diff --git a/docs/expressions/syntax.md b/docs/expressions/syntax.md index 0cf44153c..d87340edb 100644 --- a/docs/expressions/syntax.md +++ b/docs/expressions/syntax.md @@ -295,23 +295,35 @@ math.evaluate('0o77') // 63 math.evaluate('0xff') // 255 ``` -Non-decimal literals are parsed as 32 bit signed integers: +A word size suffix can be used to change the behavior of non decimal literal evaluation: ```js -math.evaluate('0xffffffff') // -1 -math.evaluate('0xfffffffff') // SyntaxError: String "0xfffffffff" is out of range +math.evaluate('0xffi8') // -1 +math.evaluate('0xffffffffi32') // -1 +math.evaluate('0xfffffffffi32') // SyntaxError: String "0xfffffffff" is out of range ``` -Numbers can be formatted as binary, octal, and hex strings using the functions -`bin`, `oct`, and `hex`: +Numbers can be formatted as binary, octal, and hex strings using the `notation` option of the `format` function: ```js -math.evaluate('bin(3)') // '0b11' -math.evaluate('oct(63)') // '0o77' -math.evaluate('hex(255)') // '0xff' -math.evaluate('hex(-1)') // '0xffffffff' -math.evaluate('hex(2.3)') // Error: Value must be an integer -math.evaluate('hex(2^35)') // Error: Value must be in range [-2^31, 2^31-1] +math.evaluate('format(3, {notation: "bin"})') // '0b11' +math.evaluate('format(63, {notation: "oct"})') // '0o77' +math.evaluate('format(255, {notation: "hex"})') // '0xff' +math.evaluate('format(-1, {notation: "hex"})') // '-0x1' +math.evaluate('format(2.3, {notation: "hex"})') // '0x2.4cccccccccccc' +``` + +The `format` function accepts a `wordSize` option to use in conjunction with the non binary notations: + +```js +math.evaluate('format(-1, {notation: "hex", wordSize: 8})') // '0xffi8' +``` + +The functions `bin`, `oct`, and `hex` are shorthand for the `format` function with `notation` set accordingly: + +```js +math.evaluate('bin(-1)') // '-0b1' +math.evaluate('bin(-1, 8)') // '0b11111111i8' ```

BigNumbers #

diff --git a/docs/reference/functions/bin.md b/docs/reference/functions/bin.md index 8198be46f..3cbce6533 100644 --- a/docs/reference/functions/bin.md +++ b/docs/reference/functions/bin.md @@ -20,6 +20,7 @@ math.bin(value) Parameter | Type | Description --------- | ---- | ----------- `value` | number | Value to be stringified +`wordSize` | number | Optional word size (see `format`)

Returns #

diff --git a/docs/reference/functions/format.md b/docs/reference/functions/format.md index ddde0aaf8..2676ab28b 100644 --- a/docs/reference/functions/format.md +++ b/docs/reference/functions/format.md @@ -41,6 +41,17 @@ math.format(value, callback) `lower` and `upper` bounds, and uses exponential notation elsewhere. Lower bound is included, upper bound is excluded. For example '123.4' and '1.4e7'. + - 'bin', 'oct, or 'hex' + Format the number using binary, octal, or hexadecimal notation. + For example '0b1101' and '0x10fe'. + - `wordSize: number` + The word size in bits to use for formatting in binary, octal, or + hexadecimal notation. To be used only with 'bin', 'oct', or 'hex' + values for 'notation' option. When this option is defined the value + is formatted as a signed twos complement integer of the given word + size and the size suffix is appended to the output. + For example format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'. + Default value is undefined. - `precision: number` A number between 0 and 16 to round the digits of the number. In case of notations 'exponential', 'engineering', and 'auto', `precision` diff --git a/docs/reference/functions/hex.md b/docs/reference/functions/hex.md index 03b481aab..85e9d8481 100644 --- a/docs/reference/functions/hex.md +++ b/docs/reference/functions/hex.md @@ -20,6 +20,7 @@ math.hex(value) Parameter | Type | Description --------- | ---- | ----------- `value` | number | Value to be stringified +`wordSize` | number | Optional word size (see `format`)

Returns #

diff --git a/docs/reference/functions/oct.md b/docs/reference/functions/oct.md index c120e9873..8e29be5af 100644 --- a/docs/reference/functions/oct.md +++ b/docs/reference/functions/oct.md @@ -20,6 +20,7 @@ math.oct(value) Parameter | Type | Description --------- | ---- | ----------- `value` | number | Value to be stringified +`wordSize` | number | Optional word size (see `format`)

Returns #

diff --git a/download.md b/download.md index 01365d62c..aaf8ab7ef 100644 --- a/download.md +++ b/download.md @@ -29,7 +29,7 @@ Math.js can be downloaded or linked from various content delivery networks: unpkg - https://unpkg.com/mathjs@8.1.1/ + https://unpkg.com/mathjs@9.0.0/ cdnjs @@ -49,8 +49,8 @@ Math.js can be downloaded or linked from various content delivery networks: Or download the full bundle directly from [unpkg](https://unpkg.com):

- - math.js (version 8.1.1, 141 kB, minified and gzipped) + + math.js (version 9.0.0, 141 kB, minified and gzipped)

diff --git a/examples/browser/angle_configuration.html b/examples/browser/angle_configuration.html index 17378ceed..1901bebc0 100644 --- a/examples/browser/angle_configuration.html +++ b/examples/browser/angle_configuration.html @@ -15,7 +15,7 @@ } - + diff --git a/examples/browser/angle_configuration.html.md b/examples/browser/angle_configuration.html.md index e11439d53..a7f73d933 100644 --- a/examples/browser/angle_configuration.html.md +++ b/examples/browser/angle_configuration.html.md @@ -24,7 +24,7 @@ File: [angle_configuration.html](angle_configuration.html) (click for a live dem } - + diff --git a/examples/browser/basic_usage.html b/examples/browser/basic_usage.html index 5c6296e87..662d31b4a 100644 --- a/examples/browser/basic_usage.html +++ b/examples/browser/basic_usage.html @@ -3,7 +3,7 @@ math.js | basic usage - + diff --git a/examples/browser/basic_usage.html.md b/examples/browser/basic_usage.html.md index 37f0f34e3..63b08b568 100644 --- a/examples/browser/basic_usage.html.md +++ b/examples/browser/basic_usage.html.md @@ -12,7 +12,7 @@ File: [basic_usage.html](basic_usage.html) (click for a live demo) math.js | basic usage - + diff --git a/examples/browser/currency_conversion.html b/examples/browser/currency_conversion.html index efc5eb9a7..b0683fd05 100644 --- a/examples/browser/currency_conversion.html +++ b/examples/browser/currency_conversion.html @@ -4,7 +4,7 @@ math.js | currency conversion - + - + diff --git a/examples/browser/custom_separators.html.md b/examples/browser/custom_separators.html.md index ccaf356fa..e573a74dc 100644 --- a/examples/browser/custom_separators.html.md +++ b/examples/browser/custom_separators.html.md @@ -24,7 +24,7 @@ File: [custom_separators.html](custom_separators.html) (click for a live demo) } - + diff --git a/examples/browser/plot.html b/examples/browser/plot.html index 5e6343a7f..dd7b3923d 100644 --- a/examples/browser/plot.html +++ b/examples/browser/plot.html @@ -3,7 +3,7 @@ math.js | plot - + diff --git a/examples/browser/plot.html.md b/examples/browser/plot.html.md index 14e0b62a5..d06482f14 100644 --- a/examples/browser/plot.html.md +++ b/examples/browser/plot.html.md @@ -12,7 +12,7 @@ File: [plot.html](plot.html) (click for a live demo) math.js | plot - + diff --git a/examples/browser/pretty_printing_with_mathjax.html b/examples/browser/pretty_printing_with_mathjax.html index 2a70dc4f3..d5da018ce 100644 --- a/examples/browser/pretty_printing_with_mathjax.html +++ b/examples/browser/pretty_printing_with_mathjax.html @@ -4,7 +4,7 @@ math.js | pretty printing with MathJax - + diff --git a/examples/browser/pretty_printing_with_mathjax.html.md b/examples/browser/pretty_printing_with_mathjax.html.md index 6f5ad5451..5fa7ab7e7 100644 --- a/examples/browser/pretty_printing_with_mathjax.html.md +++ b/examples/browser/pretty_printing_with_mathjax.html.md @@ -13,7 +13,7 @@ File: [pretty_printing_with_mathjax.html](pretty_printing_with_mathjax.html) (cl math.js | pretty printing with MathJax - + diff --git a/examples/browser/printing_html.html b/examples/browser/printing_html.html index 70e591594..87e080d12 100644 --- a/examples/browser/printing_html.html +++ b/examples/browser/printing_html.html @@ -4,7 +4,7 @@ math.js | printing HTML - + +

Rocket trajectory optimization

- This example simulates the ascent stage of the Apollo Lunar Module modeled using a system of ordinary differential equations. + This example simulates the launch of a SpaceX Falcon 9 modeled using a system of ordinary differential equations.

- - + +
- + + \ No newline at end of file diff --git a/examples/browser/rocket_trajectory_optimization.html.md b/examples/browser/rocket_trajectory_optimization.html.md index c7a9a7d2c..59af71ae7 100644 --- a/examples/browser/rocket_trajectory_optimization.html.md +++ b/examples/browser/rocket_trajectory_optimization.html.md @@ -9,157 +9,305 @@ File: [rocket_trajectory_optimization.html](rocket_trajectory_optimization.html) ```html + math.js | rocket trajectory optimization - + +

Rocket trajectory optimization

- This example simulates the ascent stage of the Apollo Lunar Module modeled using a system of ordinary differential equations. + This example simulates the launch of a SpaceX Falcon 9 modeled using a system of ordinary differential equations.

- - + +
- + ``` diff --git a/examples/browser/webworkers/index.md b/examples/browser/webworkers/index.md index 0c776e2ed..69512285f 100644 --- a/examples/browser/webworkers/index.md +++ b/examples/browser/webworkers/index.md @@ -92,7 +92,7 @@ File: [webworkers.html](webworkers.html) (click for a live demo) File: [worker.js](worker.js) ```js -importScripts('https://unpkg.com/mathjs@8.1.1/lib/browser/math.js') +importScripts('https://unpkg.com/mathjs@9.0.0/lib/browser/math.js') // create a parser const parser = self.math.parser() diff --git a/examples/browser/webworkers/worker.js b/examples/browser/webworkers/worker.js index 8715bf6af..7a07dcade 100644 --- a/examples/browser/webworkers/worker.js +++ b/examples/browser/webworkers/worker.js @@ -1,4 +1,4 @@ -importScripts('https://unpkg.com/mathjs@8.1.1/lib/browser/math.js') +importScripts('https://unpkg.com/mathjs@9.0.0/lib/browser/math.js') // create a parser const parser = self.math.parser() diff --git a/history.md b/history.md index ca8a5bf43..bf8616099 100644 --- a/history.md +++ b/history.md @@ -4,6 +4,21 @@ layout: default

History #

+

2021-01-16, version 9.0.0 #

+ +- Improved support for bin, hex, and oct literals. See #1996. Thanks @clnhlzmn. + - **Breaking change**: parse literals with prefixes `0b`, `0c`, and `0x` are + now unsigned by default. To parse them as signed, you have to specify a + suffix specifying the word size such as `i16` or `i32`. + - Function `format` now supports more notations: `bin`, 'hex', and `oct`, + for example `format(255, {notation: "hex"})`. + - The functions `format`, `bin`, `hex`, `oct` now allow specifying a wordSize, + like `bin(10, 32)` and `format(10, {notation: "bin", wordSize: 32})`. + - BigNumber support for the bin, hex, and oct literals. +- Extended and improved the example rocket_trajectory_optimization.html. + Thanks @Josef37. + +

2020-12-30, version 8.1.1 #

- Improved the performance of parsing and evaluating units a lot, see #2065. diff --git a/js/lib/math.js b/js/lib/math.js index 6b4ce3c58..7967fabd4 100644 --- a/js/lib/math.js +++ b/js/lib/math.js @@ -6,11 +6,11 @@ * It features real and complex numbers, units, matrices, a large set of * mathematical functions, and a flexible expression parser. * - * @version 8.1.1 - * @date 2020-12-30 + * @version 9.0.0 + * @date 2021-01-16 * * @license - * Copyright (C) 2013-2020 Jos de Jong + * Copyright (C) 2013-2021 Jos de Jong * * Licensed under the Apache License, Version 2.0 (the "License"); you may not * use this file except in compliance with the License. You may obtain a copy @@ -37,5 +37,5 @@ * * Copyright (c) 2015, Robert Eisele (robert@xarg.org) * Dual licensed under the MIT or GPL Version 2 licenses. - **/!function(r){"use strict";var i={s:1,n:0,d:1};function a(e){function t(){var t=Error.apply(this,arguments);t.name=this.name=e,this.stack=t.stack,this.message=t.message}function r(){}return r.prototype=Error.prototype,t.prototype=new r,t}var o=p.DivisionByZero=a("DivisionByZero"),s=p.InvalidParameter=a("InvalidParameter");function u(e,t){return isNaN(e=parseInt(e,10))&&c(),e*t}function c(){throw new s}var f=function(e,t){var r,n=0,a=1,s=1,f=0,l=0,p=0,m=1,h=1,d=0,y=1,g=1,v=1,x=1e7;if(null==e);else if(void 0!==t)s=(n=e)*(a=t);else switch(typeof e){case"object":"d"in e&&"n"in e?(n=e.n,a=e.d,"s"in e&&(n*=e.s)):0 in e?(n=e[0],1 in e&&(a=e[1])):c(),s=n*a;break;case"number":if(e<0&&(s=e,e=-e),e%1==0)n=e;else 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Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOr:{name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXor:{name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]},leftShift:{name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]},rightArithShift:{name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]},rightLogShift:{name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]},bellNumbers:{name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]},catalan:{name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]},composition:{name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]},stirlingS2:{name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]},config:{name:"config",category:"Core",syntax:["config()","config(options)"],description:"Get configuration or change configuration.",examples:["config()","1/3 + 1/4",'config({number: "Fraction"})',"1/3 + 1/4"],seealso:[]},import:{name:"import",category:"Core",syntax:["import(functions)","import(functions, options)"],description:"Import functions or constants from an object.",examples:["import({myFn: f(x)=x^2, myConstant: 32 })","myFn(2)","myConstant"],seealso:[]},typed:{name:"typed",category:"Core",syntax:["typed(signatures)","typed(name, signatures)"],description:"Create a typed function.",examples:['double = typed({ "number, number": f(x)=x+x })',"double(2)",'double("hello")'],seealso:[]},arg:{name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 + 3i)"],seealso:["re","im","conj","abs"]},conj:{name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]},re:{name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]},im:{name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]},evaluate:{name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(" + 4 + ")")'],seealso:[]},help:{name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]},distance:{name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]},intersect:{name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])"],seealso:[]},and:{name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},not:{name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},or:{name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xor:{name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},concat:{name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},cross:{name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},column:{name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row"]},ctranspose:{name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},det:{name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diag:{name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diff:{name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dot:{name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},getMatrixDataType:{name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identity:{name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},filter:{name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flatten:{name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEach:{name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["forEach([1, 2, 3], function(val) { console.log(val) })"],seealso:["map","sort","filter"]},inv:{name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},eigs:{name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},kron:{name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},map:{name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},ones:{name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelect:{name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},range:{name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},resize:{name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},reshape:{name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},rotate:{name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrix:{name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},row:{name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column"]},size:{name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sort:{name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeeze:{name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subset:{name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of a matrix or string. Indexes are one-based. Both the ranges lower-bound and upper-bound are included.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},trace:{name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transpose:{name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zeros:{name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},combinations:{name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRep:{name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorial:{name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gamma:{name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},kldivergence:{name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomial:{name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutations:{name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandom:{name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},random:{name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomInt:{name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compare:{name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNatural:{name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareText:{name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqual:{name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equal:{name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalText:{name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},larger:{name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEq:{name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smaller:{name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEq:{name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequal:{name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesian:{name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifference:{name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinct:{name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersect:{name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubset:{name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicity:{name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowerset:{name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSize:{name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifference:{name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnion:{name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erf:{name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},mad:{name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},max:{name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},mean:{name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},median:{name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},min:{name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},mode:{name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prod:{name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeq:{name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},std:{name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},sum:{name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},variance:{name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["variance(2, 4, 6)","variance([2, 4, 6, 8])",'variance([2, 4, 6, 8], "uncorrected")','variance([2, 4, 6, 8], "biased")',"variance([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]},acos:{name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","atan","asin"]},acosh:{name:"acosh",category:"Trigonometry",syntax:["acosh(x)"],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:["acosh(1.5)"],seealso:["cosh","asinh","atanh"]},acot:{name:"acot",category:"Trigonometry",syntax:["acot(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acot(0.5)","acot(cot(0.5))","acot(2)"],seealso:["cot","atan"]},acoth:{name:"acoth",category:"Trigonometry",syntax:["acoth(x)"],description:"Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:["acoth(2)","acoth(0.5)"],seealso:["acsch","asech"]},acsc:{name:"acsc",category:"Trigonometry",syntax:["acsc(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acsc(2)","acsc(csc(0.5))","acsc(0.5)"],seealso:["csc","asin","asec"]},acsch:{name:"acsch",category:"Trigonometry",syntax:["acsch(x)"],description:"Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:["acsch(0.5)"],seealso:["asech","acoth"]},asec:{name:"asec",category:"Trigonometry",syntax:["asec(x)"],description:"Calculate the inverse secant of a value.",examples:["asec(0.5)","asec(sec(0.5))","asec(2)"],seealso:["acos","acot","acsc"]},asech:{name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]},asin:{name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(0.5))"],seealso:["sin","acos","atan"]},asinh:{name:"asinh",category:"Trigonometry",syntax:["asinh(x)"],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:["asinh(0.5)"],seealso:["acosh","atanh"]},atan:{name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(0.5))"],seealso:["tan","acos","asin"]},atanh:{name:"atanh",category:"Trigonometry",syntax:["atanh(x)"],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:["atanh(0.5)"],seealso:["acosh","asinh"]},atan2:{name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]},cos:{name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]},cosh:{name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]},cot:{name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]},coth:{name:"coth",category:"Trigonometry",syntax:["coth(x)"],description:"Compute the hyperbolic cotangent of x in radians.",examples:["coth(2)","1 / tanh(2)"],seealso:["sech","csch","tanh"]},csc:{name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]},csch:{name:"csch",category:"Trigonometry",syntax:["csch(x)"],description:"Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)",examples:["csch(2)","1 / sinh(2)"],seealso:["sech","coth","sinh"]},sec:{name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]},sech:{name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)",examples:["sech(2)","1 / cosh(2)"],seealso:["coth","csch","cosh"]},sin:{name:"sin",category:"Trigonometry",syntax:["sin(x)"],description:"Compute the sine of x in radians.",examples:["sin(2)","sin(pi / 4) ^ 2","sin(90 deg)","sin(30 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["asin","cos","tan"]},sinh:{name:"sinh",category:"Trigonometry",syntax:["sinh(x)"],description:"Compute the hyperbolic sine of x in radians.",examples:["sinh(0.5)"],seealso:["cosh","tanh"]},tan:{name:"tan",category:"Trigonometry",syntax:["tan(x)"],description:"Compute the tangent of x in radians.",examples:["tan(0.5)","sin(0.5) / cos(0.5)","tan(pi / 4)","tan(45 deg)"],seealso:["atan","sin","cos"]},tanh:{name:"tanh",category:"Trigonometry",syntax:["tanh(x)"],description:"Compute the hyperbolic tangent of x in radians.",examples:["tanh(0.5)","sinh(0.5) / cosh(0.5)"],seealso:["sinh","cosh"]},to:{name:"to",category:"Units",syntax:["x to unit","to(x, unit)"],description:"Change the unit of a value.",examples:["5 inch to cm","3.2kg to g","16 bytes in bits"],seealso:[]},clone:{name:"clone",category:"Utils",syntax:["clone(x)"],description:"Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices",examples:["clone(3.5)","clone(2 - 4i)","clone(45 deg)","clone([1, 2; 3, 4])",'clone("hello world")'],seealso:[]},format:{name:"format",category:"Utils",syntax:["format(value)","format(value, precision)"],description:"Format a value of any type as string.",examples:["format(2.3)","format(3 - 4i)","format([])","format(pi, 3)"],seealso:["print"]},bin:{name:"bin",category:"Utils",syntax:["bin(value)"],description:"Format a number as binary",examples:["bin(2)"],seealso:["oct","hex"]},oct:{name:"oct",category:"Utils",syntax:["oct(value)"],description:"Format a number as octal",examples:["oct(56)"],seealso:["bin","hex"]},hex:{name:"hex",category:"Utils",syntax:["hex(value)"],description:"Format a number as hexadecimal",examples:["hex(240)"],seealso:["bin","oct"]},isNaN:{name:"isNaN",category:"Utils",syntax:["isNaN(x)"],description:"Test whether a value is NaN (not a number)",examples:["isNaN(2)","isNaN(0 / 0)","isNaN(NaN)","isNaN(Infinity)"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isInteger:{name:"isInteger",category:"Utils",syntax:["isInteger(x)"],description:"Test whether a value is an integer number.",examples:["isInteger(2)","isInteger(3.5)","isInteger([3, 0.5, -2])"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isNegative:{name:"isNegative",category:"Utils",syntax:["isNegative(x)"],description:"Test whether a value is negative: smaller than zero.",examples:["isNegative(2)","isNegative(0)","isNegative(-4)","isNegative([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isPositive","isZero"]},isNumeric:{name:"isNumeric",category:"Utils",syntax:["isNumeric(x)"],description:"Test whether a value is a numeric value. Returns true when the input is a number, BigNumber, Fraction, or boolean.",examples:["isNumeric(2)",'isNumeric("2")','hasNumericValue("2")',"isNumeric(0)","isNumeric(bignumber(500))","isNumeric(fraction(0.125))","isNumeric(2 + 3i)",'isNumeric([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","hasNumericValue"]},hasNumericValue:{name:"hasNumericValue",category:"Utils",syntax:["hasNumericValue(x)"],description:"Test whether a value is an numeric value. In case of a string, true is returned if the string contains a numeric value.",examples:["hasNumericValue(2)",'hasNumericValue("2")','isNumeric("2")',"hasNumericValue(0)","hasNumericValue(bignumber(500))","hasNumericValue(fraction(0.125))","hasNumericValue(2 + 3i)",'hasNumericValue([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","isNumeric"]},isPositive:{name:"isPositive",category:"Utils",syntax:["isPositive(x)"],description:"Test whether a value is positive: larger than zero.",examples:["isPositive(2)","isPositive(0)","isPositive(-4)","isPositive([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isNegative","isZero"]},isPrime:{name:"isPrime",category:"Utils",syntax:["isPrime(x)"],description:"Test whether a value is prime: has no divisors other than itself and one.",examples:["isPrime(3)","isPrime(-2)","isPrime([2, 17, 100])"],seealso:["isInteger","isNumeric","isNegative","isZero"]},isZero:{name:"isZero",category:"Utils",syntax:["isZero(x)"],description:"Test whether a value is zero.",examples:["isZero(2)","isZero(0)","isZero(-4)","isZero([3, 0, -2, 0])"],seealso:["isInteger","isNumeric","isNegative","isPositive"]},typeOf:{name:"typeOf",category:"Utils",syntax:["typeOf(x)"],description:"Get the type of a variable.",examples:["typeOf(3.5)","typeOf(2 - 4i)","typeOf(45 deg)",'typeOf("hello world")'],seealso:["getMatrixDataType"]},numeric:{name:"numeric",category:"Utils",syntax:["numeric(x)"],description:"Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.",examples:['numeric("4")','numeric("4", "number")','numeric("4", "BigNumber")','numeric("4", "Fraction)','numeric(4, "Fraction")','numeric(fraction(2, 5), "number)'],seealso:["number","fraction","bignumber","string","format"]}},Tu=Je("help",["typed","mathWithTransform","Help"],(function(e){var 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n(i(e[0][0],e[1][1]),i(e[1][0],e[0][1]));for(var s=o(e),u=s.U[0][0],c=1;c=t)break;for(var m=l,h=0;!p[s.p[m]];)p[s.p[m]]=!0,m=s.p[m],h++;h%2==0&&f++}return f%2==0?u:a(u)}(e.clone().valueOf(),s);throw new RangeError("Matrix must be square (size: "+ge(t)+")");default:throw new RangeError("Matrix must be two dimensional (size: "+ge(t)+")")}}})})),Iu=Je("inv",["typed","matrix","divideScalar","addScalar","multiply","unaryMinus","det","identity","abs"],(function(e){var t=e.typed,r=e.matrix,n=e.divideScalar,i=e.addScalar,a=e.multiply,o=e.unaryMinus,s=e.det,u=e.identity,c=e.abs;return t("inv",{"Array | Matrix":function(e){var t=p(e)?e.size():Me(e);switch(t.length){case 1:if(1===t[0])return p(e)?r([n(1,e.valueOf()[0])]):[n(1,e[0])];throw new RangeError("Matrix must be square (size: "+ge(t)+")");case 2:var i=t[0],a=t[1];if(i===a)return p(e)?r(f(e.valueOf(),i,a),e.storage()):f(e,i,a);throw new RangeError("Matrix must be square (size: "+ge(t)+")");default:throw new RangeError("Matrix must be two 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TypeError("Values of pointX, pointY and pointZ should be numbers or BigNumbers");if(!h(t))throw new TypeError("Values of x0, y0, z0, a, b and c should be numbers or BigNumbers");if("pointX"in e&&"pointY"in e&&"x0"in t&&"y0"in t&&"z0"in t&&"a"in t&&"b"in t&&"c"in t)return g(e.pointX,e.pointY,e.pointZ,t.x0,t.y0,t.z0,t.a,t.b,t.c);throw new TypeError("Key names do not match")}if(2===Object.keys(e).length&&2===Object.keys(t).length){if(!l(e))throw new TypeError("Values of pointOneX and pointOneY should be numbers or BigNumbers");if(!l(t))throw new TypeError("Values of pointTwoX and pointTwoY should be numbers or BigNumbers");if("pointOneX"in e&&"pointOneY"in e&&"pointTwoX"in t&&"pointTwoY"in t)return v([e.pointOneX,e.pointOneY],[t.pointTwoX,t.pointTwoY]);throw new TypeError("Key names do not match")}if(3===Object.keys(e).length&&3===Object.keys(t).length){if(!p(e))throw new TypeError("Values of pointOneX, pointOneY and pointOneZ should be numbers or BigNumbers");if(!p(t))throw new TypeError("Values of pointTwoX, pointTwoY and pointTwoZ should be numbers or BigNumbers");if("pointOneX"in e&&"pointOneY"in e&&"pointOneZ"in e&&"pointTwoX"in t&&"pointTwoY"in t&&"pointTwoZ"in t)return v([e.pointOneX,e.pointOneY,e.pointOneZ],[t.pointTwoX,t.pointTwoY,t.pointTwoZ]);throw new TypeError("Key names do not match")}throw new TypeError("Invalid Arguments: Try again")},Array:function(e){if(!function(e){if(2===e[0].length&&f(e[0][0])&&f(e[0][1])){if(e.some((function(e){return 2!==e.length||!f(e[0])||!f(e[1])})))return!1}else{if(!(3===e[0].length&&f(e[0][0])&&f(e[0][1])&&f(e[0][2])))return!1;if(e.some((function(e){return 3!==e.length||!f(e[0])||!f(e[1])||!f(e[2])})))return!1}return!0}(e))throw new TypeError("Incorrect array format entered for pairwise distance calculation");return function(e){for(var t=[],r=[],n=[],i=0;i0&&(o=e[c]);return u(o,n)}var f=a(e,(t-1)/2);return s(f)}catch(e){throw Fi(e,"median")}}var s=t({"number | BigNumber | Complex | Unit":function(e){return 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t=e.typed,r=e.add,n=e.subtract,i=e.multiply,a=e.divide,s=e.apply,u=e.isNaN;return t("variance",{"Array | Matrix":function(e){return c(e,"unbiased")},"Array | Matrix, string":c,"Array | Matrix, number | BigNumber":function(e,t){return f(e,t,"unbiased")},"Array | Matrix, number | BigNumber, string":f,"...":function(e){return c(e,"unbiased")}});function c(e,t){var s,c=0;if(0===e.length)throw new SyntaxError("Function variance requires one or more parameters (0 provided)");if(xt(e,(function(e){try{s=void 0===s?e:r(s,e),c++}catch(t){throw Fi(t,"variance",e)}})),0===c)throw new Error("Cannot calculate variance of an empty array");var f=a(s,c);if(s=void 0,xt(e,(function(e){var t=n(e,f);s=void 0===s?i(t,t):r(s,i(t,t))})),u(s))return s;switch(t){case"uncorrected":return a(s,c);case"biased":return a(s,c+1);case"unbiased":var l=o(s)?s.mul(0):0;return 1===c?l:a(s,c-1);default:throw new Error('Unknown normalization "'+t+'". 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bt(e,this)}})})),ic=Je("kldivergence",["typed","matrix","divide","sum","multiply","dotDivide","log","isNumeric"],(function(e){var t=e.typed,r=e.matrix,n=e.divide,i=e.sum,a=e.multiply,o=e.dotDivide,s=e.log,u=e.isNumeric;return t("kldivergence",{"Array, Array":function(e,t){return c(r(e),r(t))},"Matrix, Array":function(e,t){return c(e,r(t))},"Array, Matrix":function(e,t){return c(r(e),t)},"Matrix, Matrix":function(e,t){return c(e,t)}});function c(e,t){var r=t.size().length,c=e.size().length;if(r>1)throw new Error("first object must be one dimensional");if(c>1)throw new Error("second object must be one dimensional");if(r!==c)throw new Error("Length of two vectors must be equal");if(0===i(e))throw new Error("Sum of elements in first object must be non zero");if(0===i(t))throw new Error("Sum of elements in second object must be non zero");var f=n(e,i(e)),l=n(t,i(t)),p=i(a(f,s(o(f,l))));return u(p)?p:Number.NaN}})),ac=Je("multinomial",["typed","add","divide","multiply","factorial","isInteger","isPositive"],(function(e){var t=e.typed,r=e.add,n=e.divide,i=e.multiply,a=e.factorial,o=e.isInteger,s=e.isPositive;return t("multinomial",{"Array | Matrix":function(e){var t=0,u=1;return xt(e,(function(e){if(!o(e)||!s(e))throw new TypeError("Positive integer value expected in function multinomial");t=r(t,e),u=i(u,a(e))})),n(a(t),u)}})})),oc=Je("permutations",["typed","factorial"],(function(e){return(0,e.typed)("permutations",{"number | BigNumber":e.factorial,"number, number":function(e,t){if(!V(e)||e<0)throw new TypeError("Positive integer value expected in function permutations");if(!V(t)||t<0)throw new TypeError("Positive integer value expected in function permutations");if(t>e)throw new TypeError("second argument k must be less than or equal to first argument n");return Zu(e-t+1,e)},"BigNumber, BigNumber":function(e,t){var r,n;if(!sc(e)||!sc(t))throw new TypeError("Positive integer 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h=0;h=e&&(r(s.value,0)||n(s.key,s.value,this)),(s=i.extractMinimum())&&o.push(s);for(var u=0;u="0"&&e<="9"}function O(){r++,n=t.charAt(r)}function C(e){r=e,n=t.charAt(r)}function _(){var e="",t=r;if("+"===n?O():"-"===n&&(e+=n,O()),!function(e){return e>="0"&&e<="9"||"."===e}(n))return C(t),null;if("."===n){if(e+=n,O(),!A(n))return C(t),null}else{for(;A(n);)e+=n,O();"."===n&&(e+=n,O())}for(;A(n);)e+=n,O();if("E"===n||"e"===n){var i="",a=r;if(i+=n,O(),"+"!==n&&"-"!==n||(i+=n,O()),!A(n))return C(a),e;for(e+=i;A(n);)e+=n,O()}return e}function T(){for(var e="";A(n)||S.isValidAlpha(n);)e+=n,O();var t=e.charAt(0);return S.isValidAlpha(t)?e:null}function q(e){return n===e?(O(),e):null}S.prototype.type="Unit",S.prototype.isUnit=!0,S.parse=function(e,i){if(i=i||{},r=-1,n="","string"!=typeof(t=e))throw new TypeError("Invalid argument in Unit.parse, string expected");var o=new S;o.units=[];var s=1,u=!1;O(),E();var c=_(),f=null;if(c){if("BigNumber"===a.number)f=new w(c);else 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If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply","nthRoot","nthRoots","pow"]},sqrtm:{name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[1, 2], [3, 4]])"],seealso:["sqrt","abs","square","multiply"]},square:{name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},subtract:{name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]},unaryMinus:{name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]},unaryPlus:{name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]},xgcd:{name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]},bitAnd:{name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitNot:{name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]},bitOr:{name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]},bitXor:{name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. 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Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]},not:{name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]},or:{name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]},xor:{name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]},concat:{name:"concat",category:"Matrix",syntax:["concat(A, B, C, ...)","concat(A, B, C, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.",examples:["A = [1, 2; 5, 6]","B = [3, 4; 7, 8]","concat(A, B)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},cross:{name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0], [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4], [5, 6, 7])"],seealso:["multiply","dot"]},column:{name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row"]},ctranspose:{name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},det:{name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diag:{name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},diff:{name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["diff([1, 2, 4, 7, 0])","diff([1, 2, 4, 7, 0], 0)","diff(matrix([1, 2, 4, 7, 0]))","diff([[1, 2], [3, 4]])","diff([[1, 2], [3, 4]], 0)","diff([[1, 2], [3, 4]], 1)","diff([[1, 2], [3, 4]], bignumber(1))","diff(matrix([[1, 2], [3, 4]]), 1)","diff([[1, 2], matrix([3, 4])], 1)"],seealso:["subtract","partitionSelect"]},dot:{name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]},getMatrixDataType:{name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]},identity:{name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]},filter:{name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]},flatten:{name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]},forEach:{name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["forEach([1, 2, 3], function(val) { console.log(val) })"],seealso:["map","sort","filter"]},inv:{name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]},eigs:{name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and eigenvectors of a real symmetric matrix",examples:["eigs([[5, 2.3], [2.3, 1]])"],seealso:["inv"]},kron:{name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]},map:{name:"map",category:"Matrix",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], square)"],seealso:["filter","forEach"]},ones:{name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]},partitionSelect:{name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1)'],seealso:["sort"]},range:{name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]},resize:{name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]},reshape:{name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])"],seealso:["size","squeeze","resize"]},rotate:{name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], math.pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]},rotationMatrix:{name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]},row:{name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column"]},size:{name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]},sort:{name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"])',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]},squeeze:{name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]},subset:{name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of a matrix or string. Indexes are one-based. Both the ranges lower-bound and upper-bound are included.",examples:["d = [1, 2; 3, 4]","e = []","e[1, 1:2] = [5, 6]","e[2, :] = [7, 8]","f = d * e","f[2, 1]","f[:, 1]"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]},trace:{name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]},transpose:{name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]},zeros:{name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]},combinations:{name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]},combinationsWithRep:{name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]},factorial:{name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]},gamma:{name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]},kldivergence:{name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]},multinomial:{name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]},permutations:{name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]},pickRandom:{name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]},random:{name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["pickRandom","randomInt"]},randomInt:{name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]},compare:{name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]},compareNatural:{name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]},compareText:{name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]},deepEqual:{name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]},equal:{name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallerEq","largerEq","compare","deepEqual","equalText"]},equalText:{name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]},larger:{name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare"]},largerEq:{name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]},smaller:{name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallerEq","largerEq","compare"]},smallerEq:{name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]},unequal:{name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallerEq","largerEq","compare","deepEqual"]},setCartesian:{name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]},setDifference:{name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]},setDistinct:{name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]},setIntersect:{name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]},setIsSubset:{name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]},setMultiplicity:{name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]},setPowerset:{name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]},setSize:{name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]},setSymDifference:{name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]},setUnion:{name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]},erf:{name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]},mad:{name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]},max:{name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]},mean:{name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]},median:{name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]},min:{name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","median","prod","std","sum","variance"]},mode:{name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]},prod:{name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]},quantileSeq:{name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:"Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.",examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]},std:{name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]},sum:{name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]},variance:{name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, normalization)"],description:'Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["variance(2, 4, 6)","variance([2, 4, 6, 8])",'variance([2, 4, 6, 8], "uncorrected")','variance([2, 4, 6, 8], "biased")',"variance([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","min","prod","std","sum"]},acos:{name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","atan","asin"]},acosh:{name:"acosh",category:"Trigonometry",syntax:["acosh(x)"],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:["acosh(1.5)"],seealso:["cosh","asinh","atanh"]},acot:{name:"acot",category:"Trigonometry",syntax:["acot(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acot(0.5)","acot(cot(0.5))","acot(2)"],seealso:["cot","atan"]},acoth:{name:"acoth",category:"Trigonometry",syntax:["acoth(x)"],description:"Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:["acoth(2)","acoth(0.5)"],seealso:["acsch","asech"]},acsc:{name:"acsc",category:"Trigonometry",syntax:["acsc(x)"],description:"Calculate the inverse cotangent of a value.",examples:["acsc(2)","acsc(csc(0.5))","acsc(0.5)"],seealso:["csc","asin","asec"]},acsch:{name:"acsch",category:"Trigonometry",syntax:["acsch(x)"],description:"Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:["acsch(0.5)"],seealso:["asech","acoth"]},asec:{name:"asec",category:"Trigonometry",syntax:["asec(x)"],description:"Calculate the inverse secant of a value.",examples:["asec(0.5)","asec(sec(0.5))","asec(2)"],seealso:["acos","acot","acsc"]},asech:{name:"asech",category:"Trigonometry",syntax:["asech(x)"],description:"Calculate the inverse secant of a value.",examples:["asech(0.5)"],seealso:["acsch","acoth"]},asin:{name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(0.5))"],seealso:["sin","acos","atan"]},asinh:{name:"asinh",category:"Trigonometry",syntax:["asinh(x)"],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:["asinh(0.5)"],seealso:["acosh","atanh"]},atan:{name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(0.5))"],seealso:["tan","acos","asin"]},atanh:{name:"atanh",category:"Trigonometry",syntax:["atanh(x)"],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:["atanh(0.5)"],seealso:["acosh","asinh"]},atan2:{name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]},cos:{name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]},cosh:{name:"cosh",category:"Trigonometry",syntax:["cosh(x)"],description:"Compute the hyperbolic cosine of x in radians.",examples:["cosh(0.5)"],seealso:["sinh","tanh","coth"]},cot:{name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]},coth:{name:"coth",category:"Trigonometry",syntax:["coth(x)"],description:"Compute the hyperbolic cotangent of x in radians.",examples:["coth(2)","1 / tanh(2)"],seealso:["sech","csch","tanh"]},csc:{name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]},csch:{name:"csch",category:"Trigonometry",syntax:["csch(x)"],description:"Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)",examples:["csch(2)","1 / sinh(2)"],seealso:["sech","coth","sinh"]},sec:{name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]},sech:{name:"sech",category:"Trigonometry",syntax:["sech(x)"],description:"Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)",examples:["sech(2)","1 / cosh(2)"],seealso:["coth","csch","cosh"]},sin:{name:"sin",category:"Trigonometry",syntax:["sin(x)"],description:"Compute the sine of x in radians.",examples:["sin(2)","sin(pi / 4) ^ 2","sin(90 deg)","sin(30 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["asin","cos","tan"]},sinh:{name:"sinh",category:"Trigonometry",syntax:["sinh(x)"],description:"Compute the hyperbolic sine of x in radians.",examples:["sinh(0.5)"],seealso:["cosh","tanh"]},tan:{name:"tan",category:"Trigonometry",syntax:["tan(x)"],description:"Compute the tangent of x in radians.",examples:["tan(0.5)","sin(0.5) / cos(0.5)","tan(pi / 4)","tan(45 deg)"],seealso:["atan","sin","cos"]},tanh:{name:"tanh",category:"Trigonometry",syntax:["tanh(x)"],description:"Compute the hyperbolic tangent of x in radians.",examples:["tanh(0.5)","sinh(0.5) / cosh(0.5)"],seealso:["sinh","cosh"]},to:{name:"to",category:"Units",syntax:["x to unit","to(x, unit)"],description:"Change the unit of a value.",examples:["5 inch to cm","3.2kg to g","16 bytes in bits"],seealso:[]},clone:{name:"clone",category:"Utils",syntax:["clone(x)"],description:"Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices",examples:["clone(3.5)","clone(2 - 4i)","clone(45 deg)","clone([1, 2; 3, 4])",'clone("hello world")'],seealso:[]},format:{name:"format",category:"Utils",syntax:["format(value)","format(value, precision)"],description:"Format a value of any type as string.",examples:["format(2.3)","format(3 - 4i)","format([])","format(pi, 3)"],seealso:["print"]},bin:{name:"bin",category:"Utils",syntax:["bin(value)"],description:"Format a number as binary",examples:["bin(2)"],seealso:["oct","hex"]},oct:{name:"oct",category:"Utils",syntax:["oct(value)"],description:"Format a number as octal",examples:["oct(56)"],seealso:["bin","hex"]},hex:{name:"hex",category:"Utils",syntax:["hex(value)"],description:"Format a number as hexadecimal",examples:["hex(240)"],seealso:["bin","oct"]},isNaN:{name:"isNaN",category:"Utils",syntax:["isNaN(x)"],description:"Test whether a value is NaN (not a number)",examples:["isNaN(2)","isNaN(0 / 0)","isNaN(NaN)","isNaN(Infinity)"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isInteger:{name:"isInteger",category:"Utils",syntax:["isInteger(x)"],description:"Test whether a value is an integer number.",examples:["isInteger(2)","isInteger(3.5)","isInteger([3, 0.5, -2])"],seealso:["isNegative","isNumeric","isPositive","isZero"]},isNegative:{name:"isNegative",category:"Utils",syntax:["isNegative(x)"],description:"Test whether a value is negative: smaller than zero.",examples:["isNegative(2)","isNegative(0)","isNegative(-4)","isNegative([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isPositive","isZero"]},isNumeric:{name:"isNumeric",category:"Utils",syntax:["isNumeric(x)"],description:"Test whether a value is a numeric value. Returns true when the input is a number, BigNumber, Fraction, or boolean.",examples:["isNumeric(2)",'isNumeric("2")','hasNumericValue("2")',"isNumeric(0)","isNumeric(bignumber(500))","isNumeric(fraction(0.125))","isNumeric(2 + 3i)",'isNumeric([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","hasNumericValue"]},hasNumericValue:{name:"hasNumericValue",category:"Utils",syntax:["hasNumericValue(x)"],description:"Test whether a value is an numeric value. In case of a string, true is returned if the string contains a numeric value.",examples:["hasNumericValue(2)",'hasNumericValue("2")','isNumeric("2")',"hasNumericValue(0)","hasNumericValue(bignumber(500))","hasNumericValue(fraction(0.125))","hasNumericValue(2 + 3i)",'hasNumericValue([2.3, "foo", false])'],seealso:["isInteger","isZero","isNegative","isPositive","isNaN","isNumeric"]},isPositive:{name:"isPositive",category:"Utils",syntax:["isPositive(x)"],description:"Test whether a value is positive: larger than zero.",examples:["isPositive(2)","isPositive(0)","isPositive(-4)","isPositive([3, 0.5, -2])"],seealso:["isInteger","isNumeric","isNegative","isZero"]},isPrime:{name:"isPrime",category:"Utils",syntax:["isPrime(x)"],description:"Test whether a value is prime: has no divisors other than itself and one.",examples:["isPrime(3)","isPrime(-2)","isPrime([2, 17, 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Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)\n\n Math.log(a * a + b * b) / 2\n\n *\n *\n * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)\n\n var fn = function(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n var t = Math.min(a, b);\n a = Math.max(a, b);\n t = t / a;\n\n return Math.log(a) + Math.log(1 + t * t) / 2;\n };\n\n * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)\n\n Math.log(a / Math.cos(Math.atan2(b, a)))\n\n * 4. 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'-' : '') + c);\n }\n plus = minus = 0;\n }\n }\n\n // Still something on the stack\n if (plus + minus > 0) {\n parser_exit();\n }\n break;\n\n case 'number':\n z['im'] = 0;\n z['re'] = a;\n break;\n\n default:\n parser_exit();\n }\n\n if (isNaN(z['re']) || isNaN(z['im'])) {\n // If a calculation is NaN, we treat it as NaN and don't throw\n //parser_exit();\n }\n\n return z;\n };\n\n /**\n * @constructor\n * @returns {Complex}\n */\n function Complex(a, b) {\n\n if (!(this instanceof Complex)) {\n return new Complex(a, b);\n }\n\n var z = parse(a, b);\n\n this['re'] = z['re'];\n this['im'] = z['im'];\n }\n\n Complex.prototype = {\n\n 're': 0,\n 'im': 0,\n\n /**\n * Calculates the sign of a complex number, which is a normalized complex\n *\n * @returns {Complex}\n */\n 'sign': function() {\n\n var abs = this['abs']();\n\n return new Complex(\n this['re'] / abs,\n this['im'] / abs);\n },\n\n /**\n * Adds two complex numbers\n *\n * @returns {Complex}\n */\n 'add': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity + Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity + z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] + z['re'],\n this['im'] + z['im']);\n },\n\n /**\n * Subtracts two complex numbers\n *\n * @returns {Complex}\n */\n 'sub': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity - Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity - z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] - z['re'],\n this['im'] - z['im']);\n },\n\n /**\n * Multiplies two complex numbers\n *\n * @returns {Complex}\n */\n 'mul': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity * 0 = NaN\n if ((this['isInfinite']() && z['isZero']()) || (this['isZero']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity * z = Infinity { where z != 0 }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n // Short circuit for real values\n if (z['im'] === 0 && this['im'] === 0) {\n return new Complex(this['re'] * z['re'], 0);\n }\n\n return new Complex(\n this['re'] * z['re'] - this['im'] * z['im'],\n this['re'] * z['im'] + this['im'] * z['re']);\n },\n\n /**\n * Divides two complex numbers\n *\n * @returns {Complex}\n */\n 'div': function(a, b) {\n\n var z = new Complex(a, b);\n\n // 0 / 0 = NaN and Infinity / Infinity = NaN\n if ((this['isZero']() && z['isZero']()) || (this['isInfinite']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity / 0 = Infinity\n if (this['isInfinite']() || z['isZero']()) {\n return Complex['INFINITY'];\n }\n\n // 0 / Infinity = 0\n if (this['isZero']() || z['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n a = this['re'];\n b = this['im'];\n\n var c = z['re'];\n var d = z['im'];\n var t, x;\n\n if (0 === d) {\n // Divisor is real\n return new Complex(a / c, b / c);\n }\n\n if (Math.abs(c) < Math.abs(d)) {\n\n x = c / d;\n t = c * x + d;\n\n return new Complex(\n (a * x + b) / t,\n (b * x - a) / t);\n\n } else {\n\n x = d / c;\n t = d * x + c;\n\n return new Complex(\n (a + b * x) / t,\n (b - a * x) / t);\n }\n },\n\n /**\n * Calculate the power of two complex numbers\n *\n * @returns {Complex}\n */\n 'pow': function(a, b) {\n\n var z = new Complex(a, b);\n\n a = this['re'];\n b = this['im'];\n\n if (z['isZero']()) {\n return Complex['ONE'];\n }\n\n // If the exponent is real\n if (z['im'] === 0) {\n\n if (b === 0 && a >= 0) {\n\n return new Complex(Math.pow(a, z['re']), 0);\n\n } else if (a === 0) { // If base is fully imaginary\n\n switch ((z['re'] % 4 + 4) % 4) {\n case 0:\n return new Complex(Math.pow(b, z['re']), 0);\n case 1:\n return new Complex(0, Math.pow(b, z['re']));\n case 2:\n return new Complex(-Math.pow(b, z['re']), 0);\n case 3:\n return new Complex(0, -Math.pow(b, z['re']));\n }\n }\n }\n\n /* I couldn't find a good formula, so here is a derivation and optimization\n *\n * z_1^z_2 = (a + bi)^(c + di)\n * = exp((c + di) * log(a + bi)\n * = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))\n * =>...\n * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n *\n * =>...\n * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n *\n * =>\n * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))\n * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))\n *\n */\n\n if (a === 0 && b === 0 && z['re'] > 0 && z['im'] >= 0) {\n return Complex['ZERO'];\n }\n\n var arg = Math.atan2(b, a);\n var loh = logHypot(a, b);\n\n a = Math.exp(z['re'] * loh - z['im'] * arg);\n b = z['im'] * loh + z['re'] * arg;\n return new Complex(\n a * Math.cos(b),\n a * Math.sin(b));\n },\n\n /**\n * Calculate the complex square root\n *\n * @returns {Complex}\n */\n 'sqrt': function() {\n\n var a = this['re'];\n var b = this['im'];\n var r = this['abs']();\n\n var re, im;\n\n if (a >= 0) {\n\n if (b === 0) {\n return new Complex(Math.sqrt(a), 0);\n }\n\n re = 0.5 * Math.sqrt(2.0 * (r + a));\n } else {\n re = Math.abs(b) / Math.sqrt(2 * (r - a));\n }\n\n if (a <= 0) {\n im = 0.5 * Math.sqrt(2.0 * (r - a));\n } else {\n im = Math.abs(b) / Math.sqrt(2 * (r + a));\n }\n\n return new Complex(re, b < 0 ? -im : im);\n },\n\n /**\n * Calculate the complex exponent\n *\n * @returns {Complex}\n */\n 'exp': function() {\n\n var tmp = Math.exp(this['re']);\n\n if (this['im'] === 0) {\n //return new Complex(tmp, 0);\n }\n return new Complex(\n tmp * Math.cos(this['im']),\n tmp * Math.sin(this['im']));\n },\n\n /**\n * Calculate the complex exponent and subtracts one.\n *\n * This may be more accurate than `Complex(x).exp().sub(1)` if\n * `x` is small.\n *\n * @returns {Complex}\n */\n 'expm1': function() {\n\n /**\n * exp(a + i*b) - 1\n = exp(a) * (cos(b) + j*sin(b)) - 1\n = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)\n */\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.expm1(a) * Math.cos(b) + cosm1(b),\n Math.exp(a) * Math.sin(b));\n },\n\n /**\n * Calculate the natural log\n *\n * @returns {Complex}\n */\n 'log': function() {\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0 && a > 0) {\n //return new Complex(Math.log(a), 0);\n }\n\n return new Complex(\n logHypot(a, b),\n Math.atan2(b, a));\n },\n\n /**\n * Calculate the magnitude of the complex number\n *\n * @returns {number}\n */\n 'abs': function() {\n\n return hypot(this['re'], this['im']);\n },\n\n /**\n * Calculate the angle of the complex number\n *\n * @returns {number}\n */\n 'arg': function() {\n\n return Math.atan2(this['im'], this['re']);\n },\n\n /**\n * Calculate the sine of the complex number\n *\n * @returns {Complex}\n */\n 'sin': function() {\n\n // sin(c) = (e^b - e^(-b)) / (2i)\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.sin(a) * cosh(b),\n Math.cos(a) * sinh(b));\n },\n\n /**\n * Calculate the cosine\n *\n * @returns {Complex}\n */\n 'cos': function() {\n\n // cos(z) = (e^b + e^(-b)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.cos(a) * cosh(b),\n -Math.sin(a) * sinh(b));\n },\n\n /**\n * Calculate the tangent\n *\n * @returns {Complex}\n */\n 'tan': function() {\n\n // tan(c) = (e^(ci) - e^(-ci)) / (i(e^(ci) + e^(-ci)))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) + cosh(b);\n\n return new Complex(\n Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the cotangent\n *\n * @returns {Complex}\n */\n 'cot': function() {\n\n // cot(c) = i(e^(ci) + e^(-ci)) / (e^(ci) - e^(-ci))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) - cosh(b);\n\n return new Complex(\n -Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the secant\n *\n * @returns {Complex}\n */\n 'sec': function() {\n\n // sec(c) = 2 / (e^(ci) + e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) + 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.cos(a) * cosh(b) / d,\n Math.sin(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the cosecans\n *\n * @returns {Complex}\n */\n 'csc': function() {\n\n // csc(c) = 2i / (e^(ci) - e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) - 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.sin(a) * cosh(b) / d,\n -Math.cos(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the complex arcus sinus\n *\n * @returns {Complex}\n */\n 'asin': function() {\n\n // asin(c) = -i * log(ci + sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(t2['im'], -t2['re']);\n },\n\n /**\n * Calculate the complex arcus cosinus\n *\n * @returns {Complex}\n */\n 'acos': function() {\n\n // acos(c) = i * log(c - i * sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(Math.PI / 2 - t2['im'], t2['re']);\n },\n\n /**\n * Calculate the complex arcus tangent\n *\n * @returns {Complex}\n */\n 'atan': function() {\n\n // atan(c) = i / 2 log((i + x) / (i - x))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0) {\n\n if (b === 1) {\n return new Complex(0, Infinity);\n }\n\n if (b === -1) {\n return new Complex(0, -Infinity);\n }\n }\n\n var d = a * a + (1.0 - b) * (1.0 - b);\n\n var t1 = new Complex(\n (1 - b * b - a * a) / d,\n -2 * a / d).log();\n\n return new Complex(-0.5 * t1['im'], 0.5 * t1['re']);\n },\n\n /**\n * Calculate the complex arcus cotangent\n *\n * @returns {Complex}\n */\n 'acot': function() {\n\n // acot(c) = i / 2 log((c - i) / (c + i))\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n return new Complex(Math.atan2(1, a), 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atan()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atan();\n },\n\n /**\n * Calculate the complex arcus secant\n *\n * @returns {Complex}\n */\n 'asec': function() {\n\n // asec(c) = -i * log(1 / c + sqrt(1 - i / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acos()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acos();\n },\n\n /**\n * Calculate the complex arcus cosecans\n *\n * @returns {Complex}\n */\n 'acsc': function() {\n\n // acsc(c) = -i * log(i / c + sqrt(1 - 1 / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(Math.PI / 2, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asin()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asin();\n },\n\n /**\n * Calculate the complex sinh\n *\n * @returns {Complex}\n */\n 'sinh': function() {\n\n // sinh(c) = (e^c - e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n sinh(a) * Math.cos(b),\n cosh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex cosh\n *\n * @returns {Complex}\n */\n 'cosh': function() {\n\n // cosh(c) = (e^c + e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n cosh(a) * Math.cos(b),\n sinh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex tanh\n *\n * @returns {Complex}\n */\n 'tanh': function() {\n\n // tanh(c) = (e^c - e^-c) / (e^c + e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) + Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'coth': function() {\n\n // coth(c) = (e^c + e^-c) / (e^c - e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) - Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n -Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'csch': function() {\n\n // csch(c) = 2 / (e^c - e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) - cosh(2 * a);\n\n return new Complex(\n -2 * sinh(a) * Math.cos(b) / d,\n 2 * cosh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex sech\n *\n * @returns {Complex}\n */\n 'sech': function() {\n\n // sech(c) = 2 / (e^c + e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) + cosh(2 * a);\n\n return new Complex(\n 2 * cosh(a) * Math.cos(b) / d,\n -2 * sinh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'asinh': function() {\n\n // asinh(c) = log(c + sqrt(c^2 + 1))\n\n var tmp = this['im'];\n this['im'] = -this['re'];\n this['re'] = tmp;\n var res = this['asin']();\n\n this['re'] = -this['im'];\n this['im'] = tmp;\n tmp = res['re'];\n\n res['re'] = -res['im'];\n res['im'] = tmp;\n return res;\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'acosh': function() {\n\n // acosh(c) = log(c + sqrt(c^2 - 1))\n\n var res = this['acos']();\n if (res['im'] <= 0) {\n var tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n } else {\n var tmp = res['im'];\n res['im'] = -res['re'];\n res['re'] = tmp;\n }\n return res;\n },\n\n /**\n * Calculate the complex atanh\n *\n * @returns {Complex}\n */\n 'atanh': function() {\n\n // atanh(c) = log((1+c) / (1-c)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n var noIM = a > 1 && b === 0;\n var oneMinus = 1 - a;\n var onePlus = 1 + a;\n var d = oneMinus * oneMinus + b * b;\n\n var x = (d !== 0)\n ? new Complex(\n (onePlus * oneMinus - b * b) / d,\n (b * oneMinus + onePlus * b) / d)\n : new Complex(\n (a !== -1) ? (a / 0) : 0,\n (b !== 0) ? (b / 0) : 0);\n\n var temp = x['re'];\n x['re'] = logHypot(x['re'], x['im']) / 2;\n x['im'] = Math.atan2(x['im'], temp) / 2;\n if (noIM) {\n x['im'] = -x['im'];\n }\n return x;\n },\n\n /**\n * Calculate the complex acoth\n *\n * @returns {Complex}\n */\n 'acoth': function() {\n\n // acoth(c) = log((c+1) / (c-1)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Math.PI / 2);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atanh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atanh();\n },\n\n /**\n * Calculate the complex acsch\n *\n * @returns {Complex}\n */\n 'acsch': function() {\n\n // acsch(c) = log((1+sqrt(1+c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n\n return new Complex(\n (a !== 0)\n ? Math.log(a + Math.sqrt(a * a + 1))\n : Infinity, 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asinh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asinh();\n },\n\n /**\n * Calculate the complex asech\n *\n * @returns {Complex}\n */\n 'asech': function() {\n\n // asech(c) = log((1+sqrt(1-c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acosh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acosh();\n },\n\n /**\n * Calculate the complex inverse 1/z\n *\n * @returns {Complex}\n */\n 'inverse': function() {\n\n // 1 / 0 = Infinity and 1 / Infinity = 0\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n if (this['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n var a = this['re'];\n var b = this['im'];\n\n var d = a * a + b * b;\n\n return new Complex(a / d, -b / d);\n },\n\n /**\n * Returns the complex conjugate\n *\n * @returns {Complex}\n */\n 'conjugate': function() {\n\n return new Complex(this['re'], -this['im']);\n },\n\n /**\n * Gets the negated complex number\n *\n * @returns {Complex}\n */\n 'neg': function() {\n\n return new Complex(-this['re'], -this['im']);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'ceil': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.ceil(this['re'] * places) / places,\n Math.ceil(this['im'] * places) / places);\n },\n\n /**\n * Floors the actual complex number\n *\n * @returns {Complex}\n */\n 'floor': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.floor(this['re'] * places) / places,\n Math.floor(this['im'] * places) / places);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'round': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.round(this['re'] * places) / places,\n Math.round(this['im'] * places) / places);\n },\n\n /**\n * Compares two complex numbers\n *\n * **Note:** new Complex(Infinity).equals(Infinity) === false\n *\n * @returns {boolean}\n */\n 'equals': function(a, b) {\n\n var z = new Complex(a, b);\n\n return Math.abs(z['re'] - this['re']) <= Complex['EPSILON'] &&\n Math.abs(z['im'] - this['im']) <= Complex['EPSILON'];\n },\n\n /**\n * Clones the actual object\n *\n * @returns {Complex}\n */\n 'clone': function() {\n\n return new Complex(this['re'], this['im']);\n },\n\n /**\n * Gets a string of the actual complex number\n *\n * @returns {string}\n */\n 'toString': function() {\n\n var a = this['re'];\n var b = this['im'];\n var ret = '';\n\n if (this['isNaN']()) {\n return 'NaN';\n }\n\n if (this['isZero']()) {\n return '0';\n }\n\n if (this['isInfinite']()) {\n return 'Infinity';\n }\n\n if (a !== 0) {\n ret += a;\n }\n\n if (b !== 0) {\n\n if (a !== 0) {\n ret += b < 0 ? ' - ' : ' + ';\n } else if (b < 0) {\n ret += '-';\n }\n\n b = Math.abs(b);\n\n if (1 !== b) {\n ret += b;\n }\n ret += 'i';\n }\n\n if (!ret)\n return '0';\n\n return ret;\n },\n\n /**\n * Returns the actual number as a vector\n *\n * @returns {Array}\n */\n 'toVector': function() {\n\n return [this['re'], this['im']];\n },\n\n /**\n * Returns the actual real value of the current object\n *\n * @returns {number|null}\n */\n 'valueOf': function() {\n\n if (this['im'] === 0) {\n return this['re'];\n }\n return null;\n },\n\n /**\n * Determines whether a complex number is not on the Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isNaN': function() {\n return isNaN(this['re']) || isNaN(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the zero pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isZero': function() {\n return (\n (this['re'] === 0 || this['re'] === -0) &&\n (this['im'] === 0 || this['im'] === -0)\n );\n },\n\n /**\n * Determines whether a complex number is not at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isFinite': function() {\n return isFinite(this['re']) && isFinite(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isInfinite': function() {\n return !(this['isNaN']() || this['isFinite']());\n }\n };\n\n Complex['ZERO'] = new Complex(0, 0);\n Complex['ONE'] = new Complex(1, 0);\n Complex['I'] = new Complex(0, 1);\n Complex['PI'] = new Complex(Math.PI, 0);\n Complex['E'] = new Complex(Math.E, 0);\n Complex['INFINITY'] = new Complex(Infinity, Infinity);\n Complex['NAN'] = new Complex(NaN, NaN);\n Complex['EPSILON'] = 1e-16;\n\n if (typeof define === 'function' && define['amd']) {\n define([], function() {\n return Complex;\n });\n } else if (typeof exports === 'object') {\n Object.defineProperty(exports, \"__esModule\", {'value': true});\n Complex['default'] = Complex;\n Complex['Complex'] = Complex;\n module['exports'] = Complex;\n } else {\n root['Complex'] = Complex;\n }\n\n})(this);\n","module.exports = function() {\n\tthrow new Error(\"define cannot be used indirect\");\n};\n","/**\n * @license Fraction.js v4.0.12 09/09/2015\n * http://www.xarg.org/2014/03/rational-numbers-in-javascript/\n *\n * Copyright (c) 2015, Robert Eisele (robert@xarg.org)\n * Dual licensed under the MIT or GPL Version 2 licenses.\n **/\n\n\n/**\n *\n * This class offers the possibility to calculate fractions.\n * You can pass a fraction in different formats. Either as array, as double, as string or as an integer.\n *\n * Array/Object form\n * [ 0 => , 1 => ]\n * [ n => , d => ]\n *\n * Integer form\n * - Single integer value\n *\n * Double form\n * - Single double value\n *\n * String form\n * 123.456 - a simple double\n * 123/456 - a string fraction\n * 123.'456' - a double with repeating decimal places\n * 123.(456) - synonym\n * 123.45'6' - a double with repeating last place\n * 123.45(6) - synonym\n *\n * Example:\n *\n * var f = new Fraction(\"9.4'31'\");\n * f.mul([-4, 3]).div(4.9);\n *\n */\n\n(function(root) {\n\n \"use strict\";\n\n // Maximum search depth for cyclic rational numbers. 2000 should be more than enough.\n // Example: 1/7 = 0.(142857) has 6 repeating decimal places.\n // If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits\n var MAX_CYCLE_LEN = 2000;\n\n // Parsed data to avoid calling \"new\" all the time\n var P = {\n \"s\": 1,\n \"n\": 0,\n \"d\": 1\n };\n\n function createError(name) {\n\n function errorConstructor() {\n var temp = Error.apply(this, arguments);\n temp['name'] = this['name'] = name;\n this['stack'] = temp['stack'];\n this['message'] = temp['message'];\n }\n\n /**\n * Error constructor\n *\n * @constructor\n */\n function IntermediateInheritor() { }\n IntermediateInheritor.prototype = Error.prototype;\n errorConstructor.prototype = new IntermediateInheritor();\n\n return errorConstructor;\n }\n\n var DivisionByZero = Fraction['DivisionByZero'] = createError('DivisionByZero');\n var InvalidParameter = Fraction['InvalidParameter'] = createError('InvalidParameter');\n\n function assign(n, s) {\n\n if (isNaN(n = parseInt(n, 10))) {\n throwInvalidParam();\n }\n return n * s;\n }\n\n function throwInvalidParam() {\n throw new InvalidParameter();\n }\n\n var parse = function(p1, p2) {\n\n var n = 0, d = 1, s = 1;\n var v = 0, w = 0, x = 0, y = 1, z = 1;\n\n var A = 0, B = 1;\n var C = 1, D = 1;\n\n var N = 10000000;\n var M;\n\n if (p1 === undefined || p1 === null) {\n /* void */\n } else if (p2 !== undefined) {\n n = p1;\n d = p2;\n s = n * d;\n } else\n switch (typeof p1) {\n\n case \"object\":\n {\n if (\"d\" in p1 && \"n\" in p1) {\n n = p1[\"n\"];\n d = p1[\"d\"];\n if (\"s\" in p1)\n n *= p1[\"s\"];\n } else if (0 in p1) {\n n = p1[0];\n if (1 in p1)\n d = p1[1];\n } else {\n throwInvalidParam();\n }\n s = n * d;\n break;\n }\n case \"number\":\n {\n if (p1 < 0) {\n s = p1;\n p1 = -p1;\n }\n\n if (p1 % 1 === 0) {\n n = p1;\n } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow\n\n if (p1 >= 1) {\n z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10));\n p1 /= z;\n }\n\n // Using Farey Sequences\n // http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/\n\n while (B <= N && D <= N) {\n M = (A + C) / (B + D);\n\n if (p1 === M) {\n if (B + D <= N) {\n n = A + C;\n d = B + D;\n } else if (D > B) {\n n = C;\n d = D;\n } else {\n n = A;\n d = B;\n }\n break;\n\n } else {\n\n if (p1 > M) {\n A += C;\n B += D;\n } else {\n C += A;\n D += B;\n }\n\n if (B > N) {\n n = C;\n d = D;\n } else {\n n = A;\n d = B;\n }\n }\n }\n n *= z;\n } else if (isNaN(p1) || isNaN(p2)) {\n d = n = NaN;\n }\n break;\n }\n case \"string\":\n {\n B = p1.match(/\\d+|./g);\n\n if (B === null)\n throwInvalidParam();\n\n if (B[A] === '-') {// Check for minus sign at the beginning\n s = -1;\n A++;\n } else if (B[A] === '+') {// Check for plus sign at the beginning\n A++;\n }\n\n if (B.length === A + 1) { // Check if it's just a simple number \"1234\"\n w = assign(B[A++], s);\n } else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number\n\n if (B[A] !== '.') { // Handle 0.5 and .5\n v = assign(B[A++], s);\n }\n A++;\n\n // Check for decimal places\n if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === \"'\" && B[A + 3] === \"'\") {\n w = assign(B[A], s);\n y = Math.pow(10, B[A].length);\n A++;\n }\n\n // Check for repeating places\n if (B[A] === '(' && B[A + 2] === ')' || B[A] === \"'\" && B[A + 2] === \"'\") {\n x = assign(B[A + 1], s);\n z = Math.pow(10, B[A + 1].length) - 1;\n A += 3;\n }\n\n } else if (B[A + 1] === '/' || B[A + 1] === ':') { // Check for a simple fraction \"123/456\" or \"123:456\"\n w = assign(B[A], s);\n y = assign(B[A + 2], 1);\n A += 3;\n } else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction \"123 1/2\"\n v = assign(B[A], s);\n w = assign(B[A + 2], s);\n y = assign(B[A + 4], 1);\n A += 5;\n }\n\n if (B.length <= A) { // Check for more tokens on the stack\n d = y * z;\n s = /* void */\n n = x + d * v + z * w;\n break;\n }\n\n /* Fall through on error */\n }\n default:\n throwInvalidParam();\n }\n\n if (d === 0) {\n throw new DivisionByZero();\n }\n\n P[\"s\"] = s < 0 ? -1 : 1;\n P[\"n\"] = Math.abs(n);\n P[\"d\"] = Math.abs(d);\n };\n\n function modpow(b, e, m) {\n\n var r = 1;\n for (; e > 0; b = (b * b) % m, e >>= 1) {\n\n if (e & 1) {\n r = (r * b) % m;\n }\n }\n return r;\n }\n\n\n function cycleLen(n, d) {\n\n for (; d % 2 === 0;\n d /= 2) {\n }\n\n for (; d % 5 === 0;\n d /= 5) {\n }\n\n if (d === 1) // Catch non-cyclic numbers\n return 0;\n\n // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem:\n // 10^(d-1) % d == 1\n // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone,\n // as we want to translate the numbers to strings.\n\n var rem = 10 % d;\n var t = 1;\n\n for (; rem !== 1; t++) {\n rem = rem * 10 % d;\n\n if (t > MAX_CYCLE_LEN)\n return 0; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1`\n }\n return t;\n }\n\n\n function cycleStart(n, d, len) {\n\n var rem1 = 1;\n var rem2 = modpow(10, len, d);\n\n for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE)\n // Solve 10^s == 10^(s+t) (mod d)\n\n if (rem1 === rem2)\n return t;\n\n rem1 = rem1 * 10 % d;\n rem2 = rem2 * 10 % d;\n }\n return 0;\n }\n\n function gcd(a, b) {\n\n if (!a)\n return b;\n if (!b)\n return a;\n\n while (1) {\n a %= b;\n if (!a)\n return b;\n b %= a;\n if (!b)\n return a;\n }\n };\n\n /**\n * Module constructor\n *\n * @constructor\n * @param {number|Fraction=} a\n * @param {number=} b\n */\n function Fraction(a, b) {\n\n if (!(this instanceof Fraction)) {\n return new Fraction(a, b);\n }\n\n parse(a, b);\n\n if (Fraction['REDUCE']) {\n a = gcd(P[\"d\"], P[\"n\"]); // Abuse a\n } else {\n a = 1;\n }\n\n this[\"s\"] = P[\"s\"];\n this[\"n\"] = P[\"n\"] / a;\n this[\"d\"] = P[\"d\"] / a;\n }\n\n /**\n * Boolean global variable to be able to disable automatic reduction of the fraction\n *\n */\n Fraction['REDUCE'] = 1;\n\n Fraction.prototype = {\n\n \"s\": 1,\n \"n\": 0,\n \"d\": 1,\n\n /**\n * Calculates the absolute value\n *\n * Ex: new Fraction(-4).abs() => 4\n **/\n \"abs\": function() {\n\n return new Fraction(this[\"n\"], this[\"d\"]);\n },\n\n /**\n * Inverts the sign of the current fraction\n *\n * Ex: new Fraction(-4).neg() => 4\n **/\n \"neg\": function() {\n\n return new Fraction(-this[\"s\"] * this[\"n\"], this[\"d\"]);\n },\n\n /**\n * Adds two rational numbers\n *\n * Ex: new Fraction({n: 2, d: 3}).add(\"14.9\") => 467 / 30\n **/\n \"add\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * this[\"n\"] * P[\"d\"] + P[\"s\"] * this[\"d\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Subtracts two rational numbers\n *\n * Ex: new Fraction({n: 2, d: 3}).add(\"14.9\") => -427 / 30\n **/\n \"sub\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * this[\"n\"] * P[\"d\"] - P[\"s\"] * this[\"d\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Multiplies two rational numbers\n *\n * Ex: new Fraction(\"-17.(345)\").mul(3) => 5776 / 111\n **/\n \"mul\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * P[\"s\"] * this[\"n\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Divides two rational numbers\n *\n * Ex: new Fraction(\"-17.(345)\").inverse().div(3)\n **/\n \"div\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * P[\"s\"] * this[\"n\"] * P[\"d\"],\n this[\"d\"] * P[\"n\"]\n );\n },\n\n /**\n * Clones the actual object\n *\n * Ex: new Fraction(\"-17.(345)\").clone()\n **/\n \"clone\": function() {\n return new Fraction(this);\n },\n\n /**\n * Calculates the modulo of two rational numbers - a more precise fmod\n *\n * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6)\n **/\n \"mod\": function(a, b) {\n\n if (isNaN(this['n']) || isNaN(this['d'])) {\n return new Fraction(NaN);\n }\n\n if (a === undefined) {\n return new Fraction(this[\"s\"] * this[\"n\"] % this[\"d\"], 1);\n }\n\n parse(a, b);\n if (0 === P[\"n\"] && 0 === this[\"d\"]) {\n Fraction(0, 0); // Throw DivisionByZero\n }\n\n /*\n * First silly attempt, kinda slow\n *\n return that[\"sub\"]({\n \"n\": num[\"n\"] * Math.floor((this.n / this.d) / (num.n / num.d)),\n \"d\": num[\"d\"],\n \"s\": this[\"s\"]\n });*/\n\n /*\n * New attempt: a1 / b1 = a2 / b2 * q + r\n * => b2 * a1 = a2 * b1 * q + b1 * b2 * r\n * => (b2 * a1 % a2 * b1) / (b1 * b2)\n */\n return new Fraction(\n this[\"s\"] * (P[\"d\"] * this[\"n\"]) % (P[\"n\"] * this[\"d\"]),\n P[\"d\"] * this[\"d\"]\n );\n },\n\n /**\n * Calculates the fractional gcd of two rational numbers\n *\n * Ex: new Fraction(5,8).gcd(3,7) => 1/56\n */\n \"gcd\": function(a, b) {\n\n parse(a, b);\n\n // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d)\n\n return new Fraction(gcd(P[\"n\"], this[\"n\"]) * gcd(P[\"d\"], this[\"d\"]), P[\"d\"] * this[\"d\"]);\n },\n\n /**\n * Calculates the fractional lcm of two rational numbers\n *\n * Ex: new Fraction(5,8).lcm(3,7) => 15\n */\n \"lcm\": function(a, b) {\n\n parse(a, b);\n\n // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d)\n\n if (P[\"n\"] === 0 && this[\"n\"] === 0) {\n return new Fraction;\n }\n return new Fraction(P[\"n\"] * this[\"n\"], gcd(P[\"n\"], this[\"n\"]) * gcd(P[\"d\"], this[\"d\"]));\n },\n\n /**\n * Calculates the ceil of a rational number\n *\n * Ex: new Fraction('4.(3)').ceil() => (5 / 1)\n **/\n \"ceil\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.ceil(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Calculates the floor of a rational number\n *\n * Ex: new Fraction('4.(3)').floor() => (4 / 1)\n **/\n \"floor\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.floor(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Rounds a rational numbers\n *\n * Ex: new Fraction('4.(3)').round() => (4 / 1)\n **/\n \"round\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.round(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Gets the inverse of the fraction, means numerator and denominator are exchanged\n *\n * Ex: new Fraction([-3, 4]).inverse() => -4 / 3\n **/\n \"inverse\": function() {\n\n return new Fraction(this[\"s\"] * this[\"d\"], this[\"n\"]);\n },\n\n /**\n * Calculates the fraction to some integer exponent\n *\n * Ex: new Fraction(-1,2).pow(-3) => -8\n */\n \"pow\": function(m) {\n\n if (m < 0) {\n return new Fraction(Math.pow(this['s'] * this[\"d\"], -m), Math.pow(this[\"n\"], -m));\n } else {\n return new Fraction(Math.pow(this['s'] * this[\"n\"], m), Math.pow(this[\"d\"], m));\n }\n },\n\n /**\n * Check if two rational numbers are the same\n *\n * Ex: new Fraction(19.6).equals([98, 5]);\n **/\n \"equals\": function(a, b) {\n\n parse(a, b);\n return this[\"s\"] * this[\"n\"] * P[\"d\"] === P[\"s\"] * P[\"n\"] * this[\"d\"]; // Same as compare() === 0\n },\n\n /**\n * Check if two rational numbers are the same\n *\n * Ex: new Fraction(19.6).equals([98, 5]);\n **/\n \"compare\": function(a, b) {\n\n parse(a, b);\n var t = (this[\"s\"] * this[\"n\"] * P[\"d\"] - P[\"s\"] * P[\"n\"] * this[\"d\"]);\n return (0 < t) - (t < 0);\n },\n\n \"simplify\": function(eps) {\n\n // First naive implementation, needs improvement\n\n if (isNaN(this['n']) || isNaN(this['d'])) {\n return this;\n }\n\n var cont = this['abs']()['toContinued']();\n\n eps = eps || 0.001;\n\n function rec(a) {\n if (a.length === 1)\n return new Fraction(a[0]);\n return rec(a.slice(1))['inverse']()['add'](a[0]);\n }\n\n for (var i = 0; i < cont.length; i++) {\n var tmp = rec(cont.slice(0, i + 1));\n if (tmp['sub'](this['abs']())['abs']().valueOf() < eps) {\n return tmp['mul'](this['s']);\n }\n }\n return this;\n },\n\n /**\n * Check if two rational numbers are divisible\n *\n * Ex: new Fraction(19.6).divisible(1.5);\n */\n \"divisible\": function(a, b) {\n\n parse(a, b);\n return !(!(P[\"n\"] * this[\"d\"]) || ((this[\"n\"] * P[\"d\"]) % (P[\"n\"] * this[\"d\"])));\n },\n\n /**\n * Returns a decimal representation of the fraction\n *\n * Ex: new Fraction(\"100.'91823'\").valueOf() => 100.91823918239183\n **/\n 'valueOf': function() {\n\n return this[\"s\"] * this[\"n\"] / this[\"d\"];\n },\n\n /**\n * Returns a string-fraction representation of a Fraction object\n *\n * Ex: new Fraction(\"1.'3'\").toFraction() => \"4 1/3\"\n **/\n 'toFraction': function(excludeWhole) {\n\n var whole, str = \"\";\n var n = this[\"n\"];\n var d = this[\"d\"];\n if (this[\"s\"] < 0) {\n str += '-';\n }\n\n if (d === 1) {\n str += n;\n } else {\n\n if (excludeWhole && (whole = Math.floor(n / d)) > 0) {\n str += whole;\n str += \" \";\n n %= d;\n }\n\n str += n;\n str += '/';\n str += d;\n }\n return str;\n },\n\n /**\n * Returns a latex representation of a Fraction object\n *\n * Ex: new Fraction(\"1.'3'\").toLatex() => \"\\frac{4}{3}\"\n **/\n 'toLatex': function(excludeWhole) {\n\n var whole, str = \"\";\n var n = this[\"n\"];\n var d = this[\"d\"];\n if (this[\"s\"] < 0) {\n str += '-';\n }\n\n if (d === 1) {\n str += n;\n } else {\n\n if (excludeWhole && (whole = Math.floor(n / d)) > 0) {\n str += whole;\n n %= d;\n }\n\n str += \"\\\\frac{\";\n str += n;\n str += '}{';\n str += d;\n str += '}';\n }\n return str;\n },\n\n /**\n * Returns an array of continued fraction elements\n *\n * Ex: new Fraction(\"7/8\").toContinued() => [0,1,7]\n */\n 'toContinued': function() {\n\n var t;\n var a = this['n'];\n var b = this['d'];\n var res = [];\n\n if (isNaN(a) || isNaN(b)) {\n return res;\n }\n\n do {\n res.push(Math.floor(a / b));\n t = a % b;\n a = b;\n b = t;\n } while (a !== 1);\n\n return res;\n },\n\n /**\n * Creates a string representation of a fraction with all digits\n *\n * Ex: new Fraction(\"100.'91823'\").toString() => \"100.(91823)\"\n **/\n 'toString': function(dec) {\n\n var g;\n var N = this[\"n\"];\n var D = this[\"d\"];\n\n if (isNaN(N) || isNaN(D)) {\n return \"NaN\";\n }\n\n if (!Fraction['REDUCE']) {\n g = gcd(N, D);\n N /= g;\n D /= g;\n }\n\n dec = dec || 15; // 15 = decimal places when no repitation\n\n var cycLen = cycleLen(N, D); // Cycle length\n var cycOff = cycleStart(N, D, cycLen); // Cycle start\n\n var str = this['s'] === -1 ? \"-\" : \"\";\n\n str += N / D | 0;\n\n N %= D;\n N *= 10;\n\n if (N)\n str += \".\";\n\n if (cycLen) {\n\n for (var i = cycOff; i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n str += \"(\";\n for (var i = cycLen; i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n str += \")\";\n } else {\n for (var i = dec; N && i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n }\n return str;\n }\n };\n\n if (typeof define === \"function\" && define[\"amd\"]) {\n define([], function() {\n return Fraction;\n });\n } else if (typeof exports === \"object\") {\n Object.defineProperty(Fraction, \"__esModule\", { 'value': true });\n Fraction['default'] = Fraction;\n Fraction['Fraction'] = Fraction;\n module['exports'] = Fraction;\n } else {\n root['Fraction'] = Fraction;\n }\n\n})(this);\n","/*\r\n * Natural Sort algorithm for Javascript - Version 0.7 - Released under MIT license\r\n * Author: Jim Palmer (based on chunking idea from Dave Koelle)\r\n */\r\n/*jshint unused:false */\r\nmodule.exports = function naturalSort (a, b) {\r\n\t\"use strict\";\r\n\tvar re = /(^([+\\-]?(?:0|[1-9]\\d*)(?:\\.\\d*)?(?:[eE][+\\-]?\\d+)?)?$|^0x[0-9a-f]+$|\\d+)/gi,\r\n\t\tsre = /(^[ ]*|[ ]*$)/g,\r\n\t\tdre = /(^([\\w ]+,?[\\w ]+)?[\\w ]+,?[\\w ]+\\d+:\\d+(:\\d+)?[\\w ]?|^\\d{1,4}[\\/\\-]\\d{1,4}[\\/\\-]\\d{1,4}|^\\w+, \\w+ \\d+, \\d{4})/,\r\n\t\thre = /^0x[0-9a-f]+$/i,\r\n\t\tore = /^0/,\r\n\t\ti = function(s) { return naturalSort.insensitive && ('' + s).toLowerCase() || '' + s; },\r\n\t\t// convert all to strings strip whitespace\r\n\t\tx = i(a).replace(sre, '') || '',\r\n\t\ty = i(b).replace(sre, '') || '',\r\n\t\t// chunk/tokenize\r\n\t\txN = x.replace(re, '\\0$1\\0').replace(/\\0$/,'').replace(/^\\0/,'').split('\\0'),\r\n\t\tyN = y.replace(re, '\\0$1\\0').replace(/\\0$/,'').replace(/^\\0/,'').split('\\0'),\r\n\t\t// numeric, hex or date detection\r\n\t\txD = parseInt(x.match(hre), 16) || (xN.length !== 1 && x.match(dre) && Date.parse(x)),\r\n\t\tyD = parseInt(y.match(hre), 16) || xD && y.match(dre) && Date.parse(y) || null,\r\n\t\toFxNcL, oFyNcL;\r\n\t// first try and sort Hex codes or Dates\r\n\tif (yD) {\r\n\t\tif ( xD < yD ) { return -1; }\r\n\t\telse if ( xD > yD ) { return 1; }\r\n\t}\r\n\t// natural sorting through split numeric strings and default strings\r\n\tfor(var cLoc=0, numS=Math.max(xN.length, yN.length); cLoc < numS; cLoc++) {\r\n\t\t// find floats not starting with '0', string or 0 if not defined (Clint Priest)\r\n\t\toFxNcL = !(xN[cLoc] || '').match(ore) && parseFloat(xN[cLoc]) || xN[cLoc] || 0;\r\n\t\toFyNcL = !(yN[cLoc] || '').match(ore) && parseFloat(yN[cLoc]) || yN[cLoc] || 0;\r\n\t\t// handle numeric vs string comparison - number < string - (Kyle Adams)\r\n\t\tif (isNaN(oFxNcL) !== isNaN(oFyNcL)) { return (isNaN(oFxNcL)) ? 1 : -1; }\r\n\t\t// rely on string comparison if different types - i.e. '02' < 2 != '02' < '2'\r\n\t\telse if (typeof oFxNcL !== typeof oFyNcL) {\r\n\t\t\toFxNcL += '';\r\n\t\t\toFyNcL += '';\r\n\t\t}\r\n\t\tif (oFxNcL < oFyNcL) { return -1; }\r\n\t\tif (oFxNcL > oFyNcL) { return 1; }\r\n\t}\r\n\treturn 0;\r\n};\r\n","module.exports = function(module) {\n\tif (!module.webpackPolyfill) {\n\t\tmodule.deprecate = function() {};\n\t\tmodule.paths = [];\n\t\t// module.parent = undefined by default\n\t\tif (!module.children) module.children = [];\n\t\tObject.defineProperty(module, \"loaded\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.l;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"id\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.i;\n\t\t\t}\n\t\t});\n\t\tmodule.webpackPolyfill = 1;\n\t}\n\treturn module;\n};\n","/* globals __webpack_amd_options__ */\nmodule.exports = __webpack_amd_options__;\n",";(function (globalScope) {\r\n 'use strict';\r\n\r\n\r\n /*\r\n * decimal.js v10.2.1\r\n * An arbitrary-precision Decimal type for JavaScript.\r\n * https://github.com/MikeMcl/decimal.js\r\n * Copyright (c) 2020 Michael Mclaughlin \r\n * MIT Licence\r\n */\r\n\r\n\r\n // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ //\r\n\r\n\r\n // The maximum exponent magnitude.\r\n // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.\r\n var EXP_LIMIT = 9e15, // 0 to 9e15\r\n\r\n // The limit on the value of `precision`, and on the value of the first argument to\r\n // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.\r\n MAX_DIGITS = 1e9, // 0 to 1e9\r\n\r\n // Base conversion alphabet.\r\n NUMERALS = '0123456789abcdef',\r\n\r\n // The natural logarithm of 10 (1025 digits).\r\n LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',\r\n\r\n // Pi (1025 digits).\r\n PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',\r\n\r\n\r\n // The initial configuration properties of the Decimal constructor.\r\n DEFAULTS = {\r\n\r\n // These values must be integers within the stated ranges (inclusive).\r\n // Most of these values can be changed at run-time using the `Decimal.config` method.\r\n\r\n // The maximum number of significant digits of the result of a calculation or base conversion.\r\n // E.g. `Decimal.config({ precision: 20 });`\r\n precision: 20, // 1 to MAX_DIGITS\r\n\r\n // The rounding mode used when rounding to `precision`.\r\n //\r\n // ROUND_UP 0 Away from zero.\r\n // ROUND_DOWN 1 Towards zero.\r\n // ROUND_CEIL 2 Towards +Infinity.\r\n // ROUND_FLOOR 3 Towards -Infinity.\r\n // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up.\r\n // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.\r\n // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.\r\n // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.\r\n // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.\r\n //\r\n // E.g.\r\n // `Decimal.rounding = 4;`\r\n // `Decimal.rounding = Decimal.ROUND_HALF_UP;`\r\n rounding: 4, // 0 to 8\r\n\r\n // The modulo mode used when calculating the modulus: a mod n.\r\n // The quotient (q = a / n) is calculated according to the corresponding rounding mode.\r\n // The remainder (r) is calculated as: r = a - n * q.\r\n //\r\n // UP 0 The remainder is positive if the dividend is negative, else is negative.\r\n // DOWN 1 The remainder has the same sign as the dividend (JavaScript %).\r\n // FLOOR 3 The remainder has the same sign as the divisor (Python %).\r\n // HALF_EVEN 6 The IEEE 754 remainder function.\r\n // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.\r\n //\r\n // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian\r\n // division (9) are commonly used for the modulus operation. The other rounding modes can also\r\n // be used, but they may not give useful results.\r\n modulo: 1, // 0 to 9\r\n\r\n // The exponent value at and beneath which `toString` returns exponential notation.\r\n // JavaScript numbers: -7\r\n toExpNeg: -7, // 0 to -EXP_LIMIT\r\n\r\n // The exponent value at and above which `toString` returns exponential notation.\r\n // JavaScript numbers: 21\r\n toExpPos: 21, // 0 to EXP_LIMIT\r\n\r\n // The minimum exponent value, beneath which underflow to zero occurs.\r\n // JavaScript numbers: -324 (5e-324)\r\n minE: -EXP_LIMIT, // -1 to -EXP_LIMIT\r\n\r\n // The maximum exponent value, above which overflow to Infinity occurs.\r\n // JavaScript numbers: 308 (1.7976931348623157e+308)\r\n maxE: EXP_LIMIT, // 1 to EXP_LIMIT\r\n\r\n // Whether to use cryptographically-secure random number generation, if available.\r\n crypto: false // true/false\r\n },\r\n\r\n\r\n // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //\r\n\r\n\r\n Decimal, inexact, noConflict, quadrant,\r\n external = true,\r\n\r\n decimalError = '[DecimalError] ',\r\n invalidArgument = decimalError + 'Invalid argument: ',\r\n precisionLimitExceeded = decimalError + 'Precision limit exceeded',\r\n cryptoUnavailable = decimalError + 'crypto unavailable',\r\n\r\n mathfloor = Math.floor,\r\n mathpow = Math.pow,\r\n\r\n isBinary = /^0b([01]+(\\.[01]*)?|\\.[01]+)(p[+-]?\\d+)?$/i,\r\n isHex = /^0x([0-9a-f]+(\\.[0-9a-f]*)?|\\.[0-9a-f]+)(p[+-]?\\d+)?$/i,\r\n isOctal = /^0o([0-7]+(\\.[0-7]*)?|\\.[0-7]+)(p[+-]?\\d+)?$/i,\r\n isDecimal = /^(\\d+(\\.\\d*)?|\\.\\d+)(e[+-]?\\d+)?$/i,\r\n\r\n BASE = 1e7,\r\n LOG_BASE = 7,\r\n MAX_SAFE_INTEGER = 9007199254740991,\r\n\r\n LN10_PRECISION = LN10.length - 1,\r\n PI_PRECISION = PI.length - 1,\r\n\r\n // Decimal.prototype object\r\n P = { name: '[object Decimal]' };\r\n\r\n\r\n // Decimal prototype methods\r\n\r\n\r\n /*\r\n * absoluteValue abs\r\n * ceil\r\n * comparedTo cmp\r\n * cosine cos\r\n * cubeRoot cbrt\r\n * decimalPlaces dp\r\n * dividedBy div\r\n * dividedToIntegerBy divToInt\r\n * equals eq\r\n * floor\r\n * greaterThan gt\r\n * greaterThanOrEqualTo gte\r\n * hyperbolicCosine cosh\r\n * hyperbolicSine sinh\r\n * hyperbolicTangent tanh\r\n * inverseCosine acos\r\n * inverseHyperbolicCosine acosh\r\n * inverseHyperbolicSine asinh\r\n * inverseHyperbolicTangent atanh\r\n * inverseSine asin\r\n * inverseTangent atan\r\n * isFinite\r\n * isInteger isInt\r\n * isNaN\r\n * isNegative isNeg\r\n * isPositive isPos\r\n * isZero\r\n * lessThan lt\r\n * lessThanOrEqualTo lte\r\n * logarithm log\r\n * [maximum] [max]\r\n * [minimum] [min]\r\n * minus sub\r\n * modulo mod\r\n * naturalExponential exp\r\n * naturalLogarithm ln\r\n * negated neg\r\n * plus add\r\n * precision sd\r\n * round\r\n * sine sin\r\n * squareRoot sqrt\r\n * tangent tan\r\n * times mul\r\n * toBinary\r\n * toDecimalPlaces toDP\r\n * toExponential\r\n * toFixed\r\n * toFraction\r\n * toHexadecimal toHex\r\n * toNearest\r\n * toNumber\r\n * toOctal\r\n * toPower pow\r\n * toPrecision\r\n * toSignificantDigits toSD\r\n * toString\r\n * truncated trunc\r\n * valueOf toJSON\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the absolute value of this Decimal.\r\n *\r\n */\r\n P.absoluteValue = P.abs = function () {\r\n var x = new this.constructor(this);\r\n if (x.s < 0) x.s = 1;\r\n return finalise(x);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of positive Infinity.\r\n *\r\n */\r\n P.ceil = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 2);\r\n };\r\n\r\n\r\n /*\r\n * Return\r\n * 1 if the value of this Decimal is greater than the value of `y`,\r\n * -1 if the value of this Decimal is less than the value of `y`,\r\n * 0 if they have the same value,\r\n * NaN if the value of either Decimal is NaN.\r\n *\r\n */\r\n P.comparedTo = P.cmp = function (y) {\r\n var i, j, xdL, ydL,\r\n x = this,\r\n xd = x.d,\r\n yd = (y = new x.constructor(y)).d,\r\n xs = x.s,\r\n ys = y.s;\r\n\r\n // Either NaN or ±Infinity?\r\n if (!xd || !yd) {\r\n return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;\r\n }\r\n\r\n // Either zero?\r\n if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;\r\n\r\n // Signs differ?\r\n if (xs !== ys) return xs;\r\n\r\n // Compare exponents.\r\n if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;\r\n\r\n xdL = xd.length;\r\n ydL = yd.length;\r\n\r\n // Compare digit by digit.\r\n for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {\r\n if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;\r\n }\r\n\r\n // Compare lengths.\r\n return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * cos(0) = 1\r\n * cos(-0) = 1\r\n * cos(Infinity) = NaN\r\n * cos(-Infinity) = NaN\r\n * cos(NaN) = NaN\r\n *\r\n */\r\n P.cosine = P.cos = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.d) return new Ctor(NaN);\r\n\r\n // cos(0) = cos(-0) = 1\r\n if (!x.d[0]) return new Ctor(1);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;\r\n Ctor.rounding = 1;\r\n\r\n x = cosine(Ctor, toLessThanHalfPi(Ctor, x));\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n *\r\n * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * cbrt(0) = 0\r\n * cbrt(-0) = -0\r\n * cbrt(1) = 1\r\n * cbrt(-1) = -1\r\n * cbrt(N) = N\r\n * cbrt(-I) = -I\r\n * cbrt(I) = I\r\n *\r\n * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))\r\n *\r\n */\r\n P.cubeRoot = P.cbrt = function () {\r\n var e, m, n, r, rep, s, sd, t, t3, t3plusx,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n external = false;\r\n\r\n // Initial estimate.\r\n s = x.s * mathpow(x.s * x, 1 / 3);\r\n\r\n // Math.cbrt underflow/overflow?\r\n // Pass x to Math.pow as integer, then adjust the exponent of the result.\r\n if (!s || Math.abs(s) == 1 / 0) {\r\n n = digitsToString(x.d);\r\n e = x.e;\r\n\r\n // Adjust n exponent so it is a multiple of 3 away from x exponent.\r\n if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');\r\n s = mathpow(n, 1 / 3);\r\n\r\n // Rarely, e may be one less than the result exponent value.\r\n e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));\r\n\r\n if (s == 1 / 0) {\r\n n = '5e' + e;\r\n } else {\r\n n = s.toExponential();\r\n n = n.slice(0, n.indexOf('e') + 1) + e;\r\n }\r\n\r\n r = new Ctor(n);\r\n r.s = x.s;\r\n } else {\r\n r = new Ctor(s.toString());\r\n }\r\n\r\n sd = (e = Ctor.precision) + 3;\r\n\r\n // Halley's method.\r\n // TODO? Compare Newton's method.\r\n for (;;) {\r\n t = r;\r\n t3 = t.times(t).times(t);\r\n t3plusx = t3.plus(x);\r\n r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);\r\n\r\n // TODO? Replace with for-loop and checkRoundingDigits.\r\n if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {\r\n n = n.slice(sd - 3, sd + 1);\r\n\r\n // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999\r\n // , i.e. approaching a rounding boundary, continue the iteration.\r\n if (n == '9999' || !rep && n == '4999') {\r\n\r\n // On the first iteration only, check to see if rounding up gives the exact result as the\r\n // nines may infinitely repeat.\r\n if (!rep) {\r\n finalise(t, e + 1, 0);\r\n\r\n if (t.times(t).times(t).eq(x)) {\r\n r = t;\r\n break;\r\n }\r\n }\r\n\r\n sd += 4;\r\n rep = 1;\r\n } else {\r\n\r\n // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.\r\n // If not, then there are further digits and m will be truthy.\r\n if (!+n || !+n.slice(1) && n.charAt(0) == '5') {\r\n\r\n // Truncate to the first rounding digit.\r\n finalise(r, e + 1, 1);\r\n m = !r.times(r).times(r).eq(x);\r\n }\r\n\r\n break;\r\n }\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, e, Ctor.rounding, m);\r\n };\r\n\r\n\r\n /*\r\n * Return the number of decimal places of the value of this Decimal.\r\n *\r\n */\r\n P.decimalPlaces = P.dp = function () {\r\n var w,\r\n d = this.d,\r\n n = NaN;\r\n\r\n if (d) {\r\n w = d.length - 1;\r\n n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;\r\n\r\n // Subtract the number of trailing zeros of the last word.\r\n w = d[w];\r\n if (w) for (; w % 10 == 0; w /= 10) n--;\r\n if (n < 0) n = 0;\r\n }\r\n\r\n return n;\r\n };\r\n\r\n\r\n /*\r\n * n / 0 = I\r\n * n / N = N\r\n * n / I = 0\r\n * 0 / n = 0\r\n * 0 / 0 = N\r\n * 0 / N = N\r\n * 0 / I = 0\r\n * N / n = N\r\n * N / 0 = N\r\n * N / N = N\r\n * N / I = N\r\n * I / n = I\r\n * I / 0 = I\r\n * I / N = N\r\n * I / I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.dividedBy = P.div = function (y) {\r\n return divide(this, new this.constructor(y));\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the integer part of dividing the value of this Decimal\r\n * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.dividedToIntegerBy = P.divToInt = function (y) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.\r\n *\r\n */\r\n P.equals = P.eq = function (y) {\r\n return this.cmp(y) === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of negative Infinity.\r\n *\r\n */\r\n P.floor = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 3);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is greater than the value of `y`, otherwise return\r\n * false.\r\n *\r\n */\r\n P.greaterThan = P.gt = function (y) {\r\n return this.cmp(y) > 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is greater than or equal to the value of `y`,\r\n * otherwise return false.\r\n *\r\n */\r\n P.greaterThanOrEqualTo = P.gte = function (y) {\r\n var k = this.cmp(y);\r\n return k == 1 || k === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [1, Infinity]\r\n *\r\n * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...\r\n *\r\n * cosh(0) = 1\r\n * cosh(-0) = 1\r\n * cosh(Infinity) = Infinity\r\n * cosh(-Infinity) = Infinity\r\n * cosh(NaN) = NaN\r\n *\r\n * x time taken (ms) result\r\n * 1000 9 9.8503555700852349694e+433\r\n * 10000 25 4.4034091128314607936e+4342\r\n * 100000 171 1.4033316802130615897e+43429\r\n * 1000000 3817 1.5166076984010437725e+434294\r\n * 10000000 abandoned after 2 minute wait\r\n *\r\n * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))\r\n *\r\n */\r\n P.hyperbolicCosine = P.cosh = function () {\r\n var k, n, pr, rm, len,\r\n x = this,\r\n Ctor = x.constructor,\r\n one = new Ctor(1);\r\n\r\n if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);\r\n if (x.isZero()) return one;\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n len = x.d.length;\r\n\r\n // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1\r\n // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n // TODO? Estimation reused from cosine() and may not be optimal here.\r\n if (len < 32) {\r\n k = Math.ceil(len / 3);\r\n n = (1 / tinyPow(4, k)).toString();\r\n } else {\r\n k = 16;\r\n n = '2.3283064365386962890625e-10';\r\n }\r\n\r\n x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);\r\n\r\n // Reverse argument reduction\r\n var cosh2_x,\r\n i = k,\r\n d8 = new Ctor(8);\r\n for (; i--;) {\r\n cosh2_x = x.times(x);\r\n x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));\r\n }\r\n\r\n return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...\r\n *\r\n * sinh(0) = 0\r\n * sinh(-0) = -0\r\n * sinh(Infinity) = Infinity\r\n * sinh(-Infinity) = -Infinity\r\n * sinh(NaN) = NaN\r\n *\r\n * x time taken (ms)\r\n * 10 2 ms\r\n * 100 5 ms\r\n * 1000 14 ms\r\n * 10000 82 ms\r\n * 100000 886 ms 1.4033316802130615897e+43429\r\n * 200000 2613 ms\r\n * 300000 5407 ms\r\n * 400000 8824 ms\r\n * 500000 13026 ms 8.7080643612718084129e+217146\r\n * 1000000 48543 ms\r\n *\r\n * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))\r\n *\r\n */\r\n P.hyperbolicSine = P.sinh = function () {\r\n var k, pr, rm, len,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n len = x.d.length;\r\n\r\n if (len < 3) {\r\n x = taylorSeries(Ctor, 2, x, x, true);\r\n } else {\r\n\r\n // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))\r\n // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))\r\n // 3 multiplications and 1 addition\r\n\r\n // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))\r\n // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))\r\n // 4 multiplications and 2 additions\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n k = 1.4 * Math.sqrt(len);\r\n k = k > 16 ? 16 : k | 0;\r\n\r\n x = x.times(1 / tinyPow(5, k));\r\n x = taylorSeries(Ctor, 2, x, x, true);\r\n\r\n // Reverse argument reduction\r\n var sinh2_x,\r\n d5 = new Ctor(5),\r\n d16 = new Ctor(16),\r\n d20 = new Ctor(20);\r\n for (; k--;) {\r\n sinh2_x = x.times(x);\r\n x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));\r\n }\r\n }\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * tanh(x) = sinh(x) / cosh(x)\r\n *\r\n * tanh(0) = 0\r\n * tanh(-0) = -0\r\n * tanh(Infinity) = 1\r\n * tanh(-Infinity) = -1\r\n * tanh(NaN) = NaN\r\n *\r\n */\r\n P.hyperbolicTangent = P.tanh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(x.s);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 7;\r\n Ctor.rounding = 1;\r\n\r\n return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of\r\n * this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [0, pi]\r\n *\r\n * acos(x) = pi/2 - asin(x)\r\n *\r\n * acos(0) = pi/2\r\n * acos(-0) = pi/2\r\n * acos(1) = 0\r\n * acos(-1) = pi\r\n * acos(1/2) = pi/3\r\n * acos(-1/2) = 2*pi/3\r\n * acos(|x| > 1) = NaN\r\n * acos(NaN) = NaN\r\n *\r\n */\r\n P.inverseCosine = P.acos = function () {\r\n var halfPi,\r\n x = this,\r\n Ctor = x.constructor,\r\n k = x.abs().cmp(1),\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding;\r\n\r\n if (k !== -1) {\r\n return k === 0\r\n // |x| is 1\r\n ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)\r\n // |x| > 1 or x is NaN\r\n : new Ctor(NaN);\r\n }\r\n\r\n if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3\r\n\r\n Ctor.precision = pr + 6;\r\n Ctor.rounding = 1;\r\n\r\n x = x.asin();\r\n halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return halfPi.minus(x);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [1, Infinity]\r\n * Range: [0, Infinity]\r\n *\r\n * acosh(x) = ln(x + sqrt(x^2 - 1))\r\n *\r\n * acosh(x < 1) = NaN\r\n * acosh(NaN) = NaN\r\n * acosh(Infinity) = Infinity\r\n * acosh(-Infinity) = NaN\r\n * acosh(0) = NaN\r\n * acosh(-0) = NaN\r\n * acosh(1) = 0\r\n * acosh(-1) = NaN\r\n *\r\n */\r\n P.inverseHyperbolicCosine = P.acosh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);\r\n if (!x.isFinite()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n external = false;\r\n\r\n x = x.times(x).minus(1).sqrt().plus(x);\r\n\r\n external = true;\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.ln();\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * asinh(x) = ln(x + sqrt(x^2 + 1))\r\n *\r\n * asinh(NaN) = NaN\r\n * asinh(Infinity) = Infinity\r\n * asinh(-Infinity) = -Infinity\r\n * asinh(0) = 0\r\n * asinh(-0) = -0\r\n *\r\n */\r\n P.inverseHyperbolicSine = P.asinh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;\r\n Ctor.rounding = 1;\r\n external = false;\r\n\r\n x = x.times(x).plus(1).sqrt().plus(x);\r\n\r\n external = true;\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.ln();\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * atanh(x) = 0.5 * ln((1 + x) / (1 - x))\r\n *\r\n * atanh(|x| > 1) = NaN\r\n * atanh(NaN) = NaN\r\n * atanh(Infinity) = NaN\r\n * atanh(-Infinity) = NaN\r\n * atanh(0) = 0\r\n * atanh(-0) = -0\r\n * atanh(1) = Infinity\r\n * atanh(-1) = -Infinity\r\n *\r\n */\r\n P.inverseHyperbolicTangent = P.atanh = function () {\r\n var pr, rm, wpr, xsd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n xsd = x.sd();\r\n\r\n if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);\r\n\r\n Ctor.precision = wpr = xsd - x.e;\r\n\r\n x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);\r\n\r\n Ctor.precision = pr + 4;\r\n Ctor.rounding = 1;\r\n\r\n x = x.ln();\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.times(0.5);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))\r\n *\r\n * asin(0) = 0\r\n * asin(-0) = -0\r\n * asin(1/2) = pi/6\r\n * asin(-1/2) = -pi/6\r\n * asin(1) = pi/2\r\n * asin(-1) = -pi/2\r\n * asin(|x| > 1) = NaN\r\n * asin(NaN) = NaN\r\n *\r\n * TODO? Compare performance of Taylor series.\r\n *\r\n */\r\n P.inverseSine = P.asin = function () {\r\n var halfPi, k,\r\n pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n k = x.abs().cmp(1);\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n if (k !== -1) {\r\n\r\n // |x| is 1\r\n if (k === 0) {\r\n halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n halfPi.s = x.s;\r\n return halfPi;\r\n }\r\n\r\n // |x| > 1 or x is NaN\r\n return new Ctor(NaN);\r\n }\r\n\r\n // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6\r\n\r\n Ctor.precision = pr + 6;\r\n Ctor.rounding = 1;\r\n\r\n x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.times(2);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n *\r\n * atan(0) = 0\r\n * atan(-0) = -0\r\n * atan(1) = pi/4\r\n * atan(-1) = -pi/4\r\n * atan(Infinity) = pi/2\r\n * atan(-Infinity) = -pi/2\r\n * atan(NaN) = NaN\r\n *\r\n */\r\n P.inverseTangent = P.atan = function () {\r\n var i, j, k, n, px, t, r, wpr, x2,\r\n x = this,\r\n Ctor = x.constructor,\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding;\r\n\r\n if (!x.isFinite()) {\r\n if (!x.s) return new Ctor(NaN);\r\n if (pr + 4 <= PI_PRECISION) {\r\n r = getPi(Ctor, pr + 4, rm).times(0.5);\r\n r.s = x.s;\r\n return r;\r\n }\r\n } else if (x.isZero()) {\r\n return new Ctor(x);\r\n } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {\r\n r = getPi(Ctor, pr + 4, rm).times(0.25);\r\n r.s = x.s;\r\n return r;\r\n }\r\n\r\n Ctor.precision = wpr = pr + 10;\r\n Ctor.rounding = 1;\r\n\r\n // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);\r\n\r\n // Argument reduction\r\n // Ensure |x| < 0.42\r\n // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))\r\n\r\n k = Math.min(28, wpr / LOG_BASE + 2 | 0);\r\n\r\n for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));\r\n\r\n external = false;\r\n\r\n j = Math.ceil(wpr / LOG_BASE);\r\n n = 1;\r\n x2 = x.times(x);\r\n r = new Ctor(x);\r\n px = x;\r\n\r\n // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n for (; i !== -1;) {\r\n px = px.times(x2);\r\n t = r.minus(px.div(n += 2));\r\n\r\n px = px.times(x2);\r\n r = t.plus(px.div(n += 2));\r\n\r\n if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);\r\n }\r\n\r\n if (k) r = r.times(2 << (k - 1));\r\n\r\n external = true;\r\n\r\n return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is a finite number, otherwise return false.\r\n *\r\n */\r\n P.isFinite = function () {\r\n return !!this.d;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is an integer, otherwise return false.\r\n *\r\n */\r\n P.isInteger = P.isInt = function () {\r\n return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is NaN, otherwise return false.\r\n *\r\n */\r\n P.isNaN = function () {\r\n return !this.s;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is negative, otherwise return false.\r\n *\r\n */\r\n P.isNegative = P.isNeg = function () {\r\n return this.s < 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is positive, otherwise return false.\r\n *\r\n */\r\n P.isPositive = P.isPos = function () {\r\n return this.s > 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is 0 or -0, otherwise return false.\r\n *\r\n */\r\n P.isZero = function () {\r\n return !!this.d && this.d[0] === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is less than `y`, otherwise return false.\r\n *\r\n */\r\n P.lessThan = P.lt = function (y) {\r\n return this.cmp(y) < 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.\r\n *\r\n */\r\n P.lessThanOrEqualTo = P.lte = function (y) {\r\n return this.cmp(y) < 1;\r\n };\r\n\r\n\r\n /*\r\n * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * If no base is specified, return log[10](arg).\r\n *\r\n * log[base](arg) = ln(arg) / ln(base)\r\n *\r\n * The result will always be correctly rounded if the base of the log is 10, and 'almost always'\r\n * otherwise:\r\n *\r\n * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen\r\n * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error\r\n * between the result and the correctly rounded result will be one ulp (unit in the last place).\r\n *\r\n * log[-b](a) = NaN\r\n * log[0](a) = NaN\r\n * log[1](a) = NaN\r\n * log[NaN](a) = NaN\r\n * log[Infinity](a) = NaN\r\n * log[b](0) = -Infinity\r\n * log[b](-0) = -Infinity\r\n * log[b](-a) = NaN\r\n * log[b](1) = 0\r\n * log[b](Infinity) = Infinity\r\n * log[b](NaN) = NaN\r\n *\r\n * [base] {number|string|Decimal} The base of the logarithm.\r\n *\r\n */\r\n P.logarithm = P.log = function (base) {\r\n var isBase10, d, denominator, k, inf, num, sd, r,\r\n arg = this,\r\n Ctor = arg.constructor,\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding,\r\n guard = 5;\r\n\r\n // Default base is 10.\r\n if (base == null) {\r\n base = new Ctor(10);\r\n isBase10 = true;\r\n } else {\r\n base = new Ctor(base);\r\n d = base.d;\r\n\r\n // Return NaN if base is negative, or non-finite, or is 0 or 1.\r\n if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);\r\n\r\n isBase10 = base.eq(10);\r\n }\r\n\r\n d = arg.d;\r\n\r\n // Is arg negative, non-finite, 0 or 1?\r\n if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {\r\n return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);\r\n }\r\n\r\n // The result will have a non-terminating decimal expansion if base is 10 and arg is not an\r\n // integer power of 10.\r\n if (isBase10) {\r\n if (d.length > 1) {\r\n inf = true;\r\n } else {\r\n for (k = d[0]; k % 10 === 0;) k /= 10;\r\n inf = k !== 1;\r\n }\r\n }\r\n\r\n external = false;\r\n sd = pr + guard;\r\n num = naturalLogarithm(arg, sd);\r\n denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n\r\n // The result will have 5 rounding digits.\r\n r = divide(num, denominator, sd, 1);\r\n\r\n // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,\r\n // calculate 10 further digits.\r\n //\r\n // If the result is known to have an infinite decimal expansion, repeat this until it is clear\r\n // that the result is above or below the boundary. Otherwise, if after calculating the 10\r\n // further digits, the last 14 are nines, round up and assume the result is exact.\r\n // Also assume the result is exact if the last 14 are zero.\r\n //\r\n // Example of a result that will be incorrectly rounded:\r\n // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...\r\n // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it\r\n // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so\r\n // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal\r\n // place is still 2.6.\r\n if (checkRoundingDigits(r.d, k = pr, rm)) {\r\n\r\n do {\r\n sd += 10;\r\n num = naturalLogarithm(arg, sd);\r\n denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n r = divide(num, denominator, sd, 1);\r\n\r\n if (!inf) {\r\n\r\n // Check for 14 nines from the 2nd rounding digit, as the first may be 4.\r\n if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {\r\n r = finalise(r, pr + 1, 0);\r\n }\r\n\r\n break;\r\n }\r\n } while (checkRoundingDigits(r.d, k += 10, rm));\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, pr, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n P.max = function () {\r\n Array.prototype.push.call(arguments, this);\r\n return maxOrMin(this.constructor, arguments, 'lt');\r\n };\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n P.min = function () {\r\n Array.prototype.push.call(arguments, this);\r\n return maxOrMin(this.constructor, arguments, 'gt');\r\n };\r\n */\r\n\r\n\r\n /*\r\n * n - 0 = n\r\n * n - N = N\r\n * n - I = -I\r\n * 0 - n = -n\r\n * 0 - 0 = 0\r\n * 0 - N = N\r\n * 0 - I = -I\r\n * N - n = N\r\n * N - 0 = N\r\n * N - N = N\r\n * N - I = N\r\n * I - n = I\r\n * I - 0 = I\r\n * I - N = N\r\n * I - I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.minus = P.sub = function (y) {\r\n var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // If either is not finite...\r\n if (!x.d || !y.d) {\r\n\r\n // Return NaN if either is NaN.\r\n if (!x.s || !y.s) y = new Ctor(NaN);\r\n\r\n // Return y negated if x is finite and y is ±Infinity.\r\n else if (x.d) y.s = -y.s;\r\n\r\n // Return x if y is finite and x is ±Infinity.\r\n // Return x if both are ±Infinity with different signs.\r\n // Return NaN if both are ±Infinity with the same sign.\r\n else y = new Ctor(y.d || x.s !== y.s ? x : NaN);\r\n\r\n return y;\r\n }\r\n\r\n // If signs differ...\r\n if (x.s != y.s) {\r\n y.s = -y.s;\r\n return x.plus(y);\r\n }\r\n\r\n xd = x.d;\r\n yd = y.d;\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n // If either is zero...\r\n if (!xd[0] || !yd[0]) {\r\n\r\n // Return y negated if x is zero and y is non-zero.\r\n if (yd[0]) y.s = -y.s;\r\n\r\n // Return x if y is zero and x is non-zero.\r\n else if (xd[0]) y = new Ctor(x);\r\n\r\n // Return zero if both are zero.\r\n // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.\r\n else return new Ctor(rm === 3 ? -0 : 0);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n }\r\n\r\n // x and y are finite, non-zero numbers with the same sign.\r\n\r\n // Calculate base 1e7 exponents.\r\n e = mathfloor(y.e / LOG_BASE);\r\n xe = mathfloor(x.e / LOG_BASE);\r\n\r\n xd = xd.slice();\r\n k = xe - e;\r\n\r\n // If base 1e7 exponents differ...\r\n if (k) {\r\n xLTy = k < 0;\r\n\r\n if (xLTy) {\r\n d = xd;\r\n k = -k;\r\n len = yd.length;\r\n } else {\r\n d = yd;\r\n e = xe;\r\n len = xd.length;\r\n }\r\n\r\n // Numbers with massively different exponents would result in a very high number of\r\n // zeros needing to be prepended, but this can be avoided while still ensuring correct\r\n // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.\r\n i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;\r\n\r\n if (k > i) {\r\n k = i;\r\n d.length = 1;\r\n }\r\n\r\n // Prepend zeros to equalise exponents.\r\n d.reverse();\r\n for (i = k; i--;) d.push(0);\r\n d.reverse();\r\n\r\n // Base 1e7 exponents equal.\r\n } else {\r\n\r\n // Check digits to determine which is the bigger number.\r\n\r\n i = xd.length;\r\n len = yd.length;\r\n xLTy = i < len;\r\n if (xLTy) len = i;\r\n\r\n for (i = 0; i < len; i++) {\r\n if (xd[i] != yd[i]) {\r\n xLTy = xd[i] < yd[i];\r\n break;\r\n }\r\n }\r\n\r\n k = 0;\r\n }\r\n\r\n if (xLTy) {\r\n d = xd;\r\n xd = yd;\r\n yd = d;\r\n y.s = -y.s;\r\n }\r\n\r\n len = xd.length;\r\n\r\n // Append zeros to `xd` if shorter.\r\n // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.\r\n for (i = yd.length - len; i > 0; --i) xd[len++] = 0;\r\n\r\n // Subtract yd from xd.\r\n for (i = yd.length; i > k;) {\r\n\r\n if (xd[--i] < yd[i]) {\r\n for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;\r\n --xd[j];\r\n xd[i] += BASE;\r\n }\r\n\r\n xd[i] -= yd[i];\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (; xd[--len] === 0;) xd.pop();\r\n\r\n // Remove leading zeros and adjust exponent accordingly.\r\n for (; xd[0] === 0; xd.shift()) --e;\r\n\r\n // Zero?\r\n if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);\r\n\r\n y.d = xd;\r\n y.e = getBase10Exponent(xd, e);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n };\r\n\r\n\r\n /*\r\n * n % 0 = N\r\n * n % N = N\r\n * n % I = n\r\n * 0 % n = 0\r\n * -0 % n = -0\r\n * 0 % 0 = N\r\n * 0 % N = N\r\n * 0 % I = 0\r\n * N % n = N\r\n * N % 0 = N\r\n * N % N = N\r\n * N % I = N\r\n * I % n = N\r\n * I % 0 = N\r\n * I % N = N\r\n * I % I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * The result depends on the modulo mode.\r\n *\r\n */\r\n P.modulo = P.mod = function (y) {\r\n var q,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.\r\n if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);\r\n\r\n // Return x if y is ±Infinity or x is ±0.\r\n if (!y.d || x.d && !x.d[0]) {\r\n return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);\r\n }\r\n\r\n // Prevent rounding of intermediate calculations.\r\n external = false;\r\n\r\n if (Ctor.modulo == 9) {\r\n\r\n // Euclidian division: q = sign(y) * floor(x / abs(y))\r\n // result = x - q * y where 0 <= result < abs(y)\r\n q = divide(x, y.abs(), 0, 3, 1);\r\n q.s *= y.s;\r\n } else {\r\n q = divide(x, y, 0, Ctor.modulo, 1);\r\n }\r\n\r\n q = q.times(y);\r\n\r\n external = true;\r\n\r\n return x.minus(q);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of the value of this Decimal,\r\n * i.e. the base e raised to the power the value of this Decimal, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.naturalExponential = P.exp = function () {\r\n return naturalExponential(this);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,\r\n * rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.naturalLogarithm = P.ln = function () {\r\n return naturalLogarithm(this);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by\r\n * -1.\r\n *\r\n */\r\n P.negated = P.neg = function () {\r\n var x = new this.constructor(this);\r\n x.s = -x.s;\r\n return finalise(x);\r\n };\r\n\r\n\r\n /*\r\n * n + 0 = n\r\n * n + N = N\r\n * n + I = I\r\n * 0 + n = n\r\n * 0 + 0 = 0\r\n * 0 + N = N\r\n * 0 + I = I\r\n * N + n = N\r\n * N + 0 = N\r\n * N + N = N\r\n * N + I = N\r\n * I + n = I\r\n * I + 0 = I\r\n * I + N = N\r\n * I + I = I\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.plus = P.add = function (y) {\r\n var carry, d, e, i, k, len, pr, rm, xd, yd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // If either is not finite...\r\n if (!x.d || !y.d) {\r\n\r\n // Return NaN if either is NaN.\r\n if (!x.s || !y.s) y = new Ctor(NaN);\r\n\r\n // Return x if y is finite and x is ±Infinity.\r\n // Return x if both are ±Infinity with the same sign.\r\n // Return NaN if both are ±Infinity with different signs.\r\n // Return y if x is finite and y is ±Infinity.\r\n else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);\r\n\r\n return y;\r\n }\r\n\r\n // If signs differ...\r\n if (x.s != y.s) {\r\n y.s = -y.s;\r\n return x.minus(y);\r\n }\r\n\r\n xd = x.d;\r\n yd = y.d;\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n // If either is zero...\r\n if (!xd[0] || !yd[0]) {\r\n\r\n // Return x if y is zero.\r\n // Return y if y is non-zero.\r\n if (!yd[0]) y = new Ctor(x);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n }\r\n\r\n // x and y are finite, non-zero numbers with the same sign.\r\n\r\n // Calculate base 1e7 exponents.\r\n k = mathfloor(x.e / LOG_BASE);\r\n e = mathfloor(y.e / LOG_BASE);\r\n\r\n xd = xd.slice();\r\n i = k - e;\r\n\r\n // If base 1e7 exponents differ...\r\n if (i) {\r\n\r\n if (i < 0) {\r\n d = xd;\r\n i = -i;\r\n len = yd.length;\r\n } else {\r\n d = yd;\r\n e = k;\r\n len = xd.length;\r\n }\r\n\r\n // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.\r\n k = Math.ceil(pr / LOG_BASE);\r\n len = k > len ? k + 1 : len + 1;\r\n\r\n if (i > len) {\r\n i = len;\r\n d.length = 1;\r\n }\r\n\r\n // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.\r\n d.reverse();\r\n for (; i--;) d.push(0);\r\n d.reverse();\r\n }\r\n\r\n len = xd.length;\r\n i = yd.length;\r\n\r\n // If yd is longer than xd, swap xd and yd so xd points to the longer array.\r\n if (len - i < 0) {\r\n i = len;\r\n d = yd;\r\n yd = xd;\r\n xd = d;\r\n }\r\n\r\n // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.\r\n for (carry = 0; i;) {\r\n carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;\r\n xd[i] %= BASE;\r\n }\r\n\r\n if (carry) {\r\n xd.unshift(carry);\r\n ++e;\r\n }\r\n\r\n // Remove trailing zeros.\r\n // No need to check for zero, as +x + +y != 0 && -x + -y != 0\r\n for (len = xd.length; xd[--len] == 0;) xd.pop();\r\n\r\n y.d = xd;\r\n y.e = getBase10Exponent(xd, e);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n };\r\n\r\n\r\n /*\r\n * Return the number of significant digits of the value of this Decimal.\r\n *\r\n * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.\r\n *\r\n */\r\n P.precision = P.sd = function (z) {\r\n var k,\r\n x = this;\r\n\r\n if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);\r\n\r\n if (x.d) {\r\n k = getPrecision(x.d);\r\n if (z && x.e + 1 > k) k = x.e + 1;\r\n } else {\r\n k = NaN;\r\n }\r\n\r\n return k;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using\r\n * rounding mode `rounding`.\r\n *\r\n */\r\n P.round = function () {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n return finalise(new Ctor(x), x.e + 1, Ctor.rounding);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sine of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * sin(x) = x - x^3/3! + x^5/5! - ...\r\n *\r\n * sin(0) = 0\r\n * sin(-0) = -0\r\n * sin(Infinity) = NaN\r\n * sin(-Infinity) = NaN\r\n * sin(NaN) = NaN\r\n *\r\n */\r\n P.sine = P.sin = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;\r\n Ctor.rounding = 1;\r\n\r\n x = sine(Ctor, toLessThanHalfPi(Ctor, x));\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * sqrt(-n) = N\r\n * sqrt(N) = N\r\n * sqrt(-I) = N\r\n * sqrt(I) = I\r\n * sqrt(0) = 0\r\n * sqrt(-0) = -0\r\n *\r\n */\r\n P.squareRoot = P.sqrt = function () {\r\n var m, n, sd, r, rep, t,\r\n x = this,\r\n d = x.d,\r\n e = x.e,\r\n s = x.s,\r\n Ctor = x.constructor;\r\n\r\n // Negative/NaN/Infinity/zero?\r\n if (s !== 1 || !d || !d[0]) {\r\n return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);\r\n }\r\n\r\n external = false;\r\n\r\n // Initial estimate.\r\n s = Math.sqrt(+x);\r\n\r\n // Math.sqrt underflow/overflow?\r\n // Pass x to Math.sqrt as integer, then adjust the exponent of the result.\r\n if (s == 0 || s == 1 / 0) {\r\n n = digitsToString(d);\r\n\r\n if ((n.length + e) % 2 == 0) n += '0';\r\n s = Math.sqrt(n);\r\n e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);\r\n\r\n if (s == 1 / 0) {\r\n n = '5e' + e;\r\n } else {\r\n n = s.toExponential();\r\n n = n.slice(0, n.indexOf('e') + 1) + e;\r\n }\r\n\r\n r = new Ctor(n);\r\n } else {\r\n r = new Ctor(s.toString());\r\n }\r\n\r\n sd = (e = Ctor.precision) + 3;\r\n\r\n // Newton-Raphson iteration.\r\n for (;;) {\r\n t = r;\r\n r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);\r\n\r\n // TODO? Replace with for-loop and checkRoundingDigits.\r\n if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {\r\n n = n.slice(sd - 3, sd + 1);\r\n\r\n // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or\r\n // 4999, i.e. approaching a rounding boundary, continue the iteration.\r\n if (n == '9999' || !rep && n == '4999') {\r\n\r\n // On the first iteration only, check to see if rounding up gives the exact result as the\r\n // nines may infinitely repeat.\r\n if (!rep) {\r\n finalise(t, e + 1, 0);\r\n\r\n if (t.times(t).eq(x)) {\r\n r = t;\r\n break;\r\n }\r\n }\r\n\r\n sd += 4;\r\n rep = 1;\r\n } else {\r\n\r\n // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.\r\n // If not, then there are further digits and m will be truthy.\r\n if (!+n || !+n.slice(1) && n.charAt(0) == '5') {\r\n\r\n // Truncate to the first rounding digit.\r\n finalise(r, e + 1, 1);\r\n m = !r.times(r).eq(x);\r\n }\r\n\r\n break;\r\n }\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, e, Ctor.rounding, m);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * tan(0) = 0\r\n * tan(-0) = -0\r\n * tan(Infinity) = NaN\r\n * tan(-Infinity) = NaN\r\n * tan(NaN) = NaN\r\n *\r\n */\r\n P.tangent = P.tan = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 10;\r\n Ctor.rounding = 1;\r\n\r\n x = x.sin();\r\n x.s = 1;\r\n x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * n * 0 = 0\r\n * n * N = N\r\n * n * I = I\r\n * 0 * n = 0\r\n * 0 * 0 = 0\r\n * 0 * N = N\r\n * 0 * I = N\r\n * N * n = N\r\n * N * 0 = N\r\n * N * N = N\r\n * N * I = N\r\n * I * n = I\r\n * I * 0 = N\r\n * I * N = N\r\n * I * I = I\r\n *\r\n * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.times = P.mul = function (y) {\r\n var carry, e, i, k, r, rL, t, xdL, ydL,\r\n x = this,\r\n Ctor = x.constructor,\r\n xd = x.d,\r\n yd = (y = new Ctor(y)).d;\r\n\r\n y.s *= x.s;\r\n\r\n // If either is NaN, ±Infinity or ±0...\r\n if (!xd || !xd[0] || !yd || !yd[0]) {\r\n\r\n return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd\r\n\r\n // Return NaN if either is NaN.\r\n // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.\r\n ? NaN\r\n\r\n // Return ±Infinity if either is ±Infinity.\r\n // Return ±0 if either is ±0.\r\n : !xd || !yd ? y.s / 0 : y.s * 0);\r\n }\r\n\r\n e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);\r\n xdL = xd.length;\r\n ydL = yd.length;\r\n\r\n // Ensure xd points to the longer array.\r\n if (xdL < ydL) {\r\n r = xd;\r\n xd = yd;\r\n yd = r;\r\n rL = xdL;\r\n xdL = ydL;\r\n ydL = rL;\r\n }\r\n\r\n // Initialise the result array with zeros.\r\n r = [];\r\n rL = xdL + ydL;\r\n for (i = rL; i--;) r.push(0);\r\n\r\n // Multiply!\r\n for (i = ydL; --i >= 0;) {\r\n carry = 0;\r\n for (k = xdL + i; k > i;) {\r\n t = r[k] + yd[i] * xd[k - i - 1] + carry;\r\n r[k--] = t % BASE | 0;\r\n carry = t / BASE | 0;\r\n }\r\n\r\n r[k] = (r[k] + carry) % BASE | 0;\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (; !r[--rL];) r.pop();\r\n\r\n if (carry) ++e;\r\n else r.shift();\r\n\r\n y.d = r;\r\n y.e = getBase10Exponent(r, e);\r\n\r\n return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 2, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toBinary = function (sd, rm) {\r\n return toStringBinary(this, 2, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`\r\n * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.\r\n *\r\n * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toDecimalPlaces = P.toDP = function (dp, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n x = new Ctor(x);\r\n if (dp === void 0) return x;\r\n\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n return finalise(x, dp + x.e + 1, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in exponential notation rounded to\r\n * `dp` fixed decimal places using rounding mode `rounding`.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toExponential = function (dp, rm) {\r\n var str,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (dp === void 0) {\r\n str = finiteToString(x, true);\r\n } else {\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n x = finalise(new Ctor(x), dp + 1, rm);\r\n str = finiteToString(x, true, dp + 1);\r\n }\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in normal (fixed-point) notation to\r\n * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is\r\n * omitted.\r\n *\r\n * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.\r\n * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.\r\n * (-0).toFixed(3) is '0.000'.\r\n * (-0.5).toFixed(0) is '-0'.\r\n *\r\n */\r\n P.toFixed = function (dp, rm) {\r\n var str, y,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (dp === void 0) {\r\n str = finiteToString(x);\r\n } else {\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n y = finalise(new Ctor(x), dp + x.e + 1, rm);\r\n str = finiteToString(y, false, dp + y.e + 1);\r\n }\r\n\r\n // To determine whether to add the minus sign look at the value before it was rounded,\r\n // i.e. look at `x` rather than `y`.\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return an array representing the value of this Decimal as a simple fraction with an integer\r\n * numerator and an integer denominator.\r\n *\r\n * The denominator will be a positive non-zero value less than or equal to the specified maximum\r\n * denominator. If a maximum denominator is not specified, the denominator will be the lowest\r\n * value necessary to represent the number exactly.\r\n *\r\n * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.\r\n *\r\n */\r\n P.toFraction = function (maxD) {\r\n var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,\r\n x = this,\r\n xd = x.d,\r\n Ctor = x.constructor;\r\n\r\n if (!xd) return new Ctor(x);\r\n\r\n n1 = d0 = new Ctor(1);\r\n d1 = n0 = new Ctor(0);\r\n\r\n d = new Ctor(d1);\r\n e = d.e = getPrecision(xd) - x.e - 1;\r\n k = e % LOG_BASE;\r\n d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);\r\n\r\n if (maxD == null) {\r\n\r\n // d is 10**e, the minimum max-denominator needed.\r\n maxD = e > 0 ? d : n1;\r\n } else {\r\n n = new Ctor(maxD);\r\n if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);\r\n maxD = n.gt(d) ? (e > 0 ? d : n1) : n;\r\n }\r\n\r\n external = false;\r\n n = new Ctor(digitsToString(xd));\r\n pr = Ctor.precision;\r\n Ctor.precision = e = xd.length * LOG_BASE * 2;\r\n\r\n for (;;) {\r\n q = divide(n, d, 0, 1, 1);\r\n d2 = d0.plus(q.times(d1));\r\n if (d2.cmp(maxD) == 1) break;\r\n d0 = d1;\r\n d1 = d2;\r\n d2 = n1;\r\n n1 = n0.plus(q.times(d2));\r\n n0 = d2;\r\n d2 = d;\r\n d = n.minus(q.times(d2));\r\n n = d2;\r\n }\r\n\r\n d2 = divide(maxD.minus(d0), d1, 0, 1, 1);\r\n n0 = n0.plus(d2.times(n1));\r\n d0 = d0.plus(d2.times(d1));\r\n n0.s = n1.s = x.s;\r\n\r\n // Determine which fraction is closer to x, n0/d0 or n1/d1?\r\n r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1\r\n ? [n1, d1] : [n0, d0];\r\n\r\n Ctor.precision = pr;\r\n external = true;\r\n\r\n return r;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 16, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toHexadecimal = P.toHex = function (sd, rm) {\r\n return toStringBinary(this, 16, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding\r\n * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.\r\n *\r\n * The return value will always have the same sign as this Decimal, unless either this Decimal\r\n * or `y` is NaN, in which case the return value will be also be NaN.\r\n *\r\n * The return value is not affected by the value of `precision`.\r\n *\r\n * y {number|string|Decimal} The magnitude to round to a multiple of.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * 'toNearest() rounding mode not an integer: {rm}'\r\n * 'toNearest() rounding mode out of range: {rm}'\r\n *\r\n */\r\n P.toNearest = function (y, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n x = new Ctor(x);\r\n\r\n if (y == null) {\r\n\r\n // If x is not finite, return x.\r\n if (!x.d) return x;\r\n\r\n y = new Ctor(1);\r\n rm = Ctor.rounding;\r\n } else {\r\n y = new Ctor(y);\r\n if (rm === void 0) {\r\n rm = Ctor.rounding;\r\n } else {\r\n checkInt32(rm, 0, 8);\r\n }\r\n\r\n // If x is not finite, return x if y is not NaN, else NaN.\r\n if (!x.d) return y.s ? x : y;\r\n\r\n // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.\r\n if (!y.d) {\r\n if (y.s) y.s = x.s;\r\n return y;\r\n }\r\n }\r\n\r\n // If y is not zero, calculate the nearest multiple of y to x.\r\n if (y.d[0]) {\r\n external = false;\r\n x = divide(x, y, 0, rm, 1).times(y);\r\n external = true;\r\n finalise(x);\r\n\r\n // If y is zero, return zero with the sign of x.\r\n } else {\r\n y.s = x.s;\r\n x = y;\r\n }\r\n\r\n return x;\r\n };\r\n\r\n\r\n /*\r\n * Return the value of this Decimal converted to a number primitive.\r\n * Zero keeps its sign.\r\n *\r\n */\r\n P.toNumber = function () {\r\n return +this;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 8, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toOctal = function (sd, rm) {\r\n return toStringBinary(this, 8, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded\r\n * to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * ECMAScript compliant.\r\n *\r\n * pow(x, NaN) = NaN\r\n * pow(x, ±0) = 1\r\n\r\n * pow(NaN, non-zero) = NaN\r\n * pow(abs(x) > 1, +Infinity) = +Infinity\r\n * pow(abs(x) > 1, -Infinity) = +0\r\n * pow(abs(x) == 1, ±Infinity) = NaN\r\n * pow(abs(x) < 1, +Infinity) = +0\r\n * pow(abs(x) < 1, -Infinity) = +Infinity\r\n * pow(+Infinity, y > 0) = +Infinity\r\n * pow(+Infinity, y < 0) = +0\r\n * pow(-Infinity, odd integer > 0) = -Infinity\r\n * pow(-Infinity, even integer > 0) = +Infinity\r\n * pow(-Infinity, odd integer < 0) = -0\r\n * pow(-Infinity, even integer < 0) = +0\r\n * pow(+0, y > 0) = +0\r\n * pow(+0, y < 0) = +Infinity\r\n * pow(-0, odd integer > 0) = -0\r\n * pow(-0, even integer > 0) = +0\r\n * pow(-0, odd integer < 0) = -Infinity\r\n * pow(-0, even integer < 0) = +Infinity\r\n * pow(finite x < 0, finite non-integer) = NaN\r\n *\r\n * For non-integer or very large exponents pow(x, y) is calculated using\r\n *\r\n * x^y = exp(y*ln(x))\r\n *\r\n * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the\r\n * probability of an incorrectly rounded result\r\n * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14\r\n * i.e. 1 in 250,000,000,000,000\r\n *\r\n * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).\r\n *\r\n * y {number|string|Decimal} The power to which to raise this Decimal.\r\n *\r\n */\r\n P.toPower = P.pow = function (y) {\r\n var e, k, pr, r, rm, s,\r\n x = this,\r\n Ctor = x.constructor,\r\n yn = +(y = new Ctor(y));\r\n\r\n // Either ±Infinity, NaN or ±0?\r\n if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));\r\n\r\n x = new Ctor(x);\r\n\r\n if (x.eq(1)) return x;\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n if (y.eq(1)) return finalise(x, pr, rm);\r\n\r\n // y exponent\r\n e = mathfloor(y.e / LOG_BASE);\r\n\r\n // If y is a small integer use the 'exponentiation by squaring' algorithm.\r\n if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {\r\n r = intPow(Ctor, x, k, pr);\r\n return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);\r\n }\r\n\r\n s = x.s;\r\n\r\n // if x is negative\r\n if (s < 0) {\r\n\r\n // if y is not an integer\r\n if (e < y.d.length - 1) return new Ctor(NaN);\r\n\r\n // Result is positive if x is negative and the last digit of integer y is even.\r\n if ((y.d[e] & 1) == 0) s = 1;\r\n\r\n // if x.eq(-1)\r\n if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {\r\n x.s = s;\r\n return x;\r\n }\r\n }\r\n\r\n // Estimate result exponent.\r\n // x^y = 10^e, where e = y * log10(x)\r\n // log10(x) = log10(x_significand) + x_exponent\r\n // log10(x_significand) = ln(x_significand) / ln(10)\r\n k = mathpow(+x, yn);\r\n e = k == 0 || !isFinite(k)\r\n ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))\r\n : new Ctor(k + '').e;\r\n\r\n // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.\r\n\r\n // Overflow/underflow?\r\n if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);\r\n\r\n external = false;\r\n Ctor.rounding = x.s = 1;\r\n\r\n // Estimate the extra guard digits needed to ensure five correct rounding digits from\r\n // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):\r\n // new Decimal(2.32456).pow('2087987436534566.46411')\r\n // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815\r\n k = Math.min(12, (e + '').length);\r\n\r\n // r = x^y = exp(y*ln(x))\r\n r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);\r\n\r\n // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)\r\n if (r.d) {\r\n\r\n // Truncate to the required precision plus five rounding digits.\r\n r = finalise(r, pr + 5, 1);\r\n\r\n // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate\r\n // the result.\r\n if (checkRoundingDigits(r.d, pr, rm)) {\r\n e = pr + 10;\r\n\r\n // Truncate to the increased precision plus five rounding digits.\r\n r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);\r\n\r\n // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).\r\n if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {\r\n r = finalise(r, pr + 1, 0);\r\n }\r\n }\r\n }\r\n\r\n r.s = s;\r\n external = true;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(r, pr, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal rounded to `sd` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * Return exponential notation if `sd` is less than the number of digits necessary to represent\r\n * the integer part of the value in normal notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toPrecision = function (sd, rm) {\r\n var str,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (sd === void 0) {\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n } else {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n x = finalise(new Ctor(x), sd, rm);\r\n str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);\r\n }\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`\r\n * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if\r\n * omitted.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * 'toSD() digits out of range: {sd}'\r\n * 'toSD() digits not an integer: {sd}'\r\n * 'toSD() rounding mode not an integer: {rm}'\r\n * 'toSD() rounding mode out of range: {rm}'\r\n *\r\n */\r\n P.toSignificantDigits = P.toSD = function (sd, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n if (sd === void 0) {\r\n sd = Ctor.precision;\r\n rm = Ctor.rounding;\r\n } else {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n }\r\n\r\n return finalise(new Ctor(x), sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal.\r\n *\r\n * Return exponential notation if this Decimal has a positive exponent equal to or greater than\r\n * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.\r\n *\r\n */\r\n P.toString = function () {\r\n var x = this,\r\n Ctor = x.constructor,\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.\r\n *\r\n */\r\n P.truncated = P.trunc = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 1);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal.\r\n * Unlike `toString`, negative zero will include the minus sign.\r\n *\r\n */\r\n P.valueOf = P.toJSON = function () {\r\n var x = this,\r\n Ctor = x.constructor,\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n\r\n return x.isNeg() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n // Add aliases to match BigDecimal method names.\r\n // P.add = P.plus;\r\n P.subtract = P.minus;\r\n P.multiply = P.times;\r\n P.divide = P.div;\r\n P.remainder = P.mod;\r\n P.compareTo = P.cmp;\r\n P.negate = P.neg;\r\n */\r\n\r\n\r\n // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.\r\n\r\n\r\n /*\r\n * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,\r\n * finiteToString, naturalExponential, naturalLogarithm\r\n * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,\r\n * P.toPrecision, P.toSignificantDigits, toStringBinary, random\r\n * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm\r\n * convertBase toStringBinary, parseOther\r\n * cos P.cos\r\n * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,\r\n * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,\r\n * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,\r\n * taylorSeries, atan2, parseOther\r\n * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,\r\n * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,\r\n * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,\r\n * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,\r\n * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,\r\n * P.truncated, divide, getLn10, getPi, naturalExponential,\r\n * naturalLogarithm, ceil, floor, round, trunc\r\n * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,\r\n * toStringBinary\r\n * getBase10Exponent P.minus, P.plus, P.times, parseOther\r\n * getLn10 P.logarithm, naturalLogarithm\r\n * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2\r\n * getPrecision P.precision, P.toFraction\r\n * getZeroString digitsToString, finiteToString\r\n * intPow P.toPower, parseOther\r\n * isOdd toLessThanHalfPi\r\n * maxOrMin max, min\r\n * naturalExponential P.naturalExponential, P.toPower\r\n * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,\r\n * P.toPower, naturalExponential\r\n * nonFiniteToString finiteToString, toStringBinary\r\n * parseDecimal Decimal\r\n * parseOther Decimal\r\n * sin P.sin\r\n * taylorSeries P.cosh, P.sinh, cos, sin\r\n * toLessThanHalfPi P.cos, P.sin\r\n * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal\r\n * truncate intPow\r\n *\r\n * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,\r\n * naturalLogarithm, config, parseOther, random, Decimal\r\n */\r\n\r\n\r\n function digitsToString(d) {\r\n var i, k, ws,\r\n indexOfLastWord = d.length - 1,\r\n str = '',\r\n w = d[0];\r\n\r\n if (indexOfLastWord > 0) {\r\n str += w;\r\n for (i = 1; i < indexOfLastWord; i++) {\r\n ws = d[i] + '';\r\n k = LOG_BASE - ws.length;\r\n if (k) str += getZeroString(k);\r\n str += ws;\r\n }\r\n\r\n w = d[i];\r\n ws = w + '';\r\n k = LOG_BASE - ws.length;\r\n if (k) str += getZeroString(k);\r\n } else if (w === 0) {\r\n return '0';\r\n }\r\n\r\n // Remove trailing zeros of last w.\r\n for (; w % 10 === 0;) w /= 10;\r\n\r\n return str + w;\r\n }\r\n\r\n\r\n function checkInt32(i, min, max) {\r\n if (i !== ~~i || i < min || i > max) {\r\n throw Error(invalidArgument + i);\r\n }\r\n }\r\n\r\n\r\n /*\r\n * Check 5 rounding digits if `repeating` is null, 4 otherwise.\r\n * `repeating == null` if caller is `log` or `pow`,\r\n * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.\r\n */\r\n function checkRoundingDigits(d, i, rm, repeating) {\r\n var di, k, r, rd;\r\n\r\n // Get the length of the first word of the array d.\r\n for (k = d[0]; k >= 10; k /= 10) --i;\r\n\r\n // Is the rounding digit in the first word of d?\r\n if (--i < 0) {\r\n i += LOG_BASE;\r\n di = 0;\r\n } else {\r\n di = Math.ceil((i + 1) / LOG_BASE);\r\n i %= LOG_BASE;\r\n }\r\n\r\n // i is the index (0 - 6) of the rounding digit.\r\n // E.g. if within the word 3487563 the first rounding digit is 5,\r\n // then i = 4, k = 1000, rd = 3487563 % 1000 = 563\r\n k = mathpow(10, LOG_BASE - i);\r\n rd = d[di] % k | 0;\r\n\r\n if (repeating == null) {\r\n if (i < 3) {\r\n if (i == 0) rd = rd / 100 | 0;\r\n else if (i == 1) rd = rd / 10 | 0;\r\n r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;\r\n } else {\r\n r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&\r\n (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||\r\n (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;\r\n }\r\n } else {\r\n if (i < 4) {\r\n if (i == 0) rd = rd / 1000 | 0;\r\n else if (i == 1) rd = rd / 100 | 0;\r\n else if (i == 2) rd = rd / 10 | 0;\r\n r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;\r\n } else {\r\n r = ((repeating || rm < 4) && rd + 1 == k ||\r\n (!repeating && rm > 3) && rd + 1 == k / 2) &&\r\n (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;\r\n }\r\n }\r\n\r\n return r;\r\n }\r\n\r\n\r\n // Convert string of `baseIn` to an array of numbers of `baseOut`.\r\n // Eg. convertBase('255', 10, 16) returns [15, 15].\r\n // Eg. convertBase('ff', 16, 10) returns [2, 5, 5].\r\n function convertBase(str, baseIn, baseOut) {\r\n var j,\r\n arr = [0],\r\n arrL,\r\n i = 0,\r\n strL = str.length;\r\n\r\n for (; i < strL;) {\r\n for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;\r\n arr[0] += NUMERALS.indexOf(str.charAt(i++));\r\n for (j = 0; j < arr.length; j++) {\r\n if (arr[j] > baseOut - 1) {\r\n if (arr[j + 1] === void 0) arr[j + 1] = 0;\r\n arr[j + 1] += arr[j] / baseOut | 0;\r\n arr[j] %= baseOut;\r\n }\r\n }\r\n }\r\n\r\n return arr.reverse();\r\n }\r\n\r\n\r\n /*\r\n * cos(x) = 1 - x^2/2! + x^4/4! - ...\r\n * |x| < pi/2\r\n *\r\n */\r\n function cosine(Ctor, x) {\r\n var k, y,\r\n len = x.d.length;\r\n\r\n // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1\r\n // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n if (len < 32) {\r\n k = Math.ceil(len / 3);\r\n y = (1 / tinyPow(4, k)).toString();\r\n } else {\r\n k = 16;\r\n y = '2.3283064365386962890625e-10';\r\n }\r\n\r\n Ctor.precision += k;\r\n\r\n x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1));\r\n\r\n // Reverse argument reduction\r\n for (var i = k; i--;) {\r\n var cos2x = x.times(x);\r\n x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);\r\n }\r\n\r\n Ctor.precision -= k;\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Perform division in the specified base.\r\n */\r\n var divide = (function () {\r\n\r\n // Assumes non-zero x and k, and hence non-zero result.\r\n function multiplyInteger(x, k, base) {\r\n var temp,\r\n carry = 0,\r\n i = x.length;\r\n\r\n for (x = x.slice(); i--;) {\r\n temp = x[i] * k + carry;\r\n x[i] = temp % base | 0;\r\n carry = temp / base | 0;\r\n }\r\n\r\n if (carry) x.unshift(carry);\r\n\r\n return x;\r\n }\r\n\r\n function compare(a, b, aL, bL) {\r\n var i, r;\r\n\r\n if (aL != bL) {\r\n r = aL > bL ? 1 : -1;\r\n } else {\r\n for (i = r = 0; i < aL; i++) {\r\n if (a[i] != b[i]) {\r\n r = a[i] > b[i] ? 1 : -1;\r\n break;\r\n }\r\n }\r\n }\r\n\r\n return r;\r\n }\r\n\r\n function subtract(a, b, aL, base) {\r\n var i = 0;\r\n\r\n // Subtract b from a.\r\n for (; aL--;) {\r\n a[aL] -= i;\r\n i = a[aL] < b[aL] ? 1 : 0;\r\n a[aL] = i * base + a[aL] - b[aL];\r\n }\r\n\r\n // Remove leading zeros.\r\n for (; !a[0] && a.length > 1;) a.shift();\r\n }\r\n\r\n return function (x, y, pr, rm, dp, base) {\r\n var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,\r\n yL, yz,\r\n Ctor = x.constructor,\r\n sign = x.s == y.s ? 1 : -1,\r\n xd = x.d,\r\n yd = y.d;\r\n\r\n // Either NaN, Infinity or 0?\r\n if (!xd || !xd[0] || !yd || !yd[0]) {\r\n\r\n return new Ctor(// Return NaN if either NaN, or both Infinity or 0.\r\n !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :\r\n\r\n // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.\r\n xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);\r\n }\r\n\r\n if (base) {\r\n logBase = 1;\r\n e = x.e - y.e;\r\n } else {\r\n base = BASE;\r\n logBase = LOG_BASE;\r\n e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);\r\n }\r\n\r\n yL = yd.length;\r\n xL = xd.length;\r\n q = new Ctor(sign);\r\n qd = q.d = [];\r\n\r\n // Result exponent may be one less than e.\r\n // The digit array of a Decimal from toStringBinary may have trailing zeros.\r\n for (i = 0; yd[i] == (xd[i] || 0); i++);\r\n\r\n if (yd[i] > (xd[i] || 0)) e--;\r\n\r\n if (pr == null) {\r\n sd = pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n } else if (dp) {\r\n sd = pr + (x.e - y.e) + 1;\r\n } else {\r\n sd = pr;\r\n }\r\n\r\n if (sd < 0) {\r\n qd.push(1);\r\n more = true;\r\n } else {\r\n\r\n // Convert precision in number of base 10 digits to base 1e7 digits.\r\n sd = sd / logBase + 2 | 0;\r\n i = 0;\r\n\r\n // divisor < 1e7\r\n if (yL == 1) {\r\n k = 0;\r\n yd = yd[0];\r\n sd++;\r\n\r\n // k is the carry.\r\n for (; (i < xL || k) && sd--; i++) {\r\n t = k * base + (xd[i] || 0);\r\n qd[i] = t / yd | 0;\r\n k = t % yd | 0;\r\n }\r\n\r\n more = k || i < xL;\r\n\r\n // divisor >= 1e7\r\n } else {\r\n\r\n // Normalise xd and yd so highest order digit of yd is >= base/2\r\n k = base / (yd[0] + 1) | 0;\r\n\r\n if (k > 1) {\r\n yd = multiplyInteger(yd, k, base);\r\n xd = multiplyInteger(xd, k, base);\r\n yL = yd.length;\r\n xL = xd.length;\r\n }\r\n\r\n xi = yL;\r\n rem = xd.slice(0, yL);\r\n remL = rem.length;\r\n\r\n // Add zeros to make remainder as long as divisor.\r\n for (; remL < yL;) rem[remL++] = 0;\r\n\r\n yz = yd.slice();\r\n yz.unshift(0);\r\n yd0 = yd[0];\r\n\r\n if (yd[1] >= base / 2) ++yd0;\r\n\r\n do {\r\n k = 0;\r\n\r\n // Compare divisor and remainder.\r\n cmp = compare(yd, rem, yL, remL);\r\n\r\n // If divisor < remainder.\r\n if (cmp < 0) {\r\n\r\n // Calculate trial digit, k.\r\n rem0 = rem[0];\r\n if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);\r\n\r\n // k will be how many times the divisor goes into the current remainder.\r\n k = rem0 / yd0 | 0;\r\n\r\n // Algorithm:\r\n // 1. product = divisor * trial digit (k)\r\n // 2. if product > remainder: product -= divisor, k--\r\n // 3. remainder -= product\r\n // 4. if product was < remainder at 2:\r\n // 5. compare new remainder and divisor\r\n // 6. If remainder > divisor: remainder -= divisor, k++\r\n\r\n if (k > 1) {\r\n if (k >= base) k = base - 1;\r\n\r\n // product = divisor * trial digit.\r\n prod = multiplyInteger(yd, k, base);\r\n prodL = prod.length;\r\n remL = rem.length;\r\n\r\n // Compare product and remainder.\r\n cmp = compare(prod, rem, prodL, remL);\r\n\r\n // product > remainder.\r\n if (cmp == 1) {\r\n k--;\r\n\r\n // Subtract divisor from product.\r\n subtract(prod, yL < prodL ? yz : yd, prodL, base);\r\n }\r\n } else {\r\n\r\n // cmp is -1.\r\n // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1\r\n // to avoid it. If k is 1 there is a need to compare yd and rem again below.\r\n if (k == 0) cmp = k = 1;\r\n prod = yd.slice();\r\n }\r\n\r\n prodL = prod.length;\r\n if (prodL < remL) prod.unshift(0);\r\n\r\n // Subtract product from remainder.\r\n subtract(rem, prod, remL, base);\r\n\r\n // If product was < previous remainder.\r\n if (cmp == -1) {\r\n remL = rem.length;\r\n\r\n // Compare divisor and new remainder.\r\n cmp = compare(yd, rem, yL, remL);\r\n\r\n // If divisor < new remainder, subtract divisor from remainder.\r\n if (cmp < 1) {\r\n k++;\r\n\r\n // Subtract divisor from remainder.\r\n subtract(rem, yL < remL ? yz : yd, remL, base);\r\n }\r\n }\r\n\r\n remL = rem.length;\r\n } else if (cmp === 0) {\r\n k++;\r\n rem = [0];\r\n } // if cmp === 1, k will be 0\r\n\r\n // Add the next digit, k, to the result array.\r\n qd[i++] = k;\r\n\r\n // Update the remainder.\r\n if (cmp && rem[0]) {\r\n rem[remL++] = xd[xi] || 0;\r\n } else {\r\n rem = [xd[xi]];\r\n remL = 1;\r\n }\r\n\r\n } while ((xi++ < xL || rem[0] !== void 0) && sd--);\r\n\r\n more = rem[0] !== void 0;\r\n }\r\n\r\n // Leading zero?\r\n if (!qd[0]) qd.shift();\r\n }\r\n\r\n // logBase is 1 when divide is being used for base conversion.\r\n if (logBase == 1) {\r\n q.e = e;\r\n inexact = more;\r\n } else {\r\n\r\n // To calculate q.e, first get the number of digits of qd[0].\r\n for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;\r\n q.e = i + e * logBase - 1;\r\n\r\n finalise(q, dp ? pr + q.e + 1 : pr, rm, more);\r\n }\r\n\r\n return q;\r\n };\r\n })();\r\n\r\n\r\n /*\r\n * Round `x` to `sd` significant digits using rounding mode `rm`.\r\n * Check for over/under-flow.\r\n */\r\n function finalise(x, sd, rm, isTruncated) {\r\n var digits, i, j, k, rd, roundUp, w, xd, xdi,\r\n Ctor = x.constructor;\r\n\r\n // Don't round if sd is null or undefined.\r\n out: if (sd != null) {\r\n xd = x.d;\r\n\r\n // Infinity/NaN.\r\n if (!xd) return x;\r\n\r\n // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.\r\n // w: the word of xd containing rd, a base 1e7 number.\r\n // xdi: the index of w within xd.\r\n // digits: the number of digits of w.\r\n // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if\r\n // they had leading zeros)\r\n // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).\r\n\r\n // Get the length of the first word of the digits array xd.\r\n for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;\r\n i = sd - digits;\r\n\r\n // Is the rounding digit in the first word of xd?\r\n if (i < 0) {\r\n i += LOG_BASE;\r\n j = sd;\r\n w = xd[xdi = 0];\r\n\r\n // Get the rounding digit at index j of w.\r\n rd = w / mathpow(10, digits - j - 1) % 10 | 0;\r\n } else {\r\n xdi = Math.ceil((i + 1) / LOG_BASE);\r\n k = xd.length;\r\n if (xdi >= k) {\r\n if (isTruncated) {\r\n\r\n // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.\r\n for (; k++ <= xdi;) xd.push(0);\r\n w = rd = 0;\r\n digits = 1;\r\n i %= LOG_BASE;\r\n j = i - LOG_BASE + 1;\r\n } else {\r\n break out;\r\n }\r\n } else {\r\n w = k = xd[xdi];\r\n\r\n // Get the number of digits of w.\r\n for (digits = 1; k >= 10; k /= 10) digits++;\r\n\r\n // Get the index of rd within w.\r\n i %= LOG_BASE;\r\n\r\n // Get the index of rd within w, adjusted for leading zeros.\r\n // The number of leading zeros of w is given by LOG_BASE - digits.\r\n j = i - LOG_BASE + digits;\r\n\r\n // Get the rounding digit at index j of w.\r\n rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;\r\n }\r\n }\r\n\r\n // Are there any non-zero digits after the rounding digit?\r\n isTruncated = isTruncated || sd < 0 ||\r\n xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));\r\n\r\n // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right\r\n // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression\r\n // will give 714.\r\n\r\n roundUp = rm < 4\r\n ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))\r\n : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&\r\n\r\n // Check whether the digit to the left of the rounding digit is odd.\r\n ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||\r\n rm == (x.s < 0 ? 8 : 7));\r\n\r\n if (sd < 1 || !xd[0]) {\r\n xd.length = 0;\r\n if (roundUp) {\r\n\r\n // Convert sd to decimal places.\r\n sd -= x.e + 1;\r\n\r\n // 1, 0.1, 0.01, 0.001, 0.0001 etc.\r\n xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);\r\n x.e = -sd || 0;\r\n } else {\r\n\r\n // Zero.\r\n xd[0] = x.e = 0;\r\n }\r\n\r\n return x;\r\n }\r\n\r\n // Remove excess digits.\r\n if (i == 0) {\r\n xd.length = xdi;\r\n k = 1;\r\n xdi--;\r\n } else {\r\n xd.length = xdi + 1;\r\n k = mathpow(10, LOG_BASE - i);\r\n\r\n // E.g. 56700 becomes 56000 if 7 is the rounding digit.\r\n // j > 0 means i > number of leading zeros of w.\r\n xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;\r\n }\r\n\r\n if (roundUp) {\r\n for (;;) {\r\n\r\n // Is the digit to be rounded up in the first word of xd?\r\n if (xdi == 0) {\r\n\r\n // i will be the length of xd[0] before k is added.\r\n for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;\r\n j = xd[0] += k;\r\n for (k = 1; j >= 10; j /= 10) k++;\r\n\r\n // if i != k the length has increased.\r\n if (i != k) {\r\n x.e++;\r\n if (xd[0] == BASE) xd[0] = 1;\r\n }\r\n\r\n break;\r\n } else {\r\n xd[xdi] += k;\r\n if (xd[xdi] != BASE) break;\r\n xd[xdi--] = 0;\r\n k = 1;\r\n }\r\n }\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (i = xd.length; xd[--i] === 0;) xd.pop();\r\n }\r\n\r\n if (external) {\r\n\r\n // Overflow?\r\n if (x.e > Ctor.maxE) {\r\n\r\n // Infinity.\r\n x.d = null;\r\n x.e = NaN;\r\n\r\n // Underflow?\r\n } else if (x.e < Ctor.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n // Ctor.underflow = true;\r\n } // else Ctor.underflow = false;\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n function finiteToString(x, isExp, sd) {\r\n if (!x.isFinite()) return nonFiniteToString(x);\r\n var k,\r\n e = x.e,\r\n str = digitsToString(x.d),\r\n len = str.length;\r\n\r\n if (isExp) {\r\n if (sd && (k = sd - len) > 0) {\r\n str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);\r\n } else if (len > 1) {\r\n str = str.charAt(0) + '.' + str.slice(1);\r\n }\r\n\r\n str = str + (x.e < 0 ? 'e' : 'e+') + x.e;\r\n } else if (e < 0) {\r\n str = '0.' + getZeroString(-e - 1) + str;\r\n if (sd && (k = sd - len) > 0) str += getZeroString(k);\r\n } else if (e >= len) {\r\n str += getZeroString(e + 1 - len);\r\n if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);\r\n } else {\r\n if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);\r\n if (sd && (k = sd - len) > 0) {\r\n if (e + 1 === len) str += '.';\r\n str += getZeroString(k);\r\n }\r\n }\r\n\r\n return str;\r\n }\r\n\r\n\r\n // Calculate the base 10 exponent from the base 1e7 exponent.\r\n function getBase10Exponent(digits, e) {\r\n var w = digits[0];\r\n\r\n // Add the number of digits of the first word of the digits array.\r\n for ( e *= LOG_BASE; w >= 10; w /= 10) e++;\r\n return e;\r\n }\r\n\r\n\r\n function getLn10(Ctor, sd, pr) {\r\n if (sd > LN10_PRECISION) {\r\n\r\n // Reset global state in case the exception is caught.\r\n external = true;\r\n if (pr) Ctor.precision = pr;\r\n throw Error(precisionLimitExceeded);\r\n }\r\n return finalise(new Ctor(LN10), sd, 1, true);\r\n }\r\n\r\n\r\n function getPi(Ctor, sd, rm) {\r\n if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);\r\n return finalise(new Ctor(PI), sd, rm, true);\r\n }\r\n\r\n\r\n function getPrecision(digits) {\r\n var w = digits.length - 1,\r\n len = w * LOG_BASE + 1;\r\n\r\n w = digits[w];\r\n\r\n // If non-zero...\r\n if (w) {\r\n\r\n // Subtract the number of trailing zeros of the last word.\r\n for (; w % 10 == 0; w /= 10) len--;\r\n\r\n // Add the number of digits of the first word.\r\n for (w = digits[0]; w >= 10; w /= 10) len++;\r\n }\r\n\r\n return len;\r\n }\r\n\r\n\r\n function getZeroString(k) {\r\n var zs = '';\r\n for (; k--;) zs += '0';\r\n return zs;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an\r\n * integer of type number.\r\n *\r\n * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.\r\n *\r\n */\r\n function intPow(Ctor, x, n, pr) {\r\n var isTruncated,\r\n r = new Ctor(1),\r\n\r\n // Max n of 9007199254740991 takes 53 loop iterations.\r\n // Maximum digits array length; leaves [28, 34] guard digits.\r\n k = Math.ceil(pr / LOG_BASE + 4);\r\n\r\n external = false;\r\n\r\n for (;;) {\r\n if (n % 2) {\r\n r = r.times(x);\r\n if (truncate(r.d, k)) isTruncated = true;\r\n }\r\n\r\n n = mathfloor(n / 2);\r\n if (n === 0) {\r\n\r\n // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.\r\n n = r.d.length - 1;\r\n if (isTruncated && r.d[n] === 0) ++r.d[n];\r\n break;\r\n }\r\n\r\n x = x.times(x);\r\n truncate(x.d, k);\r\n }\r\n\r\n external = true;\r\n\r\n return r;\r\n }\r\n\r\n\r\n function isOdd(n) {\r\n return n.d[n.d.length - 1] & 1;\r\n }\r\n\r\n\r\n /*\r\n * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.\r\n */\r\n function maxOrMin(Ctor, args, ltgt) {\r\n var y,\r\n x = new Ctor(args[0]),\r\n i = 0;\r\n\r\n for (; ++i < args.length;) {\r\n y = new Ctor(args[i]);\r\n if (!y.s) {\r\n x = y;\r\n break;\r\n } else if (x[ltgt](y)) {\r\n x = y;\r\n }\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant\r\n * digits.\r\n *\r\n * Taylor/Maclaurin series.\r\n *\r\n * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...\r\n *\r\n * Argument reduction:\r\n * Repeat x = x / 32, k += 5, until |x| < 0.1\r\n * exp(x) = exp(x / 2^k)^(2^k)\r\n *\r\n * Previously, the argument was initially reduced by\r\n * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10)\r\n * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was\r\n * found to be slower than just dividing repeatedly by 32 as above.\r\n *\r\n * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000\r\n * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000\r\n * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)\r\n *\r\n * exp(Infinity) = Infinity\r\n * exp(-Infinity) = 0\r\n * exp(NaN) = NaN\r\n * exp(±0) = 1\r\n *\r\n * exp(x) is non-terminating for any finite, non-zero x.\r\n *\r\n * The result will always be correctly rounded.\r\n *\r\n */\r\n function naturalExponential(x, sd) {\r\n var denominator, guard, j, pow, sum, t, wpr,\r\n rep = 0,\r\n i = 0,\r\n k = 0,\r\n Ctor = x.constructor,\r\n rm = Ctor.rounding,\r\n pr = Ctor.precision;\r\n\r\n // 0/NaN/Infinity?\r\n if (!x.d || !x.d[0] || x.e > 17) {\r\n\r\n return new Ctor(x.d\r\n ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0\r\n : x.s ? x.s < 0 ? 0 : x : 0 / 0);\r\n }\r\n\r\n if (sd == null) {\r\n external = false;\r\n wpr = pr;\r\n } else {\r\n wpr = sd;\r\n }\r\n\r\n t = new Ctor(0.03125);\r\n\r\n // while abs(x) >= 0.1\r\n while (x.e > -2) {\r\n\r\n // x = x / 2^5\r\n x = x.times(t);\r\n k += 5;\r\n }\r\n\r\n // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision\r\n // necessary to ensure the first 4 rounding digits are correct.\r\n guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;\r\n wpr += guard;\r\n denominator = pow = sum = new Ctor(1);\r\n Ctor.precision = wpr;\r\n\r\n for (;;) {\r\n pow = finalise(pow.times(x), wpr, 1);\r\n denominator = denominator.times(++i);\r\n t = sum.plus(divide(pow, denominator, wpr, 1));\r\n\r\n if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {\r\n j = k;\r\n while (j--) sum = finalise(sum.times(sum), wpr, 1);\r\n\r\n // Check to see if the first 4 rounding digits are [49]999.\r\n // If so, repeat the summation with a higher precision, otherwise\r\n // e.g. with precision: 18, rounding: 1\r\n // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)\r\n // `wpr - guard` is the index of first rounding digit.\r\n if (sd == null) {\r\n\r\n if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {\r\n Ctor.precision = wpr += 10;\r\n denominator = pow = t = new Ctor(1);\r\n i = 0;\r\n rep++;\r\n } else {\r\n return finalise(sum, Ctor.precision = pr, rm, external = true);\r\n }\r\n } else {\r\n Ctor.precision = pr;\r\n return sum;\r\n }\r\n }\r\n\r\n sum = t;\r\n }\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant\r\n * digits.\r\n *\r\n * ln(-n) = NaN\r\n * ln(0) = -Infinity\r\n * ln(-0) = -Infinity\r\n * ln(1) = 0\r\n * ln(Infinity) = Infinity\r\n * ln(-Infinity) = NaN\r\n * ln(NaN) = NaN\r\n *\r\n * ln(n) (n != 1) is non-terminating.\r\n *\r\n */\r\n function naturalLogarithm(y, sd) {\r\n var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,\r\n n = 1,\r\n guard = 10,\r\n x = y,\r\n xd = x.d,\r\n Ctor = x.constructor,\r\n rm = Ctor.rounding,\r\n pr = Ctor.precision;\r\n\r\n // Is x negative or Infinity, NaN, 0 or 1?\r\n if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {\r\n return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);\r\n }\r\n\r\n if (sd == null) {\r\n external = false;\r\n wpr = pr;\r\n } else {\r\n wpr = sd;\r\n }\r\n\r\n Ctor.precision = wpr += guard;\r\n c = digitsToString(xd);\r\n c0 = c.charAt(0);\r\n\r\n if (Math.abs(e = x.e) < 1.5e15) {\r\n\r\n // Argument reduction.\r\n // The series converges faster the closer the argument is to 1, so using\r\n // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b\r\n // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,\r\n // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can\r\n // later be divided by this number, then separate out the power of 10 using\r\n // ln(a*10^b) = ln(a) + b*ln(10).\r\n\r\n // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).\r\n //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {\r\n // max n is 6 (gives 0.7 - 1.3)\r\n while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {\r\n x = x.times(y);\r\n c = digitsToString(x.d);\r\n c0 = c.charAt(0);\r\n n++;\r\n }\r\n\r\n e = x.e;\r\n\r\n if (c0 > 1) {\r\n x = new Ctor('0.' + c);\r\n e++;\r\n } else {\r\n x = new Ctor(c0 + '.' + c.slice(1));\r\n }\r\n } else {\r\n\r\n // The argument reduction method above may result in overflow if the argument y is a massive\r\n // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this\r\n // function using ln(x*10^e) = ln(x) + e*ln(10).\r\n t = getLn10(Ctor, wpr + 2, pr).times(e + '');\r\n x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);\r\n Ctor.precision = pr;\r\n\r\n return sd == null ? finalise(x, pr, rm, external = true) : x;\r\n }\r\n\r\n // x1 is x reduced to a value near 1.\r\n x1 = x;\r\n\r\n // Taylor series.\r\n // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)\r\n // where x = (y - 1)/(y + 1) (|x| < 1)\r\n sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);\r\n x2 = finalise(x.times(x), wpr, 1);\r\n denominator = 3;\r\n\r\n for (;;) {\r\n numerator = finalise(numerator.times(x2), wpr, 1);\r\n t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));\r\n\r\n if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {\r\n sum = sum.times(2);\r\n\r\n // Reverse the argument reduction. Check that e is not 0 because, besides preventing an\r\n // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.\r\n if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));\r\n sum = divide(sum, new Ctor(n), wpr, 1);\r\n\r\n // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has\r\n // been repeated previously) and the first 4 rounding digits 9999?\r\n // If so, restart the summation with a higher precision, otherwise\r\n // e.g. with precision: 12, rounding: 1\r\n // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.\r\n // `wpr - guard` is the index of first rounding digit.\r\n if (sd == null) {\r\n if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {\r\n Ctor.precision = wpr += guard;\r\n t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);\r\n x2 = finalise(x.times(x), wpr, 1);\r\n denominator = rep = 1;\r\n } else {\r\n return finalise(sum, Ctor.precision = pr, rm, external = true);\r\n }\r\n } else {\r\n Ctor.precision = pr;\r\n return sum;\r\n }\r\n }\r\n\r\n sum = t;\r\n denominator += 2;\r\n }\r\n }\r\n\r\n\r\n // ±Infinity, NaN.\r\n function nonFiniteToString(x) {\r\n // Unsigned.\r\n return String(x.s * x.s / 0);\r\n }\r\n\r\n\r\n /*\r\n * Parse the value of a new Decimal `x` from string `str`.\r\n */\r\n function parseDecimal(x, str) {\r\n var e, i, len;\r\n\r\n // Decimal point?\r\n if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');\r\n\r\n // Exponential form?\r\n if ((i = str.search(/e/i)) > 0) {\r\n\r\n // Determine exponent.\r\n if (e < 0) e = i;\r\n e += +str.slice(i + 1);\r\n str = str.substring(0, i);\r\n } else if (e < 0) {\r\n\r\n // Integer.\r\n e = str.length;\r\n }\r\n\r\n // Determine leading zeros.\r\n for (i = 0; str.charCodeAt(i) === 48; i++);\r\n\r\n // Determine trailing zeros.\r\n for (len = str.length; str.charCodeAt(len - 1) === 48; --len);\r\n str = str.slice(i, len);\r\n\r\n if (str) {\r\n len -= i;\r\n x.e = e = e - i - 1;\r\n x.d = [];\r\n\r\n // Transform base\r\n\r\n // e is the base 10 exponent.\r\n // i is where to slice str to get the first word of the digits array.\r\n i = (e + 1) % LOG_BASE;\r\n if (e < 0) i += LOG_BASE;\r\n\r\n if (i < len) {\r\n if (i) x.d.push(+str.slice(0, i));\r\n for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));\r\n str = str.slice(i);\r\n i = LOG_BASE - str.length;\r\n } else {\r\n i -= len;\r\n }\r\n\r\n for (; i--;) str += '0';\r\n x.d.push(+str);\r\n\r\n if (external) {\r\n\r\n // Overflow?\r\n if (x.e > x.constructor.maxE) {\r\n\r\n // Infinity.\r\n x.d = null;\r\n x.e = NaN;\r\n\r\n // Underflow?\r\n } else if (x.e < x.constructor.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n // x.constructor.underflow = true;\r\n } // else x.constructor.underflow = false;\r\n }\r\n } else {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.\r\n */\r\n function parseOther(x, str) {\r\n var base, Ctor, divisor, i, isFloat, len, p, xd, xe;\r\n\r\n if (str === 'Infinity' || str === 'NaN') {\r\n if (!+str) x.s = NaN;\r\n x.e = NaN;\r\n x.d = null;\r\n return x;\r\n }\r\n\r\n if (isHex.test(str)) {\r\n base = 16;\r\n str = str.toLowerCase();\r\n } else if (isBinary.test(str)) {\r\n base = 2;\r\n } else if (isOctal.test(str)) {\r\n base = 8;\r\n } else {\r\n throw Error(invalidArgument + str);\r\n }\r\n\r\n // Is there a binary exponent part?\r\n i = str.search(/p/i);\r\n\r\n if (i > 0) {\r\n p = +str.slice(i + 1);\r\n str = str.substring(2, i);\r\n } else {\r\n str = str.slice(2);\r\n }\r\n\r\n // Convert `str` as an integer then divide the result by `base` raised to a power such that the\r\n // fraction part will be restored.\r\n i = str.indexOf('.');\r\n isFloat = i >= 0;\r\n Ctor = x.constructor;\r\n\r\n if (isFloat) {\r\n str = str.replace('.', '');\r\n len = str.length;\r\n i = len - i;\r\n\r\n // log[10](16) = 1.2041... , log[10](88) = 1.9444....\r\n divisor = intPow(Ctor, new Ctor(base), i, i * 2);\r\n }\r\n\r\n xd = convertBase(str, base, BASE);\r\n xe = xd.length - 1;\r\n\r\n // Remove trailing zeros.\r\n for (i = xe; xd[i] === 0; --i) xd.pop();\r\n if (i < 0) return new Ctor(x.s * 0);\r\n x.e = getBase10Exponent(xd, xe);\r\n x.d = xd;\r\n external = false;\r\n\r\n // At what precision to perform the division to ensure exact conversion?\r\n // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)\r\n // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412\r\n // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.\r\n // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount\r\n // Therefore using 4 * the number of digits of str will always be enough.\r\n if (isFloat) x = divide(x, divisor, len * 4);\r\n\r\n // Multiply by the binary exponent part if present.\r\n if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));\r\n external = true;\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * sin(x) = x - x^3/3! + x^5/5! - ...\r\n * |x| < pi/2\r\n *\r\n */\r\n function sine(Ctor, x) {\r\n var k,\r\n len = x.d.length;\r\n\r\n if (len < 3) return taylorSeries(Ctor, 2, x, x);\r\n\r\n // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)\r\n // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)\r\n // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n k = 1.4 * Math.sqrt(len);\r\n k = k > 16 ? 16 : k | 0;\r\n\r\n x = x.times(1 / tinyPow(5, k));\r\n x = taylorSeries(Ctor, 2, x, x);\r\n\r\n // Reverse argument reduction\r\n var sin2_x,\r\n d5 = new Ctor(5),\r\n d16 = new Ctor(16),\r\n d20 = new Ctor(20);\r\n for (; k--;) {\r\n sin2_x = x.times(x);\r\n x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.\r\n function taylorSeries(Ctor, n, x, y, isHyperbolic) {\r\n var j, t, u, x2,\r\n i = 1,\r\n pr = Ctor.precision,\r\n k = Math.ceil(pr / LOG_BASE);\r\n\r\n external = false;\r\n x2 = x.times(x);\r\n u = new Ctor(y);\r\n\r\n for (;;) {\r\n t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);\r\n u = isHyperbolic ? y.plus(t) : y.minus(t);\r\n y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);\r\n t = u.plus(y);\r\n\r\n if (t.d[k] !== void 0) {\r\n for (j = k; t.d[j] === u.d[j] && j--;);\r\n if (j == -1) break;\r\n }\r\n\r\n j = u;\r\n u = y;\r\n y = t;\r\n t = j;\r\n i++;\r\n }\r\n\r\n external = true;\r\n t.d.length = k + 1;\r\n\r\n return t;\r\n }\r\n\r\n\r\n // Exponent e must be positive and non-zero.\r\n function tinyPow(b, e) {\r\n var n = b;\r\n while (--e) n *= b;\r\n return n;\r\n }\r\n\r\n\r\n // Return the absolute value of `x` reduced to less than or equal to half pi.\r\n function toLessThanHalfPi(Ctor, x) {\r\n var t,\r\n isNeg = x.s < 0,\r\n pi = getPi(Ctor, Ctor.precision, 1),\r\n halfPi = pi.times(0.5);\r\n\r\n x = x.abs();\r\n\r\n if (x.lte(halfPi)) {\r\n quadrant = isNeg ? 4 : 1;\r\n return x;\r\n }\r\n\r\n t = x.divToInt(pi);\r\n\r\n if (t.isZero()) {\r\n quadrant = isNeg ? 3 : 2;\r\n } else {\r\n x = x.minus(t.times(pi));\r\n\r\n // 0 <= x < pi\r\n if (x.lte(halfPi)) {\r\n quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);\r\n return x;\r\n }\r\n\r\n quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);\r\n }\r\n\r\n return x.minus(pi).abs();\r\n }\r\n\r\n\r\n /*\r\n * Return the value of Decimal `x` as a string in base `baseOut`.\r\n *\r\n * If the optional `sd` argument is present include a binary exponent suffix.\r\n */\r\n function toStringBinary(x, baseOut, sd, rm) {\r\n var base, e, i, k, len, roundUp, str, xd, y,\r\n Ctor = x.constructor,\r\n isExp = sd !== void 0;\r\n\r\n if (isExp) {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n } else {\r\n sd = Ctor.precision;\r\n rm = Ctor.rounding;\r\n }\r\n\r\n if (!x.isFinite()) {\r\n str = nonFiniteToString(x);\r\n } else {\r\n str = finiteToString(x);\r\n i = str.indexOf('.');\r\n\r\n // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:\r\n // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))\r\n // minBinaryExponent = floor(decimalExponent * log[2](10))\r\n // log[2](10) = 3.321928094887362347870319429489390175864\r\n\r\n if (isExp) {\r\n base = 2;\r\n if (baseOut == 16) {\r\n sd = sd * 4 - 3;\r\n } else if (baseOut == 8) {\r\n sd = sd * 3 - 2;\r\n }\r\n } else {\r\n base = baseOut;\r\n }\r\n\r\n // Convert the number as an integer then divide the result by its base raised to a power such\r\n // that the fraction part will be restored.\r\n\r\n // Non-integer.\r\n if (i >= 0) {\r\n str = str.replace('.', '');\r\n y = new Ctor(1);\r\n y.e = str.length - i;\r\n y.d = convertBase(finiteToString(y), 10, base);\r\n y.e = y.d.length;\r\n }\r\n\r\n xd = convertBase(str, 10, base);\r\n e = len = xd.length;\r\n\r\n // Remove trailing zeros.\r\n for (; xd[--len] == 0;) xd.pop();\r\n\r\n if (!xd[0]) {\r\n str = isExp ? '0p+0' : '0';\r\n } else {\r\n if (i < 0) {\r\n e--;\r\n } else {\r\n x = new Ctor(x);\r\n x.d = xd;\r\n x.e = e;\r\n x = divide(x, y, sd, rm, 0, base);\r\n xd = x.d;\r\n e = x.e;\r\n roundUp = inexact;\r\n }\r\n\r\n // The rounding digit, i.e. the digit after the digit that may be rounded up.\r\n i = xd[sd];\r\n k = base / 2;\r\n roundUp = roundUp || xd[sd + 1] !== void 0;\r\n\r\n roundUp = rm < 4\r\n ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))\r\n : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||\r\n rm === (x.s < 0 ? 8 : 7));\r\n\r\n xd.length = sd;\r\n\r\n if (roundUp) {\r\n\r\n // Rounding up may mean the previous digit has to be rounded up and so on.\r\n for (; ++xd[--sd] > base - 1;) {\r\n xd[sd] = 0;\r\n if (!sd) {\r\n ++e;\r\n xd.unshift(1);\r\n }\r\n }\r\n }\r\n\r\n // Determine trailing zeros.\r\n for (len = xd.length; !xd[len - 1]; --len);\r\n\r\n // E.g. [4, 11, 15] becomes 4bf.\r\n for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);\r\n\r\n // Add binary exponent suffix?\r\n if (isExp) {\r\n if (len > 1) {\r\n if (baseOut == 16 || baseOut == 8) {\r\n i = baseOut == 16 ? 4 : 3;\r\n for (--len; len % i; len++) str += '0';\r\n xd = convertBase(str, base, baseOut);\r\n for (len = xd.length; !xd[len - 1]; --len);\r\n\r\n // xd[0] will always be be 1\r\n for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);\r\n } else {\r\n str = str.charAt(0) + '.' + str.slice(1);\r\n }\r\n }\r\n\r\n str = str + (e < 0 ? 'p' : 'p+') + e;\r\n } else if (e < 0) {\r\n for (; ++e;) str = '0' + str;\r\n str = '0.' + str;\r\n } else {\r\n if (++e > len) for (e -= len; e-- ;) str += '0';\r\n else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);\r\n }\r\n }\r\n\r\n str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;\r\n }\r\n\r\n return x.s < 0 ? '-' + str : str;\r\n }\r\n\r\n\r\n // Does not strip trailing zeros.\r\n function truncate(arr, len) {\r\n if (arr.length > len) {\r\n arr.length = len;\r\n return true;\r\n }\r\n }\r\n\r\n\r\n // Decimal methods\r\n\r\n\r\n /*\r\n * abs\r\n * acos\r\n * acosh\r\n * add\r\n * asin\r\n * asinh\r\n * atan\r\n * atanh\r\n * atan2\r\n * cbrt\r\n * ceil\r\n * clone\r\n * config\r\n * cos\r\n * cosh\r\n * div\r\n * exp\r\n * floor\r\n * hypot\r\n * ln\r\n * log\r\n * log2\r\n * log10\r\n * max\r\n * min\r\n * mod\r\n * mul\r\n * pow\r\n * random\r\n * round\r\n * set\r\n * sign\r\n * sin\r\n * sinh\r\n * sqrt\r\n * sub\r\n * tan\r\n * tanh\r\n * trunc\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the absolute value of `x`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function abs(x) {\r\n return new this(x).abs();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arccosine in radians of `x`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function acos(x) {\r\n return new this(x).acos();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function acosh(x) {\r\n return new this(x).acosh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function add(x, y) {\r\n return new this(x).plus(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function asin(x) {\r\n return new this(x).asin();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function asinh(x) {\r\n return new this(x).asinh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function atan(x) {\r\n return new this(x).atan();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function atanh(x) {\r\n return new this(x).atanh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi\r\n * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi, pi]\r\n *\r\n * y {number|string|Decimal} The y-coordinate.\r\n * x {number|string|Decimal} The x-coordinate.\r\n *\r\n * atan2(±0, -0) = ±pi\r\n * atan2(±0, +0) = ±0\r\n * atan2(±0, -x) = ±pi for x > 0\r\n * atan2(±0, x) = ±0 for x > 0\r\n * atan2(-y, ±0) = -pi/2 for y > 0\r\n * atan2(y, ±0) = pi/2 for y > 0\r\n * atan2(±y, -Infinity) = ±pi for finite y > 0\r\n * atan2(±y, +Infinity) = ±0 for finite y > 0\r\n * atan2(±Infinity, x) = ±pi/2 for finite x\r\n * atan2(±Infinity, -Infinity) = ±3*pi/4\r\n * atan2(±Infinity, +Infinity) = ±pi/4\r\n * atan2(NaN, x) = NaN\r\n * atan2(y, NaN) = NaN\r\n *\r\n */\r\n function atan2(y, x) {\r\n y = new this(y);\r\n x = new this(x);\r\n var r,\r\n pr = this.precision,\r\n rm = this.rounding,\r\n wpr = pr + 4;\r\n\r\n // Either NaN\r\n if (!y.s || !x.s) {\r\n r = new this(NaN);\r\n\r\n // Both ±Infinity\r\n } else if (!y.d && !x.d) {\r\n r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);\r\n r.s = y.s;\r\n\r\n // x is ±Infinity or y is ±0\r\n } else if (!x.d || y.isZero()) {\r\n r = x.s < 0 ? getPi(this, pr, rm) : new this(0);\r\n r.s = y.s;\r\n\r\n // y is ±Infinity or x is ±0\r\n } else if (!y.d || x.isZero()) {\r\n r = getPi(this, wpr, 1).times(0.5);\r\n r.s = y.s;\r\n\r\n // Both non-zero and finite\r\n } else if (x.s < 0) {\r\n this.precision = wpr;\r\n this.rounding = 1;\r\n r = this.atan(divide(y, x, wpr, 1));\r\n x = getPi(this, wpr, 1);\r\n this.precision = pr;\r\n this.rounding = rm;\r\n r = y.s < 0 ? r.minus(x) : r.plus(x);\r\n } else {\r\n r = this.atan(divide(y, x, wpr, 1));\r\n }\r\n\r\n return r;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function cbrt(x) {\r\n return new this(x).cbrt();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function ceil(x) {\r\n return finalise(x = new this(x), x.e + 1, 2);\r\n }\r\n\r\n\r\n /*\r\n * Configure global settings for a Decimal constructor.\r\n *\r\n * `obj` is an object with one or more of the following properties,\r\n *\r\n * precision {number}\r\n * rounding {number}\r\n * toExpNeg {number}\r\n * toExpPos {number}\r\n * maxE {number}\r\n * minE {number}\r\n * modulo {number}\r\n * crypto {boolean|number}\r\n * defaults {true}\r\n *\r\n * E.g. Decimal.config({ precision: 20, rounding: 4 })\r\n *\r\n */\r\n function config(obj) {\r\n if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');\r\n var i, p, v,\r\n useDefaults = obj.defaults === true,\r\n ps = [\r\n 'precision', 1, MAX_DIGITS,\r\n 'rounding', 0, 8,\r\n 'toExpNeg', -EXP_LIMIT, 0,\r\n 'toExpPos', 0, EXP_LIMIT,\r\n 'maxE', 0, EXP_LIMIT,\r\n 'minE', -EXP_LIMIT, 0,\r\n 'modulo', 0, 9\r\n ];\r\n\r\n for (i = 0; i < ps.length; i += 3) {\r\n if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];\r\n if ((v = obj[p]) !== void 0) {\r\n if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;\r\n else throw Error(invalidArgument + p + ': ' + v);\r\n }\r\n }\r\n\r\n if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];\r\n if ((v = obj[p]) !== void 0) {\r\n if (v === true || v === false || v === 0 || v === 1) {\r\n if (v) {\r\n if (typeof crypto != 'undefined' && crypto &&\r\n (crypto.getRandomValues || crypto.randomBytes)) {\r\n this[p] = true;\r\n } else {\r\n throw Error(cryptoUnavailable);\r\n }\r\n } else {\r\n this[p] = false;\r\n }\r\n } else {\r\n throw Error(invalidArgument + p + ': ' + v);\r\n }\r\n }\r\n\r\n return this;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function cos(x) {\r\n return new this(x).cos();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function cosh(x) {\r\n return new this(x).cosh();\r\n }\r\n\r\n\r\n /*\r\n * Create and return a Decimal constructor with the same configuration properties as this Decimal\r\n * constructor.\r\n *\r\n */\r\n function clone(obj) {\r\n var i, p, ps;\r\n\r\n /*\r\n * The Decimal constructor and exported function.\r\n * Return a new Decimal instance.\r\n *\r\n * v {number|string|Decimal} A numeric value.\r\n *\r\n */\r\n function Decimal(v) {\r\n var e, i, t,\r\n x = this;\r\n\r\n // Decimal called without new.\r\n if (!(x instanceof Decimal)) return new Decimal(v);\r\n\r\n // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor\r\n // which points to Object.\r\n x.constructor = Decimal;\r\n\r\n // Duplicate.\r\n if (v instanceof Decimal) {\r\n x.s = v.s;\r\n\r\n if (external) {\r\n if (!v.d || v.e > Decimal.maxE) {\r\n\r\n // Infinity.\r\n x.e = NaN;\r\n x.d = null;\r\n } else if (v.e < Decimal.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n } else {\r\n x.e = v.e;\r\n x.d = v.d.slice();\r\n }\r\n } else {\r\n x.e = v.e;\r\n x.d = v.d ? v.d.slice() : v.d;\r\n }\r\n\r\n return;\r\n }\r\n\r\n t = typeof v;\r\n\r\n if (t === 'number') {\r\n if (v === 0) {\r\n x.s = 1 / v < 0 ? -1 : 1;\r\n x.e = 0;\r\n x.d = [0];\r\n return;\r\n }\r\n\r\n if (v < 0) {\r\n v = -v;\r\n x.s = -1;\r\n } else {\r\n x.s = 1;\r\n }\r\n\r\n // Fast path for small integers.\r\n if (v === ~~v && v < 1e7) {\r\n for (e = 0, i = v; i >= 10; i /= 10) e++;\r\n\r\n if (external) {\r\n if (e > Decimal.maxE) {\r\n x.e = NaN;\r\n x.d = null;\r\n } else if (e < Decimal.minE) {\r\n x.e = 0;\r\n x.d = [0];\r\n } else {\r\n x.e = e;\r\n x.d = [v];\r\n }\r\n } else {\r\n x.e = e;\r\n x.d = [v];\r\n }\r\n\r\n return;\r\n\r\n // Infinity, NaN.\r\n } else if (v * 0 !== 0) {\r\n if (!v) x.s = NaN;\r\n x.e = NaN;\r\n x.d = null;\r\n return;\r\n }\r\n\r\n return parseDecimal(x, v.toString());\r\n\r\n } else if (t !== 'string') {\r\n throw Error(invalidArgument + v);\r\n }\r\n\r\n // Minus sign?\r\n if ((i = v.charCodeAt(0)) === 45) {\r\n v = v.slice(1);\r\n x.s = -1;\r\n } else {\r\n // Plus sign?\r\n if (i === 43) v = v.slice(1);\r\n x.s = 1;\r\n }\r\n\r\n return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);\r\n }\r\n\r\n Decimal.prototype = P;\r\n\r\n Decimal.ROUND_UP = 0;\r\n Decimal.ROUND_DOWN = 1;\r\n Decimal.ROUND_CEIL = 2;\r\n Decimal.ROUND_FLOOR = 3;\r\n Decimal.ROUND_HALF_UP = 4;\r\n Decimal.ROUND_HALF_DOWN = 5;\r\n Decimal.ROUND_HALF_EVEN = 6;\r\n Decimal.ROUND_HALF_CEIL = 7;\r\n Decimal.ROUND_HALF_FLOOR = 8;\r\n Decimal.EUCLID = 9;\r\n\r\n Decimal.config = Decimal.set = config;\r\n Decimal.clone = clone;\r\n Decimal.isDecimal = isDecimalInstance;\r\n\r\n Decimal.abs = abs;\r\n Decimal.acos = acos;\r\n Decimal.acosh = acosh; // ES6\r\n Decimal.add = add;\r\n Decimal.asin = asin;\r\n Decimal.asinh = asinh; // ES6\r\n Decimal.atan = atan;\r\n Decimal.atanh = atanh; // ES6\r\n Decimal.atan2 = atan2;\r\n Decimal.cbrt = cbrt; // ES6\r\n Decimal.ceil = ceil;\r\n Decimal.cos = cos;\r\n Decimal.cosh = cosh; // ES6\r\n Decimal.div = div;\r\n Decimal.exp = exp;\r\n Decimal.floor = floor;\r\n Decimal.hypot = hypot; // ES6\r\n Decimal.ln = ln;\r\n Decimal.log = log;\r\n Decimal.log10 = log10; // ES6\r\n Decimal.log2 = log2; // ES6\r\n Decimal.max = max;\r\n Decimal.min = min;\r\n Decimal.mod = mod;\r\n Decimal.mul = mul;\r\n Decimal.pow = pow;\r\n Decimal.random = random;\r\n Decimal.round = round;\r\n Decimal.sign = sign; // ES6\r\n Decimal.sin = sin;\r\n Decimal.sinh = sinh; // ES6\r\n Decimal.sqrt = sqrt;\r\n Decimal.sub = sub;\r\n Decimal.tan = tan;\r\n Decimal.tanh = tanh; // ES6\r\n Decimal.trunc = trunc; // ES6\r\n\r\n if (obj === void 0) obj = {};\r\n if (obj) {\r\n if (obj.defaults !== true) {\r\n ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];\r\n for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];\r\n }\r\n }\r\n\r\n Decimal.config(obj);\r\n\r\n return Decimal;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function div(x, y) {\r\n return new this(x).div(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} The power to which to raise the base of the natural log.\r\n *\r\n */\r\n function exp(x) {\r\n return new this(x).exp();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function floor(x) {\r\n return finalise(x = new this(x), x.e + 1, 3);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,\r\n * rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function hypot() {\r\n var i, n,\r\n t = new this(0);\r\n\r\n external = false;\r\n\r\n for (i = 0; i < arguments.length;) {\r\n n = new this(arguments[i++]);\r\n if (!n.d) {\r\n if (n.s) {\r\n external = true;\r\n return new this(1 / 0);\r\n }\r\n t = n;\r\n } else if (t.d) {\r\n t = t.plus(n.times(n));\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return t.sqrt();\r\n }\r\n\r\n\r\n /*\r\n * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),\r\n * otherwise return false.\r\n *\r\n */\r\n function isDecimalInstance(obj) {\r\n return obj instanceof Decimal || obj && obj.name === '[object Decimal]' || false;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function ln(x) {\r\n return new this(x).ln();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base\r\n * is specified, rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * log[y](x)\r\n *\r\n * x {number|string|Decimal} The argument of the logarithm.\r\n * y {number|string|Decimal} The base of the logarithm.\r\n *\r\n */\r\n function log(x, y) {\r\n return new this(x).log(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function log2(x) {\r\n return new this(x).log(2);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function log10(x) {\r\n return new this(x).log(10);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the maximum of the arguments.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function max() {\r\n return maxOrMin(this, arguments, 'lt');\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the minimum of the arguments.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function min() {\r\n return maxOrMin(this, arguments, 'gt');\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function mod(x, y) {\r\n return new this(x).mod(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function mul(x, y) {\r\n return new this(x).mul(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} The base.\r\n * y {number|string|Decimal} The exponent.\r\n *\r\n */\r\n function pow(x, y) {\r\n return new this(x).pow(y);\r\n }\r\n\r\n\r\n /*\r\n * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with\r\n * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros\r\n * are produced).\r\n *\r\n * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.\r\n *\r\n */\r\n function random(sd) {\r\n var d, e, k, n,\r\n i = 0,\r\n r = new this(1),\r\n rd = [];\r\n\r\n if (sd === void 0) sd = this.precision;\r\n else checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n k = Math.ceil(sd / LOG_BASE);\r\n\r\n if (!this.crypto) {\r\n for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;\r\n\r\n // Browsers supporting crypto.getRandomValues.\r\n } else if (crypto.getRandomValues) {\r\n d = crypto.getRandomValues(new Uint32Array(k));\r\n\r\n for (; i < k;) {\r\n n = d[i];\r\n\r\n // 0 <= n < 4294967296\r\n // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).\r\n if (n >= 4.29e9) {\r\n d[i] = crypto.getRandomValues(new Uint32Array(1))[0];\r\n } else {\r\n\r\n // 0 <= n <= 4289999999\r\n // 0 <= (n % 1e7) <= 9999999\r\n rd[i++] = n % 1e7;\r\n }\r\n }\r\n\r\n // Node.js supporting crypto.randomBytes.\r\n } else if (crypto.randomBytes) {\r\n\r\n // buffer\r\n d = crypto.randomBytes(k *= 4);\r\n\r\n for (; i < k;) {\r\n\r\n // 0 <= n < 2147483648\r\n n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);\r\n\r\n // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).\r\n if (n >= 2.14e9) {\r\n crypto.randomBytes(4).copy(d, i);\r\n } else {\r\n\r\n // 0 <= n <= 2139999999\r\n // 0 <= (n % 1e7) <= 9999999\r\n rd.push(n % 1e7);\r\n i += 4;\r\n }\r\n }\r\n\r\n i = k / 4;\r\n } else {\r\n throw Error(cryptoUnavailable);\r\n }\r\n\r\n k = rd[--i];\r\n sd %= LOG_BASE;\r\n\r\n // Convert trailing digits to zeros according to sd.\r\n if (k && sd) {\r\n n = mathpow(10, LOG_BASE - sd);\r\n rd[i] = (k / n | 0) * n;\r\n }\r\n\r\n // Remove trailing words which are zero.\r\n for (; rd[i] === 0; i--) rd.pop();\r\n\r\n // Zero?\r\n if (i < 0) {\r\n e = 0;\r\n rd = [0];\r\n } else {\r\n e = -1;\r\n\r\n // Remove leading words which are zero and adjust exponent accordingly.\r\n for (; rd[0] === 0; e -= LOG_BASE) rd.shift();\r\n\r\n // Count the digits of the first word of rd to determine leading zeros.\r\n for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;\r\n\r\n // Adjust the exponent for leading zeros of the first word of rd.\r\n if (k < LOG_BASE) e -= LOG_BASE - k;\r\n }\r\n\r\n r.e = e;\r\n r.d = rd;\r\n\r\n return r;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.\r\n *\r\n * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function round(x) {\r\n return finalise(x = new this(x), x.e + 1, this.rounding);\r\n }\r\n\r\n\r\n /*\r\n * Return\r\n * 1 if x > 0,\r\n * -1 if x < 0,\r\n * 0 if x is 0,\r\n * -0 if x is -0,\r\n * NaN otherwise\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function sign(x) {\r\n x = new this(x);\r\n return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function sin(x) {\r\n return new this(x).sin();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function sinh(x) {\r\n return new this(x).sinh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function sqrt(x) {\r\n return new this(x).sqrt();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function sub(x, y) {\r\n return new this(x).sub(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function tan(x) {\r\n return new this(x).tan();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function tanh(x) {\r\n return new this(x).tanh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` truncated to an integer.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function trunc(x) {\r\n return finalise(x = new this(x), x.e + 1, 1);\r\n }\r\n\r\n\r\n // Create and configure initial Decimal constructor.\r\n Decimal = clone(DEFAULTS);\r\n\r\n Decimal['default'] = Decimal.Decimal = Decimal;\r\n\r\n // Create the internal constants from their string values.\r\n LN10 = new Decimal(LN10);\r\n PI = new Decimal(PI);\r\n\r\n\r\n // Export.\r\n\r\n\r\n // AMD.\r\n if (typeof define == 'function' && define.amd) {\r\n define(function () {\r\n return Decimal;\r\n });\r\n\r\n // Node and other environments that support module.exports.\r\n } else if (typeof module != 'undefined' && module.exports) {\r\n if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {\r\n P[Symbol.for('nodejs.util.inspect.custom')] = P.toString;\r\n P[Symbol.toStringTag] = 'Decimal';\r\n }\r\n\r\n module.exports = Decimal;\r\n\r\n // Browser.\r\n } else {\r\n if (!globalScope) {\r\n globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;\r\n }\r\n\r\n noConflict = globalScope.Decimal;\r\n Decimal.noConflict = function () {\r\n globalScope.Decimal = noConflict;\r\n return Decimal;\r\n };\r\n\r\n globalScope.Decimal = Decimal;\r\n }\r\n})(this);\r\n","/**\n * typed-function\n *\n * Type checking for JavaScript functions\n *\n * https://github.com/josdejong/typed-function\n */\n'use strict';\n\n(function (root, factory) {\n if (typeof define === 'function' && define.amd) {\n // AMD. Register as an anonymous module.\n define([], factory);\n } else if (typeof exports === 'object') {\n // OldNode. Does not work with strict CommonJS, but\n // only CommonJS-like environments that support module.exports,\n // like OldNode.\n module.exports = factory();\n } else {\n // Browser globals (root is window)\n root.typed = factory();\n }\n}(this, function () {\n\n function ok () {\n return true;\n }\n\n function notOk () {\n return false;\n }\n\n function undef () {\n return undefined;\n }\n\n /**\n * @typedef {{\n * params: Param[],\n * fn: function\n * }} Signature\n *\n * @typedef {{\n * types: Type[],\n * restParam: boolean\n * }} Param\n *\n * @typedef {{\n * name: string,\n * typeIndex: number,\n * test: function,\n * conversion?: ConversionDef,\n * conversionIndex: number,\n * }} Type\n *\n * @typedef {{\n * from: string,\n * to: string,\n * convert: function (*) : *\n * }} ConversionDef\n *\n * @typedef {{\n * name: string,\n * test: function(*) : boolean\n * }} TypeDef\n */\n\n // create a new instance of typed-function\n function create () {\n // data type tests\n var _types = [\n { name: 'number', test: function (x) { return typeof x === 'number' } },\n { name: 'string', test: function (x) { return typeof x === 'string' } },\n { name: 'boolean', test: function (x) { return typeof x === 'boolean' } },\n { name: 'Function', test: function (x) { return typeof x === 'function'} },\n { name: 'Array', test: Array.isArray },\n { name: 'Date', test: function (x) { return x instanceof Date } },\n { name: 'RegExp', test: function (x) { return x instanceof RegExp } },\n { name: 'Object', test: function (x) {\n return typeof x === 'object' && x !== null && x.constructor === Object\n }},\n { name: 'null', test: function (x) { return x === null } },\n { name: 'undefined', test: function (x) { return x === undefined } }\n ];\n\n var anyType = {\n name: 'any',\n test: ok\n }\n\n // types which need to be ignored\n var _ignore = [];\n\n // type conversions\n var _conversions = [];\n\n // This is a temporary object, will be replaced with a typed function at the end\n var typed = {\n types: _types,\n conversions: _conversions,\n ignore: _ignore\n };\n\n /**\n * Find the test function for a type\n * @param {String} typeName\n * @return {TypeDef} Returns the type definition when found,\n * Throws a TypeError otherwise\n */\n function findTypeByName (typeName) {\n var entry = findInArray(typed.types, function (entry) {\n return entry.name === typeName;\n });\n\n if (entry) {\n return entry;\n }\n\n if (typeName === 'any') { // special baked-in case 'any'\n return anyType;\n }\n\n var hint = findInArray(typed.types, function (entry) {\n return entry.name.toLowerCase() === typeName.toLowerCase();\n });\n\n throw new TypeError('Unknown type \"' + typeName + '\"' +\n (hint ? ('. Did you mean \"' + hint.name + '\"?') : ''));\n }\n\n /**\n * Find the index of a type definition. Handles special case 'any'\n * @param {TypeDef} type\n * @return {number}\n */\n function findTypeIndex(type) {\n if (type === anyType) {\n return 999;\n }\n\n return typed.types.indexOf(type);\n }\n\n /**\n * Find a type that matches a value.\n * @param {*} value\n * @return {string} Returns the name of the first type for which\n * the type test matches the value.\n */\n function findTypeName(value) {\n var entry = findInArray(typed.types, function (entry) {\n return entry.test(value);\n });\n\n if (entry) {\n return entry.name;\n }\n\n throw new TypeError('Value has unknown type. Value: ' + value);\n }\n\n /**\n * Find a specific signature from a (composed) typed function, for example:\n *\n * typed.find(fn, ['number', 'string'])\n * typed.find(fn, 'number, string')\n *\n * Function find only only works for exact matches.\n *\n * @param {Function} fn A typed-function\n * @param {string | string[]} signature Signature to be found, can be\n * an array or a comma separated string.\n * @return {Function} Returns the matching signature, or\n * throws an error when no signature\n * is found.\n */\n function find (fn, signature) {\n if (!fn.signatures) {\n throw new TypeError('Function is no typed-function');\n }\n\n // normalize input\n var arr;\n if (typeof signature === 'string') {\n arr = signature.split(',');\n for (var i = 0; i < arr.length; i++) {\n arr[i] = arr[i].trim();\n }\n }\n else if (Array.isArray(signature)) {\n arr = signature;\n }\n else {\n throw new TypeError('String array or a comma separated string expected');\n }\n\n var str = arr.join(',');\n\n // find an exact match\n var match = fn.signatures[str];\n if (match) {\n return match;\n }\n\n // TODO: extend find to match non-exact signatures\n\n throw new TypeError('Signature not found (signature: ' + (fn.name || 'unnamed') + '(' + arr.join(', ') + '))');\n }\n\n /**\n * Convert a given value to another data type.\n * @param {*} value\n * @param {string} type\n */\n function convert (value, type) {\n var from = findTypeName(value);\n\n // check conversion is needed\n if (type === from) {\n return value;\n }\n\n for (var i = 0; i < typed.conversions.length; i++) {\n var conversion = typed.conversions[i];\n if (conversion.from === from && conversion.to === type) {\n return conversion.convert(value);\n }\n }\n\n throw new Error('Cannot convert from ' + from + ' to ' + type);\n }\n \n /**\n * Stringify parameters in a normalized way\n * @param {Param[]} params\n * @return {string}\n */\n function stringifyParams (params) {\n return params\n .map(function (param) {\n var typeNames = param.types.map(getTypeName);\n\n return (param.restParam ? '...' : '') + typeNames.join('|');\n })\n .join(',');\n }\n\n /**\n * Parse a parameter, like \"...number | boolean\"\n * @param {string} param\n * @param {ConversionDef[]} conversions\n * @return {Param} param\n */\n function parseParam (param, conversions) {\n var restParam = param.indexOf('...') === 0;\n var types = (!restParam)\n ? param\n : (param.length > 3)\n ? param.slice(3)\n : 'any';\n\n var typeNames = types.split('|').map(trim)\n .filter(notEmpty)\n .filter(notIgnore);\n\n var matchingConversions = filterConversions(conversions, typeNames);\n\n var exactTypes = typeNames.map(function (typeName) {\n var type = findTypeByName(typeName);\n\n return {\n name: typeName,\n typeIndex: findTypeIndex(type),\n test: type.test,\n conversion: null,\n conversionIndex: -1\n };\n });\n\n var convertibleTypes = matchingConversions.map(function (conversion) {\n var type = findTypeByName(conversion.from);\n\n return {\n name: conversion.from,\n typeIndex: findTypeIndex(type),\n test: type.test,\n conversion: conversion,\n conversionIndex: conversions.indexOf(conversion)\n };\n });\n\n return {\n types: exactTypes.concat(convertibleTypes),\n restParam: restParam\n };\n }\n\n /**\n * Parse a signature with comma separated parameters,\n * like \"number | boolean, ...string\"\n * @param {string} signature\n * @param {function} fn\n * @param {ConversionDef[]} conversions\n * @return {Signature | null} signature\n */\n function parseSignature (signature, fn, conversions) {\n var params = [];\n\n if (signature.trim() !== '') {\n params = signature\n .split(',')\n .map(trim)\n .map(function (param, index, array) {\n var parsedParam = parseParam(param, conversions);\n\n if (parsedParam.restParam && (index !== array.length - 1)) {\n throw new SyntaxError('Unexpected rest parameter \"' + param + '\": ' +\n 'only allowed for the last parameter');\n }\n\n return parsedParam;\n });\n }\n\n if (params.some(isInvalidParam)) {\n // invalid signature: at least one parameter has no types\n // (they may have been filtered)\n return null;\n }\n\n return {\n params: params,\n fn: fn\n };\n }\n\n /**\n * Test whether a set of params contains a restParam\n * @param {Param[]} params\n * @return {boolean} Returns true when the last parameter is a restParam\n */\n function hasRestParam(params) {\n var param = last(params)\n return param ? param.restParam : false;\n }\n\n /**\n * Test whether a parameter contains conversions\n * @param {Param} param\n * @return {boolean} Returns true when at least one of the parameters\n * contains a conversion.\n */\n function hasConversions(param) {\n return param.types.some(function (type) {\n return type.conversion != null;\n });\n }\n\n /**\n * Create a type test for a single parameter, which can have one or multiple\n * types.\n * @param {Param} param\n * @return {function(x: *) : boolean} Returns a test function\n */\n function compileTest(param) {\n if (!param || param.types.length === 0) {\n // nothing to do\n return ok;\n }\n else if (param.types.length === 1) {\n return findTypeByName(param.types[0].name).test;\n }\n else if (param.types.length === 2) {\n var test0 = findTypeByName(param.types[0].name).test;\n var test1 = findTypeByName(param.types[1].name).test;\n return function or(x) {\n return test0(x) || test1(x);\n }\n }\n else { // param.types.length > 2\n var tests = param.types.map(function (type) {\n return findTypeByName(type.name).test;\n })\n return function or(x) {\n for (var i = 0; i < tests.length; i++) {\n if (tests[i](x)) {\n return true;\n }\n }\n return false;\n }\n }\n }\n\n /**\n * Create a test for all parameters of a signature\n * @param {Param[]} params\n * @return {function(args: Array<*>) : boolean}\n */\n function compileTests(params) {\n var tests, test0, test1;\n\n if (hasRestParam(params)) {\n // variable arguments like '...number'\n tests = initial(params).map(compileTest);\n var varIndex = tests.length;\n var lastTest = compileTest(last(params));\n var testRestParam = function (args) {\n for (var i = varIndex; i < args.length; i++) {\n if (!lastTest(args[i])) {\n return false;\n }\n }\n return true;\n }\n\n return function testArgs(args) {\n for (var i = 0; i < tests.length; i++) {\n if (!tests[i](args[i])) {\n return false;\n }\n }\n return testRestParam(args) && (args.length >= varIndex + 1);\n };\n }\n else {\n // no variable arguments\n if (params.length === 0) {\n return function testArgs(args) {\n return args.length === 0;\n };\n }\n else if (params.length === 1) {\n test0 = compileTest(params[0]);\n return function testArgs(args) {\n return test0(args[0]) && args.length === 1;\n };\n }\n else if (params.length === 2) {\n test0 = compileTest(params[0]);\n test1 = compileTest(params[1]);\n return function testArgs(args) {\n return test0(args[0]) && test1(args[1]) && args.length === 2;\n };\n }\n else { // arguments.length > 2\n tests = params.map(compileTest);\n return function testArgs(args) {\n for (var i = 0; i < tests.length; i++) {\n if (!tests[i](args[i])) {\n return false;\n }\n }\n return args.length === tests.length;\n };\n }\n }\n }\n\n /**\n * Find the parameter at a specific index of a signature.\n * Handles rest parameters.\n * @param {Signature} signature\n * @param {number} index\n * @return {Param | null} Returns the matching parameter when found,\n * null otherwise.\n */\n function getParamAtIndex(signature, index) {\n return index < signature.params.length\n ? signature.params[index]\n : hasRestParam(signature.params)\n ? last(signature.params)\n : null\n }\n\n /**\n * Get all type names of a parameter\n * @param {Signature} signature\n * @param {number} index\n * @param {boolean} excludeConversions\n * @return {string[]} Returns an array with type names\n */\n function getExpectedTypeNames (signature, index, excludeConversions) {\n var param = getParamAtIndex(signature, index);\n var types = param\n ? excludeConversions\n ? param.types.filter(isExactType)\n : param.types\n : [];\n\n return types.map(getTypeName);\n }\n\n /**\n * Returns the name of a type\n * @param {Type} type\n * @return {string} Returns the type name\n */\n function getTypeName(type) {\n return type.name;\n }\n\n /**\n * Test whether a type is an exact type or conversion\n * @param {Type} type\n * @return {boolean} Returns true when\n */\n function isExactType(type) {\n return type.conversion === null || type.conversion === undefined;\n }\n\n /**\n * Helper function for creating error messages: create an array with\n * all available types on a specific argument index.\n * @param {Signature[]} signatures\n * @param {number} index\n * @return {string[]} Returns an array with available types\n */\n function mergeExpectedParams(signatures, index) {\n var typeNames = uniq(flatMap(signatures, function (signature) {\n return getExpectedTypeNames(signature, index, false);\n }));\n\n return (typeNames.indexOf('any') !== -1) ? ['any'] : typeNames;\n }\n\n /**\n * Create\n * @param {string} name The name of the function\n * @param {array.<*>} args The actual arguments passed to the function\n * @param {Signature[]} signatures A list with available signatures\n * @return {TypeError} Returns a type error with additional data\n * attached to it in the property `data`\n */\n function createError(name, args, signatures) {\n var err, expected;\n var _name = name || 'unnamed';\n\n // test for wrong type at some index\n var matchingSignatures = signatures;\n var index;\n for (index = 0; index < args.length; index++) {\n var nextMatchingDefs = matchingSignatures.filter(function (signature) {\n var test = compileTest(getParamAtIndex(signature, index));\n return (index < signature.params.length || hasRestParam(signature.params)) &&\n test(args[index]);\n });\n\n if (nextMatchingDefs.length === 0) {\n // no matching signatures anymore, throw error \"wrong type\"\n expected = mergeExpectedParams(matchingSignatures, index);\n if (expected.length > 0) {\n var actualType = findTypeName(args[index]);\n\n err = new TypeError('Unexpected type of argument in function ' + _name +\n ' (expected: ' + expected.join(' or ') +\n ', actual: ' + actualType + ', index: ' + index + ')');\n err.data = {\n category: 'wrongType',\n fn: _name,\n index: index,\n actual: actualType,\n expected: expected\n }\n return err;\n }\n }\n else {\n matchingSignatures = nextMatchingDefs;\n }\n }\n\n // test for too few arguments\n var lengths = matchingSignatures.map(function (signature) {\n return hasRestParam(signature.params) ? Infinity : signature.params.length;\n });\n if (args.length < Math.min.apply(null, lengths)) {\n expected = mergeExpectedParams(matchingSignatures, index);\n err = new TypeError('Too few arguments in function ' + _name +\n ' (expected: ' + expected.join(' or ') +\n ', index: ' + args.length + ')');\n err.data = {\n category: 'tooFewArgs',\n fn: _name,\n index: args.length,\n expected: expected\n }\n return err;\n }\n\n // test for too many arguments\n var maxLength = Math.max.apply(null, lengths);\n if (args.length > maxLength) {\n err = new TypeError('Too many arguments in function ' + _name +\n ' (expected: ' + maxLength + ', actual: ' + args.length + ')');\n err.data = {\n category: 'tooManyArgs',\n fn: _name,\n index: args.length,\n expectedLength: maxLength\n }\n return err;\n }\n\n err = new TypeError('Arguments of type \"' + args.join(', ') +\n '\" do not match any of the defined signatures of function ' + _name + '.');\n err.data = {\n category: 'mismatch',\n actual: args.map(findTypeName)\n }\n return err;\n }\n\n /**\n * Find the lowest index of all exact types of a parameter (no conversions)\n * @param {Param} param\n * @return {number} Returns the index of the lowest type in typed.types\n */\n function getLowestTypeIndex (param) {\n var min = 999;\n\n for (var i = 0; i < param.types.length; i++) {\n if (isExactType(param.types[i])) {\n min = Math.min(min, param.types[i].typeIndex);\n }\n }\n\n return min;\n }\n\n /**\n * Find the lowest index of the conversion of all types of the parameter\n * having a conversion\n * @param {Param} param\n * @return {number} Returns the lowest index of the conversions of this type\n */\n function getLowestConversionIndex (param) {\n var min = 999;\n\n for (var i = 0; i < param.types.length; i++) {\n if (!isExactType(param.types[i])) {\n min = Math.min(min, param.types[i].conversionIndex);\n }\n }\n\n return min;\n }\n\n /**\n * Compare two params\n * @param {Param} param1\n * @param {Param} param2\n * @return {number} returns a negative number when param1 must get a lower\n * index than param2, a positive number when the opposite,\n * or zero when both are equal\n */\n function compareParams (param1, param2) {\n var c;\n\n // compare having a rest parameter or not\n c = param1.restParam - param2.restParam;\n if (c !== 0) {\n return c;\n }\n\n // compare having conversions or not\n c = hasConversions(param1) - hasConversions(param2);\n if (c !== 0) {\n return c;\n }\n\n // compare the index of the types\n c = getLowestTypeIndex(param1) - getLowestTypeIndex(param2);\n if (c !== 0) {\n return c;\n }\n\n // compare the index of any conversion\n return getLowestConversionIndex(param1) - getLowestConversionIndex(param2);\n }\n\n /**\n * Compare two signatures\n * @param {Signature} signature1\n * @param {Signature} signature2\n * @return {number} returns a negative number when param1 must get a lower\n * index than param2, a positive number when the opposite,\n * or zero when both are equal\n */\n function compareSignatures (signature1, signature2) {\n var len = Math.min(signature1.params.length, signature2.params.length);\n var i;\n var c;\n\n // compare whether the params have conversions at all or not\n c = signature1.params.some(hasConversions) - signature2.params.some(hasConversions)\n if (c !== 0) {\n return c;\n }\n\n // next compare whether the params have conversions one by one\n for (i = 0; i < len; i++) {\n c = hasConversions(signature1.params[i]) - hasConversions(signature2.params[i]);\n if (c !== 0) {\n return c;\n }\n }\n\n // compare the types of the params one by one\n for (i = 0; i < len; i++) {\n c = compareParams(signature1.params[i], signature2.params[i]);\n if (c !== 0) {\n return c;\n }\n }\n\n // compare the number of params\n return signature1.params.length - signature2.params.length;\n }\n\n /**\n * Get params containing all types that can be converted to the defined types.\n *\n * @param {ConversionDef[]} conversions\n * @param {string[]} typeNames\n * @return {ConversionDef[]} Returns the conversions that are available\n * for every type (if any)\n */\n function filterConversions(conversions, typeNames) {\n var matches = {};\n\n conversions.forEach(function (conversion) {\n if (typeNames.indexOf(conversion.from) === -1 &&\n typeNames.indexOf(conversion.to) !== -1 &&\n !matches[conversion.from]) {\n matches[conversion.from] = conversion;\n }\n });\n\n return Object.keys(matches).map(function (from) {\n return matches[from];\n });\n }\n\n /**\n * Preprocess arguments before calling the original function:\n * - if needed convert the parameters\n * - in case of rest parameters, move the rest parameters into an Array\n * @param {Param[]} params\n * @param {function} fn\n * @return {function} Returns a wrapped function\n */\n function compileArgsPreprocessing(params, fn) {\n var fnConvert = fn;\n\n // TODO: can we make this wrapper function smarter/simpler?\n\n if (params.some(hasConversions)) {\n var restParam = hasRestParam(params);\n var compiledConversions = params.map(compileArgConversion)\n\n fnConvert = function convertArgs() {\n var args = [];\n var last = restParam ? arguments.length - 1 : arguments.length;\n for (var i = 0; i < last; i++) {\n args[i] = compiledConversions[i](arguments[i]);\n }\n if (restParam) {\n args[last] = arguments[last].map(compiledConversions[last]);\n }\n\n return fn.apply(this, args);\n }\n }\n\n var fnPreprocess = fnConvert;\n if (hasRestParam(params)) {\n var offset = params.length - 1;\n\n fnPreprocess = function preprocessRestParams () {\n return fnConvert.apply(this,\n slice(arguments, 0, offset).concat([slice(arguments, offset)]));\n }\n }\n\n return fnPreprocess;\n }\n\n /**\n * Compile conversion for a parameter to the right type\n * @param {Param} param\n * @return {function} Returns the wrapped function that will convert arguments\n *\n */\n function compileArgConversion(param) {\n var test0, test1, conversion0, conversion1;\n var tests = [];\n var conversions = [];\n\n param.types.forEach(function (type) {\n if (type.conversion) {\n tests.push(findTypeByName(type.conversion.from).test);\n conversions.push(type.conversion.convert);\n }\n });\n\n // create optimized conversion functions depending on the number of conversions\n switch (conversions.length) {\n case 0:\n return function convertArg(arg) {\n return arg;\n }\n\n case 1:\n test0 = tests[0]\n conversion0 = conversions[0];\n return function convertArg(arg) {\n if (test0(arg)) {\n return conversion0(arg)\n }\n return arg;\n }\n\n case 2:\n test0 = tests[0]\n test1 = tests[1]\n conversion0 = conversions[0];\n conversion1 = conversions[1];\n return function convertArg(arg) {\n if (test0(arg)) {\n return conversion0(arg)\n }\n if (test1(arg)) {\n return conversion1(arg)\n }\n return arg;\n }\n\n default:\n return function convertArg(arg) {\n for (var i = 0; i < conversions.length; i++) {\n if (tests[i](arg)) {\n return conversions[i](arg);\n }\n }\n return arg;\n }\n }\n }\n\n /**\n * Convert an array with signatures into a map with signatures,\n * where signatures with union types are split into separate signatures\n *\n * Throws an error when there are conflicting types\n *\n * @param {Signature[]} signatures\n * @return {Object.} Returns a map with signatures\n * as key and the original function\n * of this signature as value.\n */\n function createSignaturesMap(signatures) {\n var signaturesMap = {};\n signatures.forEach(function (signature) {\n if (!signature.params.some(hasConversions)) {\n splitParams(signature.params, true).forEach(function (params) {\n signaturesMap[stringifyParams(params)] = signature.fn;\n });\n }\n });\n\n return signaturesMap;\n }\n\n /**\n * Split params with union types in to separate params.\n *\n * For example:\n *\n * splitParams([['Array', 'Object'], ['string', 'RegExp'])\n * // returns:\n * // [\n * // ['Array', 'string'],\n * // ['Array', 'RegExp'],\n * // ['Object', 'string'],\n * // ['Object', 'RegExp']\n * // ]\n *\n * @param {Param[]} params\n * @param {boolean} ignoreConversionTypes\n * @return {Param[]}\n */\n function splitParams(params, ignoreConversionTypes) {\n function _splitParams(params, index, types) {\n if (index < params.length) {\n var param = params[index]\n var filteredTypes = ignoreConversionTypes\n ? param.types.filter(isExactType)\n : param.types;\n var typeGroups\n\n if (param.restParam) {\n // split the types of a rest parameter in two:\n // one with only exact types, and one with exact types and conversions\n var exactTypes = filteredTypes.filter(isExactType)\n typeGroups = exactTypes.length < filteredTypes.length\n ? [exactTypes, filteredTypes]\n : [filteredTypes]\n\n }\n else {\n // split all the types of a regular parameter into one type per group\n typeGroups = filteredTypes.map(function (type) {\n return [type]\n })\n }\n\n // recurse over the groups with types\n return flatMap(typeGroups, function (typeGroup) {\n return _splitParams(params, index + 1, types.concat([typeGroup]));\n });\n\n }\n else {\n // we've reached the end of the parameters. Now build a new Param\n var splittedParams = types.map(function (type, typeIndex) {\n return {\n types: type,\n restParam: (typeIndex === params.length - 1) && hasRestParam(params)\n }\n });\n\n return [splittedParams];\n }\n }\n\n return _splitParams(params, 0, []);\n }\n\n /**\n * Test whether two signatures have a conflicting signature\n * @param {Signature} signature1\n * @param {Signature} signature2\n * @return {boolean} Returns true when the signatures conflict, false otherwise.\n */\n function hasConflictingParams(signature1, signature2) {\n var ii = Math.max(signature1.params.length, signature2.params.length);\n\n for (var i = 0; i < ii; i++) {\n var typesNames1 = getExpectedTypeNames(signature1, i, true);\n var typesNames2 = getExpectedTypeNames(signature2, i, true);\n\n if (!hasOverlap(typesNames1, typesNames2)) {\n return false;\n }\n }\n\n var len1 = signature1.params.length;\n var len2 = signature2.params.length;\n var restParam1 = hasRestParam(signature1.params);\n var restParam2 = hasRestParam(signature2.params);\n\n return restParam1\n ? restParam2 ? (len1 === len2) : (len2 >= len1)\n : restParam2 ? (len1 >= len2) : (len1 === len2)\n }\n\n /**\n * Create a typed function\n * @param {String} name The name for the typed function\n * @param {Object.} signaturesMap\n * An object with one or\n * multiple signatures as key, and the\n * function corresponding to the\n * signature as value.\n * @return {function} Returns the created typed function.\n */\n function createTypedFunction(name, signaturesMap) {\n if (Object.keys(signaturesMap).length === 0) {\n throw new SyntaxError('No signatures provided');\n }\n\n // parse the signatures, and check for conflicts\n var parsedSignatures = [];\n Object.keys(signaturesMap)\n .map(function (signature) {\n return parseSignature(signature, signaturesMap[signature], typed.conversions);\n })\n .filter(notNull)\n .forEach(function (parsedSignature) {\n // check whether this parameter conflicts with already parsed signatures\n var conflictingSignature = findInArray(parsedSignatures, function (s) {\n return hasConflictingParams(s, parsedSignature)\n });\n if (conflictingSignature) {\n throw new TypeError('Conflicting signatures \"' +\n stringifyParams(conflictingSignature.params) + '\" and \"' +\n stringifyParams(parsedSignature.params) + '\".');\n }\n\n parsedSignatures.push(parsedSignature);\n });\n\n // split and filter the types of the signatures, and then order them\n var signatures = flatMap(parsedSignatures, function (parsedSignature) {\n var params = parsedSignature ? splitParams(parsedSignature.params, false) : []\n\n return params.map(function (params) {\n return {\n params: params,\n fn: parsedSignature.fn\n };\n });\n }).filter(notNull);\n\n signatures.sort(compareSignatures);\n\n // we create a highly optimized checks for the first couple of signatures with max 2 arguments\n var ok0 = signatures[0] && signatures[0].params.length <= 2 && !hasRestParam(signatures[0].params);\n var ok1 = signatures[1] && signatures[1].params.length <= 2 && !hasRestParam(signatures[1].params);\n var ok2 = signatures[2] && signatures[2].params.length <= 2 && !hasRestParam(signatures[2].params);\n var ok3 = signatures[3] && signatures[3].params.length <= 2 && !hasRestParam(signatures[3].params);\n var ok4 = signatures[4] && signatures[4].params.length <= 2 && !hasRestParam(signatures[4].params);\n var ok5 = signatures[5] && signatures[5].params.length <= 2 && !hasRestParam(signatures[5].params);\n var allOk = ok0 && ok1 && ok2 && ok3 && ok4 && ok5;\n\n // compile the tests\n var tests = signatures.map(function (signature) {\n return compileTests(signature.params);\n });\n\n var test00 = ok0 ? compileTest(signatures[0].params[0]) : notOk;\n var test10 = ok1 ? compileTest(signatures[1].params[0]) : notOk;\n var test20 = ok2 ? compileTest(signatures[2].params[0]) : notOk;\n var test30 = ok3 ? compileTest(signatures[3].params[0]) : notOk;\n var test40 = ok4 ? compileTest(signatures[4].params[0]) : notOk;\n var test50 = ok5 ? compileTest(signatures[5].params[0]) : notOk;\n\n var test01 = ok0 ? compileTest(signatures[0].params[1]) : notOk;\n var test11 = ok1 ? compileTest(signatures[1].params[1]) : notOk;\n var test21 = ok2 ? compileTest(signatures[2].params[1]) : notOk;\n var test31 = ok3 ? compileTest(signatures[3].params[1]) : notOk;\n var test41 = ok4 ? compileTest(signatures[4].params[1]) : notOk;\n var test51 = ok5 ? compileTest(signatures[5].params[1]) : notOk;\n\n // compile the functions\n var fns = signatures.map(function(signature) {\n return compileArgsPreprocessing(signature.params, signature.fn);\n });\n\n var fn0 = ok0 ? fns[0] : undef;\n var fn1 = ok1 ? fns[1] : undef;\n var fn2 = ok2 ? fns[2] : undef;\n var fn3 = ok3 ? fns[3] : undef;\n var fn4 = ok4 ? fns[4] : undef;\n var fn5 = ok5 ? fns[5] : undef;\n\n var len0 = ok0 ? signatures[0].params.length : -1;\n var len1 = ok1 ? signatures[1].params.length : -1;\n var len2 = ok2 ? signatures[2].params.length : -1;\n var len3 = ok3 ? signatures[3].params.length : -1;\n var len4 = ok4 ? signatures[4].params.length : -1;\n var len5 = ok5 ? signatures[5].params.length : -1;\n\n // simple and generic, but also slow\n var iStart = allOk ? 6 : 0;\n var iEnd = signatures.length;\n var generic = function generic() {\n 'use strict';\n\n for (var i = iStart; i < iEnd; i++) {\n if (tests[i](arguments)) {\n return fns[i].apply(this, arguments);\n }\n }\n\n throw createError(name, arguments, signatures);\n }\n\n // create the typed function\n // fast, specialized version. Falls back to the slower, generic one if needed\n var fn = function fn(arg0, arg1) {\n 'use strict';\n\n if (arguments.length === len0 && test00(arg0) && test01(arg1)) { return fn0.apply(fn, arguments); }\n if (arguments.length === len1 && test10(arg0) && test11(arg1)) { return fn1.apply(fn, arguments); }\n if (arguments.length === len2 && test20(arg0) && test21(arg1)) { return fn2.apply(fn, arguments); }\n if (arguments.length === len3 && test30(arg0) && test31(arg1)) { return fn3.apply(fn, arguments); }\n if (arguments.length === len4 && test40(arg0) && test41(arg1)) { return fn4.apply(fn, arguments); }\n if (arguments.length === len5 && test50(arg0) && test51(arg1)) { return fn5.apply(fn, arguments); }\n\n return generic.apply(fn, arguments);\n }\n\n // attach name the typed function\n try {\n Object.defineProperty(fn, 'name', {value: name});\n }\n catch (err) {\n // old browsers do not support Object.defineProperty and some don't support setting the name property\n // the function name is not essential for the functioning, it's mostly useful for debugging,\n // so it's fine to have unnamed functions.\n }\n\n // attach signatures to the function\n fn.signatures = createSignaturesMap(signatures);\n\n return fn;\n }\n\n /**\n * Test whether a type should be NOT be ignored\n * @param {string} typeName\n * @return {boolean}\n */\n function notIgnore(typeName) {\n return typed.ignore.indexOf(typeName) === -1;\n }\n\n /**\n * trim a string\n * @param {string} str\n * @return {string}\n */\n function trim(str) {\n return str.trim();\n }\n\n /**\n * Test whether a string is not empty\n * @param {string} str\n * @return {boolean}\n */\n function notEmpty(str) {\n return !!str;\n }\n\n /**\n * test whether a value is not strict equal to null\n * @param {*} value\n * @return {boolean}\n */\n function notNull(value) {\n return value !== null;\n }\n\n /**\n * Test whether a parameter has no types defined\n * @param {Param} param\n * @return {boolean}\n */\n function isInvalidParam (param) {\n return param.types.length === 0;\n }\n\n /**\n * Return all but the last items of an array\n * @param {Array} arr\n * @return {Array}\n */\n function initial(arr) {\n return arr.slice(0, arr.length - 1);\n }\n\n /**\n * return the last item of an array\n * @param {Array} arr\n * @return {*}\n */\n function last(arr) {\n return arr[arr.length - 1];\n }\n\n /**\n * Slice an array or function Arguments\n * @param {Array | Arguments | IArguments} arr\n * @param {number} start\n * @param {number} [end]\n * @return {Array}\n */\n function slice(arr, start, end) {\n return Array.prototype.slice.call(arr, start, end);\n }\n\n /**\n * Test whether an array contains some item\n * @param {Array} array\n * @param {*} item\n * @return {boolean} Returns true if array contains item, false if not.\n */\n function contains(array, item) {\n return array.indexOf(item) !== -1;\n }\n\n /**\n * Test whether two arrays have overlapping items\n * @param {Array} array1\n * @param {Array} array2\n * @return {boolean} Returns true when at least one item exists in both arrays\n */\n function hasOverlap(array1, array2) {\n for (var i = 0; i < array1.length; i++) {\n if (contains(array2, array1[i])) {\n return true;\n }\n }\n\n return false;\n }\n\n /**\n * Return the first item from an array for which test(arr[i]) returns true\n * @param {Array} arr\n * @param {function} test\n * @return {* | undefined} Returns the first matching item\n * or undefined when there is no match\n */\n function findInArray(arr, test) {\n for (var i = 0; i < arr.length; i++) {\n if (test(arr[i])) {\n return arr[i];\n }\n }\n return undefined;\n }\n\n /**\n * Filter unique items of an array with strings\n * @param {string[]} arr\n * @return {string[]}\n */\n function uniq(arr) {\n var entries = {}\n for (var i = 0; i < arr.length; i++) {\n entries[arr[i]] = true;\n }\n return Object.keys(entries);\n }\n\n /**\n * Flat map the result invoking a callback for every item in an array.\n * https://gist.github.com/samgiles/762ee337dff48623e729\n * @param {Array} arr\n * @param {function} callback\n * @return {Array}\n */\n function flatMap(arr, callback) {\n return Array.prototype.concat.apply([], arr.map(callback));\n }\n\n /**\n * Retrieve the function name from a set of typed functions,\n * and check whether the name of all functions match (if given)\n * @param {function[]} fns\n */\n function getName (fns) {\n var name = '';\n\n for (var i = 0; i < fns.length; i++) {\n var fn = fns[i];\n\n // check whether the names are the same when defined\n if ((typeof fn.signatures === 'object' || typeof fn.signature === 'string') && fn.name !== '') {\n if (name === '') {\n name = fn.name;\n }\n else if (name !== fn.name) {\n var err = new Error('Function names do not match (expected: ' + name + ', actual: ' + fn.name + ')');\n err.data = {\n actual: fn.name,\n expected: name\n };\n throw err;\n }\n }\n }\n\n return name;\n }\n\n // extract and merge all signatures of a list with typed functions\n function extractSignatures(fns) {\n var err;\n var signaturesMap = {};\n\n function validateUnique(_signature, _fn) {\n if (signaturesMap.hasOwnProperty(_signature) && _fn !== signaturesMap[_signature]) {\n err = new Error('Signature \"' + _signature + '\" is defined twice');\n err.data = {signature: _signature};\n throw err;\n // else: both signatures point to the same function, that's fine\n }\n }\n\n for (var i = 0; i < fns.length; i++) {\n var fn = fns[i];\n\n // test whether this is a typed-function\n if (typeof fn.signatures === 'object') {\n // merge the signatures\n for (var signature in fn.signatures) {\n if (fn.signatures.hasOwnProperty(signature)) {\n validateUnique(signature, fn.signatures[signature]);\n signaturesMap[signature] = fn.signatures[signature];\n }\n }\n }\n else if (typeof fn.signature === 'string') {\n validateUnique(fn.signature, fn);\n signaturesMap[fn.signature] = fn;\n }\n else {\n err = new TypeError('Function is no typed-function (index: ' + i + ')');\n err.data = {index: i};\n throw err;\n }\n }\n\n return signaturesMap;\n }\n\n typed = createTypedFunction('typed', {\n 'string, Object': createTypedFunction,\n 'Object': function (signaturesMap) {\n // find existing name\n var fns = [];\n for (var signature in signaturesMap) {\n if (signaturesMap.hasOwnProperty(signature)) {\n fns.push(signaturesMap[signature]);\n }\n }\n var name = getName(fns);\n return createTypedFunction(name, signaturesMap);\n },\n '...Function': function (fns) {\n return createTypedFunction(getName(fns), extractSignatures(fns));\n },\n 'string, ...Function': function (name, fns) {\n return createTypedFunction(name, extractSignatures(fns));\n }\n });\n\n typed.create = create;\n typed.types = _types;\n typed.conversions = _conversions;\n typed.ignore = _ignore;\n typed.convert = convert;\n typed.find = find;\n\n /**\n * add a type\n * @param {{name: string, test: function}} type\n * @param {boolean} [beforeObjectTest=true]\n * If true, the new test will be inserted before\n * the test with name 'Object' (if any), since\n * tests for Object match Array and classes too.\n */\n typed.addType = function (type, beforeObjectTest) {\n if (!type || typeof type.name !== 'string' || typeof type.test !== 'function') {\n throw new TypeError('Object with properties {name: string, test: function} expected');\n }\n\n if (beforeObjectTest !== false) {\n for (var i = 0; i < typed.types.length; i++) {\n if (typed.types[i].name === 'Object') {\n typed.types.splice(i, 0, type);\n return\n }\n }\n }\n\n typed.types.push(type);\n };\n\n // add a conversion\n typed.addConversion = function (conversion) {\n if (!conversion\n || typeof conversion.from !== 'string'\n || typeof conversion.to !== 'string'\n || typeof conversion.convert !== 'function') {\n throw new TypeError('Object with properties {from: string, to: string, convert: function} expected');\n }\n\n typed.conversions.push(conversion);\n };\n\n return typed;\n }\n\n return create();\n}));\n","// A library of seedable RNGs implemented in Javascript.\n//\n// Usage:\n//\n// var seedrandom = require('seedrandom');\n// var random = seedrandom(1); // or any seed.\n// var x = random(); // 0 <= x < 1. Every bit is random.\n// var x = random.quick(); // 0 <= x < 1. 32 bits of randomness.\n\n// alea, a 53-bit multiply-with-carry generator by Johannes Baagøe.\n// Period: ~2^116\n// Reported to pass all BigCrush tests.\nvar alea = require('./lib/alea');\n\n// xor128, a pure xor-shift generator by George Marsaglia.\n// Period: 2^128-1.\n// Reported to fail: MatrixRank and LinearComp.\nvar xor128 = require('./lib/xor128');\n\n// xorwow, George Marsaglia's 160-bit xor-shift combined plus weyl.\n// Period: 2^192-2^32\n// Reported to fail: CollisionOver, SimpPoker, and LinearComp.\nvar xorwow = require('./lib/xorwow');\n\n// xorshift7, by François Panneton and Pierre L'ecuyer, takes\n// a different approach: it adds robustness by allowing more shifts\n// than Marsaglia's original three. It is a 7-shift generator\n// with 256 bits, that passes BigCrush with no systmatic failures.\n// Period 2^256-1.\n// No systematic BigCrush failures reported.\nvar xorshift7 = require('./lib/xorshift7');\n\n// xor4096, by Richard Brent, is a 4096-bit xor-shift with a\n// very long period that also adds a Weyl generator. It also passes\n// BigCrush with no systematic failures. Its long period may\n// be useful if you have many generators and need to avoid\n// collisions.\n// Period: 2^4128-2^32.\n// No systematic BigCrush failures reported.\nvar xor4096 = require('./lib/xor4096');\n\n// Tyche-i, by Samuel Neves and Filipe Araujo, is a bit-shifting random\n// number generator derived from ChaCha, a modern stream cipher.\n// https://eden.dei.uc.pt/~sneves/pubs/2011-snfa2.pdf\n// Period: ~2^127\n// No systematic BigCrush failures reported.\nvar tychei = require('./lib/tychei');\n\n// The original ARC4-based prng included in this library.\n// Period: ~2^1600\nvar sr = require('./seedrandom');\n\nsr.alea = alea;\nsr.xor128 = xor128;\nsr.xorwow = xorwow;\nsr.xorshift7 = xorshift7;\nsr.xor4096 = xor4096;\nsr.tychei = tychei;\n\nmodule.exports = sr;\n","function E () {\n // Keep this empty so it's easier to inherit from\n // (via https://github.com/lipsmack from https://github.com/scottcorgan/tiny-emitter/issues/3)\n}\n\nE.prototype = {\n on: function (name, callback, ctx) {\n var e = this.e || (this.e = {});\n\n (e[name] || (e[name] = [])).push({\n fn: callback,\n ctx: ctx\n });\n\n return this;\n },\n\n once: function (name, callback, ctx) {\n var self = this;\n function listener () {\n self.off(name, listener);\n callback.apply(ctx, arguments);\n };\n\n listener._ = callback\n return this.on(name, listener, ctx);\n },\n\n emit: function (name) {\n var data = [].slice.call(arguments, 1);\n var evtArr = ((this.e || (this.e = {}))[name] || []).slice();\n var i = 0;\n var len = evtArr.length;\n\n for (i; i < len; i++) {\n evtArr[i].fn.apply(evtArr[i].ctx, data);\n }\n\n return this;\n },\n\n off: function (name, callback) {\n var e = this.e || (this.e = {});\n var evts = e[name];\n var liveEvents = [];\n\n if (evts && callback) {\n for (var i = 0, len = evts.length; i < len; i++) {\n if (evts[i].fn !== callback && evts[i].fn._ !== callback)\n liveEvents.push(evts[i]);\n }\n }\n\n // Remove event from queue to prevent memory leak\n // Suggested by https://github.com/lazd\n // Ref: https://github.com/scottcorgan/tiny-emitter/commit/c6ebfaa9bc973b33d110a84a307742b7cf94c953#commitcomment-5024910\n\n (liveEvents.length)\n ? e[name] = liveEvents\n : delete e[name];\n\n return this;\n }\n};\n\nmodule.exports = E;\nmodule.exports.TinyEmitter = E;\n","\"use strict\";\n\n// Map the characters to escape to their escaped values. The list is derived\n// from http://www.cespedes.org/blog/85/how-to-escape-latex-special-characters\n\nvar _extends = Object.assign || function (target) { for (var i = 1; i < arguments.length; i++) { var source = arguments[i]; for (var key in source) { if (Object.prototype.hasOwnProperty.call(source, key)) { target[key] = source[key]; } } } return target; };\n\nvar defaultEscapes = {\n \"{\": \"\\\\{\",\n \"}\": \"\\\\}\",\n \"\\\\\": \"\\\\textbackslash{}\",\n \"#\": \"\\\\#\",\n $: \"\\\\$\",\n \"%\": \"\\\\%\",\n \"&\": \"\\\\&\",\n \"^\": \"\\\\textasciicircum{}\",\n _: \"\\\\_\",\n \"~\": \"\\\\textasciitilde{}\"\n};\nvar formatEscapes = {\n \"\\u2013\": \"\\\\--\",\n \"\\u2014\": \"\\\\---\",\n \" \": \"~\",\n \"\\t\": \"\\\\qquad{}\",\n \"\\r\\n\": \"\\\\newline{}\",\n \"\\n\": \"\\\\newline{}\"\n};\n\nvar defaultEscapeMapFn = function defaultEscapeMapFn(defaultEscapes, formatEscapes) {\n return _extends({}, defaultEscapes, formatEscapes);\n};\n\n/**\n * Escape a string to be used in LaTeX documents.\n * @param {string} str the string to be escaped.\n * @param {boolean} params.preserveFormatting whether formatting escapes should\n * be performed (default: false).\n * @param {function} params.escapeMapFn the function to modify the escape maps.\n * @return {string} the escaped string, ready to be used in LaTeX.\n */\nmodule.exports = function (str) {\n var _ref = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {},\n _ref$preserveFormatti = _ref.preserveFormatting,\n preserveFormatting = _ref$preserveFormatti === undefined ? false : _ref$preserveFormatti,\n _ref$escapeMapFn = _ref.escapeMapFn,\n escapeMapFn = _ref$escapeMapFn === undefined ? defaultEscapeMapFn : _ref$escapeMapFn;\n\n var runningStr = String(str);\n var result = \"\";\n\n var escapes = escapeMapFn(_extends({}, defaultEscapes), preserveFormatting ? _extends({}, formatEscapes) : {});\n var escapeKeys = Object.keys(escapes); // as it is reused later on\n\n // Algorithm: Go through the string character by character, if it matches\n // with one of the special characters then we'll replace it with the escaped\n // version.\n\n var _loop = function _loop() {\n var specialCharFound = false;\n escapeKeys.forEach(function (key, index) {\n if (specialCharFound) {\n return;\n }\n if (runningStr.length >= key.length && runningStr.slice(0, key.length) === key) {\n result += escapes[escapeKeys[index]];\n runningStr = runningStr.slice(key.length, runningStr.length);\n specialCharFound = true;\n }\n });\n if (!specialCharFound) {\n result += runningStr.slice(0, 1);\n runningStr = runningStr.slice(1, runningStr.length);\n }\n };\n\n while (runningStr) {\n _loop();\n }\n return result;\n};","// A port of an algorithm by Johannes Baagøe , 2010\n// http://baagoe.com/en/RandomMusings/javascript/\n// https://github.com/nquinlan/better-random-numbers-for-javascript-mirror\n// Original work is under MIT license -\n\n// Copyright (C) 2010 by Johannes Baagøe \n//\n// Permission is hereby granted, free of charge, to any person obtaining a copy\n// of this software and associated documentation files (the \"Software\"), to deal\n// in the Software without restriction, including without limitation the rights\n// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n// copies of the Software, and to permit persons to whom the Software is\n// furnished to do so, subject to the following conditions:\n//\n// The above copyright notice and this permission notice shall be included in\n// all copies or substantial portions of the Software.\n//\n// THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n// THE SOFTWARE.\n\n\n\n(function(global, module, define) {\n\nfunction Alea(seed) {\n var me = this, mash = Mash();\n\n me.next = function() {\n var t = 2091639 * me.s0 + me.c * 2.3283064365386963e-10; // 2^-32\n me.s0 = me.s1;\n me.s1 = me.s2;\n return me.s2 = t - (me.c = t | 0);\n };\n\n // Apply the seeding algorithm from Baagoe.\n me.c = 1;\n me.s0 = mash(' ');\n me.s1 = mash(' ');\n me.s2 = mash(' ');\n me.s0 -= mash(seed);\n if (me.s0 < 0) { me.s0 += 1; }\n me.s1 -= mash(seed);\n if (me.s1 < 0) { me.s1 += 1; }\n me.s2 -= mash(seed);\n if (me.s2 < 0) { me.s2 += 1; }\n mash = null;\n}\n\nfunction copy(f, t) {\n t.c = f.c;\n t.s0 = f.s0;\n t.s1 = f.s1;\n t.s2 = f.s2;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new Alea(seed),\n state = opts && opts.state,\n prng = xg.next;\n prng.int32 = function() { return (xg.next() * 0x100000000) | 0; }\n prng.double = function() {\n return prng() + (prng() * 0x200000 | 0) * 1.1102230246251565e-16; // 2^-53\n };\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nfunction Mash() {\n var n = 0xefc8249d;\n\n var mash = function(data) {\n data = String(data);\n for (var i = 0; i < data.length; i++) {\n n += data.charCodeAt(i);\n var h = 0.02519603282416938 * n;\n n = h >>> 0;\n h -= n;\n h *= n;\n n = h >>> 0;\n h -= n;\n n += h * 0x100000000; // 2^32\n }\n return (n >>> 0) * 2.3283064365386963e-10; // 2^-32\n };\n\n return mash;\n}\n\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.alea = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xor128\" prng algorithm by\n// George Marsaglia. See http://www.jstatsoft.org/v08/i14/paper\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n me.x = 0;\n me.y = 0;\n me.z = 0;\n me.w = 0;\n\n // Set up generator function.\n me.next = function() {\n var t = me.x ^ (me.x << 11);\n me.x = me.y;\n me.y = me.z;\n me.z = me.w;\n return me.w ^= (me.w >>> 19) ^ t ^ (t >>> 8);\n };\n\n if (seed === (seed | 0)) {\n // Integer seed.\n me.x = seed;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 64; k++) {\n me.x ^= strseed.charCodeAt(k) | 0;\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.x = f.x;\n t.y = f.y;\n t.z = f.z;\n t.w = f.w;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xor128 = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xorwow\" prng algorithm by\n// George Marsaglia. See http://www.jstatsoft.org/v08/i14/paper\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n // Set up generator function.\n me.next = function() {\n var t = (me.x ^ (me.x >>> 2));\n me.x = me.y; me.y = me.z; me.z = me.w; me.w = me.v;\n return (me.d = (me.d + 362437 | 0)) +\n (me.v = (me.v ^ (me.v << 4)) ^ (t ^ (t << 1))) | 0;\n };\n\n me.x = 0;\n me.y = 0;\n me.z = 0;\n me.w = 0;\n me.v = 0;\n\n if (seed === (seed | 0)) {\n // Integer seed.\n me.x = seed;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 64; k++) {\n me.x ^= strseed.charCodeAt(k) | 0;\n if (k == strseed.length) {\n me.d = me.x << 10 ^ me.x >>> 4;\n }\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.x = f.x;\n t.y = f.y;\n t.z = f.z;\n t.w = f.w;\n t.v = f.v;\n t.d = f.d;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xorwow = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xorshift7\" algorithm by\n// François Panneton and Pierre L'ecuyer:\n// \"On the Xorgshift Random Number Generators\"\n// http://saluc.engr.uconn.edu/refs/crypto/rng/panneton05onthexorshift.pdf\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this;\n\n // Set up generator function.\n me.next = function() {\n // Update xor generator.\n var X = me.x, i = me.i, t, v, w;\n t = X[i]; t ^= (t >>> 7); v = t ^ (t << 24);\n t = X[(i + 1) & 7]; v ^= t ^ (t >>> 10);\n t = X[(i + 3) & 7]; v ^= t ^ (t >>> 3);\n t = X[(i + 4) & 7]; v ^= t ^ (t << 7);\n t = X[(i + 7) & 7]; t = t ^ (t << 13); v ^= t ^ (t << 9);\n X[i] = v;\n me.i = (i + 1) & 7;\n return v;\n };\n\n function init(me, seed) {\n var j, w, X = [];\n\n if (seed === (seed | 0)) {\n // Seed state array using a 32-bit integer.\n w = X[0] = seed;\n } else {\n // Seed state using a string.\n seed = '' + seed;\n for (j = 0; j < seed.length; ++j) {\n X[j & 7] = (X[j & 7] << 15) ^\n (seed.charCodeAt(j) + X[(j + 1) & 7] << 13);\n }\n }\n // Enforce an array length of 8, not all zeroes.\n while (X.length < 8) X.push(0);\n for (j = 0; j < 8 && X[j] === 0; ++j);\n if (j == 8) w = X[7] = -1; else w = X[j];\n\n me.x = X;\n me.i = 0;\n\n // Discard an initial 256 values.\n for (j = 256; j > 0; --j) {\n me.next();\n }\n }\n\n init(me, seed);\n}\n\nfunction copy(f, t) {\n t.x = f.x.slice();\n t.i = f.i;\n return t;\n}\n\nfunction impl(seed, opts) {\n if (seed == null) seed = +(new Date);\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (state.x) copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xorshift7 = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n","// A Javascript implementaion of Richard Brent's Xorgens xor4096 algorithm.\n//\n// This fast non-cryptographic random number generator is designed for\n// use in Monte-Carlo algorithms. It combines a long-period xorshift\n// generator with a Weyl generator, and it passes all common batteries\n// of stasticial tests for randomness while consuming only a few nanoseconds\n// for each prng generated. For background on the generator, see Brent's\n// paper: \"Some long-period random number generators using shifts and xors.\"\n// http://arxiv.org/pdf/1004.3115v1.pdf\n//\n// Usage:\n//\n// var xor4096 = require('xor4096');\n// random = xor4096(1); // Seed with int32 or string.\n// assert.equal(random(), 0.1520436450538547); // (0, 1) range, 53 bits.\n// assert.equal(random.int32(), 1806534897); // signed int32, 32 bits.\n//\n// For nonzero numeric keys, this impelementation provides a sequence\n// identical to that by Brent's xorgens 3 implementaion in C. This\n// implementation also provides for initalizing the generator with\n// string seeds, or for saving and restoring the state of the generator.\n//\n// On Chrome, this prng benchmarks about 2.1 times slower than\n// Javascript's built-in Math.random().\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this;\n\n // Set up generator function.\n me.next = function() {\n var w = me.w,\n X = me.X, i = me.i, t, v;\n // Update Weyl generator.\n me.w = w = (w + 0x61c88647) | 0;\n // Update xor generator.\n v = X[(i + 34) & 127];\n t = X[i = ((i + 1) & 127)];\n v ^= v << 13;\n t ^= t << 17;\n v ^= v >>> 15;\n t ^= t >>> 12;\n // Update Xor generator array state.\n v = X[i] = v ^ t;\n me.i = i;\n // Result is the combination.\n return (v + (w ^ (w >>> 16))) | 0;\n };\n\n function init(me, seed) {\n var t, v, i, j, w, X = [], limit = 128;\n if (seed === (seed | 0)) {\n // Numeric seeds initialize v, which is used to generates X.\n v = seed;\n seed = null;\n } else {\n // String seeds are mixed into v and X one character at a time.\n seed = seed + '\\0';\n v = 0;\n limit = Math.max(limit, seed.length);\n }\n // Initialize circular array and weyl value.\n for (i = 0, j = -32; j < limit; ++j) {\n // Put the unicode characters into the array, and shuffle them.\n if (seed) v ^= seed.charCodeAt((j + 32) % seed.length);\n // After 32 shuffles, take v as the starting w value.\n if (j === 0) w = v;\n v ^= v << 10;\n v ^= v >>> 15;\n v ^= v << 4;\n v ^= v >>> 13;\n if (j >= 0) {\n w = (w + 0x61c88647) | 0; // Weyl.\n t = (X[j & 127] ^= (v + w)); // Combine xor and weyl to init array.\n i = (0 == t) ? i + 1 : 0; // Count zeroes.\n }\n }\n // We have detected all zeroes; make the key nonzero.\n if (i >= 128) {\n X[(seed && seed.length || 0) & 127] = -1;\n }\n // Run the generator 512 times to further mix the state before using it.\n // Factoring this as a function slows the main generator, so it is just\n // unrolled here. The weyl generator is not advanced while warming up.\n i = 127;\n for (j = 4 * 128; j > 0; --j) {\n v = X[(i + 34) & 127];\n t = X[i = ((i + 1) & 127)];\n v ^= v << 13;\n t ^= t << 17;\n v ^= v >>> 15;\n t ^= t >>> 12;\n X[i] = v ^ t;\n }\n // Storing state as object members is faster than using closure variables.\n me.w = w;\n me.X = X;\n me.i = i;\n }\n\n init(me, seed);\n}\n\nfunction copy(f, t) {\n t.i = f.i;\n t.w = f.w;\n t.X = f.X.slice();\n return t;\n};\n\nfunction impl(seed, opts) {\n if (seed == null) seed = +(new Date);\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (state.X) copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xor4096 = impl;\n}\n\n})(\n this, // window object or global\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n","// A Javascript implementaion of the \"Tyche-i\" prng algorithm by\n// Samuel Neves and Filipe Araujo.\n// See https://eden.dei.uc.pt/~sneves/pubs/2011-snfa2.pdf\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n // Set up generator function.\n me.next = function() {\n var b = me.b, c = me.c, d = me.d, a = me.a;\n b = (b << 25) ^ (b >>> 7) ^ c;\n c = (c - d) | 0;\n d = (d << 24) ^ (d >>> 8) ^ a;\n a = (a - b) | 0;\n me.b = b = (b << 20) ^ (b >>> 12) ^ c;\n me.c = c = (c - d) | 0;\n me.d = (d << 16) ^ (c >>> 16) ^ a;\n return me.a = (a - b) | 0;\n };\n\n /* The following is non-inverted tyche, which has better internal\n * bit diffusion, but which is about 25% slower than tyche-i in JS.\n me.next = function() {\n var a = me.a, b = me.b, c = me.c, d = me.d;\n a = (me.a + me.b | 0) >>> 0;\n d = me.d ^ a; d = d << 16 ^ d >>> 16;\n c = me.c + d | 0;\n b = me.b ^ c; b = b << 12 ^ d >>> 20;\n me.a = a = a + b | 0;\n d = d ^ a; me.d = d = d << 8 ^ d >>> 24;\n me.c = c = c + d | 0;\n b = b ^ c;\n return me.b = (b << 7 ^ b >>> 25);\n }\n */\n\n me.a = 0;\n me.b = 0;\n me.c = 2654435769 | 0;\n me.d = 1367130551;\n\n if (seed === Math.floor(seed)) {\n // Integer seed.\n me.a = (seed / 0x100000000) | 0;\n me.b = seed | 0;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 20; k++) {\n me.b ^= strseed.charCodeAt(k) | 0;\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.a = f.a;\n t.b = f.b;\n t.c = f.c;\n t.d = f.d;\n return t;\n};\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.tychei = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","/*\nCopyright 2019 David Bau.\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.\nIN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY\nCLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,\nTORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE\nSOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n\n*/\n\n(function (global, pool, math) {\n//\n// The following constants are related to IEEE 754 limits.\n//\n\nvar width = 256, // each RC4 output is 0 <= x < 256\n chunks = 6, // at least six RC4 outputs for each double\n digits = 52, // there are 52 significant digits in a double\n rngname = 'random', // rngname: name for Math.random and Math.seedrandom\n startdenom = math.pow(width, chunks),\n significance = math.pow(2, digits),\n overflow = significance * 2,\n mask = width - 1,\n nodecrypto; // node.js crypto module, initialized at the bottom.\n\n//\n// seedrandom()\n// This is the seedrandom function described above.\n//\nfunction seedrandom(seed, options, callback) {\n var key = [];\n options = (options == true) ? { entropy: true } : (options || {});\n\n // Flatten the seed string or build one from local entropy if needed.\n var shortseed = mixkey(flatten(\n options.entropy ? [seed, tostring(pool)] :\n (seed == null) ? autoseed() : seed, 3), key);\n\n // Use the seed to initialize an ARC4 generator.\n var arc4 = new ARC4(key);\n\n // This function returns a random double in [0, 1) that contains\n // randomness in every bit of the mantissa of the IEEE 754 value.\n var prng = function() {\n var n = arc4.g(chunks), // Start with a numerator n < 2 ^ 48\n d = startdenom, // and denominator d = 2 ^ 48.\n x = 0; // and no 'extra last byte'.\n while (n < significance) { // Fill up all significant digits by\n n = (n + x) * width; // shifting numerator and\n d *= width; // denominator and generating a\n x = arc4.g(1); // new least-significant-byte.\n }\n while (n >= overflow) { // To avoid rounding up, before adding\n n /= 2; // last byte, shift everything\n d /= 2; // right using integer math until\n x >>>= 1; // we have exactly the desired bits.\n }\n return (n + x) / d; // Form the number within [0, 1).\n };\n\n prng.int32 = function() { return arc4.g(4) | 0; }\n prng.quick = function() { return arc4.g(4) / 0x100000000; }\n prng.double = prng;\n\n // Mix the randomness into accumulated entropy.\n mixkey(tostring(arc4.S), pool);\n\n // Calling convention: what to return as a function of prng, seed, is_math.\n return (options.pass || callback ||\n function(prng, seed, is_math_call, state) {\n if (state) {\n // Load the arc4 state from the given state if it has an S array.\n if (state.S) { copy(state, arc4); }\n // Only provide the .state method if requested via options.state.\n prng.state = function() { return copy(arc4, {}); }\n }\n\n // If called as a method of Math (Math.seedrandom()), mutate\n // Math.random because that is how seedrandom.js has worked since v1.0.\n if (is_math_call) { math[rngname] = prng; return seed; }\n\n // Otherwise, it is a newer calling convention, so return the\n // prng directly.\n else return prng;\n })(\n prng,\n shortseed,\n 'global' in options ? options.global : (this == math),\n options.state);\n}\n\n//\n// ARC4\n//\n// An ARC4 implementation. The constructor takes a key in the form of\n// an array of at most (width) integers that should be 0 <= x < (width).\n//\n// The g(count) method returns a pseudorandom integer that concatenates\n// the next (count) outputs from ARC4. Its return value is a number x\n// that is in the range 0 <= x < (width ^ count).\n//\nfunction ARC4(key) {\n var t, keylen = key.length,\n me = this, i = 0, j = me.i = me.j = 0, s = me.S = [];\n\n // The empty key [] is treated as [0].\n if (!keylen) { key = [keylen++]; }\n\n // Set up S using the standard key scheduling algorithm.\n while (i < width) {\n s[i] = i++;\n }\n for (i = 0; i < width; i++) {\n s[i] = s[j = mask & (j + key[i % keylen] + (t = s[i]))];\n s[j] = t;\n }\n\n // The \"g\" method returns the next (count) outputs as one number.\n (me.g = function(count) {\n // Using instance members instead of closure state nearly doubles speed.\n var t, r = 0,\n i = me.i, j = me.j, s = me.S;\n while (count--) {\n t = s[i = mask & (i + 1)];\n r = r * width + s[mask & ((s[i] = s[j = mask & (j + t)]) + (s[j] = t))];\n }\n me.i = i; me.j = j;\n return r;\n // For robust unpredictability, the function call below automatically\n // discards an initial batch of values. This is called RC4-drop[256].\n // See http://google.com/search?q=rsa+fluhrer+response&btnI\n })(width);\n}\n\n//\n// copy()\n// Copies internal state of ARC4 to or from a plain object.\n//\nfunction copy(f, t) {\n t.i = f.i;\n t.j = f.j;\n t.S = f.S.slice();\n return t;\n};\n\n//\n// flatten()\n// Converts an object tree to nested arrays of strings.\n//\nfunction flatten(obj, depth) {\n var result = [], typ = (typeof obj), prop;\n if (depth && typ == 'object') {\n for (prop in obj) {\n try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}\n }\n }\n return (result.length ? result : typ == 'string' ? obj : obj + '\\0');\n}\n\n//\n// mixkey()\n// Mixes a string seed into a key that is an array of integers, and\n// returns a shortened string seed that is equivalent to the result key.\n//\nfunction mixkey(seed, key) {\n var stringseed = seed + '', smear, j = 0;\n while (j < stringseed.length) {\n key[mask & j] =\n mask & ((smear ^= key[mask & j] * 19) + stringseed.charCodeAt(j++));\n }\n return tostring(key);\n}\n\n//\n// autoseed()\n// Returns an object for autoseeding, using window.crypto and Node crypto\n// module if available.\n//\nfunction autoseed() {\n try {\n var out;\n if (nodecrypto && (out = nodecrypto.randomBytes)) {\n // The use of 'out' to remember randomBytes makes tight minified code.\n out = out(width);\n } else {\n out = new Uint8Array(width);\n (global.crypto || global.msCrypto).getRandomValues(out);\n }\n return tostring(out);\n } catch (e) {\n var browser = global.navigator,\n plugins = browser && browser.plugins;\n return [+new Date, global, plugins, global.screen, tostring(pool)];\n }\n}\n\n//\n// tostring()\n// Converts an array of charcodes to a string\n//\nfunction tostring(a) {\n return String.fromCharCode.apply(0, a);\n}\n\n//\n// When seedrandom.js is loaded, we immediately mix a few bits\n// from the built-in RNG into the entropy pool. Because we do\n// not want to interfere with deterministic PRNG state later,\n// seedrandom will not call math.random on its own again after\n// initialization.\n//\nmixkey(math.random(), pool);\n\n//\n// Nodejs and AMD support: export the implementation as a module using\n// either convention.\n//\nif ((typeof module) == 'object' && module.exports) {\n module.exports = seedrandom;\n // When in node.js, try using crypto package for autoseeding.\n try {\n nodecrypto = require('crypto');\n } catch (ex) {}\n} else if ((typeof define) == 'function' && define.amd) {\n define(function() { return seedrandom; });\n} else {\n // When included as a plain script, set up Math.seedrandom global.\n math['seed' + rngname] = seedrandom;\n}\n\n\n// End anonymous scope, and pass initial values.\n})(\n // global: `self` in browsers (including strict mode and web workers),\n // otherwise `this` in Node and other environments\n (typeof self !== 'undefined') ? self : this,\n [], // pool: entropy pool starts empty\n Math // math: package containing random, pow, and seedrandom\n);\n","if(typeof __WEBPACK_EXTERNAL_MODULE__19__ === 'undefined') {var e = new Error(\"Cannot find module 'crypto'\"); e.code = 'MODULE_NOT_FOUND'; throw e;}\nmodule.exports = __WEBPACK_EXTERNAL_MODULE__19__;","// type checks for all known types\n//\n// note that:\n//\n// - check by duck-typing on a property like `isUnit`, instead of checking instanceof.\n// instanceof cannot be used because that would not allow to pass data from\n// one instance of math.js to another since each has it's own instance of Unit.\n// - check the `isUnit` property via the constructor, so there will be no\n// matches for \"fake\" instances like plain objects with a property `isUnit`.\n// That is important for security reasons.\n// - It must not be possible to override the type checks used internally,\n// for security reasons, so these functions are not exposed in the expression\n// parser.\n\nexport function isNumber (x) {\n return typeof x === 'number'\n}\n\nexport function isBigNumber (x) {\n return (x && x.constructor.prototype.isBigNumber === true) || false\n}\n\nexport function isComplex (x) {\n return (x && typeof x === 'object' && Object.getPrototypeOf(x).isComplex === true) || false\n}\n\nexport function isFraction (x) {\n return (x && typeof x === 'object' && Object.getPrototypeOf(x).isFraction === true) || false\n}\n\nexport function isUnit (x) {\n return (x && x.constructor.prototype.isUnit === true) || false\n}\n\nexport function isString (x) {\n return typeof x === 'string'\n}\n\nexport const isArray = Array.isArray\n\nexport function isMatrix (x) {\n return (x && x.constructor.prototype.isMatrix === true) || false\n}\n\n/**\n * Test whether a value is a collection: an Array or Matrix\n * @param {*} x\n * @returns {boolean} isCollection\n */\nexport function isCollection (x) {\n return Array.isArray(x) || isMatrix(x)\n}\n\nexport function isDenseMatrix (x) {\n return (x && x.isDenseMatrix && x.constructor.prototype.isMatrix === true) || false\n}\n\nexport function isSparseMatrix (x) {\n return (x && x.isSparseMatrix && x.constructor.prototype.isMatrix === true) || false\n}\n\nexport function isRange (x) {\n return (x && x.constructor.prototype.isRange === true) || false\n}\n\nexport function isIndex (x) {\n return (x && x.constructor.prototype.isIndex === true) || false\n}\n\nexport function isBoolean (x) {\n return typeof x === 'boolean'\n}\n\nexport function isResultSet (x) {\n return (x && x.constructor.prototype.isResultSet === true) || false\n}\n\nexport function isHelp (x) {\n return (x && x.constructor.prototype.isHelp === true) || false\n}\n\nexport function isFunction (x) {\n return typeof x === 'function'\n}\n\nexport function isDate (x) {\n return x instanceof Date\n}\n\nexport function isRegExp (x) {\n return x instanceof RegExp\n}\n\nexport function isObject (x) {\n return !!(x &&\n typeof x === 'object' &&\n x.constructor === Object &&\n !isComplex(x) &&\n !isFraction(x))\n}\n\nexport function isNull (x) {\n return x === null\n}\n\nexport function isUndefined (x) {\n return x === undefined\n}\n\nexport function isAccessorNode (x) {\n return (x && x.isAccessorNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isArrayNode (x) {\n return (x && x.isArrayNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isAssignmentNode (x) {\n return (x && x.isAssignmentNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isBlockNode (x) {\n return (x && x.isBlockNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isConditionalNode (x) {\n return (x && x.isConditionalNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isConstantNode (x) {\n return (x && x.isConstantNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isFunctionAssignmentNode (x) {\n return (x && x.isFunctionAssignmentNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isFunctionNode (x) {\n return (x && x.isFunctionNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isIndexNode (x) {\n return (x && x.isIndexNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isNode (x) {\n return (x && x.isNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isObjectNode (x) {\n return (x && x.isObjectNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isOperatorNode (x) {\n return (x && x.isOperatorNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isParenthesisNode (x) {\n return (x && x.isParenthesisNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isRangeNode (x) {\n return (x && x.isRangeNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isSymbolNode (x) {\n return (x && x.isSymbolNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isChain (x) {\n return (x && x.constructor.prototype.isChain === true) || false\n}\n\nexport function typeOf (x) {\n const t = typeof x\n\n if (t === 'object') {\n // JavaScript types\n if (x === null) return 'null'\n if (Array.isArray(x)) return 'Array'\n if (x instanceof Date) return 'Date'\n if (x instanceof RegExp) return 'RegExp'\n\n // math.js types\n if (isBigNumber(x)) return 'BigNumber'\n if (isComplex(x)) return 'Complex'\n if (isFraction(x)) return 'Fraction'\n if (isMatrix(x)) return 'Matrix'\n if (isUnit(x)) return 'Unit'\n if (isIndex(x)) return 'Index'\n if (isRange(x)) return 'Range'\n if (isResultSet(x)) return 'ResultSet'\n if (isNode(x)) return x.type\n if (isChain(x)) return 'Chain'\n if (isHelp(x)) return 'Help'\n\n return 'Object'\n }\n\n if (t === 'function') return 'Function'\n\n return t // can be 'string', 'number', 'boolean', ...\n}\n","import { isNumber } from './is.js'\n\n/**\n * @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue\n */\n\n/**\n * Check if a number is integer\n * @param {number | boolean} value\n * @return {boolean} isInteger\n */\nexport function isInteger (value) {\n if (typeof value === 'boolean') {\n return true\n }\n\n return isFinite(value)\n ? (value === Math.round(value))\n : false\n // Note: we use ==, not ===, as we can have Booleans as well\n}\n\n/**\n * Calculate the sign of a number\n * @param {number} x\n * @returns {number}\n */\nexport const sign = /* #__PURE__ */ Math.sign || function (x) {\n if (x > 0) {\n return 1\n } else if (x < 0) {\n return -1\n } else {\n return 0\n }\n}\n\n/**\n * Calculate the base-2 logarithm of a number\n * @param {number} x\n * @returns {number}\n */\nexport const log2 = /* #__PURE__ */ Math.log2 || function log2 (x) {\n return Math.log(x) / Math.LN2\n}\n\n/**\n * Calculate the base-10 logarithm of a number\n * @param {number} x\n * @returns {number}\n */\nexport const log10 = /* #__PURE__ */ Math.log10 || function log10 (x) {\n return Math.log(x) / Math.LN10\n}\n\n/**\n * Calculate the natural logarithm of a number + 1\n * @param {number} x\n * @returns {number}\n */\nexport const log1p = /* #__PURE__ */ Math.log1p || function (x) {\n return Math.log(x + 1)\n}\n\n/**\n * Calculate cubic root for a number\n *\n * Code from es6-shim.js:\n * https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577\n *\n * @param {number} x\n * @returns {number} Returns the cubic root of x\n */\nexport const cbrt = /* #__PURE__ */ Math.cbrt || function cbrt (x) {\n if (x === 0) {\n return x\n }\n\n const negate = x < 0\n let result\n if (negate) {\n x = -x\n }\n\n if (isFinite(x)) {\n result = Math.exp(Math.log(x) / 3)\n // from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods\n result = (x / (result * result) + (2 * result)) / 3\n } else {\n result = x\n }\n\n return negate ? -result : result\n}\n\n/**\n * Calculates exponentiation minus 1\n * @param {number} x\n * @return {number} res\n */\nexport const expm1 = /* #__PURE__ */ Math.expm1 || function expm1 (x) {\n return (x >= 2e-4 || x <= -2e-4)\n ? Math.exp(x) - 1\n : x + x * x / 2 + x * x * x / 6\n}\n\n/**\n * Convert a number to a formatted string representation.\n *\n * Syntax:\n *\n * format(value)\n * format(value, options)\n * format(value, precision)\n * format(value, fn)\n *\n * Where:\n *\n * {number} value The value to be formatted\n * {Object} options An object with formatting options. Available options:\n * {string} notation\n * Number notation. Choose from:\n * 'fixed' Always use regular number notation.\n * For example '123.40' and '14000000'\n * 'exponential' Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * 'engineering' Always use engineering notation.\n * For example '123.4e+0' and '14.0e+6'\n * 'auto' (default) Regular number notation for numbers\n * having an absolute value between\n * `lowerExp` and `upperExp` bounds, and\n * uses exponential notation elsewhere.\n * Lower bound is included, upper bound\n * is excluded.\n * For example '123.4' and '1.4e7'.\n * {number} precision A number between 0 and 16 to round\n * the digits of the number.\n * In case of notations 'exponential',\n * 'engineering', and 'auto',\n * `precision` defines the total\n * number of significant digits returned.\n * In case of notation 'fixed',\n * `precision` defines the number of\n * significant digits after the decimal\n * point.\n * `precision` is undefined by default,\n * not rounding any digits.\n * {number} lowerExp Exponent determining the lower boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `-3`.\n * {number} upperExp Exponent determining the upper boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `5`.\n * {Function} fn A custom formatting function. Can be used to override the\n * built-in notations. Function `fn` is called with `value` as\n * parameter and must return a string. Is useful for example to\n * format all values inside a matrix in a particular way.\n *\n * Examples:\n *\n * format(6.4) // '6.4'\n * format(1240000) // '1.24e6'\n * format(1/3) // '0.3333333333333333'\n * format(1/3, 3) // '0.333'\n * format(21385, 2) // '21000'\n * format(12.071, {notation: 'fixed'}) // '12'\n * format(2.3, {notation: 'fixed', precision: 2}) // '2.30'\n * format(52.8, {notation: 'exponential'}) // '5.28e+1'\n * format(12345678, {notation: 'engineering'}) // '12.345678e+6'\n *\n * @param {number} value\n * @param {Object | Function | number} [options]\n * @return {string} str The formatted value\n */\nexport function format (value, options) {\n if (typeof options === 'function') {\n // handle format(value, fn)\n return options(value)\n }\n\n // handle special cases\n if (value === Infinity) {\n return 'Infinity'\n } else if (value === -Infinity) {\n return '-Infinity'\n } else if (isNaN(value)) {\n return 'NaN'\n }\n\n // default values for options\n let notation = 'auto'\n let precision\n\n if (options) {\n // determine notation from options\n if (options.notation) {\n notation = options.notation\n }\n\n // determine precision from options\n if (isNumber(options)) {\n precision = options\n } else if (isNumber(options.precision)) {\n precision = options.precision\n }\n }\n\n // handle the various notations\n switch (notation) {\n case 'fixed':\n return toFixed(value, precision)\n\n case 'exponential':\n return toExponential(value, precision)\n\n case 'engineering':\n return toEngineering(value, precision)\n\n case 'auto':\n // remove trailing zeros after the decimal point\n return toPrecision(value, precision, options && options)\n .replace(/((\\.\\d*?)(0+))($|e)/, function () {\n const digits = arguments[2]\n const e = arguments[4]\n return (digits !== '.') ? digits + e : e\n })\n\n default:\n throw new Error('Unknown notation \"' + notation + '\". ' +\n 'Choose \"auto\", \"exponential\", or \"fixed\".')\n }\n}\n\n/**\n * Split a number into sign, coefficients, and exponent\n * @param {number | string} value\n * @return {SplitValue}\n * Returns an object containing sign, coefficients, and exponent\n */\nexport function splitNumber (value) {\n // parse the input value\n const match = String(value).toLowerCase().match(/^0*?(-?)(\\d+\\.?\\d*)(e([+-]?\\d+))?$/)\n if (!match) {\n throw new SyntaxError('Invalid number ' + value)\n }\n\n const sign = match[1]\n const digits = match[2]\n let exponent = parseFloat(match[4] || '0')\n\n const dot = digits.indexOf('.')\n exponent += (dot !== -1) ? (dot - 1) : (digits.length - 1)\n\n const coefficients = digits\n .replace('.', '') // remove the dot (must be removed before removing leading zeros)\n .replace(/^0*/, function (zeros) {\n // remove leading zeros, add their count to the exponent\n exponent -= zeros.length\n return ''\n })\n .replace(/0*$/, '') // remove trailing zeros\n .split('')\n .map(function (d) {\n return parseInt(d)\n })\n\n if (coefficients.length === 0) {\n coefficients.push(0)\n exponent++\n }\n\n return {\n sign: sign,\n coefficients: coefficients,\n exponent: exponent\n }\n}\n\n/**\n * Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'\n * @param {number | string} value\n * @param {number} [precision] Optional number of significant figures to return.\n */\nexport function toEngineering (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n const split = splitNumber(value)\n const rounded = roundDigits(split, precision)\n\n const e = rounded.exponent\n const c = rounded.coefficients\n\n // find nearest lower multiple of 3 for exponent\n const newExp = e % 3 === 0 ? e : (e < 0 ? (e - 3) - (e % 3) : e - (e % 3))\n\n if (isNumber(precision)) {\n // add zeroes to give correct sig figs\n while (precision > c.length || (e - newExp) + 1 > c.length) {\n c.push(0)\n }\n } else {\n // concatenate coefficients with necessary zeros\n // add zeros if necessary (for example: 1e+8 -> 100e+6)\n const missingZeros = Math.abs(e - newExp) - (c.length - 1)\n for (let i = 0; i < missingZeros; i++) {\n c.push(0)\n }\n }\n\n // find difference in exponents\n let expDiff = Math.abs(e - newExp)\n let decimalIdx = 1\n\n // push decimal index over by expDiff times\n while (expDiff > 0) {\n decimalIdx++\n expDiff--\n }\n\n // if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.\n // otherwise concat with the rest of the coefficients\n const decimals = c.slice(decimalIdx).join('')\n const decimalVal = ((isNumber(precision) && decimals.length) || decimals.match(/[1-9]/)) ? ('.' + decimals) : ''\n\n const str = c.slice(0, decimalIdx).join('') +\n decimalVal +\n 'e' + (e >= 0 ? '+' : '') + newExp.toString()\n return rounded.sign + str\n}\n\n/**\n * Format a number with fixed notation.\n * @param {number | string} value\n * @param {number} [precision=undefined] Optional number of decimals after the\n * decimal point. null by default.\n */\nexport function toFixed (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n const splitValue = splitNumber(value)\n const rounded = (typeof precision === 'number')\n ? roundDigits(splitValue, splitValue.exponent + 1 + precision)\n : splitValue\n let c = rounded.coefficients\n let p = rounded.exponent + 1 // exponent may have changed\n\n // append zeros if needed\n const pp = p + (precision || 0)\n if (c.length < pp) {\n c = c.concat(zeros(pp - c.length))\n }\n\n // prepend zeros if needed\n if (p < 0) {\n c = zeros(-p + 1).concat(c)\n p = 1\n }\n\n // insert a dot if needed\n if (p < c.length) {\n c.splice(p, 0, (p === 0) ? '0.' : '.')\n }\n\n return rounded.sign + c.join('')\n}\n\n/**\n * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'\n * @param {number | string} value\n * @param {number} [precision] Number of digits in formatted output.\n * If not provided, the maximum available digits\n * is used.\n */\nexport function toExponential (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n // round if needed, else create a clone\n const split = splitNumber(value)\n const rounded = precision ? roundDigits(split, precision) : split\n let c = rounded.coefficients\n const e = rounded.exponent\n\n // append zeros if needed\n if (c.length < precision) {\n c = c.concat(zeros(precision - c.length))\n }\n\n // format as `C.CCCe+EEE` or `C.CCCe-EEE`\n const first = c.shift()\n return rounded.sign + first + (c.length > 0 ? ('.' + c.join('')) : '') +\n 'e' + (e >= 0 ? '+' : '') + e\n}\n\n/**\n * Format a number with a certain precision\n * @param {number | string} value\n * @param {number} [precision=undefined] Optional number of digits.\n * @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]\n * By default:\n * lowerExp = -3 (incl)\n * upper = +5 (excl)\n * @return {string}\n */\nexport function toPrecision (value, precision, options) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n // determine lower and upper bound for exponential notation.\n const lowerExp = (options && options.lowerExp !== undefined) ? options.lowerExp : -3\n const upperExp = (options && options.upperExp !== undefined) ? options.upperExp : 5\n\n const split = splitNumber(value)\n const rounded = precision ? roundDigits(split, precision) : split\n if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {\n // exponential notation\n return toExponential(value, precision)\n } else {\n let c = rounded.coefficients\n const e = rounded.exponent\n\n // append trailing zeros\n if (c.length < precision) {\n c = c.concat(zeros(precision - c.length))\n }\n\n // append trailing zeros\n // TODO: simplify the next statement\n c = c.concat(zeros(e - c.length + 1 +\n (c.length < precision ? precision - c.length : 0)))\n\n // prepend zeros\n c = zeros(-e).concat(c)\n\n const dot = e > 0 ? e : 0\n if (dot < c.length - 1) {\n c.splice(dot + 1, 0, '.')\n }\n\n return rounded.sign + c.join('')\n }\n}\n\n/**\n * Round the number of digits of a number *\n * @param {SplitValue} split A value split with .splitNumber(value)\n * @param {number} precision A positive integer\n * @return {SplitValue}\n * Returns an object containing sign, coefficients, and exponent\n * with rounded digits\n */\nexport function roundDigits (split, precision) {\n // create a clone\n const rounded = {\n sign: split.sign,\n coefficients: split.coefficients,\n exponent: split.exponent\n }\n const c = rounded.coefficients\n\n // prepend zeros if needed\n while (precision <= 0) {\n c.unshift(0)\n rounded.exponent++\n precision++\n }\n\n if (c.length > precision) {\n const removed = c.splice(precision, c.length - precision)\n\n if (removed[0] >= 5) {\n let i = precision - 1\n c[i]++\n while (c[i] === 10) {\n c.pop()\n if (i === 0) {\n c.unshift(0)\n rounded.exponent++\n i++\n }\n i--\n c[i]++\n }\n }\n }\n\n return rounded\n}\n\n/**\n * Create an array filled with zeros.\n * @param {number} length\n * @return {Array}\n */\nfunction zeros (length) {\n const arr = []\n for (let i = 0; i < length; i++) {\n arr.push(0)\n }\n return arr\n}\n\n/**\n * Count the number of significant digits of a number.\n *\n * For example:\n * 2.34 returns 3\n * 0.0034 returns 2\n * 120.5e+30 returns 4\n *\n * @param {number} value\n * @return {number} digits Number of significant digits\n */\nexport function digits (value) {\n return value\n .toExponential()\n .replace(/e.*$/, '') // remove exponential notation\n .replace(/^0\\.?0*|\\./, '') // remove decimal point and leading zeros\n .length\n}\n\n/**\n * Minimum number added to one that makes the result different than one\n */\nexport const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16\n\n/**\n * Compares two floating point numbers.\n * @param {number} x First value to compare\n * @param {number} y Second value to compare\n * @param {number} [epsilon] The maximum relative difference between x and y\n * If epsilon is undefined or null, the function will\n * test whether x and y are exactly equal.\n * @return {boolean} whether the two numbers are nearly equal\n*/\nexport function nearlyEqual (x, y, epsilon) {\n // if epsilon is null or undefined, test whether x and y are exactly equal\n if (epsilon === null || epsilon === undefined) {\n return x === y\n }\n\n if (x === y) {\n return true\n }\n\n // NaN\n if (isNaN(x) || isNaN(y)) {\n return false\n }\n\n // at this point x and y should be finite\n if (isFinite(x) && isFinite(y)) {\n // check numbers are very close, needed when comparing numbers near zero\n const diff = Math.abs(x - y)\n if (diff < DBL_EPSILON) {\n return true\n } else {\n // use relative error\n return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon\n }\n }\n\n // Infinite and Number or negative Infinite and positive Infinite cases\n return false\n}\n\n/**\n * Calculate the hyperbolic arccos of a number\n * @param {number} x\n * @return {number}\n */\nexport const acosh = Math.acosh || function (x) {\n return Math.log(Math.sqrt(x * x - 1) + x)\n}\n\nexport const asinh = Math.asinh || function (x) {\n return Math.log(Math.sqrt(x * x + 1) + x)\n}\n\n/**\n * Calculate the hyperbolic arctangent of a number\n * @param {number} x\n * @return {number}\n */\nexport const atanh = Math.atanh || function (x) {\n return Math.log((1 + x) / (1 - x)) / 2\n}\n\n/**\n * Calculate the hyperbolic cosine of a number\n * @param {number} x\n * @returns {number}\n */\nexport const cosh = Math.cosh || function (x) {\n return (Math.exp(x) + Math.exp(-x)) / 2\n}\n\n/**\n * Calculate the hyperbolic sine of a number\n * @param {number} x\n * @returns {number}\n */\nexport const sinh = Math.sinh || function (x) {\n return (Math.exp(x) - Math.exp(-x)) / 2\n}\n\n/**\n * Calculate the hyperbolic tangent of a number\n * @param {number} x\n * @returns {number}\n */\nexport const tanh = Math.tanh || function (x) {\n const e = Math.exp(2 * x)\n return (e - 1) / (e + 1)\n}\n","/**\n * Convert a BigNumber to a formatted string representation.\n *\n * Syntax:\n *\n * format(value)\n * format(value, options)\n * format(value, precision)\n * format(value, fn)\n *\n * Where:\n *\n * {number} value The value to be formatted\n * {Object} options An object with formatting options. Available options:\n * {string} notation\n * Number notation. Choose from:\n * 'fixed' Always use regular number notation.\n * For example '123.40' and '14000000'\n * 'exponential' Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * 'auto' (default) Regular number notation for numbers\n * having an absolute value between\n * `lower` and `upper` bounds, and uses\n * exponential notation elsewhere.\n * Lower bound is included, upper bound\n * is excluded.\n * For example '123.4' and '1.4e7'.\n * {number} precision A number between 0 and 16 to round\n * the digits of the number.\n * In case of notations 'exponential',\n * 'engineering', and 'auto',\n * `precision` defines the total\n * number of significant digits returned.\n * In case of notation 'fixed',\n * `precision` defines the number of\n * significant digits after the decimal\n * point.\n * `precision` is undefined by default.\n * {number} lowerExp Exponent determining the lower boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `-3`.\n * {number} upperExp Exponent determining the upper boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `5`.\n * {Function} fn A custom formatting function. Can be used to override the\n * built-in notations. Function `fn` is called with `value` as\n * parameter and must return a string. Is useful for example to\n * format all values inside a matrix in a particular way.\n *\n * Examples:\n *\n * format(6.4) // '6.4'\n * format(1240000) // '1.24e6'\n * format(1/3) // '0.3333333333333333'\n * format(1/3, 3) // '0.333'\n * format(21385, 2) // '21000'\n * format(12e8, {notation: 'fixed'}) // returns '1200000000'\n * format(2.3, {notation: 'fixed', precision: 4}) // returns '2.3000'\n * format(52.8, {notation: 'exponential'}) // returns '5.28e+1'\n * format(12400, {notation: 'engineering'}) // returns '12.400e+3'\n *\n * @param {BigNumber} value\n * @param {Object | Function | number} [options]\n * @return {string} str The formatted value\n */\nexport function format (value, options) {\n if (typeof options === 'function') {\n // handle format(value, fn)\n return options(value)\n }\n\n // handle special cases\n if (!value.isFinite()) {\n return value.isNaN() ? 'NaN' : (value.gt(0) ? 'Infinity' : '-Infinity')\n }\n\n // default values for options\n let notation = 'auto'\n let precision\n\n if (options !== undefined) {\n // determine notation from options\n if (options.notation) {\n notation = options.notation\n }\n\n // determine precision from options\n if (typeof options === 'number') {\n precision = options\n } else if (options.precision) {\n precision = options.precision\n }\n }\n\n // handle the various notations\n switch (notation) {\n case 'fixed':\n return toFixed(value, precision)\n\n case 'exponential':\n return toExponential(value, precision)\n\n case 'engineering':\n return toEngineering(value, precision)\n\n case 'auto':\n {\n // determine lower and upper bound for exponential notation.\n // TODO: implement support for upper and lower to be BigNumbers themselves\n const lowerExp = (options && options.lowerExp !== undefined) ? options.lowerExp : -3\n const upperExp = (options && options.upperExp !== undefined) ? options.upperExp : 5\n\n // handle special case zero\n if (value.isZero()) return '0'\n\n // determine whether or not to output exponential notation\n let str\n const rounded = value.toSignificantDigits(precision)\n const exp = rounded.e\n if (exp >= lowerExp && exp < upperExp) {\n // normal number notation\n str = rounded.toFixed()\n } else {\n // exponential notation\n str = toExponential(value, precision)\n }\n\n // remove trailing zeros after the decimal point\n return str.replace(/((\\.\\d*?)(0+))($|e)/, function () {\n const digits = arguments[2]\n const e = arguments[4]\n return (digits !== '.') ? digits + e : e\n })\n }\n default:\n throw new Error('Unknown notation \"' + notation + '\". ' +\n 'Choose \"auto\", \"exponential\", or \"fixed\".')\n }\n}\n\n/**\n * Format a BigNumber in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'\n * @param {BigNumber | string} value\n * @param {number} [precision] Optional number of significant figures to return.\n */\nexport function toEngineering (value, precision) {\n // find nearest lower multiple of 3 for exponent\n const e = value.e\n const newExp = e % 3 === 0 ? e : (e < 0 ? (e - 3) - (e % 3) : e - (e % 3))\n\n // find difference in exponents, and calculate the value without exponent\n const valueWithoutExp = value.mul(Math.pow(10, -newExp))\n\n let valueStr = valueWithoutExp.toPrecision(precision)\n if (valueStr.indexOf('e') !== -1) {\n valueStr = valueWithoutExp.toString()\n }\n\n return valueStr + 'e' + (e >= 0 ? '+' : '') + newExp.toString()\n}\n\n/**\n * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'\n * @param {BigNumber} value\n * @param {number} [precision] Number of digits in formatted output.\n * If not provided, the maximum available digits\n * is used.\n * @returns {string} str\n */\nexport function toExponential (value, precision) {\n if (precision !== undefined) {\n return value.toExponential(precision - 1) // Note the offset of one\n } else {\n return value.toExponential()\n }\n}\n\n/**\n * Format a number with fixed notation.\n * @param {BigNumber} value\n * @param {number} [precision=undefined] Optional number of decimals after the\n * decimal point. Undefined by default.\n */\nexport function toFixed (value, precision) {\n return value.toFixed(precision)\n}\n","import { isBigNumber, isString, typeOf } from './is.js'\nimport { format as formatNumber } from './number.js'\nimport { format as formatBigNumber } from './bignumber/formatter.js'\n\n/**\n * Check if a text ends with a certain string.\n * @param {string} text\n * @param {string} search\n */\nexport function endsWith (text, search) {\n const start = text.length - search.length\n const end = text.length\n return (text.substring(start, end) === search)\n}\n\n/**\n * Format a value of any type into a string.\n *\n * Usage:\n * math.format(value)\n * math.format(value, precision)\n *\n * When value is a function:\n *\n * - When the function has a property `syntax`, it returns this\n * syntax description.\n * - In other cases, a string `'function'` is returned.\n *\n * When `value` is an Object:\n *\n * - When the object contains a property `format` being a function, this\n * function is invoked as `value.format(options)` and the result is returned.\n * - When the object has its own `toString` method, this method is invoked\n * and the result is returned.\n * - In other cases the function will loop over all object properties and\n * return JSON object notation like '{\"a\": 2, \"b\": 3}'.\n *\n * Example usage:\n * math.format(2/7) // '0.2857142857142857'\n * math.format(math.pi, 3) // '3.14'\n * math.format(new Complex(2, 3)) // '2 + 3i'\n * math.format('hello') // '\"hello\"'\n *\n * @param {*} value Value to be stringified\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string} str\n */\nexport function format (value, options) {\n if (typeof value === 'number') {\n return formatNumber(value, options)\n }\n\n if (isBigNumber(value)) {\n return formatBigNumber(value, options)\n }\n\n // note: we use unsafe duck-typing here to check for Fractions, this is\n // ok here since we're only invoking toString or concatenating its values\n if (looksLikeFraction(value)) {\n if (!options || options.fraction !== 'decimal') {\n // output as ratio, like '1/3'\n return (value.s * value.n) + '/' + value.d\n } else {\n // output as decimal, like '0.(3)'\n return value.toString()\n }\n }\n\n if (Array.isArray(value)) {\n return formatArray(value, options)\n }\n\n if (isString(value)) {\n return '\"' + value + '\"'\n }\n\n if (typeof value === 'function') {\n return value.syntax ? String(value.syntax) : 'function'\n }\n\n if (value && typeof value === 'object') {\n if (typeof value.format === 'function') {\n return value.format(options)\n } else if (value && value.toString(options) !== {}.toString()) {\n // this object has a non-native toString method, use that one\n return value.toString(options)\n } else {\n const entries = Object.keys(value).map(key => {\n return '\"' + key + '\": ' + format(value[key], options)\n })\n\n return '{' + entries.join(', ') + '}'\n }\n }\n\n return String(value)\n}\n\n/**\n * Stringify a value into a string enclosed in double quotes.\n * Unescaped double quotes and backslashes inside the value are escaped.\n * @param {*} value\n * @return {string}\n */\nexport function stringify (value) {\n const text = String(value)\n let escaped = ''\n let i = 0\n while (i < text.length) {\n let c = text.charAt(i)\n\n if (c === '\\\\') {\n escaped += c\n i++\n\n c = text.charAt(i)\n if (c === '' || '\"\\\\/bfnrtu'.indexOf(c) === -1) {\n escaped += '\\\\' // no valid escape character -> escape it\n }\n escaped += c\n } else if (c === '\"') {\n escaped += '\\\\\"'\n } else {\n escaped += c\n }\n i++\n }\n\n return '\"' + escaped + '\"'\n}\n\n/**\n * Escape special HTML characters\n * @param {*} value\n * @return {string}\n */\nexport function escape (value) {\n let text = String(value)\n text = text.replace(/&/g, '&')\n .replace(/\"/g, '"')\n .replace(/'/g, ''')\n .replace(//g, '>')\n\n return text\n}\n\n/**\n * Recursively format an n-dimensional matrix\n * Example output: \"[[1, 2], [3, 4]]\"\n * @param {Array} array\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\nfunction formatArray (array, options) {\n if (Array.isArray(array)) {\n let str = '['\n const len = array.length\n for (let i = 0; i < len; i++) {\n if (i !== 0) {\n str += ', '\n }\n str += formatArray(array[i], options)\n }\n str += ']'\n return str\n } else {\n return format(array, options)\n }\n}\n\n/**\n * Check whether a value looks like a Fraction (unsafe duck-type check)\n * @param {*} value\n * @return {boolean}\n */\nfunction looksLikeFraction (value) {\n return (value &&\n typeof value === 'object' &&\n typeof value.s === 'number' &&\n typeof value.n === 'number' &&\n typeof value.d === 'number') || false\n}\n\n/**\n * Compare two strings\n * @param {string} x\n * @param {string} y\n * @returns {number}\n */\nexport function compareText (x, y) {\n // we don't want to convert numbers to string, only accept string input\n if (!isString(x)) {\n throw new TypeError('Unexpected type of argument in function compareText ' +\n '(expected: string or Array or Matrix, actual: ' + typeOf(x) + ', index: 0)')\n }\n if (!isString(y)) {\n throw new TypeError('Unexpected type of argument in function compareText ' +\n '(expected: string or Array or Matrix, actual: ' + typeOf(y) + ', index: 1)')\n }\n\n return (x === y)\n ? 0\n : (x > y ? 1 : -1)\n}\n","/**\n * Create a range error with the message:\n * 'Dimension mismatch ( != )'\n * @param {number | number[]} actual The actual size\n * @param {number | number[]} expected The expected size\n * @param {string} [relation='!='] Optional relation between actual\n * and expected size: '!=', '<', etc.\n * @extends RangeError\n */\nexport function DimensionError (actual, expected, relation) {\n if (!(this instanceof DimensionError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.actual = actual\n this.expected = expected\n this.relation = relation\n\n this.message = 'Dimension mismatch (' +\n (Array.isArray(actual) ? ('[' + actual.join(', ') + ']') : actual) +\n ' ' + (this.relation || '!=') + ' ' +\n (Array.isArray(expected) ? ('[' + expected.join(', ') + ']') : expected) +\n ')'\n\n this.stack = (new Error()).stack\n}\n\nDimensionError.prototype = new RangeError()\nDimensionError.prototype.constructor = RangeError\nDimensionError.prototype.name = 'DimensionError'\nDimensionError.prototype.isDimensionError = true\n","/**\n * Create a range error with the message:\n * 'Index out of range (index < min)'\n * 'Index out of range (index < max)'\n *\n * @param {number} index The actual index\n * @param {number} [min=0] Minimum index (included)\n * @param {number} [max] Maximum index (excluded)\n * @extends RangeError\n */\nexport function IndexError (index, min, max) {\n if (!(this instanceof IndexError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.index = index\n if (arguments.length < 3) {\n this.min = 0\n this.max = min\n } else {\n this.min = min\n this.max = max\n }\n\n if (this.min !== undefined && this.index < this.min) {\n this.message = 'Index out of range (' + this.index + ' < ' + this.min + ')'\n } else if (this.max !== undefined && this.index >= this.max) {\n this.message = 'Index out of range (' + this.index + ' > ' + (this.max - 1) + ')'\n } else {\n this.message = 'Index out of range (' + this.index + ')'\n }\n\n this.stack = (new Error()).stack\n}\n\nIndexError.prototype = new RangeError()\nIndexError.prototype.constructor = RangeError\nIndexError.prototype.name = 'IndexError'\nIndexError.prototype.isIndexError = true\n","import { isInteger } from './number.js'\nimport { isNumber } from './is.js'\nimport { format } from './string.js'\nimport { DimensionError } from '../error/DimensionError.js'\nimport { IndexError } from '../error/IndexError.js'\n\n/**\n * Calculate the size of a multi dimensional array.\n * This function checks the size of the first entry, it does not validate\n * whether all dimensions match. (use function `validate` for that)\n * @param {Array} x\n * @Return {Number[]} size\n */\nexport function arraySize (x) {\n const s = []\n\n while (Array.isArray(x)) {\n s.push(x.length)\n x = x[0]\n }\n\n return s\n}\n\n/**\n * Recursively validate whether each element in a multi dimensional array\n * has a size corresponding to the provided size array.\n * @param {Array} array Array to be validated\n * @param {number[]} size Array with the size of each dimension\n * @param {number} dim Current dimension\n * @throws DimensionError\n * @private\n */\nfunction _validate (array, size, dim) {\n let i\n const len = array.length\n\n if (len !== size[dim]) {\n throw new DimensionError(len, size[dim])\n }\n\n if (dim < size.length - 1) {\n // recursively validate each child array\n const dimNext = dim + 1\n for (i = 0; i < len; i++) {\n const child = array[i]\n if (!Array.isArray(child)) {\n throw new DimensionError(size.length - 1, size.length, '<')\n }\n _validate(array[i], size, dimNext)\n }\n } else {\n // last dimension. none of the childs may be an array\n for (i = 0; i < len; i++) {\n if (Array.isArray(array[i])) {\n throw new DimensionError(size.length + 1, size.length, '>')\n }\n }\n }\n}\n\n/**\n * Validate whether each element in a multi dimensional array has\n * a size corresponding to the provided size array.\n * @param {Array} array Array to be validated\n * @param {number[]} size Array with the size of each dimension\n * @throws DimensionError\n */\nexport function validate (array, size) {\n const isScalar = (size.length === 0)\n if (isScalar) {\n // scalar\n if (Array.isArray(array)) {\n throw new DimensionError(array.length, 0)\n }\n } else {\n // array\n _validate(array, size, 0)\n }\n}\n\n/**\n * Test whether index is an integer number with index >= 0 and index < length\n * when length is provided\n * @param {number} index Zero-based index\n * @param {number} [length] Length of the array\n */\nexport function validateIndex (index, length) {\n if (!isNumber(index) || !isInteger(index)) {\n throw new TypeError('Index must be an integer (value: ' + index + ')')\n }\n if (index < 0 || (typeof length === 'number' && index >= length)) {\n throw new IndexError(index, length)\n }\n}\n\n/**\n * Resize a multi dimensional array. The resized array is returned.\n * @param {Array} array Array to be resized\n * @param {Array.} size Array with the size of each dimension\n * @param {*} [defaultValue=0] Value to be filled in in new entries,\n * zero by default. Specify for example `null`,\n * to clearly see entries that are not explicitly\n * set.\n * @return {Array} array The resized array\n */\nexport function resize (array, size, defaultValue) {\n // TODO: add support for scalars, having size=[] ?\n\n // check the type of the arguments\n if (!Array.isArray(array) || !Array.isArray(size)) {\n throw new TypeError('Array expected')\n }\n if (size.length === 0) {\n throw new Error('Resizing to scalar is not supported')\n }\n\n // check whether size contains positive integers\n size.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n })\n\n // recursively resize the array\n const _defaultValue = (defaultValue !== undefined) ? defaultValue : 0\n _resize(array, size, 0, _defaultValue)\n\n return array\n}\n\n/**\n * Recursively resize a multi dimensional array\n * @param {Array} array Array to be resized\n * @param {number[]} size Array with the size of each dimension\n * @param {number} dim Current dimension\n * @param {*} [defaultValue] Value to be filled in in new entries,\n * undefined by default.\n * @private\n */\nfunction _resize (array, size, dim, defaultValue) {\n let i\n let elem\n const oldLen = array.length\n const newLen = size[dim]\n const minLen = Math.min(oldLen, newLen)\n\n // apply new length\n array.length = newLen\n\n if (dim < size.length - 1) {\n // non-last dimension\n const dimNext = dim + 1\n\n // resize existing child arrays\n for (i = 0; i < minLen; i++) {\n // resize child array\n elem = array[i]\n if (!Array.isArray(elem)) {\n elem = [elem] // add a dimension\n array[i] = elem\n }\n _resize(elem, size, dimNext, defaultValue)\n }\n\n // create new child arrays\n for (i = minLen; i < newLen; i++) {\n // get child array\n elem = []\n array[i] = elem\n\n // resize new child array\n _resize(elem, size, dimNext, defaultValue)\n }\n } else {\n // last dimension\n\n // remove dimensions of existing values\n for (i = 0; i < minLen; i++) {\n while (Array.isArray(array[i])) {\n array[i] = array[i][0]\n }\n }\n\n // fill new elements with the default value\n for (i = minLen; i < newLen; i++) {\n array[i] = defaultValue\n }\n }\n}\n\n/**\n * Re-shape a multi dimensional array to fit the specified dimensions\n * @param {Array} array Array to be reshaped\n * @param {Array.} sizes List of sizes for each dimension\n * @returns {Array} Array whose data has been formatted to fit the\n * specified dimensions\n *\n * @throws {DimensionError} If the product of the new dimension sizes does\n * not equal that of the old ones\n */\nexport function reshape (array, sizes) {\n const flatArray = flatten(array)\n let newArray\n\n function product (arr) {\n return arr.reduce((prev, curr) => prev * curr)\n }\n\n if (!Array.isArray(array) || !Array.isArray(sizes)) {\n throw new TypeError('Array expected')\n }\n\n if (sizes.length === 0) {\n throw new DimensionError(0, product(arraySize(array)), '!=')\n }\n\n let totalSize = 1\n for (let sizeIndex = 0; sizeIndex < sizes.length; sizeIndex++) {\n totalSize *= sizes[sizeIndex]\n }\n\n if (flatArray.length !== totalSize) {\n throw new DimensionError(\n product(sizes),\n product(arraySize(array)),\n '!='\n )\n }\n\n try {\n newArray = _reshape(flatArray, sizes)\n } catch (e) {\n if (e instanceof DimensionError) {\n throw new DimensionError(\n product(sizes),\n product(arraySize(array)),\n '!='\n )\n }\n throw e\n }\n\n return newArray\n}\n\n/**\n * Iteratively re-shape a multi dimensional array to fit the specified dimensions\n * @param {Array} array Array to be reshaped\n * @param {Array.} sizes List of sizes for each dimension\n * @returns {Array} Array whose data has been formatted to fit the\n * specified dimensions\n */\n\nfunction _reshape (array, sizes) {\n // testing if there are enough elements for the requested shape\n let tmpArray = array\n let tmpArray2\n // for each dimensions starting by the last one and ignoring the first one\n for (let sizeIndex = sizes.length - 1; sizeIndex > 0; sizeIndex--) {\n const size = sizes[sizeIndex]\n tmpArray2 = []\n\n // aggregate the elements of the current tmpArray in elements of the requested size\n const length = tmpArray.length / size\n for (let i = 0; i < length; i++) {\n tmpArray2.push(tmpArray.slice(i * size, (i + 1) * size))\n }\n // set it as the new tmpArray for the next loop turn or for return\n tmpArray = tmpArray2\n }\n\n return tmpArray\n}\n\n/**\n * Squeeze a multi dimensional array\n * @param {Array} array\n * @param {Array} [size]\n * @returns {Array} returns the array itself\n */\nexport function squeeze (array, size) {\n const s = size || arraySize(array)\n\n // squeeze outer dimensions\n while (Array.isArray(array) && array.length === 1) {\n array = array[0]\n s.shift()\n }\n\n // find the first dimension to be squeezed\n let dims = s.length\n while (s[dims - 1] === 1) {\n dims--\n }\n\n // squeeze inner dimensions\n if (dims < s.length) {\n array = _squeeze(array, dims, 0)\n s.length = dims\n }\n\n return array\n}\n\n/**\n * Recursively squeeze a multi dimensional array\n * @param {Array} array\n * @param {number} dims Required number of dimensions\n * @param {number} dim Current dimension\n * @returns {Array | *} Returns the squeezed array\n * @private\n */\nfunction _squeeze (array, dims, dim) {\n let i, ii\n\n if (dim < dims) {\n const next = dim + 1\n for (i = 0, ii = array.length; i < ii; i++) {\n array[i] = _squeeze(array[i], dims, next)\n }\n } else {\n while (Array.isArray(array)) {\n array = array[0]\n }\n }\n\n return array\n}\n\n/**\n * Unsqueeze a multi dimensional array: add dimensions when missing\n *\n * Paramter `size` will be mutated to match the new, unqueezed matrix size.\n *\n * @param {Array} array\n * @param {number} dims Desired number of dimensions of the array\n * @param {number} [outer] Number of outer dimensions to be added\n * @param {Array} [size] Current size of array.\n * @returns {Array} returns the array itself\n * @private\n */\nexport function unsqueeze (array, dims, outer, size) {\n const s = size || arraySize(array)\n\n // unsqueeze outer dimensions\n if (outer) {\n for (let i = 0; i < outer; i++) {\n array = [array]\n s.unshift(1)\n }\n }\n\n // unsqueeze inner dimensions\n array = _unsqueeze(array, dims, 0)\n while (s.length < dims) {\n s.push(1)\n }\n\n return array\n}\n\n/**\n * Recursively unsqueeze a multi dimensional array\n * @param {Array} array\n * @param {number} dims Required number of dimensions\n * @param {number} dim Current dimension\n * @returns {Array | *} Returns the squeezed array\n * @private\n */\nfunction _unsqueeze (array, dims, dim) {\n let i, ii\n\n if (Array.isArray(array)) {\n const next = dim + 1\n for (i = 0, ii = array.length; i < ii; i++) {\n array[i] = _unsqueeze(array[i], dims, next)\n }\n } else {\n for (let d = dim; d < dims; d++) {\n array = [array]\n }\n }\n\n return array\n}\n/**\n * Flatten a multi dimensional array, put all elements in a one dimensional\n * array\n * @param {Array} array A multi dimensional array\n * @return {Array} The flattened array (1 dimensional)\n */\nexport function flatten (array) {\n if (!Array.isArray(array)) {\n // if not an array, return as is\n return array\n }\n const flat = []\n\n array.forEach(function callback (value) {\n if (Array.isArray(value)) {\n value.forEach(callback) // traverse through sub-arrays recursively\n } else {\n flat.push(value)\n }\n })\n\n return flat\n}\n\n/**\n * A safe map\n * @param {Array} array\n * @param {function} callback\n */\nexport function map (array, callback) {\n return Array.prototype.map.call(array, callback)\n}\n\n/**\n * A safe forEach\n * @param {Array} array\n * @param {function} callback\n */\nexport function forEach (array, callback) {\n Array.prototype.forEach.call(array, callback)\n}\n\n/**\n * A safe filter\n * @param {Array} array\n * @param {function} callback\n */\nexport function filter (array, callback) {\n if (arraySize(array).length !== 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n\n return Array.prototype.filter.call(array, callback)\n}\n\n/**\n * Filter values in a callback given a regular expression\n * @param {Array} array\n * @param {RegExp} regexp\n * @return {Array} Returns the filtered array\n * @private\n */\nexport function filterRegExp (array, regexp) {\n if (arraySize(array).length !== 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n\n return Array.prototype.filter.call(array, (entry) => regexp.test(entry))\n}\n\n/**\n * A safe join\n * @param {Array} array\n * @param {string} separator\n */\nexport function join (array, separator) {\n return Array.prototype.join.call(array, separator)\n}\n\n/**\n * Assign a numeric identifier to every element of a sorted array\n * @param {Array} a An array\n * @return {Array} An array of objects containing the original value and its identifier\n */\nexport function identify (a) {\n if (!Array.isArray(a)) {\n throw new TypeError('Array input expected')\n }\n\n if (a.length === 0) {\n return a\n }\n\n const b = []\n let count = 0\n b[0] = { value: a[0], identifier: 0 }\n for (let i = 1; i < a.length; i++) {\n if (a[i] === a[i - 1]) {\n count++\n } else {\n count = 0\n }\n b.push({ value: a[i], identifier: count })\n }\n return b\n}\n\n/**\n * Remove the numeric identifier from the elements\n * @param {array} a An array\n * @return {array} An array of values without identifiers\n */\nexport function generalize (a) {\n if (!Array.isArray(a)) {\n throw new TypeError('Array input expected')\n }\n\n if (a.length === 0) {\n return a\n }\n\n const b = []\n for (let i = 0; i < a.length; i++) {\n b.push(a[i].value)\n }\n return b\n}\n\n/**\n * Check the datatype of a given object\n * This is a low level implementation that should only be used by\n * parent Matrix classes such as SparseMatrix or DenseMatrix\n * This method does not validate Array Matrix shape\n * @param {Array} array\n * @param {function} typeOf Callback function to use to determine the type of a value\n * @return string\n */\nexport function getArrayDataType (array, typeOf) {\n let type // to hold type info\n let length = 0 // to hold length value to ensure it has consistent sizes\n\n for (let i = 0; i < array.length; i++) {\n const item = array[i]\n const isArray = Array.isArray(item)\n\n // Saving the target matrix row size\n if (i === 0 && isArray) {\n length = item.length\n }\n\n // If the current item is an array but the length does not equal the targetVectorSize\n if (isArray && item.length !== length) {\n return undefined\n }\n\n const itemType = isArray\n ? getArrayDataType(item, typeOf) // recurse into a nested array\n : typeOf(item)\n\n if (type === undefined) {\n type = itemType // first item\n } else if (type !== itemType) {\n return 'mixed'\n } else {\n // we're good, everything has the same type so far\n }\n }\n\n return type\n}\n\n/**\n * Return the last item from an array\n * @param array\n * @returns {*}\n */\nexport function last (array) {\n return array[array.length - 1]\n}\n\n/**\n * Get all but the last element of array.\n */\nexport function initial (array) {\n return array.slice(0, array.length - 1)\n}\n\n/**\n * Test whether an array or string contains an item\n * @param {Array | string} array\n * @param {*} item\n * @return {boolean}\n */\nexport function contains (array, item) {\n return array.indexOf(item) !== -1\n}\n","import { isBigNumber } from './is.js'\n\n/**\n * Clone an object\n *\n * clone(x)\n *\n * Can clone any primitive type, array, and object.\n * If x has a function clone, this function will be invoked to clone the object.\n *\n * @param {*} x\n * @return {*} clone\n */\nexport function clone (x) {\n const type = typeof x\n\n // immutable primitive types\n if (type === 'number' || type === 'string' || type === 'boolean' ||\n x === null || x === undefined) {\n return x\n }\n\n // use clone function of the object when available\n if (typeof x.clone === 'function') {\n return x.clone()\n }\n\n // array\n if (Array.isArray(x)) {\n return x.map(function (value) {\n return clone(value)\n })\n }\n\n if (x instanceof Date) return new Date(x.valueOf())\n if (isBigNumber(x)) return x // bignumbers are immutable\n if (x instanceof RegExp) throw new TypeError('Cannot clone ' + x) // TODO: clone a RegExp\n\n // object\n return mapObject(x, clone)\n}\n\n/**\n * Apply map to all properties of an object\n * @param {Object} object\n * @param {function} callback\n * @return {Object} Returns a copy of the object with mapped properties\n */\nexport function mapObject (object, callback) {\n const clone = {}\n\n for (const key in object) {\n if (hasOwnProperty(object, key)) {\n clone[key] = callback(object[key])\n }\n }\n\n return clone\n}\n\n/**\n * Extend object a with the properties of object b\n * @param {Object} a\n * @param {Object} b\n * @return {Object} a\n */\nexport function extend (a, b) {\n for (const prop in b) {\n if (hasOwnProperty(b, prop)) {\n a[prop] = b[prop]\n }\n }\n return a\n}\n\n/**\n * Deep extend an object a with the properties of object b\n * @param {Object} a\n * @param {Object} b\n * @returns {Object}\n */\nexport function deepExtend (a, b) {\n // TODO: add support for Arrays to deepExtend\n if (Array.isArray(b)) {\n throw new TypeError('Arrays are not supported by deepExtend')\n }\n\n for (const prop in b) {\n // We check against prop not being in Object.prototype or Function.prototype\n // to prevent polluting for example Object.__proto__.\n if (hasOwnProperty(b, prop) && !(prop in Object.prototype) && !(prop in Function.prototype)) {\n if (b[prop] && b[prop].constructor === Object) {\n if (a[prop] === undefined) {\n a[prop] = {}\n }\n if (a[prop] && a[prop].constructor === Object) {\n deepExtend(a[prop], b[prop])\n } else {\n a[prop] = b[prop]\n }\n } else if (Array.isArray(b[prop])) {\n throw new TypeError('Arrays are not supported by deepExtend')\n } else {\n a[prop] = b[prop]\n }\n }\n }\n return a\n}\n\n/**\n * Deep test equality of all fields in two pairs of arrays or objects.\n * Compares values and functions strictly (ie. 2 is not the same as '2').\n * @param {Array | Object} a\n * @param {Array | Object} b\n * @returns {boolean}\n */\nexport function deepStrictEqual (a, b) {\n let prop, i, len\n if (Array.isArray(a)) {\n if (!Array.isArray(b)) {\n return false\n }\n\n if (a.length !== b.length) {\n return false\n }\n\n for (i = 0, len = a.length; i < len; i++) {\n if (!deepStrictEqual(a[i], b[i])) {\n return false\n }\n }\n return true\n } else if (typeof a === 'function') {\n return (a === b)\n } else if (a instanceof Object) {\n if (Array.isArray(b) || !(b instanceof Object)) {\n return false\n }\n\n for (prop in a) {\n // noinspection JSUnfilteredForInLoop\n if (!(prop in b) || !deepStrictEqual(a[prop], b[prop])) {\n return false\n }\n }\n for (prop in b) {\n // noinspection JSUnfilteredForInLoop\n if (!(prop in a) || !deepStrictEqual(a[prop], b[prop])) {\n return false\n }\n }\n return true\n } else {\n return (a === b)\n }\n}\n\n/**\n * Recursively flatten a nested object.\n * @param {Object} nestedObject\n * @return {Object} Returns the flattened object\n */\nexport function deepFlatten (nestedObject) {\n const flattenedObject = {}\n\n _deepFlatten(nestedObject, flattenedObject)\n\n return flattenedObject\n}\n\n// helper function used by deepFlatten\nfunction _deepFlatten (nestedObject, flattenedObject) {\n for (const prop in nestedObject) {\n if (hasOwnProperty(nestedObject, prop)) {\n const value = nestedObject[prop]\n if (typeof value === 'object' && value !== null) {\n _deepFlatten(value, flattenedObject)\n } else {\n flattenedObject[prop] = value\n }\n }\n }\n}\n\n/**\n * Test whether the current JavaScript engine supports Object.defineProperty\n * @returns {boolean} returns true if supported\n */\nexport function canDefineProperty () {\n // test needed for broken IE8 implementation\n try {\n if (Object.defineProperty) {\n Object.defineProperty({}, 'x', { get: function () {} })\n return true\n }\n } catch (e) {}\n\n return false\n}\n\n/**\n * Attach a lazy loading property to a constant.\n * The given function `fn` is called once when the property is first requested.\n *\n * @param {Object} object Object where to add the property\n * @param {string} prop Property name\n * @param {Function} valueResolver Function returning the property value. Called\n * without arguments.\n */\nexport function lazy (object, prop, valueResolver) {\n let _uninitialized = true\n let _value\n\n Object.defineProperty(object, prop, {\n get: function () {\n if (_uninitialized) {\n _value = valueResolver()\n _uninitialized = false\n }\n return _value\n },\n\n set: function (value) {\n _value = value\n _uninitialized = false\n },\n\n configurable: true,\n enumerable: true\n })\n}\n\n/**\n * Traverse a path into an object.\n * When a namespace is missing, it will be created\n * @param {Object} object\n * @param {string | string[]} path A dot separated string like 'name.space'\n * @return {Object} Returns the object at the end of the path\n */\nexport function traverse (object, path) {\n if (path && typeof path === 'string') {\n return traverse(object, path.split('.'))\n }\n\n let obj = object\n\n if (path) {\n for (let i = 0; i < path.length; i++) {\n const key = path[i]\n if (!(key in obj)) {\n obj[key] = {}\n }\n obj = obj[key]\n }\n }\n\n return obj\n}\n\n/**\n * A safe hasOwnProperty\n * @param {Object} object\n * @param {string} property\n */\nexport function hasOwnProperty (object, property) {\n return object && Object.hasOwnProperty.call(object, property)\n}\n\n/**\n * Test whether an object is a factory. a factory has fields:\n *\n * - factory: function (type: Object, config: Object, load: function, typed: function [, math: Object]) (required)\n * - name: string (optional)\n * - path: string A dot separated path (optional)\n * - math: boolean If true (false by default), the math namespace is passed\n * as fifth argument of the factory function\n *\n * @param {*} object\n * @returns {boolean}\n */\nexport function isLegacyFactory (object) {\n return object && typeof object.factory === 'function'\n}\n\n/**\n * Get a nested property from an object\n * @param {Object} object\n * @param {string | string[]} path\n * @returns {Object}\n */\nexport function get (object, path) {\n if (typeof path === 'string') {\n if (isPath(path)) {\n return get(object, path.split('.'))\n } else {\n return object[path]\n }\n }\n\n let child = object\n\n for (let i = 0; i < path.length; i++) {\n const key = path[i]\n child = child ? child[key] : undefined\n }\n\n return child\n}\n\n/**\n * Set a nested property in an object\n * Mutates the object itself\n * If the path doesn't exist, it will be created\n * @param {Object} object\n * @param {string | string[]} path\n * @param {*} value\n * @returns {Object}\n */\nexport function set (object, path, value) {\n if (typeof path === 'string') {\n if (isPath(path)) {\n return set(object, path.split('.'), value)\n } else {\n object[path] = value\n return object\n }\n }\n\n let child = object\n for (let i = 0; i < path.length - 1; i++) {\n const key = path[i]\n if (child[key] === undefined) {\n child[key] = {}\n }\n child = child[key]\n }\n\n if (path.length > 0) {\n const lastKey = path[path.length - 1]\n child[lastKey] = value\n }\n\n return object\n}\n\n/**\n * Create an object composed of the picked object properties\n * @param {Object} object\n * @param {string[]} properties\n * @param {function} [transform] Optional value to transform a value when picking it\n * @return {Object}\n */\nexport function pick (object, properties, transform) {\n const copy = {}\n\n for (let i = 0; i < properties.length; i++) {\n const key = properties[i]\n const value = get(object, key)\n if (value !== undefined) {\n set(copy, key, transform ? transform(value, key) : value)\n }\n }\n\n return copy\n}\n\n/**\n * Shallow version of pick, creating an object composed of the picked object properties\n * but not for nested properties\n * @param {Object} object\n * @param {string[]} properties\n * @return {Object}\n */\nexport function pickShallow (object, properties) {\n const copy = {}\n\n for (let i = 0; i < properties.length; i++) {\n const key = properties[i]\n const value = object[key]\n if (value !== undefined) {\n copy[key] = value\n }\n }\n\n return copy\n}\n\nexport function values (object) {\n return Object.keys(object).map(key => object[key])\n}\n\n// helper function to test whether a string contains a path like 'user.name'\nfunction isPath (str) {\n return str.indexOf('.') !== -1\n}\n","import { contains } from './array.js'\nimport { pickShallow } from './object.js'\n\n/**\n * Create a factory function, which can be used to inject dependencies.\n *\n * The created functions are memoized, a consecutive call of the factory\n * with the exact same inputs will return the same function instance.\n * The memoized cache is exposed on `factory.cache` and can be cleared\n * if needed.\n *\n * Example:\n *\n * const name = 'log'\n * const dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n *\n * export const createLog = factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n * // ... create the function log here and return it\n * }\n *\n * @param {string} name Name of the function to be created\n * @param {string[]} dependencies The names of all required dependencies\n * @param {function} create Callback function called with an object with all dependencies\n * @param {Object} [meta] Optional object with meta information that will be attached\n * to the created factory function as property `meta`.\n * @returns {function}\n */\nexport function factory (name, dependencies, create, meta) {\n function assertAndCreate (scope) {\n // we only pass the requested dependencies to the factory function\n // to prevent functions to rely on dependencies that are not explicitly\n // requested.\n const deps = pickShallow(scope, dependencies.map(stripOptionalNotation))\n\n assertDependencies(name, dependencies, scope)\n\n return create(deps)\n }\n\n assertAndCreate.isFactory = true\n assertAndCreate.fn = name\n assertAndCreate.dependencies = dependencies.slice().sort()\n if (meta) {\n assertAndCreate.meta = meta\n }\n\n return assertAndCreate\n}\n\n/**\n * Sort all factories such that when loading in order, the dependencies are resolved.\n *\n * @param {Array} factories\n * @returns {Array} Returns a new array with the sorted factories.\n */\nexport function sortFactories (factories) {\n const factoriesByName = {}\n\n factories.forEach(factory => {\n factoriesByName[factory.fn] = factory\n })\n\n function containsDependency (factory, dependency) {\n // TODO: detect circular references\n if (isFactory(factory)) {\n if (contains(factory.dependencies, dependency.fn || dependency.name)) {\n return true\n }\n\n if (factory.dependencies.some(d => containsDependency(factoriesByName[d], dependency))) {\n return true\n }\n }\n\n return false\n }\n\n const sorted = []\n\n function addFactory (factory) {\n let index = 0\n while (index < sorted.length && !containsDependency(sorted[index], factory)) {\n index++\n }\n\n sorted.splice(index, 0, factory)\n }\n\n // sort regular factory functions\n factories\n .filter(isFactory)\n .forEach(addFactory)\n\n // sort legacy factory functions AFTER the regular factory functions\n factories\n .filter(factory => !isFactory(factory))\n .forEach(addFactory)\n\n return sorted\n}\n\n// TODO: comment or cleanup if unused in the end\nexport function create (factories, scope = {}) {\n sortFactories(factories)\n .forEach(factory => factory(scope))\n\n return scope\n}\n\n/**\n * Test whether an object is a factory. This is the case when it has\n * properties name, dependencies, and a function create.\n * @param {*} obj\n * @returns {boolean}\n */\nexport function isFactory (obj) {\n return typeof obj === 'function' &&\n typeof obj.fn === 'string' &&\n Array.isArray(obj.dependencies)\n}\n\n/**\n * Assert that all dependencies of a list with dependencies are available in the provided scope.\n *\n * Will throw an exception when there are dependencies missing.\n *\n * @param {string} name Name for the function to be created. Used to generate a useful error message\n * @param {string[]} dependencies\n * @param {Object} scope\n */\nexport function assertDependencies (name, dependencies, scope) {\n const allDefined = dependencies\n .filter(dependency => !isOptionalDependency(dependency)) // filter optionals\n .every(dependency => scope[dependency] !== undefined)\n\n if (!allDefined) {\n const missingDependencies = dependencies.filter(dependency => scope[dependency] === undefined)\n\n // TODO: create a custom error class for this, a MathjsError or something like that\n throw new Error(`Cannot create function \"${name}\", ` +\n `some dependencies are missing: ${missingDependencies.map(d => `\"${d}\"`).join(', ')}.`)\n }\n}\n\nexport function isOptionalDependency (dependency) {\n return dependency && dependency[0] === '?'\n}\n\nexport function stripOptionalNotation (dependency) {\n return dependency && dependency[0] === '?'\n ? dependency.slice(1)\n : dependency\n}\n","/**\n * Create a typed-function which checks the types of the arguments and\n * can match them against multiple provided signatures. The typed-function\n * automatically converts inputs in order to find a matching signature.\n * Typed functions throw informative errors in case of wrong input arguments.\n *\n * See the library [typed-function](https://github.com/josdejong/typed-function)\n * for detailed documentation.\n *\n * Syntax:\n *\n * math.typed(name, signatures) : function\n * math.typed(signatures) : function\n *\n * Examples:\n *\n * // create a typed function with multiple types per argument (type union)\n * const fn2 = typed({\n * 'number | boolean': function (b) {\n * return 'b is a number or boolean'\n * },\n * 'string, number | boolean': function (a, b) {\n * return 'a is a string, b is a number or boolean'\n * }\n * })\n *\n * // create a typed function with an any type argument\n * const log = typed({\n * 'string, any': function (event, data) {\n * console.log('event: ' + event + ', data: ' + JSON.stringify(data))\n * }\n * })\n *\n * @param {string} [name] Optional name for the typed-function\n * @param {Object} signatures Object with one or multiple function signatures\n * @returns {function} The created typed-function.\n */\n\nimport {\n isAccessorNode,\n isArray,\n isArrayNode,\n isAssignmentNode,\n isBigNumber,\n isBlockNode,\n isBoolean,\n isChain,\n isComplex,\n isConditionalNode,\n isConstantNode,\n isDate,\n isDenseMatrix,\n isFraction,\n isFunction,\n isFunctionAssignmentNode,\n isFunctionNode,\n isHelp,\n isIndex,\n isIndexNode,\n isMatrix,\n isNode,\n isNull,\n isNumber,\n isObject,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRange,\n isRangeNode,\n isRegExp,\n isResultSet,\n isSparseMatrix,\n isString,\n isSymbolNode,\n isUndefined,\n isUnit\n} from '../../utils/is.js'\nimport typedFunction from 'typed-function'\nimport { digits } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\n// returns a new instance of typed-function\nlet _createTyped = function () {\n // initially, return the original instance of typed-function\n // consecutively, return a new instance from typed.create.\n _createTyped = typedFunction.create\n return typedFunction\n}\n\nconst dependencies = [\n '?BigNumber',\n '?Complex',\n '?DenseMatrix',\n '?Fraction'\n]\n\n/**\n * Factory function for creating a new typed instance\n * @param {Object} dependencies Object with data types like Complex and BigNumber\n * @returns {Function}\n */\nexport const createTyped = /* #__PURE__ */ factory('typed', dependencies, function createTyped ({ BigNumber, Complex, DenseMatrix, Fraction }) {\n // TODO: typed-function must be able to silently ignore signatures with unknown data types\n\n // get a new instance of typed-function\n const typed = _createTyped()\n\n // define all types. The order of the types determines in which order function\n // arguments are type-checked (so for performance it's important to put the\n // most used types first).\n typed.types = [\n { name: 'number', test: isNumber },\n { name: 'Complex', test: isComplex },\n { name: 'BigNumber', test: isBigNumber },\n { name: 'Fraction', test: isFraction },\n { name: 'Unit', test: isUnit },\n { name: 'string', test: isString },\n { name: 'Chain', test: isChain },\n { name: 'Array', test: isArray },\n { name: 'Matrix', test: isMatrix },\n { name: 'DenseMatrix', test: isDenseMatrix },\n { name: 'SparseMatrix', test: isSparseMatrix },\n { name: 'Range', test: isRange },\n { name: 'Index', test: isIndex },\n { name: 'boolean', test: isBoolean },\n { name: 'ResultSet', test: isResultSet },\n { name: 'Help', test: isHelp },\n { name: 'function', test: isFunction },\n { name: 'Date', test: isDate },\n { name: 'RegExp', test: isRegExp },\n { name: 'null', test: isNull },\n { name: 'undefined', test: isUndefined },\n\n { name: 'AccessorNode', test: isAccessorNode },\n { name: 'ArrayNode', test: isArrayNode },\n { name: 'AssignmentNode', test: isAssignmentNode },\n { name: 'BlockNode', test: isBlockNode },\n { name: 'ConditionalNode', test: isConditionalNode },\n { name: 'ConstantNode', test: isConstantNode },\n { name: 'FunctionNode', test: isFunctionNode },\n { name: 'FunctionAssignmentNode', test: isFunctionAssignmentNode },\n { name: 'IndexNode', test: isIndexNode },\n { name: 'Node', test: isNode },\n { name: 'ObjectNode', test: isObjectNode },\n { name: 'OperatorNode', test: isOperatorNode },\n { name: 'ParenthesisNode', test: isParenthesisNode },\n { name: 'RangeNode', test: isRangeNode },\n { name: 'SymbolNode', test: isSymbolNode },\n\n { name: 'Object', test: isObject } // order 'Object' last, it matches on other classes too\n ]\n\n typed.conversions = [\n {\n from: 'number',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n // note: conversion from number to BigNumber can fail if x has >15 digits\n if (digits(x) > 15) {\n throw new TypeError('Cannot implicitly convert a number with >15 significant digits to BigNumber ' +\n '(value: ' + x + '). ' +\n 'Use function bignumber(x) to convert to BigNumber.')\n }\n return new BigNumber(x)\n }\n }, {\n from: 'number',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x, 0)\n }\n }, {\n from: 'number',\n to: 'string',\n convert: function (x) {\n return x + ''\n }\n }, {\n from: 'BigNumber',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x.toNumber(), 0)\n }\n }, {\n from: 'Fraction',\n to: 'BigNumber',\n convert: function (x) {\n throw new TypeError('Cannot implicitly convert a Fraction to BigNumber or vice versa. ' +\n 'Use function bignumber(x) to convert to BigNumber or fraction(x) to convert to Fraction.')\n }\n }, {\n from: 'Fraction',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x.valueOf(), 0)\n }\n }, {\n from: 'number',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n const f = new Fraction(x)\n if (f.valueOf() !== x) {\n throw new TypeError('Cannot implicitly convert a number to a Fraction when there will be a loss of precision ' +\n '(value: ' + x + '). ' +\n 'Use function fraction(x) to convert to Fraction.')\n }\n return f\n }\n }, {\n // FIXME: add conversion from Fraction to number, for example for `sqrt(fraction(1,3))`\n // from: 'Fraction',\n // to: 'number',\n // convert: function (x) {\n // return x.valueOf()\n // }\n // }, {\n from: 'string',\n to: 'number',\n convert: function (x) {\n const n = Number(x)\n if (isNaN(n)) {\n throw new Error('Cannot convert \"' + x + '\" to a number')\n }\n return n\n }\n }, {\n from: 'string',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n try {\n return new BigNumber(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to BigNumber')\n }\n }\n }, {\n from: 'string',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n try {\n return new Fraction(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to Fraction')\n }\n }\n }, {\n from: 'string',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n try {\n return new Complex(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to Complex')\n }\n }\n }, {\n from: 'boolean',\n to: 'number',\n convert: function (x) {\n return +x\n }\n }, {\n from: 'boolean',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n return new BigNumber(+x)\n }\n }, {\n from: 'boolean',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n return new Fraction(+x)\n }\n }, {\n from: 'boolean',\n to: 'string',\n convert: function (x) {\n return String(x)\n }\n }, {\n from: 'Array',\n to: 'Matrix',\n convert: function (array) {\n if (!DenseMatrix) {\n throwNoMatrix()\n }\n\n return new DenseMatrix(array)\n }\n }, {\n from: 'Matrix',\n to: 'Array',\n convert: function (matrix) {\n return matrix.valueOf()\n }\n }\n ]\n\n return typed\n})\n\nfunction throwNoBignumber (x) {\n throw new Error(`Cannot convert value ${x} into a BigNumber: no class 'BigNumber' provided`)\n}\n\nfunction throwNoComplex (x) {\n throw new Error(`Cannot convert value ${x} into a Complex number: no class 'Complex' provided`)\n}\n\nfunction throwNoMatrix () {\n throw new Error('Cannot convert array into a Matrix: no class \\'DenseMatrix\\' provided')\n}\n\nfunction throwNoFraction (x) {\n throw new Error(`Cannot convert value ${x} into a Fraction, no class 'Fraction' provided.`)\n}\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'ResultSet'\nconst dependencies = []\n\nexport const createResultSet = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * A ResultSet contains a list or results\n * @class ResultSet\n * @param {Array} entries\n * @constructor ResultSet\n */\n function ResultSet (entries) {\n if (!(this instanceof ResultSet)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.entries = entries || []\n }\n\n /**\n * Attach type information\n */\n ResultSet.prototype.type = 'ResultSet'\n ResultSet.prototype.isResultSet = true\n\n /**\n * Returns the array with results hold by this ResultSet\n * @memberof ResultSet\n * @returns {Array} entries\n */\n ResultSet.prototype.valueOf = function () {\n return this.entries\n }\n\n /**\n * Returns the stringified results of the ResultSet\n * @memberof ResultSet\n * @returns {string} string\n */\n ResultSet.prototype.toString = function () {\n return '[' + this.entries.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the ResultSet\n * @memberof ResultSet\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"ResultSet\", \"entries\": [...]}`\n */\n ResultSet.prototype.toJSON = function () {\n return {\n mathjs: 'ResultSet',\n entries: this.entries\n }\n }\n\n /**\n * Instantiate a ResultSet from a JSON object\n * @memberof ResultSet\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"ResultSet\", \"entries\": [...]}`\n * @return {ResultSet}\n */\n ResultSet.fromJSON = function (json) {\n return new ResultSet(json.entries)\n }\n\n return ResultSet\n}, { isClass: true })\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'BigNumber'\nconst dependencies = ['?on', 'config']\n\nexport const createBigNumberClass = /* #__PURE__ */ factory(name, dependencies, ({ on, config }) => {\n const EUCLID = 9 // Use euclidian division for mod calculation\n const BigNumber = Decimal.clone({ precision: config.precision, modulo: EUCLID })\n\n /**\n * Attach type information\n */\n BigNumber.prototype.type = 'BigNumber'\n BigNumber.prototype.isBigNumber = true\n\n /**\n * Get a JSON representation of a BigNumber containing\n * type information\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"BigNumber\", \"value\": \"0.2\"}`\n */\n BigNumber.prototype.toJSON = function () {\n return {\n mathjs: 'BigNumber',\n value: this.toString()\n }\n }\n\n /**\n * Instantiate a BigNumber from a JSON object\n * @param {Object} json a JSON object structured as:\n * `{\"mathjs\": \"BigNumber\", \"value\": \"0.2\"}`\n * @return {BigNumber}\n */\n BigNumber.fromJSON = function (json) {\n return new BigNumber(json.value)\n }\n\n if (on) {\n // listen for changed in the configuration, automatically apply changed precision\n on('config', function (curr, prev) {\n if (curr.precision !== prev.precision) {\n BigNumber.config({ precision: curr.precision })\n }\n })\n }\n\n return BigNumber\n}, { isClass: true })\n","import Complex from 'complex.js'\nimport { format } from '../../utils/number.js'\nimport { isNumber, isUnit } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Complex'\nconst dependencies = []\n\nexport const createComplexClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Attach type information\n */\n Complex.prototype.type = 'Complex'\n Complex.prototype.isComplex = true\n\n /**\n * Get a JSON representation of the complex number\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Complex\", \"re\": 2, \"im\": 3}`\n */\n Complex.prototype.toJSON = function () {\n return {\n mathjs: 'Complex',\n re: this.re,\n im: this.im\n }\n }\n\n /*\n * Return the value of the complex number in polar notation\n * The angle phi will be set in the interval of [-pi, pi].\n * @return {{r: number, phi: number}} Returns and object with properties r and phi.\n */\n Complex.prototype.toPolar = function () {\n return {\n r: this.abs(),\n phi: this.arg()\n }\n }\n\n /**\n * Get a string representation of the complex number,\n * with optional formatting options.\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string} str\n */\n Complex.prototype.format = function (options) {\n let str = ''\n let im = this.im\n let re = this.re\n const strRe = format(this.re, options)\n const strIm = format(this.im, options)\n\n // round either re or im when smaller than the configured precision\n const precision = isNumber(options) ? options : options ? options.precision : null\n if (precision !== null) {\n const epsilon = Math.pow(10, -precision)\n if (Math.abs(re / im) < epsilon) {\n re = 0\n }\n if (Math.abs(im / re) < epsilon) {\n im = 0\n }\n }\n\n if (im === 0) {\n // real value\n str = strRe\n } else if (re === 0) {\n // purely complex value\n if (im === 1) {\n str = 'i'\n } else if (im === -1) {\n str = '-i'\n } else {\n str = strIm + 'i'\n }\n } else {\n // complex value\n if (im < 0) {\n if (im === -1) {\n str = strRe + ' - i'\n } else {\n str = strRe + ' - ' + strIm.substring(1) + 'i'\n }\n } else {\n if (im === 1) {\n str = strRe + ' + i'\n } else {\n str = strRe + ' + ' + strIm + 'i'\n }\n }\n }\n return str\n }\n\n /**\n * Create a complex number from polar coordinates\n *\n * Usage:\n *\n * Complex.fromPolar(r: number, phi: number) : Complex\n * Complex.fromPolar({r: number, phi: number}) : Complex\n *\n * @param {*} args...\n * @return {Complex}\n */\n Complex.fromPolar = function (args) {\n switch (arguments.length) {\n case 1:\n {\n const arg = arguments[0]\n if (typeof arg === 'object') {\n return Complex(arg)\n } else {\n throw new TypeError('Input has to be an object with r and phi keys.')\n }\n }\n case 2:\n {\n const r = arguments[0]\n let phi = arguments[1]\n if (isNumber(r)) {\n if (isUnit(phi) && phi.hasBase('ANGLE')) {\n // convert unit to a number in radians\n phi = phi.toNumber('rad')\n }\n\n if (isNumber(phi)) {\n return new Complex({ r: r, phi: phi })\n }\n\n throw new TypeError('Phi is not a number nor an angle unit.')\n } else {\n throw new TypeError('Radius r is not a number.')\n }\n }\n\n default:\n throw new SyntaxError('Wrong number of arguments in function fromPolar')\n }\n }\n\n Complex.prototype.valueOf = Complex.prototype.toString\n\n /**\n * Create a Complex number from a JSON object\n * @param {Object} json A JSON Object structured as\n * {\"mathjs\": \"Complex\", \"re\": 2, \"im\": 3}\n * All properties are optional, default values\n * for `re` and `im` are 0.\n * @return {Complex} Returns a new Complex number\n */\n Complex.fromJSON = function (json) {\n return new Complex(json)\n }\n\n /**\n * Compare two complex numbers, `a` and `b`:\n *\n * - Returns 1 when the real part of `a` is larger than the real part of `b`\n * - Returns -1 when the real part of `a` is smaller than the real part of `b`\n * - Returns 1 when the real parts are equal\n * and the imaginary part of `a` is larger than the imaginary part of `b`\n * - Returns -1 when the real parts are equal\n * and the imaginary part of `a` is smaller than the imaginary part of `b`\n * - Returns 0 when both real and imaginary parts are equal.\n *\n * @params {Complex} a\n * @params {Complex} b\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n Complex.compare = function (a, b) {\n if (a.re > b.re) { return 1 }\n if (a.re < b.re) { return -1 }\n\n if (a.im > b.im) { return 1 }\n if (a.im < b.im) { return -1 }\n\n return 0\n }\n\n return Complex\n}, { isClass: true })\n","import Fraction from 'fraction.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Fraction'\nconst dependencies = []\n\nexport const createFractionClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Attach type information\n */\n Fraction.prototype.type = 'Fraction'\n Fraction.prototype.isFraction = true\n\n /**\n * Get a JSON representation of a Fraction containing type information\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Fraction\", \"n\": 3, \"d\": 8}`\n */\n Fraction.prototype.toJSON = function () {\n return {\n mathjs: 'Fraction',\n n: this.s * this.n,\n d: this.d\n }\n }\n\n /**\n * Instantiate a Fraction from a JSON object\n * @param {Object} json a JSON object structured as:\n * `{\"mathjs\": \"Fraction\", \"n\": 3, \"d\": 8}`\n * @return {BigNumber}\n */\n Fraction.fromJSON = function (json) {\n return new Fraction(json)\n }\n\n return Fraction\n}, { isClass: true })\n","import { isBigNumber } from '../../utils/is.js'\nimport { format, sign } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Range'\nconst dependencies = []\n\nexport const createRangeClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Create a range. A range has a start, step, and end, and contains functions\n * to iterate over the range.\n *\n * A range can be constructed as:\n *\n * const range = new Range(start, end)\n * const range = new Range(start, end, step)\n *\n * To get the result of the range:\n * range.forEach(function (x) {\n * console.log(x)\n * })\n * range.map(function (x) {\n * return math.sin(x)\n * })\n * range.toArray()\n *\n * Example usage:\n *\n * const c = new Range(2, 6) // 2:1:5\n * c.toArray() // [2, 3, 4, 5]\n * const d = new Range(2, -3, -1) // 2:-1:-2\n * d.toArray() // [2, 1, 0, -1, -2]\n *\n * @class Range\n * @constructor Range\n * @param {number} start included lower bound\n * @param {number} end excluded upper bound\n * @param {number} [step] step size, default value is 1\n */\n function Range (start, end, step) {\n if (!(this instanceof Range)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n const hasStart = start !== null && start !== undefined\n const hasEnd = end !== null && end !== undefined\n const hasStep = step !== null && step !== undefined\n\n if (hasStart) {\n if (isBigNumber(start)) {\n start = start.toNumber()\n } else if (typeof start !== 'number') {\n throw new TypeError('Parameter start must be a number')\n }\n }\n if (hasEnd) {\n if (isBigNumber(end)) {\n end = end.toNumber()\n } else if (typeof end !== 'number') {\n throw new TypeError('Parameter end must be a number')\n }\n }\n if (hasStep) {\n if (isBigNumber(step)) {\n step = step.toNumber()\n } else if (typeof step !== 'number') {\n throw new TypeError('Parameter step must be a number')\n }\n }\n\n this.start = hasStart ? parseFloat(start) : 0\n this.end = hasEnd ? parseFloat(end) : 0\n this.step = hasStep ? parseFloat(step) : 1\n }\n\n /**\n * Attach type information\n */\n Range.prototype.type = 'Range'\n Range.prototype.isRange = true\n\n /**\n * Parse a string into a range,\n * The string contains the start, optional step, and end, separated by a colon.\n * If the string does not contain a valid range, null is returned.\n * For example str='0:2:11'.\n * @memberof Range\n * @param {string} str\n * @return {Range | null} range\n */\n Range.parse = function (str) {\n if (typeof str !== 'string') {\n return null\n }\n\n const args = str.split(':')\n const nums = args.map(function (arg) {\n return parseFloat(arg)\n })\n\n const invalid = nums.some(function (num) {\n return isNaN(num)\n })\n if (invalid) {\n return null\n }\n\n switch (nums.length) {\n case 2:\n return new Range(nums[0], nums[1])\n case 3:\n return new Range(nums[0], nums[2], nums[1])\n default:\n return null\n }\n }\n\n /**\n * Create a clone of the range\n * @return {Range} clone\n */\n Range.prototype.clone = function () {\n return new Range(this.start, this.end, this.step)\n }\n\n /**\n * Retrieve the size of the range.\n * Returns an array containing one number, the number of elements in the range.\n * @memberof Range\n * @returns {number[]} size\n */\n Range.prototype.size = function () {\n let len = 0\n const start = this.start\n const step = this.step\n const end = this.end\n const diff = end - start\n\n if (sign(step) === sign(diff)) {\n len = Math.ceil((diff) / step)\n } else if (diff === 0) {\n len = 0\n }\n\n if (isNaN(len)) {\n len = 0\n }\n return [len]\n }\n\n /**\n * Calculate the minimum value in the range\n * @memberof Range\n * @return {number | undefined} min\n */\n Range.prototype.min = function () {\n const size = this.size()[0]\n\n if (size > 0) {\n if (this.step > 0) {\n // positive step\n return this.start\n } else {\n // negative step\n return this.start + (size - 1) * this.step\n }\n } else {\n return undefined\n }\n }\n\n /**\n * Calculate the maximum value in the range\n * @memberof Range\n * @return {number | undefined} max\n */\n Range.prototype.max = function () {\n const size = this.size()[0]\n\n if (size > 0) {\n if (this.step > 0) {\n // positive step\n return this.start + (size - 1) * this.step\n } else {\n // negative step\n return this.start\n }\n } else {\n return undefined\n }\n }\n\n /**\n * Execute a callback function for each value in the range.\n * @memberof Range\n * @param {function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Range being traversed.\n */\n Range.prototype.forEach = function (callback) {\n let x = this.start\n const step = this.step\n const end = this.end\n let i = 0\n\n if (step > 0) {\n while (x < end) {\n callback(x, [i], this)\n x += step\n i++\n }\n } else if (step < 0) {\n while (x > end) {\n callback(x, [i], this)\n x += step\n i++\n }\n }\n }\n\n /**\n * Execute a callback function for each value in the Range, and return the\n * results as an array\n * @memberof Range\n * @param {function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @returns {Array} array\n */\n Range.prototype.map = function (callback) {\n const array = []\n this.forEach(function (value, index, obj) {\n array[index[0]] = callback(value, index, obj)\n })\n return array\n }\n\n /**\n * Create an Array with a copy of the Ranges data\n * @memberof Range\n * @returns {Array} array\n */\n Range.prototype.toArray = function () {\n const array = []\n this.forEach(function (value, index) {\n array[index[0]] = value\n })\n return array\n }\n\n /**\n * Get the primitive value of the Range, a one dimensional array\n * @memberof Range\n * @returns {Array} array\n */\n Range.prototype.valueOf = function () {\n // TODO: implement a caching mechanism for range.valueOf()\n return this.toArray()\n }\n\n /**\n * Get a string representation of the range, with optional formatting options.\n * Output is formatted as 'start:step:end', for example '2:6' or '0:0.2:11'\n * @memberof Range\n * @param {Object | number | function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n Range.prototype.format = function (options) {\n let str = format(this.start, options)\n\n if (this.step !== 1) {\n str += ':' + format(this.step, options)\n }\n str += ':' + format(this.end, options)\n return str\n }\n\n /**\n * Get a string representation of the range.\n * @memberof Range\n * @returns {string}\n */\n Range.prototype.toString = function () {\n return this.format()\n }\n\n /**\n * Get a JSON representation of the range\n * @memberof Range\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Range\", \"start\": 2, \"end\": 4, \"step\": 1}`\n */\n Range.prototype.toJSON = function () {\n return {\n mathjs: 'Range',\n start: this.start,\n end: this.end,\n step: this.step\n }\n }\n\n /**\n * Instantiate a Range from a JSON object\n * @memberof Range\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Range\", \"start\": 2, \"end\": 4, \"step\": 1}`\n * @return {Range}\n */\n Range.fromJSON = function (json) {\n return new Range(json.start, json.end, json.step)\n }\n\n return Range\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'Matrix'\nconst dependencies = []\n\nexport const createMatrixClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * @constructor Matrix\n *\n * A Matrix is a wrapper around an Array. A matrix can hold a multi dimensional\n * array. A matrix can be constructed as:\n *\n * let matrix = math.matrix(data)\n *\n * Matrix contains the functions to resize, get and set values, get the size,\n * clone the matrix and to convert the matrix to a vector, array, or scalar.\n * Furthermore, one can iterate over the matrix using map and forEach.\n * The internal Array of the Matrix can be accessed using the function valueOf.\n *\n * Example usage:\n *\n * let matrix = math.matrix([[1, 2], [3, 4]])\n * matix.size() // [2, 2]\n * matrix.resize([3, 2], 5)\n * matrix.valueOf() // [[1, 2], [3, 4], [5, 5]]\n * matrix.subset([1,2]) // 3 (indexes are zero-based)\n *\n */\n function Matrix () {\n if (!(this instanceof Matrix)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n }\n\n /**\n * Attach type information\n */\n Matrix.prototype.type = 'Matrix'\n Matrix.prototype.isMatrix = true\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @return {string} The storage format.\n */\n Matrix.prototype.storage = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke storage on a Matrix interface')\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @return {string} The datatype.\n */\n Matrix.prototype.datatype = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke datatype on a Matrix interface')\n }\n\n /**\n * Create a new Matrix With the type of the current matrix instance\n * @param {Array | Object} data\n * @param {string} [datatype]\n */\n Matrix.prototype.create = function (data, datatype) {\n throw new Error('Cannot invoke create on a Matrix interface')\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n Matrix.prototype.subset = function (index, replacement, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke subset on a Matrix interface')\n }\n\n /**\n * Get a single element from the matrix.\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n Matrix.prototype.get = function (index) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke get on a Matrix interface')\n }\n\n /**\n * Replace a single element in the matrix.\n * @param {number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {Matrix} self\n */\n Matrix.prototype.set = function (index, value, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke set on a Matrix interface')\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @param {number[]} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n Matrix.prototype.resize = function (size, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke resize on a Matrix interface')\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n Matrix.prototype.reshape = function (size, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke reshape on a Matrix interface')\n }\n\n /**\n * Create a clone of the matrix\n * @return {Matrix} clone\n */\n Matrix.prototype.clone = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke clone on a Matrix interface')\n }\n\n /**\n * Retrieve the size of the matrix.\n * @returns {number[]} size\n */\n Matrix.prototype.size = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke size on a Matrix interface')\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {Matrix} matrix\n */\n Matrix.prototype.map = function (callback, skipZeros) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke map on a Matrix interface')\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n */\n Matrix.prototype.forEach = function (callback) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke forEach on a Matrix interface')\n }\n\n /**\n * Create an Array with a copy of the data of the Matrix\n * @returns {Array} array\n */\n Matrix.prototype.toArray = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke toArray on a Matrix interface')\n }\n\n /**\n * Get the primitive value of the Matrix: a multidimensional array\n * @returns {Array} array\n */\n Matrix.prototype.valueOf = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke valueOf on a Matrix interface')\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n Matrix.prototype.format = function (options) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke format on a Matrix interface')\n }\n\n /**\n * Get a string representation of the matrix\n * @returns {string} str\n */\n Matrix.prototype.toString = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke toString on a Matrix interface')\n }\n\n return Matrix\n}, { isClass: true })\n","import { isArray, isBigNumber, isCollection, isIndex, isMatrix, isNumber, isString, typeOf } from '../../utils/is.js'\nimport { arraySize, getArrayDataType, reshape, resize, unsqueeze, validate, validateIndex } from '../../utils/array.js'\nimport { format } from '../../utils/string.js'\nimport { isInteger } from '../../utils/number.js'\nimport { clone, deepStrictEqual } from '../../utils/object.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'DenseMatrix'\nconst dependencies = [\n 'Matrix'\n]\n\nexport const createDenseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ Matrix }) => {\n /**\n * Dense Matrix implementation. A regular, dense matrix, supporting multi-dimensional matrices. This is the default matrix type.\n * @class DenseMatrix\n */\n function DenseMatrix (data, datatype) {\n if (!(this instanceof DenseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data)) {\n // check data is a DenseMatrix\n if (data.type === 'DenseMatrix') {\n // clone data & size\n this._data = clone(data._data)\n this._size = clone(data._size)\n this._datatype = datatype || data._datatype\n } else {\n // build data from existing matrix\n this._data = data.toArray()\n this._size = data.size()\n this._datatype = datatype || data._datatype\n }\n } else if (data && isArray(data.data) && isArray(data.size)) {\n // initialize fields from JSON representation\n this._data = data.data\n this._size = data.size\n // verify the dimensions of the array\n validate(this._data, this._size)\n this._datatype = datatype || data.datatype\n } else if (isArray(data)) {\n // replace nested Matrices with Arrays\n this._data = preprocess(data)\n // get the dimensions of the array\n this._size = arraySize(this._data)\n // verify the dimensions of the array, TODO: compute size while processing array\n validate(this._data, this._size)\n // data type unknown\n this._datatype = datatype\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._data = []\n this._size = [0]\n this._datatype = datatype\n }\n }\n\n DenseMatrix.prototype = new Matrix()\n\n /**\n * Create a new DenseMatrix\n */\n DenseMatrix.prototype.createDenseMatrix = function (data, datatype) {\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Attach type information\n */\n DenseMatrix.prototype.type = 'DenseMatrix'\n DenseMatrix.prototype.isDenseMatrix = true\n\n /**\n * Get the matrix type\n *\n * Usage:\n * const matrixType = matrix.getDataType() // retrieves the matrix type\n *\n * @memberOf DenseMatrix\n * @return {string} type information; if multiple types are found from the Matrix, it will return \"mixed\"\n */\n DenseMatrix.prototype.getDataType = function () {\n return getArrayDataType(this._data, typeOf)\n }\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @memberof DenseMatrix\n * @return {string} The storage format.\n */\n DenseMatrix.prototype.storage = function () {\n return 'dense'\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @memberof DenseMatrix\n * @return {string} The datatype.\n */\n DenseMatrix.prototype.datatype = function () {\n return this._datatype\n }\n\n /**\n * Create a new DenseMatrix\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {string} [datatype]\n */\n DenseMatrix.prototype.create = function (data, datatype) {\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @memberof DenseMatrix\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n DenseMatrix.prototype.subset = function (index, replacement, defaultValue) {\n switch (arguments.length) {\n case 1:\n return _get(this, index)\n\n // intentional fall through\n case 2:\n case 3:\n return _set(this, index, replacement, defaultValue)\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n /**\n * Get a single element from the matrix.\n * @memberof DenseMatrix\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n DenseMatrix.prototype.get = function (index) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check index\n for (let x = 0; x < index.length; x++) { validateIndex(index[x], this._size[x]) }\n\n let data = this._data\n for (let i = 0, ii = index.length; i < ii; i++) {\n const indexI = index[i]\n validateIndex(indexI, data.length)\n data = data[indexI]\n }\n\n return data\n }\n\n /**\n * Replace a single element in the matrix.\n * @memberof DenseMatrix\n * @param {number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {DenseMatrix} self\n */\n DenseMatrix.prototype.set = function (index, value, defaultValue) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length < this._size.length) { throw new DimensionError(index.length, this._size.length, '<') }\n\n let i, ii, indexI\n\n // enlarge matrix when needed\n const size = index.map(function (i) {\n return i + 1\n })\n _fit(this, size, defaultValue)\n\n // traverse over the dimensions\n let data = this._data\n for (i = 0, ii = index.length - 1; i < ii; i++) {\n indexI = index[i]\n validateIndex(indexI, data.length)\n data = data[indexI]\n }\n\n // set new value\n indexI = index[index.length - 1]\n validateIndex(indexI, data.length)\n data[indexI] = value\n\n return this\n }\n\n /**\n * Get a submatrix of this matrix\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix\n * @param {Index} index Zero-based index\n * @private\n */\n function _get (matrix, index) {\n if (!isIndex(index)) {\n throw new TypeError('Invalid index')\n }\n\n const isScalar = index.isScalar()\n if (isScalar) {\n // return a scalar\n return matrix.get(index.min())\n } else {\n // validate dimensions\n const size = index.size()\n if (size.length !== matrix._size.length) {\n throw new DimensionError(size.length, matrix._size.length)\n }\n\n // validate if any of the ranges in the index is out of range\n const min = index.min()\n const max = index.max()\n for (let i = 0, ii = matrix._size.length; i < ii; i++) {\n validateIndex(min[i], matrix._size[i])\n validateIndex(max[i], matrix._size[i])\n }\n\n // retrieve submatrix\n // TODO: more efficient when creating an empty matrix and setting _data and _size manually\n return new DenseMatrix(_getSubmatrix(matrix._data, index, size.length, 0), matrix._datatype)\n }\n }\n\n /**\n * Recursively get a submatrix of a multi dimensional matrix.\n * Index is not checked for correct number or length of dimensions.\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {Index} index\n * @param {number} dims Total number of dimensions\n * @param {number} dim Current dimension\n * @return {Array} submatrix\n * @private\n */\n function _getSubmatrix (data, index, dims, dim) {\n const last = (dim === dims - 1)\n const range = index.dimension(dim)\n\n if (last) {\n return range.map(function (i) {\n validateIndex(i, data.length)\n return data[i]\n }).valueOf()\n } else {\n return range.map(function (i) {\n validateIndex(i, data.length)\n const child = data[i]\n return _getSubmatrix(child, index, dims, dim + 1)\n }).valueOf()\n }\n }\n\n /**\n * Replace a submatrix in this matrix\n * Indexes are zero-based.\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix\n * @param {Index} index\n * @param {DenseMatrix | Array | *} submatrix\n * @param {*} defaultValue Default value, filled in on new entries when\n * the matrix is resized.\n * @return {DenseMatrix} matrix\n * @private\n */\n function _set (matrix, index, submatrix, defaultValue) {\n if (!index || index.isIndex !== true) {\n throw new TypeError('Invalid index')\n }\n\n // get index size and check whether the index contains a single value\n const iSize = index.size()\n const isScalar = index.isScalar()\n\n // calculate the size of the submatrix, and convert it into an Array if needed\n let sSize\n if (isMatrix(submatrix)) {\n sSize = submatrix.size()\n submatrix = submatrix.valueOf()\n } else {\n sSize = arraySize(submatrix)\n }\n\n if (isScalar) {\n // set a scalar\n\n // check whether submatrix is a scalar\n if (sSize.length !== 0) {\n throw new TypeError('Scalar expected')\n }\n\n matrix.set(index.min(), submatrix, defaultValue)\n } else {\n // set a submatrix\n\n // validate dimensions\n if (iSize.length < matrix._size.length) {\n throw new DimensionError(iSize.length, matrix._size.length, '<')\n }\n\n if (sSize.length < iSize.length) {\n // calculate number of missing outer dimensions\n let i = 0\n let outer = 0\n while (iSize[i] === 1 && sSize[i] === 1) {\n i++\n }\n while (iSize[i] === 1) {\n outer++\n i++\n }\n\n // unsqueeze both outer and inner dimensions\n submatrix = unsqueeze(submatrix, iSize.length, outer, sSize)\n }\n\n // check whether the size of the submatrix matches the index size\n if (!deepStrictEqual(iSize, sSize)) {\n throw new DimensionError(iSize, sSize, '>')\n }\n\n // enlarge matrix when needed\n const size = index.max().map(function (i) {\n return i + 1\n })\n _fit(matrix, size, defaultValue)\n\n // insert the sub matrix\n const dims = iSize.length\n const dim = 0\n _setSubmatrix(matrix._data, index, submatrix, dims, dim)\n }\n\n return matrix\n }\n\n /**\n * Replace a submatrix of a multi dimensional matrix.\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {Index} index\n * @param {Array} submatrix\n * @param {number} dims Total number of dimensions\n * @param {number} dim\n * @private\n */\n function _setSubmatrix (data, index, submatrix, dims, dim) {\n const last = (dim === dims - 1)\n const range = index.dimension(dim)\n\n if (last) {\n range.forEach(function (dataIndex, subIndex) {\n validateIndex(dataIndex)\n data[dataIndex] = submatrix[subIndex[0]]\n })\n } else {\n range.forEach(function (dataIndex, subIndex) {\n validateIndex(dataIndex)\n _setSubmatrix(data[dataIndex], index, submatrix[subIndex[0]], dims, dim + 1)\n })\n }\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @memberof DenseMatrix\n * @param {number[] || Matrix} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n DenseMatrix.prototype.resize = function (size, defaultValue, copy) {\n // validate arguments\n if (!isCollection(size)) {\n throw new TypeError('Array or Matrix expected')\n }\n\n // SparseMatrix input is always 2d, flatten this into 1d if it's indeed a vector\n const sizeArray = size.valueOf().map(value => {\n return Array.isArray(value) && value.length === 1\n ? value[0]\n : value\n })\n\n // matrix to resize\n const m = copy ? this.clone() : this\n // resize matrix\n return _resize(m, sizeArray, defaultValue)\n }\n\n function _resize (matrix, size, defaultValue) {\n // check size\n if (size.length === 0) {\n // first value in matrix\n let v = matrix._data\n // go deep\n while (isArray(v)) {\n v = v[0]\n }\n return v\n }\n // resize matrix\n matrix._size = size.slice(0) // copy the array\n matrix._data = resize(matrix._data, matrix._size, defaultValue)\n // return matrix\n return matrix\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * NOTE: This might be better suited to copy by default, instead of modifying\n * in place. For now, it operates in place to remain consistent with\n * resize().\n *\n * @memberof DenseMatrix\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n DenseMatrix.prototype.reshape = function (size, copy) {\n const m = copy ? this.clone() : this\n\n m._data = reshape(m._data, size)\n m._size = size.slice(0)\n return m\n }\n\n /**\n * Enlarge the matrix when it is smaller than given size.\n * If the matrix is larger or equal sized, nothing is done.\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix The matrix to be resized\n * @param {number[]} size\n * @param {*} defaultValue Default value, filled in on new entries.\n * @private\n */\n function _fit (matrix, size, defaultValue) {\n const // copy the array\n newSize = matrix._size.slice(0)\n\n let changed = false\n\n // add dimensions when needed\n while (newSize.length < size.length) {\n newSize.push(0)\n changed = true\n }\n\n // enlarge size when needed\n for (let i = 0, ii = size.length; i < ii; i++) {\n if (size[i] > newSize[i]) {\n newSize[i] = size[i]\n changed = true\n }\n }\n\n if (changed) {\n // resize only when size is changed\n _resize(matrix, newSize, defaultValue)\n }\n }\n\n /**\n * Create a clone of the matrix\n * @memberof DenseMatrix\n * @return {DenseMatrix} clone\n */\n DenseMatrix.prototype.clone = function () {\n const m = new DenseMatrix({\n data: clone(this._data),\n size: clone(this._size),\n datatype: this._datatype\n })\n return m\n }\n\n /**\n * Retrieve the size of the matrix.\n * @memberof DenseMatrix\n * @returns {number[]} size\n */\n DenseMatrix.prototype.size = function () {\n return this._size.slice(0) // return a clone of _size\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @memberof DenseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n *\n * @return {DenseMatrix} matrix\n */\n DenseMatrix.prototype.map = function (callback) {\n // matrix instance\n const me = this\n const recurse = function (value, index) {\n if (isArray(value)) {\n return value.map(function (child, i) {\n return recurse(child, index.concat(i))\n })\n } else {\n return callback(value, index, me)\n }\n }\n\n // determine the new datatype when the original matrix has datatype defined\n // TODO: should be done in matrix constructor instead\n const data = recurse(this._data, [])\n const datatype = this._datatype !== undefined\n ? getArrayDataType(data, typeOf)\n : undefined\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @memberof DenseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n */\n DenseMatrix.prototype.forEach = function (callback) {\n // matrix instance\n const me = this\n const recurse = function (value, index) {\n if (isArray(value)) {\n value.forEach(function (child, i) {\n recurse(child, index.concat(i))\n })\n } else {\n callback(value, index, me)\n }\n }\n recurse(this._data, [])\n }\n\n /**\n * Create an Array with a copy of the data of the DenseMatrix\n * @memberof DenseMatrix\n * @returns {Array} array\n */\n DenseMatrix.prototype.toArray = function () {\n return clone(this._data)\n }\n\n /**\n * Get the primitive value of the DenseMatrix: a multidimensional array\n * @memberof DenseMatrix\n * @returns {Array} array\n */\n DenseMatrix.prototype.valueOf = function () {\n return this._data\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @memberof DenseMatrix\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n DenseMatrix.prototype.format = function (options) {\n return format(this._data, options)\n }\n\n /**\n * Get a string representation of the matrix\n * @memberof DenseMatrix\n * @returns {string} str\n */\n DenseMatrix.prototype.toString = function () {\n return format(this._data)\n }\n\n /**\n * Get a JSON representation of the matrix\n * @memberof DenseMatrix\n * @returns {Object}\n */\n DenseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'DenseMatrix',\n data: this._data,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Get the kth Matrix diagonal.\n *\n * @memberof DenseMatrix\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will retrieved.\n *\n * @returns {Matrix} The matrix with the diagonal values.\n */\n DenseMatrix.prototype.diagonal = function (k) {\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n\n // number diagonal values\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // x is a matrix get diagonal from matrix\n const data = []\n\n // loop rows\n for (let i = 0; i < n; i++) {\n data[i] = this._data[i + kSub][i + kSuper]\n }\n\n // create DenseMatrix\n return new DenseMatrix({\n data: data,\n size: [n],\n datatype: this._datatype\n })\n }\n\n /**\n * Create a diagonal matrix.\n *\n * @memberof DenseMatrix\n * @param {Array} size The matrix size.\n * @param {number | Matrix | Array } value The values for the diagonal.\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will be filled in.\n * @param {number} [defaultValue] The default value for non-diagonal\n * @param {string} [datatype] The datatype for the diagonal\n *\n * @returns {DenseMatrix}\n */\n DenseMatrix.diagonal = function (size, value, k, defaultValue) {\n if (!isArray(size)) { throw new TypeError('Array expected, size parameter') }\n if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // map size & validate\n size = size.map(function (s) {\n // check it is a big number\n if (isBigNumber(s)) {\n // convert it\n s = s.toNumber()\n }\n // validate arguments\n if (!isNumber(s) || !isInteger(s) || s < 1) {\n throw new Error('Size values must be positive integers')\n }\n return s\n })\n\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // number of non-zero items\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // value extraction function\n let _value\n\n // check value\n if (isArray(value)) {\n // validate array\n if (value.length !== n) {\n // number of values in array must be n\n throw new Error('Invalid value array length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value[i]\n }\n } else if (isMatrix(value)) {\n // matrix size\n const ms = value.size()\n // validate matrix\n if (ms.length !== 1 || ms[0] !== n) {\n // number of values in array must be n\n throw new Error('Invalid matrix length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value.get([i])\n }\n } else {\n // define function\n _value = function () {\n // return value\n return value\n }\n }\n\n // discover default value if needed\n if (!defaultValue) {\n // check first value in array\n defaultValue = isBigNumber(_value(0))\n ? _value(0).mul(0) // trick to create a BigNumber with value zero\n : 0\n }\n\n // empty array\n let data = []\n\n // check we need to resize array\n if (size.length > 0) {\n // resize array\n data = resize(data, size, defaultValue)\n // fill diagonal\n for (let d = 0; d < n; d++) {\n data[d + kSub][d + kSuper] = _value(d)\n }\n }\n\n // create DenseMatrix\n return new DenseMatrix({\n data: data,\n size: [rows, columns]\n })\n }\n\n /**\n * Generate a matrix from a JSON object\n * @memberof DenseMatrix\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"DenseMatrix\", data: [], size: []}`,\n * where mathjs is optional\n * @returns {DenseMatrix}\n */\n DenseMatrix.fromJSON = function (json) {\n return new DenseMatrix(json)\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @memberof DenseMatrix\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n DenseMatrix.prototype.swapRows = function (i, j) {\n // check index\n if (!isNumber(i) || !isInteger(i) || !isNumber(j) || !isInteger(j)) {\n throw new Error('Row index must be positive integers')\n }\n // check dimensions\n if (this._size.length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n // validate index\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[0])\n\n // swap rows\n DenseMatrix._swapRows(i, j, this._data)\n // return current instance\n return this\n }\n\n /**\n * Swap rows i and j in Dense Matrix data structure.\n *\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n * @param {Array} data Matrix data\n */\n DenseMatrix._swapRows = function (i, j, data) {\n // swap values i <-> j\n const vi = data[i]\n data[i] = data[j]\n data[j] = vi\n }\n\n /**\n * Preprocess data, which can be an Array or DenseMatrix with nested Arrays and\n * Matrices. Replaces all nested Matrices with Arrays\n * @memberof DenseMatrix\n * @param {Array} data\n * @return {Array} data\n */\n function preprocess (data) {\n for (let i = 0, ii = data.length; i < ii; i++) {\n const elem = data[i]\n if (isArray(elem)) {\n data[i] = preprocess(elem)\n } else if (elem && elem.isMatrix === true) {\n data[i] = preprocess(elem.valueOf())\n }\n }\n\n return data\n }\n\n return DenseMatrix\n}, { isClass: true })\n","import { clone as objectClone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'clone'\nconst dependencies = ['typed']\n\nexport const createClone = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Clone an object. Will make a deep copy of the data.\n *\n * Syntax:\n *\n * math.clone(x)\n *\n * Examples:\n *\n * math.clone(3.5) // returns number 3.5\n * math.clone(math.complex('2-4i') // returns Complex 2 - 4i\n * math.clone(math.unit(45, 'deg')) // returns Unit 45 deg\n * math.clone([[1, 2], [3, 4]]) // returns Array [[1, 2], [3, 4]]\n * math.clone(\"hello world\") // returns string \"hello world\"\n *\n * @param {*} x Object to be cloned\n * @return {*} A clone of object x\n */\n return typed(name, {\n any: objectClone\n })\n})\n","import { isCollection, isMatrix } from './is.js'\nimport { IndexError } from '../error/IndexError.js'\nimport { arraySize } from './array.js'\n\n/**\n * Test whether an array contains collections\n * @param {Array} array\n * @returns {boolean} Returns true when the array contains one or multiple\n * collections (Arrays or Matrices). Returns false otherwise.\n */\nexport function containsCollections (array) {\n for (let i = 0; i < array.length; i++) {\n if (isCollection(array[i])) {\n return true\n }\n }\n return false\n}\n\n/**\n * Recursively loop over all elements in a given multi dimensional array\n * and invoke the callback on each of the elements.\n * @param {Array | Matrix} array\n * @param {Function} callback The callback method is invoked with one\n * parameter: the current element in the array\n */\nexport function deepForEach (array, callback) {\n if (isMatrix(array)) {\n array = array.valueOf()\n }\n\n for (let i = 0, ii = array.length; i < ii; i++) {\n const value = array[i]\n\n if (Array.isArray(value)) {\n deepForEach(value, callback)\n } else {\n callback(value)\n }\n }\n}\n\n/**\n * Execute the callback function element wise for each element in array and any\n * nested array\n * Returns an array with the results\n * @param {Array | Matrix} array\n * @param {Function} callback The callback is called with two parameters:\n * value1 and value2, which contain the current\n * element of both arrays.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {Array | Matrix} res\n */\nexport function deepMap (array, callback, skipZeros) {\n if (array && (typeof array.map === 'function')) {\n // TODO: replace array.map with a for loop to improve performance\n return array.map(function (x) {\n return deepMap(x, callback, skipZeros)\n })\n } else {\n return callback(array)\n }\n}\n\n/**\n * Reduce a given matrix or array to a new matrix or\n * array with one less dimension, applying the given\n * callback in the selected dimension.\n * @param {Array | Matrix} mat\n * @param {number} dim\n * @param {Function} callback\n * @return {Array | Matrix} res\n */\nexport function reduce (mat, dim, callback) {\n const size = Array.isArray(mat) ? arraySize(mat) : mat.size()\n if (dim < 0 || (dim >= size.length)) {\n // TODO: would be more clear when throwing a DimensionError here\n throw new IndexError(dim, size.length)\n }\n\n if (isMatrix(mat)) {\n return mat.create(_reduce(mat.valueOf(), dim, callback))\n } else {\n return _reduce(mat, dim, callback)\n }\n}\n\n/**\n * Recursively reduce a matrix\n * @param {Array} mat\n * @param {number} dim\n * @param {Function} callback\n * @returns {Array} ret\n * @private\n */\nfunction _reduce (mat, dim, callback) {\n let i, ret, val, tran\n\n if (dim <= 0) {\n if (!Array.isArray(mat[0])) {\n val = mat[0]\n for (i = 1; i < mat.length; i++) {\n val = callback(val, mat[i])\n }\n return val\n } else {\n tran = _switch(mat)\n ret = []\n for (i = 0; i < tran.length; i++) {\n ret[i] = _reduce(tran[i], dim - 1, callback)\n }\n return ret\n }\n } else {\n ret = []\n for (i = 0; i < mat.length; i++) {\n ret[i] = _reduce(mat[i], dim - 1, callback)\n }\n return ret\n }\n}\n\n/**\n * Transpose a matrix\n * @param {Array} mat\n * @returns {Array} ret\n * @private\n */\nfunction _switch (mat) {\n const I = mat.length\n const J = mat[0].length\n let i, j\n const ret = []\n for (j = 0; j < J; j++) {\n const tmp = []\n for (i = 0; i < I; i++) {\n tmp.push(mat[i][j])\n }\n ret.push(tmp)\n }\n return ret\n}\n\n// TODO: document function scatter\nexport function scatter (a, j, w, x, u, mark, cindex, f, inverse, update, value) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n\n // vars\n let k, k0, k1, i\n\n // check we need to process values (pattern matrix)\n if (x) {\n // values in j\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check value exists in current j\n if (w[i] !== mark) {\n // i is new entry in j\n w[i] = mark\n // add i to pattern of C\n cindex.push(i)\n // x(i) = A, check we need to call function this time\n if (update) {\n // copy value to workspace calling callback function\n x[i] = inverse ? f(avalues[k], value) : f(value, avalues[k])\n // function was called on current row\n u[i] = mark\n } else {\n // copy value to workspace\n x[i] = avalues[k]\n }\n } else {\n // i exists in C already\n x[i] = inverse ? f(avalues[k], x[i]) : f(x[i], avalues[k])\n // function was called on current row\n u[i] = mark\n }\n }\n } else {\n // values in j\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check value exists in current j\n if (w[i] !== mark) {\n // i is new entry in j\n w[i] = mark\n // add i to pattern of C\n cindex.push(i)\n } else {\n // indicate function was called on current row\n u[i] = mark\n }\n }\n }\n}\n","import { deepMap } from '../../utils/collection.js'\nimport { isInteger as isIntegerNumber } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isInteger'\nconst dependencies = ['typed']\n\nexport const createIsInteger = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is an integer number.\n * The function supports `number`, `BigNumber`, and `Fraction`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isInteger(x)\n *\n * Examples:\n *\n * math.isInteger(2) // returns true\n * math.isInteger(0) // returns true\n * math.isInteger(0.5) // returns false\n * math.isInteger(math.bignumber(500)) // returns true\n * math.isInteger(math.fraction(4)) // returns true\n * math.isInteger('3') // returns true\n * math.isInteger([3, 0.5, -2]) // returns [true, false, true]\n * math.isInteger(math.complex('2-4i') // throws an error\n *\n * See also:\n *\n * isNumeric, isPositive, isNegative, isZero\n *\n * @param {number | BigNumber | Fraction | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` contains a numeric, integer value.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isIntegerNumber, // TODO: what to do with isInteger(add(0.1, 0.2)) ?\n\n BigNumber: function (x) {\n return x.isInt()\n },\n\n Fraction: function (x) {\n return x.d === 1 && isFinite(x.n)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { isInteger } from '../../utils/number.js'\n\nconst n1 = 'number'\n\nexport function isIntegerNumber (x) {\n return isInteger(x)\n}\nisIntegerNumber.signature = n1\n\nexport function isNegativeNumber (x) {\n return x < 0\n}\nisNegativeNumber.signature = n1\n\nexport function isPositiveNumber (x) {\n return x > 0\n}\nisPositiveNumber.signature = n1\n\nexport function isZeroNumber (x) {\n return x === 0\n}\nisZeroNumber.signature = n1\n\nexport function isNaNNumber (x) {\n return Number.isNaN(x)\n}\nisNaNNumber.signature = n1\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isNegativeNumber } from '../../plain/number/index.js'\n\nconst name = 'isNegative'\nconst dependencies = ['typed']\n\nexport const createIsNegative = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is negative: smaller than zero.\n * The function supports types `number`, `BigNumber`, `Fraction`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNegative(x)\n *\n * Examples:\n *\n * math.isNegative(3) // returns false\n * math.isNegative(-2) // returns true\n * math.isNegative(0) // returns false\n * math.isNegative(-0) // returns false\n * math.isNegative(math.bignumber(2)) // returns false\n * math.isNegative(math.fraction(-2, 5)) // returns true\n * math.isNegative('-2') // returns true\n * math.isNegative([2, 0, -3]') // returns [false, false, true]\n *\n * See also:\n *\n * isNumeric, isPositive, isZero, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isNegativeNumber,\n\n BigNumber: function (x) {\n return x.isNeg() && !x.isZero() && !x.isNaN()\n },\n\n Fraction: function (x) {\n return x.s < 0 // It's enough to decide on the sign\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isNumeric'\nconst dependencies = ['typed']\n\nexport const createIsNumeric = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is an numeric value.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNumeric(x)\n *\n * Examples:\n *\n * math.isNumeric(2) // returns true\n * math.isNumeric('2') // returns false\n * math.hasNumericValue('2') // returns true\n * math.isNumeric(0) // returns true\n * math.isNumeric(math.bignumber(500)) // returns true\n * math.isNumeric(math.fraction(4)) // returns true\n * math.isNumeric(math.complex('2-4i') // returns false\n * math.isNumeric([2.3, 'foo', false]) // returns [true, false, true]\n *\n * See also:\n *\n * isZero, isPositive, isNegative, isInteger, hasNumericValue\n *\n * @param {*} x Value to be tested\n * @return {boolean} Returns true when `x` is a `number`, `BigNumber`,\n * `Fraction`, or `boolean`. Returns false for other types.\n * Throws an error in case of unknown types.\n */\n return typed(name, {\n 'number | BigNumber | Fraction | boolean': function () {\n return true\n },\n\n 'Complex | Unit | string | null | undefined | Node': function () {\n return false\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'hasNumericValue'\nconst dependencies = ['typed', 'isNumeric']\n\nexport const createHasNumericValue = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNumeric }) => {\n /**\n * Test whether a value is an numeric value.\n *\n * In case of a string, true is returned if the string contains a numeric value.\n *\n * Syntax:\n *\n * math.hasNumericValue(x)\n *\n * Examples:\n *\n * math.hasNumericValue(2) // returns true\n * math.hasNumericValue('2') // returns true\n * math.isNumeric('2') // returns false\n * math.hasNumericValue(0) // returns true\n * math.hasNumericValue(math.bignumber(500)) // returns true\n * math.hasNumericValue(math.fraction(4)) // returns true\n * math.hasNumericValue(math.complex('2-4i') // returns false\n * math.hasNumericValue([2.3, 'foo', false]) // returns [true, false, true]\n *\n * See also:\n *\n * isZero, isPositive, isNegative, isInteger, isNumeric\n *\n * @param {*} x Value to be tested\n * @return {boolean} Returns true when `x` is a `number`, `BigNumber`,\n * `Fraction`, `Boolean`, or a `String` containing number. Returns false for other types.\n * Throws an error in case of unknown types.\n */\n return typed(name, {\n string: function (x) {\n return x.trim().length > 0 && !isNaN(Number(x))\n },\n any: function (x) {\n return isNumeric(x)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isPositiveNumber } from '../../plain/number/index.js'\n\nconst name = 'isPositive'\nconst dependencies = ['typed']\n\nexport const createIsPositive = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is positive: larger than zero.\n * The function supports types `number`, `BigNumber`, `Fraction`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isPositive(x)\n *\n * Examples:\n *\n * math.isPositive(3) // returns true\n * math.isPositive(-2) // returns false\n * math.isPositive(0) // returns false\n * math.isPositive(-0) // returns false\n * math.isPositive(0.5) // returns true\n * math.isPositive(math.bignumber(2)) // returns true\n * math.isPositive(math.fraction(-2, 5)) // returns false\n * math.isPositive(math.fraction(1,3)) // returns false\n * math.isPositive('2') // returns true\n * math.isPositive([2, 0, -3]) // returns [true, false, false]\n *\n * See also:\n *\n * isNumeric, isZero, isNegative, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isPositiveNumber,\n\n BigNumber: function (x) {\n return !x.isNeg() && !x.isZero() && !x.isNaN()\n },\n\n Fraction: function (x) {\n return x.s > 0 && x.n > 0\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isZeroNumber } from '../../plain/number/index.js'\n\nconst name = 'isZero'\nconst dependencies = ['typed']\n\nexport const createIsZero = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is zero.\n * The function can check for zero for types `number`, `BigNumber`, `Fraction`,\n * `Complex`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isZero(x)\n *\n * Examples:\n *\n * math.isZero(0) // returns true\n * math.isZero(2) // returns false\n * math.isZero(0.5) // returns false\n * math.isZero(math.bignumber(0)) // returns true\n * math.isZero(math.fraction(0)) // returns true\n * math.isZero(math.fraction(1,3)) // returns false\n * math.isZero(math.complex('2 - 4i') // returns false\n * math.isZero(math.complex('0i') // returns true\n * math.isZero('0') // returns true\n * math.isZero('2') // returns false\n * math.isZero([2, 0, -3]') // returns [false, true, false]\n *\n * See also:\n *\n * isNumeric, isPositive, isNegative, isInteger\n *\n * @param {number | BigNumber | Complex | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isZeroNumber,\n\n BigNumber: function (x) {\n return x.isZero()\n },\n\n Complex: function (x) {\n return x.re === 0 && x.im === 0\n },\n\n Fraction: function (x) {\n return x.d === 1 && x.n === 0\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isNaNNumber } from '../../plain/number/index.js'\n\nconst name = 'isNaN'\nconst dependencies = ['typed']\n\nexport const createIsNaN = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is NaN (not a number).\n * The function supports types `number`, `BigNumber`, `Fraction`, `Unit` and `Complex`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNaN(x)\n *\n * Examples:\n *\n * math.isNaN(3) // returns false\n * math.isNaN(NaN) // returns true\n * math.isNaN(0) // returns false\n * math.isNaN(math.bignumber(NaN)) // returns true\n * math.isNaN(math.bignumber(0)) // returns false\n * math.isNaN(math.fraction(-2, 5)) // returns false\n * math.isNaN('-2') // returns false\n * math.isNaN([2, 0, -3, NaN]') // returns [false, false, false, true]\n *\n * See also:\n *\n * isNumeric, isNegative, isPositive, isZero, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is NaN.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isNaNNumber,\n\n BigNumber: function (x) {\n return x.isNaN()\n },\n\n Fraction: function (x) {\n return false\n },\n\n Complex: function (x) {\n return x.isNaN()\n },\n\n Unit: function (x) {\n return Number.isNaN(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, Number.isNaN)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { typeOf as _typeOf } from '../../utils/is.js'\n\nconst name = 'typeOf'\nconst dependencies = ['typed']\n\nexport const createTypeOf = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Determine the type of a variable.\n *\n * Function `typeOf` recognizes the following types of objects:\n *\n * Object | Returns | Example\n * ---------------------- | ------------- | ------------------------------------------\n * null | `'null'` | `math.typeOf(null)`\n * number | `'number'` | `math.typeOf(3.5)`\n * boolean | `'boolean'` | `math.typeOf(true)`\n * string | `'string'` | `math.typeOf('hello world')`\n * Array | `'Array'` | `math.typeOf([1, 2, 3])`\n * Date | `'Date'` | `math.typeOf(new Date())`\n * Function | `'Function'` | `math.typeOf(function () {})`\n * Object | `'Object'` | `math.typeOf({a: 2, b: 3})`\n * RegExp | `'RegExp'` | `math.typeOf(/a regexp/)`\n * undefined | `'undefined'` | `math.typeOf(undefined)`\n * math.BigNumber | `'BigNumber'` | `math.typeOf(math.bignumber('2.3e500'))`\n * math.Chain | `'Chain'` | `math.typeOf(math.chain(2))`\n * math.Complex | `'Complex'` | `math.typeOf(math.complex(2, 3))`\n * math.Fraction | `'Fraction'` | `math.typeOf(math.fraction(1, 3))`\n * math.Help | `'Help'` | `math.typeOf(math.help('sqrt'))`\n * math.Help | `'Help'` | `math.typeOf(math.help('sqrt'))`\n * math.Index | `'Index'` | `math.typeOf(math.index(1, 3))`\n * math.Matrix | `'Matrix'` | `math.typeOf(math.matrix([[1,2], [3, 4]]))`\n * math.Range | `'Range'` | `math.typeOf(math.range(0, 10))`\n * math.ResultSet | `'ResultSet'` | `math.typeOf(math.evaluate('a=2\\nb=3'))`\n * math.Unit | `'Unit'` | `math.typeOf(math.unit('45 deg'))`\n * math.AccessorNode | `'AccessorNode'` | `math.typeOf(math.parse('A[2]'))`\n * math.ArrayNode | `'ArrayNode'` | `math.typeOf(math.parse('[1,2,3]'))`\n * math.AssignmentNode | `'AssignmentNode'` | `math.typeOf(math.parse('x=2'))`\n * math.BlockNode | `'BlockNode'` | `math.typeOf(math.parse('a=2; b=3'))`\n * math.ConditionalNode | `'ConditionalNode'` | `math.typeOf(math.parse('x<0 ? -x : x'))`\n * math.ConstantNode | `'ConstantNode'` | `math.typeOf(math.parse('2.3'))`\n * math.FunctionAssignmentNode | `'FunctionAssignmentNode'` | `math.typeOf(math.parse('f(x)=x^2'))`\n * math.FunctionNode | `'FunctionNode'` | `math.typeOf(math.parse('sqrt(4)'))`\n * math.IndexNode | `'IndexNode'` | `math.typeOf(math.parse('A[2]').index)`\n * math.ObjectNode | `'ObjectNode'` | `math.typeOf(math.parse('{a:2}'))`\n * math.ParenthesisNode | `'ParenthesisNode'` | `math.typeOf(math.parse('(2+3)'))`\n * math.RangeNode | `'RangeNode'` | `math.typeOf(math.parse('1:10'))`\n * math.SymbolNode | `'SymbolNode'` | `math.typeOf(math.parse('x'))`\n *\n * Syntax:\n *\n * math.typeOf(x)\n *\n * Examples:\n *\n * math.typeOf(3.5) // returns 'number'\n * math.typeOf(math.complex('2-4i')) // returns 'Complex'\n * math.typeOf(math.unit('45 deg')) // returns 'Unit'\n * math.typeOf('hello world') // returns 'string'\n *\n * @param {*} x The variable for which to test the type.\n * @return {string} Returns the name of the type. Primitive types are lower case,\n * non-primitive types are upper-camel-case.\n * For example 'number', 'string', 'Array', 'Date'.\n */\n return typed(name, {\n any: _typeOf\n })\n})\n","/**\n * Compares two BigNumbers.\n * @param {BigNumber} x First value to compare\n * @param {BigNumber} y Second value to compare\n * @param {number} [epsilon] The maximum relative difference between x and y\n * If epsilon is undefined or null, the function will\n * test whether x and y are exactly equal.\n * @return {boolean} whether the two numbers are nearly equal\n */\nexport function nearlyEqual (x, y, epsilon) {\n // if epsilon is null or undefined, test whether x and y are exactly equal\n if (epsilon === null || epsilon === undefined) {\n return x.eq(y)\n }\n\n // use \"==\" operator, handles infinities\n if (x.eq(y)) {\n return true\n }\n\n // NaN\n if (x.isNaN() || y.isNaN()) {\n return false\n }\n\n // at this point x and y should be finite\n if (x.isFinite() && y.isFinite()) {\n // check numbers are very close, needed when comparing numbers near zero\n const diff = x.minus(y).abs()\n if (diff.isZero()) {\n return true\n } else {\n // use relative error\n const max = x.constructor.max(x.abs(), y.abs())\n return diff.lte(max.times(epsilon))\n }\n }\n\n // Infinite and Number or negative Infinite and positive Infinite cases\n return false\n}\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { complexEquals } from '../../utils/complex.js'\n\nconst name = 'equalScalar'\nconst dependencies = ['typed', 'config']\n\nexport const createEqualScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed, config }) => {\n /**\n * Test whether two scalar values are nearly equal.\n *\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Complex} y Second value to compare\n * @return {boolean} Returns true when the compared values are equal, else returns false\n * @private\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x === y\n },\n\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.eq(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.equals(y)\n },\n\n 'Complex, Complex': function (x, y) {\n return complexEquals(x, y, config.epsilon)\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n }\n })\n})\n\nexport const createEqualScalarNumber = factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual } from './number.js'\n\n/**\n * Test whether two complex values are equal provided a given epsilon.\n * Does not use or change the global Complex.EPSILON setting\n * @param {Complex} x\n * @param {Complex} y\n * @param {number} epsilon\n * @returns {boolean}\n */\nexport function complexEquals (x, y, epsilon) {\n return nearlyEqual(x.re, y.re, epsilon) && nearlyEqual(x.im, y.im, epsilon)\n}\n","import { isArray, isBigNumber, isCollection, isIndex, isMatrix, isNumber, isString, typeOf } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { format } from '../../utils/string.js'\nimport { clone, deepStrictEqual } from '../../utils/object.js'\nimport { arraySize, getArrayDataType, unsqueeze, validateIndex } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { DimensionError } from '../../error/DimensionError.js'\n\nconst name = 'SparseMatrix'\nconst dependencies = [\n 'typed',\n 'equalScalar',\n 'Matrix'\n]\n\nexport const createSparseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar, Matrix }) => {\n /**\n * Sparse Matrix implementation. This type implements a Compressed Column Storage format\n * for sparse matrices.\n * @class SparseMatrix\n */\n function SparseMatrix (data, datatype) {\n if (!(this instanceof SparseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data)) {\n // create from matrix\n _createFromMatrix(this, data, datatype)\n } else if (data && isArray(data.index) && isArray(data.ptr) && isArray(data.size)) {\n // initialize fields\n this._values = data.values\n this._index = data.index\n this._ptr = data.ptr\n this._size = data.size\n this._datatype = datatype || data.datatype\n } else if (isArray(data)) {\n // create from array\n _createFromArray(this, data, datatype)\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._values = []\n this._index = []\n this._ptr = [0]\n this._size = [0, 0]\n this._datatype = datatype\n }\n }\n\n function _createFromMatrix (matrix, source, datatype) {\n // check matrix type\n if (source.type === 'SparseMatrix') {\n // clone arrays\n matrix._values = source._values ? clone(source._values) : undefined\n matrix._index = clone(source._index)\n matrix._ptr = clone(source._ptr)\n matrix._size = clone(source._size)\n matrix._datatype = datatype || source._datatype\n } else {\n // build from matrix data\n _createFromArray(matrix, source.valueOf(), datatype || source._datatype)\n }\n }\n\n function _createFromArray (matrix, data, datatype) {\n // initialize fields\n matrix._values = []\n matrix._index = []\n matrix._ptr = []\n matrix._datatype = datatype\n // discover rows & columns, do not use math.size() to avoid looping array twice\n const rows = data.length\n let columns = 0\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, datatype)\n }\n\n // check we have rows (empty array)\n if (rows > 0) {\n // column index\n let j = 0\n do {\n // store pointer to values index\n matrix._ptr.push(matrix._index.length)\n // loop rows\n for (let i = 0; i < rows; i++) {\n // current row\n const row = data[i]\n // check row is an array\n if (isArray(row)) {\n // update columns if needed (only on first column)\n if (j === 0 && columns < row.length) { columns = row.length }\n // check row has column\n if (j < row.length) {\n // value\n const v = row[j]\n // check value != 0\n if (!eq(v, zero)) {\n // store value\n matrix._values.push(v)\n // index\n matrix._index.push(i)\n }\n }\n } else {\n // update columns if needed (only on first column)\n if (j === 0 && columns < 1) { columns = 1 }\n // check value != 0 (row is a scalar)\n if (!eq(row, zero)) {\n // store value\n matrix._values.push(row)\n // index\n matrix._index.push(i)\n }\n }\n }\n // increment index\n j++\n }\n while (j < columns)\n }\n // store number of values in ptr\n matrix._ptr.push(matrix._index.length)\n // size\n matrix._size = [rows, columns]\n }\n\n SparseMatrix.prototype = new Matrix()\n\n /**\n * Create a new SparseMatrix\n */\n SparseMatrix.prototype.createSparseMatrix = function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n\n /**\n * Attach type information\n */\n SparseMatrix.prototype.type = 'SparseMatrix'\n SparseMatrix.prototype.isSparseMatrix = true\n\n /**\n * Get the matrix type\n *\n * Usage:\n * const matrixType = matrix.getDataType() // retrieves the matrix type\n *\n * @memberOf SparseMatrix\n * @return {string} type information; if multiple types are found from the Matrix, it will return \"mixed\"\n */\n SparseMatrix.prototype.getDataType = function () {\n return getArrayDataType(this._values, typeOf)\n }\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @memberof SparseMatrix\n * @return {string} The storage format.\n */\n SparseMatrix.prototype.storage = function () {\n return 'sparse'\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @memberof SparseMatrix\n * @return {string} The datatype.\n */\n SparseMatrix.prototype.datatype = function () {\n return this._datatype\n }\n\n /**\n * Create a new SparseMatrix\n * @memberof SparseMatrix\n * @param {Array} data\n * @param {string} [datatype]\n */\n SparseMatrix.prototype.create = function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n\n /**\n * Get the matrix density.\n *\n * Usage:\n * const density = matrix.density() // retrieve matrix density\n *\n * @memberof SparseMatrix\n * @return {number} The matrix density.\n */\n SparseMatrix.prototype.density = function () {\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n // calculate density\n return rows !== 0 && columns !== 0 ? (this._index.length / (rows * columns)) : 0\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @memberof SparseMatrix\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n SparseMatrix.prototype.subset = function (index, replacement, defaultValue) { // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke subset on a Pattern only matrix') }\n\n // check arguments\n switch (arguments.length) {\n case 1:\n return _getsubset(this, index)\n\n // intentional fall through\n case 2:\n case 3:\n return _setsubset(this, index, replacement, defaultValue)\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n function _getsubset (matrix, idx) {\n // check idx\n if (!isIndex(idx)) {\n throw new TypeError('Invalid index')\n }\n\n const isScalar = idx.isScalar()\n if (isScalar) {\n // return a scalar\n return matrix.get(idx.min())\n }\n // validate dimensions\n const size = idx.size()\n if (size.length !== matrix._size.length) {\n throw new DimensionError(size.length, matrix._size.length)\n }\n\n // vars\n let i, ii, k, kk\n\n // validate if any of the ranges in the index is out of range\n const min = idx.min()\n const max = idx.max()\n for (i = 0, ii = matrix._size.length; i < ii; i++) {\n validateIndex(min[i], matrix._size[i])\n validateIndex(max[i], matrix._size[i])\n }\n\n // matrix arrays\n const mvalues = matrix._values\n const mindex = matrix._index\n const mptr = matrix._ptr\n\n // rows & columns dimensions for result matrix\n const rows = idx.dimension(0)\n const columns = idx.dimension(1)\n\n // workspace & permutation vector\n const w = []\n const pv = []\n\n // loop rows in resulting matrix\n rows.forEach(function (i, r) {\n // update permutation vector\n pv[i] = r[0]\n // mark i in workspace\n w[i] = true\n })\n\n // result matrix arrays\n const values = mvalues ? [] : undefined\n const index = []\n const ptr = []\n\n // loop columns in result matrix\n columns.forEach(function (j) {\n // update ptr\n ptr.push(index.length)\n // loop values in column j\n for (k = mptr[j], kk = mptr[j + 1]; k < kk; k++) {\n // row\n i = mindex[k]\n // check row is in result matrix\n if (w[i] === true) {\n // push index\n index.push(pv[i])\n // check we need to process values\n if (values) { values.push(mvalues[k]) }\n }\n }\n })\n // update ptr\n ptr.push(index.length)\n\n // return matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: size,\n datatype: matrix._datatype\n })\n }\n\n function _setsubset (matrix, index, submatrix, defaultValue) {\n // check index\n if (!index || index.isIndex !== true) {\n throw new TypeError('Invalid index')\n }\n\n // get index size and check whether the index contains a single value\n const iSize = index.size()\n const isScalar = index.isScalar()\n\n // calculate the size of the submatrix, and convert it into an Array if needed\n let sSize\n if (isMatrix(submatrix)) {\n // submatrix size\n sSize = submatrix.size()\n // use array representation\n submatrix = submatrix.toArray()\n } else {\n // get submatrix size (array, scalar)\n sSize = arraySize(submatrix)\n }\n\n // check index is a scalar\n if (isScalar) {\n // verify submatrix is a scalar\n if (sSize.length !== 0) {\n throw new TypeError('Scalar expected')\n }\n // set value\n matrix.set(index.min(), submatrix, defaultValue)\n } else {\n // validate dimensions, index size must be one or two dimensions\n if (iSize.length !== 1 && iSize.length !== 2) {\n throw new DimensionError(iSize.length, matrix._size.length, '<')\n }\n\n // check submatrix and index have the same dimensions\n if (sSize.length < iSize.length) {\n // calculate number of missing outer dimensions\n let i = 0\n let outer = 0\n while (iSize[i] === 1 && sSize[i] === 1) {\n i++\n }\n while (iSize[i] === 1) {\n outer++\n i++\n }\n // unsqueeze both outer and inner dimensions\n submatrix = unsqueeze(submatrix, iSize.length, outer, sSize)\n }\n\n // check whether the size of the submatrix matches the index size\n if (!deepStrictEqual(iSize, sSize)) {\n throw new DimensionError(iSize, sSize, '>')\n }\n\n // offsets\n const x0 = index.min()[0]\n const y0 = index.min()[1]\n\n // submatrix rows and columns\n const m = sSize[0]\n const n = sSize[1]\n\n // loop submatrix\n for (let x = 0; x < m; x++) {\n // loop columns\n for (let y = 0; y < n; y++) {\n // value at i, j\n const v = submatrix[x][y]\n // invoke set (zero value will remove entry from matrix)\n matrix.set([x + x0, y + y0], v, defaultValue)\n }\n }\n }\n return matrix\n }\n\n /**\n * Get a single element from the matrix.\n * @memberof SparseMatrix\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n SparseMatrix.prototype.get = function (index) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke get on a Pattern only matrix') }\n\n // row and column\n const i = index[0]\n const j = index[1]\n\n // check i, j are valid\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[1])\n\n // find value index\n const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)\n // check k is prior to next column k and it is in the correct row\n if (k < this._ptr[j + 1] && this._index[k] === i) { return this._values[k] }\n\n return 0\n }\n\n /**\n * Replace a single element in the matrix.\n * @memberof SparseMatrix\n * @param {number[]} index Zero-based index\n * @param {*} v\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be set to zero.\n * @return {SparseMatrix} self\n */\n SparseMatrix.prototype.set = function (index, v, defaultValue) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke set on a Pattern only matrix') }\n\n // row and column\n const i = index[0]\n const j = index[1]\n\n // rows & columns\n let rows = this._size[0]\n let columns = this._size[1]\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(this._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [this._datatype, this._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, this._datatype)\n }\n\n // check we need to resize matrix\n if (i > rows - 1 || j > columns - 1) {\n // resize matrix\n _resize(this, Math.max(i + 1, rows), Math.max(j + 1, columns), defaultValue)\n // update rows & columns\n rows = this._size[0]\n columns = this._size[1]\n }\n\n // check i, j are valid\n validateIndex(i, rows)\n validateIndex(j, columns)\n\n // find value index\n const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)\n // check k is prior to next column k and it is in the correct row\n if (k < this._ptr[j + 1] && this._index[k] === i) {\n // check value != 0\n if (!eq(v, zero)) {\n // update value\n this._values[k] = v\n } else {\n // remove value from matrix\n _remove(k, j, this._values, this._index, this._ptr)\n }\n } else {\n // insert value @ (i, j)\n _insert(k, i, j, v, this._values, this._index, this._ptr)\n }\n\n return this\n }\n\n function _getValueIndex (i, top, bottom, index) {\n // check row is on the bottom side\n if (bottom - top === 0) { return bottom }\n // loop rows [top, bottom[\n for (let r = top; r < bottom; r++) {\n // check we found value index\n if (index[r] === i) { return r }\n }\n // we did not find row\n return top\n }\n\n function _remove (k, j, values, index, ptr) {\n // remove value @ k\n values.splice(k, 1)\n index.splice(k, 1)\n // update pointers\n for (let x = j + 1; x < ptr.length; x++) { ptr[x]-- }\n }\n\n function _insert (k, i, j, v, values, index, ptr) {\n // insert value\n values.splice(k, 0, v)\n // update row for k\n index.splice(k, 0, i)\n // update column pointers\n for (let x = j + 1; x < ptr.length; x++) { ptr[x]++ }\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @memberof SparseMatrix\n * @param {number[] | Matrix} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n SparseMatrix.prototype.resize = function (size, defaultValue, copy) {\n // validate arguments\n if (!isCollection(size)) {\n throw new TypeError('Array or Matrix expected')\n }\n\n // SparseMatrix input is always 2d, flatten this into 1d if it's indeed a vector\n const sizeArray = size.valueOf().map(value => {\n return Array.isArray(value) && value.length === 1\n ? value[0]\n : value\n })\n\n if (sizeArray.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // check sizes\n sizeArray.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(sizeArray) + ')')\n }\n })\n\n // matrix to resize\n const m = copy ? this.clone() : this\n // resize matrix\n return _resize(m, sizeArray[0], sizeArray[1], defaultValue)\n }\n\n function _resize (matrix, rows, columns, defaultValue) {\n // value to insert at the time of growing matrix\n let value = defaultValue || 0\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(matrix._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, matrix._datatype)\n // convert value to the same datatype\n value = typed.convert(value, matrix._datatype)\n }\n\n // should we insert the value?\n const ins = !eq(value, zero)\n\n // old columns and rows\n const r = matrix._size[0]\n let c = matrix._size[1]\n\n let i, j, k\n\n // check we need to increase columns\n if (columns > c) {\n // loop new columns\n for (j = c; j < columns; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._values.length\n // check we need to insert matrix._values\n if (ins) {\n // loop rows\n for (i = 0; i < r; i++) {\n // add new matrix._values\n matrix._values.push(value)\n // update matrix._index\n matrix._index.push(i)\n }\n }\n }\n // store number of matrix._values in matrix._ptr\n matrix._ptr[columns] = matrix._values.length\n } else if (columns < c) {\n // truncate matrix._ptr\n matrix._ptr.splice(columns + 1, c - columns)\n // truncate matrix._values and matrix._index\n matrix._values.splice(matrix._ptr[columns], matrix._values.length)\n matrix._index.splice(matrix._ptr[columns], matrix._index.length)\n }\n // update columns\n c = columns\n\n // check we need to increase rows\n if (rows > r) {\n // check we have to insert values\n if (ins) {\n // inserts\n let n = 0\n // loop columns\n for (j = 0; j < c; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._ptr[j] + n\n // where to insert matrix._values\n k = matrix._ptr[j + 1] + n\n // pointer\n let p = 0\n // loop new rows, initialize pointer\n for (i = r; i < rows; i++, p++) {\n // add value\n matrix._values.splice(k + p, 0, value)\n // update matrix._index\n matrix._index.splice(k + p, 0, i)\n // increment inserts\n n++\n }\n }\n // store number of matrix._values in matrix._ptr\n matrix._ptr[c] = matrix._values.length\n }\n } else if (rows < r) {\n // deletes\n let d = 0\n // loop columns\n for (j = 0; j < c; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._ptr[j] - d\n // where matrix._values start for next column\n const k0 = matrix._ptr[j]\n const k1 = matrix._ptr[j + 1] - d\n // loop matrix._index\n for (k = k0; k < k1; k++) {\n // row\n i = matrix._index[k]\n // check we need to delete value and matrix._index\n if (i > rows - 1) {\n // remove value\n matrix._values.splice(k, 1)\n // remove item from matrix._index\n matrix._index.splice(k, 1)\n // increase deletes\n d++\n }\n }\n }\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._values.length\n }\n // update matrix._size\n matrix._size[0] = rows\n matrix._size[1] = columns\n // return matrix\n return matrix\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * NOTE: This might be better suited to copy by default, instead of modifying\n * in place. For now, it operates in place to remain consistent with\n * resize().\n *\n * @memberof SparseMatrix\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n SparseMatrix.prototype.reshape = function (size, copy) {\n // validate arguments\n if (!isArray(size)) { throw new TypeError('Array expected') }\n if (size.length !== 2) { throw new Error('Sparse matrices can only be reshaped in two dimensions') }\n\n // check sizes\n size.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n })\n\n // m * n must not change\n if (this._size[0] * this._size[1] !== size[0] * size[1]) {\n throw new Error('Reshaping sparse matrix will result in the wrong number of elements')\n }\n\n // matrix to reshape\n const m = copy ? this.clone() : this\n\n // return unchanged if the same shape\n if (this._size[0] === size[0] && this._size[1] === size[1]) {\n return m\n }\n\n // Convert to COO format (generate a column index)\n const colIndex = []\n for (let i = 0; i < m._ptr.length; i++) {\n for (let j = 0; j < m._ptr[i + 1] - m._ptr[i]; j++) {\n colIndex.push(i)\n }\n }\n\n // Clone the values array\n const values = m._values.slice()\n\n // Clone the row index array\n const rowIndex = m._index.slice()\n\n // Transform the (row, column) indices\n for (let i = 0; i < m._index.length; i++) {\n const r1 = rowIndex[i]\n const c1 = colIndex[i]\n const flat = r1 * m._size[1] + c1\n colIndex[i] = flat % size[1]\n rowIndex[i] = Math.floor(flat / size[1])\n }\n\n // Now reshaping is supposed to preserve the row-major order, BUT these sparse matrices are stored\n // in column-major order, so we have to reorder the value array now. One option is to use a multisort,\n // sorting several arrays based on some other array.\n\n // OR, we could easily just:\n\n // 1. Remove all values from the matrix\n m._values.length = 0\n m._index.length = 0\n m._ptr.length = size[1] + 1\n m._size = size.slice()\n for (let i = 0; i < m._ptr.length; i++) {\n m._ptr[i] = 0\n }\n\n // 2. Re-insert all elements in the proper order (simplified code from SparseMatrix.prototype.set)\n // This step is probably the most time-consuming\n for (let h = 0; h < values.length; h++) {\n const i = rowIndex[h]\n const j = colIndex[h]\n const v = values[h]\n const k = _getValueIndex(i, m._ptr[j], m._ptr[j + 1], m._index)\n _insert(k, i, j, v, m._values, m._index, m._ptr)\n }\n\n // The value indices are inserted out of order, but apparently that's... still OK?\n\n return m\n }\n\n /**\n * Create a clone of the matrix\n * @memberof SparseMatrix\n * @return {SparseMatrix} clone\n */\n SparseMatrix.prototype.clone = function () {\n const m = new SparseMatrix({\n values: this._values ? clone(this._values) : undefined,\n index: clone(this._index),\n ptr: clone(this._ptr),\n size: clone(this._size),\n datatype: this._datatype\n })\n return m\n }\n\n /**\n * Retrieve the size of the matrix.\n * @memberof SparseMatrix\n * @returns {number[]} size\n */\n SparseMatrix.prototype.size = function () {\n return this._size.slice(0) // copy the Array\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @memberof SparseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {SparseMatrix} matrix\n */\n SparseMatrix.prototype.map = function (callback, skipZeros) {\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke map on a Pattern only matrix') }\n // matrix instance\n const me = this\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // invoke callback\n const invoke = function (v, i, j) {\n // invoke callback\n return callback(v, [i, j], me)\n }\n // invoke _map\n return _map(this, 0, rows - 1, 0, columns - 1, invoke, skipZeros)\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on the interval\n * [minRow..maxRow, minColumn..maxColumn].\n */\n function _map (matrix, minRow, maxRow, minColumn, maxColumn, callback, skipZeros) {\n // result arrays\n const values = []\n const index = []\n const ptr = []\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(matrix._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, matrix._datatype)\n }\n\n // invoke callback\n const invoke = function (v, x, y) {\n // invoke callback\n v = callback(v, x, y)\n // check value != 0\n if (!eq(v, zero)) {\n // store value\n values.push(v)\n // index\n index.push(x)\n }\n }\n // loop columns\n for (let j = minColumn; j <= maxColumn; j++) {\n // store pointer to values index\n ptr.push(values.length)\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = matrix._ptr[j]\n const k1 = matrix._ptr[j + 1]\n\n if (skipZeros) {\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = matrix._index[k]\n // check i is in range\n if (i >= minRow && i <= maxRow) {\n // value @ k\n invoke(matrix._values[k], i - minRow, j - minColumn)\n }\n }\n } else {\n // create a cache holding all defined values\n const values = {}\n for (let k = k0; k < k1; k++) {\n const i = matrix._index[k]\n values[i] = matrix._values[k]\n }\n\n // loop over all rows (indexes can be unordered so we can't use that),\n // and either read the value or zero\n for (let i = minRow; i <= maxRow; i++) {\n const value = (i in values) ? values[i] : 0\n invoke(value, i - minRow, j - minColumn)\n }\n }\n }\n\n // store number of values in ptr\n ptr.push(values.length)\n // return sparse matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [maxRow - minRow + 1, maxColumn - minColumn + 1]\n })\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @memberof SparseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n */\n SparseMatrix.prototype.forEach = function (callback, skipZeros) {\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke forEach on a Pattern only matrix') }\n // matrix instance\n const me = this\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n\n if (skipZeros) {\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = this._index[k]\n\n // value @ k\n callback(this._values[k], [i, j], me)\n }\n } else {\n // create a cache holding all defined values\n const values = {}\n for (let k = k0; k < k1; k++) {\n const i = this._index[k]\n values[i] = this._values[k]\n }\n\n // loop over all rows (indexes can be unordered so we can't use that),\n // and either read the value or zero\n for (let i = 0; i < rows; i++) {\n const value = (i in values) ? values[i] : 0\n callback(value, [i, j], me)\n }\n }\n }\n }\n\n /**\n * Create an Array with a copy of the data of the SparseMatrix\n * @memberof SparseMatrix\n * @returns {Array} array\n */\n SparseMatrix.prototype.toArray = function () {\n return _toArray(this._values, this._index, this._ptr, this._size, true)\n }\n\n /**\n * Get the primitive value of the SparseMatrix: a two dimensions array\n * @memberof SparseMatrix\n * @returns {Array} array\n */\n SparseMatrix.prototype.valueOf = function () {\n return _toArray(this._values, this._index, this._ptr, this._size, false)\n }\n\n function _toArray (values, index, ptr, size, copy) {\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n // result\n const a = []\n // vars\n let i, j\n // initialize array\n for (i = 0; i < rows; i++) {\n a[i] = []\n for (j = 0; j < columns; j++) { a[i][j] = 0 }\n }\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n i = index[k]\n // set value (use one for pattern matrix)\n a[i][j] = values ? (copy ? clone(values[k]) : values[k]) : 1\n }\n }\n return a\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @memberof SparseMatrix\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n SparseMatrix.prototype.format = function (options) {\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // density\n const density = this.density()\n // rows & columns\n let str = 'Sparse Matrix [' + format(rows, options) + ' x ' + format(columns, options) + '] density: ' + format(density, options) + '\\n'\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = this._index[k]\n // append value\n str += '\\n (' + format(i, options) + ', ' + format(j, options) + ') ==> ' + (this._values ? format(this._values[k], options) : 'X')\n }\n }\n return str\n }\n\n /**\n * Get a string representation of the matrix\n * @memberof SparseMatrix\n * @returns {string} str\n */\n SparseMatrix.prototype.toString = function () {\n return format(this.toArray())\n }\n\n /**\n * Get a JSON representation of the matrix\n * @memberof SparseMatrix\n * @returns {Object}\n */\n SparseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'SparseMatrix',\n values: this._values,\n index: this._index,\n ptr: this._ptr,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Get the kth Matrix diagonal.\n *\n * @memberof SparseMatrix\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will retrieved.\n *\n * @returns {Matrix} The matrix vector with the diagonal values.\n */\n SparseMatrix.prototype.diagonal = function (k) {\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n\n // number diagonal values\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // diagonal arrays\n const values = []\n const index = []\n const ptr = []\n // initial ptr value\n ptr[0] = 0\n // loop columns\n for (let j = kSuper; j < columns && values.length < n; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n // loop x within [k0, k1[\n for (let x = k0; x < k1; x++) {\n // row index\n const i = this._index[x]\n // check row\n if (i === j - kSuper + kSub) {\n // value on this column\n values.push(this._values[x])\n // store row\n index[values.length - 1] = i - kSub\n // exit loop\n break\n }\n }\n }\n // close ptr\n ptr.push(values.length)\n // return matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [n, 1]\n })\n }\n\n /**\n * Generate a matrix from a JSON object\n * @memberof SparseMatrix\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SparseMatrix\", \"values\": [], \"index\": [], \"ptr\": [], \"size\": []}`,\n * where mathjs is optional\n * @returns {SparseMatrix}\n */\n SparseMatrix.fromJSON = function (json) {\n return new SparseMatrix(json)\n }\n\n /**\n * Create a diagonal matrix.\n *\n * @memberof SparseMatrix\n * @param {Array} size The matrix size.\n * @param {number | Array | Matrix } value The values for the diagonal.\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will be filled in.\n * @param {number} [defaultValue] The default value for non-diagonal\n * @param {string} [datatype] The Matrix datatype, values must be of this datatype.\n *\n * @returns {SparseMatrix}\n */\n SparseMatrix.diagonal = function (size, value, k, defaultValue, datatype) {\n if (!isArray(size)) { throw new TypeError('Array expected, size parameter') }\n if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // map size & validate\n size = size.map(function (s) {\n // check it is a big number\n if (isBigNumber(s)) {\n // convert it\n s = s.toNumber()\n }\n // validate arguments\n if (!isNumber(s) || !isInteger(s) || s < 1) {\n throw new Error('Size values must be positive integers')\n }\n return s\n })\n\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, datatype)\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // number of non-zero items\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // value extraction function\n let _value\n\n // check value\n if (isArray(value)) {\n // validate array\n if (value.length !== n) {\n // number of values in array must be n\n throw new Error('Invalid value array length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value[i]\n }\n } else if (isMatrix(value)) {\n // matrix size\n const ms = value.size()\n // validate matrix\n if (ms.length !== 1 || ms[0] !== n) {\n // number of values in array must be n\n throw new Error('Invalid matrix length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value.get([i])\n }\n } else {\n // define function\n _value = function () {\n // return value\n return value\n }\n }\n\n // create arrays\n const values = []\n const index = []\n const ptr = []\n\n // loop items\n for (let j = 0; j < columns; j++) {\n // number of rows with value\n ptr.push(values.length)\n // diagonal index\n const i = j - kSuper\n // check we need to set diagonal value\n if (i >= 0 && i < n) {\n // get value @ i\n const v = _value(i)\n // check for zero\n if (!eq(v, zero)) {\n // column\n index.push(i + kSub)\n // add value\n values.push(v)\n }\n }\n }\n // last value should be number of values\n ptr.push(values.length)\n // create SparseMatrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [rows, columns]\n })\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @memberof SparseMatrix\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n SparseMatrix.prototype.swapRows = function (i, j) {\n // check index\n if (!isNumber(i) || !isInteger(i) || !isNumber(j) || !isInteger(j)) {\n throw new Error('Row index must be positive integers')\n }\n // check dimensions\n if (this._size.length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n // validate index\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[0])\n\n // swap rows\n SparseMatrix._swapRows(i, j, this._size[1], this._values, this._index, this._ptr)\n // return current instance\n return this\n }\n\n /**\n * Loop rows with data in column j.\n *\n * @param {number} j Column\n * @param {Array} values Matrix values\n * @param {Array} index Matrix row indeces\n * @param {Array} ptr Matrix column pointers\n * @param {Function} callback Callback function invoked for every row in column j\n */\n SparseMatrix._forEachRow = function (j, values, index, ptr, callback) {\n // indeces for column j\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop\n for (let k = k0; k < k1; k++) {\n // invoke callback\n callback(index[k], values[k])\n }\n }\n\n /**\n * Swap rows x and y in Sparse Matrix data structures.\n *\n * @param {number} x Matrix row index 1\n * @param {number} y Matrix row index 2\n * @param {number} columns Number of columns in matrix\n * @param {Array} values Matrix values\n * @param {Array} index Matrix row indeces\n * @param {Array} ptr Matrix column pointers\n */\n SparseMatrix._swapRows = function (x, y, columns, values, index, ptr) {\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // find value index @ x\n const kx = _getValueIndex(x, k0, k1, index)\n // find value index @ x\n const ky = _getValueIndex(y, k0, k1, index)\n // check both rows exist in matrix\n if (kx < k1 && ky < k1 && index[kx] === x && index[ky] === y) {\n // swap values (check for pattern matrix)\n if (values) {\n const v = values[kx]\n values[kx] = values[ky]\n values[ky] = v\n }\n // next column\n continue\n }\n // check x row exist & no y row\n if (kx < k1 && index[kx] === x && (ky >= k1 || index[ky] !== y)) {\n // value @ x (check for pattern matrix)\n const vx = values ? values[kx] : undefined\n // insert value @ y\n index.splice(ky, 0, y)\n if (values) { values.splice(ky, 0, vx) }\n // remove value @ x (adjust array index if needed)\n index.splice(ky <= kx ? kx + 1 : kx, 1)\n if (values) { values.splice(ky <= kx ? kx + 1 : kx, 1) }\n // next column\n continue\n }\n // check y row exist & no x row\n if (ky < k1 && index[ky] === y && (kx >= k1 || index[kx] !== x)) {\n // value @ y (check for pattern matrix)\n const vy = values ? values[ky] : undefined\n // insert value @ x\n index.splice(kx, 0, x)\n if (values) { values.splice(kx, 0, vy) }\n // remove value @ y (adjust array index if needed)\n index.splice(kx <= ky ? ky + 1 : ky, 1)\n if (values) { values.splice(kx <= ky ? ky + 1 : ky, 1) }\n }\n }\n }\n\n return SparseMatrix\n}, { isClass: true })\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\n\nconst name = 'number'\nconst dependencies = ['typed']\n\nexport const createNumber = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a number or convert a string, boolean, or unit to a number.\n * When value is a matrix, all elements will be converted to number.\n *\n * Syntax:\n *\n * math.number(value)\n * math.number(unit, valuelessUnit)\n *\n * Examples:\n *\n * math.number(2) // returns number 2\n * math.number('7.2') // returns number 7.2\n * math.number(true) // returns number 1\n * math.number([true, false, true, true]) // returns [1, 0, 1, 1]\n * math.number(math.unit('52cm'), 'm') // returns 0.52\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, string, unit\n *\n * @param {string | number | BigNumber | Fraction | boolean | Array | Matrix | Unit | null} [value] Value to be converted\n * @param {Unit | string} [valuelessUnit] A valueless unit, used to convert a unit to a number\n * @return {number | Array | Matrix} The created number\n */\n const number = typed('number', {\n '': function () {\n return 0\n },\n\n number: function (x) {\n return x\n },\n\n string: function (x) {\n if (x === 'NaN') return NaN\n let num = Number(x)\n if (isNaN(num)) {\n throw new SyntaxError('String \"' + x + '\" is no valid number')\n }\n if (['0b', '0o', '0x'].includes(x.substring(0, 2))) {\n if (num > 2 ** 32 - 1) {\n throw new SyntaxError(`String \"${x}\" is out of range`)\n }\n if (num & 0x80000000) {\n num = -1 * ~(num - 1)\n }\n }\n return num\n },\n\n BigNumber: function (x) {\n return x.toNumber()\n },\n\n Fraction: function (x) {\n return x.valueOf()\n },\n\n Unit: function (x) {\n throw new Error('Second argument with valueless unit expected')\n },\n\n null: function (x) {\n return 0\n },\n\n 'Unit, string | Unit': function (unit, valuelessUnit) {\n return unit.toNumber(valuelessUnit)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n\n // reviver function to parse a JSON object like:\n //\n // {\"mathjs\":\"number\",\"value\":\"2.3\"}\n //\n // into a number 2.3\n number.fromJSON = function (json) {\n return parseFloat(json.value)\n }\n\n return number\n})\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\nimport { format } from '../utils/number.js'\n\nconst name = 'string'\nconst dependencies = ['typed']\n\nexport const createString = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a string or convert any object into a string.\n * Elements of Arrays and Matrices are processed element wise.\n *\n * Syntax:\n *\n * math.string(value)\n *\n * Examples:\n *\n * math.string(4.2) // returns string '4.2'\n * math.string(math.complex(3, 2) // returns string '3 + 2i'\n *\n * const u = math.unit(5, 'km')\n * math.string(u.to('m')) // returns string '5000 m'\n *\n * math.string([true, false]) // returns ['true', 'false']\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, number, unit\n *\n * @param {* | Array | Matrix | null} [value] A value to convert to a string\n * @return {string | Array | Matrix} The created string\n */\n return typed(name, {\n '': function () {\n return ''\n },\n\n number: format,\n\n null: function (x) {\n return 'null'\n },\n\n boolean: function (x) {\n return x + ''\n },\n\n string: function (x) {\n return x\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n any: function (x) {\n return String(x)\n }\n })\n})\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\n\nconst name = 'boolean'\nconst dependencies = ['typed']\n\nexport const createBoolean = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a boolean or convert a string or number to a boolean.\n * In case of a number, `true` is returned for non-zero numbers, and `false` in\n * case of zero.\n * Strings can be `'true'` or `'false'`, or can contain a number.\n * When value is a matrix, all elements will be converted to boolean.\n *\n * Syntax:\n *\n * math.boolean(x)\n *\n * Examples:\n *\n * math.boolean(0) // returns false\n * math.boolean(1) // returns true\n * math.boolean(-3) // returns true\n * math.boolean('true') // returns true\n * math.boolean('false') // returns false\n * math.boolean([1, 0, 1, 1]) // returns [true, false, true, true]\n *\n * See also:\n *\n * bignumber, complex, index, matrix, string, unit\n *\n * @param {string | number | boolean | Array | Matrix | null} value A value of any type\n * @return {boolean | Array | Matrix} The boolean value\n */\n return typed(name, {\n '': function () {\n return false\n },\n\n boolean: function (x) {\n return x\n },\n\n number: function (x) {\n return !!x\n },\n\n null: function (x) {\n return false\n },\n\n BigNumber: function (x) {\n return !x.isZero()\n },\n\n string: function (x) {\n // try case insensitive\n const lcase = x.toLowerCase()\n if (lcase === 'true') {\n return true\n } else if (lcase === 'false') {\n return false\n }\n\n // test whether value is a valid number\n const num = Number(x)\n if (x !== '' && !isNaN(num)) {\n return !!num\n }\n\n throw new Error('Cannot convert \"' + x + '\" to a boolean')\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'bignumber'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createBignumber = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Create a BigNumber, which can store numbers with arbitrary precision.\n * When a matrix is provided, all elements will be converted to BigNumber.\n *\n * Syntax:\n *\n * math.bignumber(x)\n *\n * Examples:\n *\n * 0.1 + 0.2 // returns number 0.30000000000000004\n * math.bignumber(0.1) + math.bignumber(0.2) // returns BigNumber 0.3\n *\n *\n * 7.2e500 // returns number Infinity\n * math.bignumber('7.2e500') // returns BigNumber 7.2e500\n *\n * See also:\n *\n * boolean, complex, index, matrix, string, unit\n *\n * @param {number | string | Fraction | BigNumber | Array | Matrix | boolean | null} [value] Value for the big number,\n * 0 by default.\n * @returns {BigNumber} The created bignumber\n */\n return typed('bignumber', {\n '': function () {\n return new BigNumber(0)\n },\n\n number: function (x) {\n // convert to string to prevent errors in case of >15 digits\n return new BigNumber(x + '')\n },\n\n string: function (x) {\n return new BigNumber(x)\n },\n\n BigNumber: function (x) {\n // we assume a BigNumber is immutable\n return x\n },\n\n Fraction: function (x) {\n return new BigNumber(x.n).div(x.d).times(x.s)\n },\n\n null: function (x) {\n return new BigNumber(0)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'complex'\nconst dependencies = ['typed', 'Complex']\n\nexport const createComplex = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex }) => {\n /**\n * Create a complex value or convert a value to a complex value.\n *\n * Syntax:\n *\n * math.complex() // creates a complex value with zero\n * // as real and imaginary part.\n * math.complex(re : number, im : string) // creates a complex value with provided\n * // values for real and imaginary part.\n * math.complex(re : number) // creates a complex value with provided\n * // real value and zero imaginary part.\n * math.complex(complex : Complex) // clones the provided complex value.\n * math.complex(arg : string) // parses a string into a complex value.\n * math.complex(array : Array) // converts the elements of the array\n * // or matrix element wise into a\n * // complex value.\n * math.complex({re: number, im: number}) // creates a complex value with provided\n * // values for real an imaginary part.\n * math.complex({r: number, phi: number}) // creates a complex value with provided\n * // polar coordinates\n *\n * Examples:\n *\n * const a = math.complex(3, -4) // a = Complex 3 - 4i\n * a.re = 5 // a = Complex 5 - 4i\n * const i = a.im // Number -4\n * const b = math.complex('2 + 6i') // Complex 2 + 6i\n * const c = math.complex() // Complex 0 + 0i\n * const d = math.add(a, b) // Complex 5 + 2i\n *\n * See also:\n *\n * bignumber, boolean, index, matrix, number, string, unit\n *\n * @param {* | Array | Matrix} [args]\n * Arguments specifying the real and imaginary part of the complex number\n * @return {Complex | Array | Matrix} Returns a complex value\n */\n return typed('complex', {\n '': function () {\n return Complex.ZERO\n },\n\n number: function (x) {\n return new Complex(x, 0)\n },\n\n 'number, number': function (re, im) {\n return new Complex(re, im)\n },\n\n // TODO: this signature should be redundant\n 'BigNumber, BigNumber': function (re, im) {\n return new Complex(re.toNumber(), im.toNumber())\n },\n\n Fraction: function (x) {\n return new Complex(x.valueOf(), 0)\n },\n\n Complex: function (x) {\n return x.clone()\n },\n\n string: function (x) {\n return Complex(x) // for example '2 + 3i'\n },\n\n null: function (x) {\n return Complex(0)\n },\n\n Object: function (x) {\n if ('re' in x && 'im' in x) {\n return new Complex(x.re, x.im)\n }\n\n if (('r' in x && 'phi' in x) || ('abs' in x && 'arg' in x)) {\n return new Complex(x)\n }\n\n throw new Error('Expected object with properties (re and im) or (r and phi) or (abs and arg)')\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'fraction'\nconst dependencies = ['typed', 'Fraction']\n\nexport const createFraction = /* #__PURE__ */ factory(name, dependencies, ({ typed, Fraction }) => {\n /**\n * Create a fraction convert a value to a fraction.\n *\n * Syntax:\n * math.fraction(numerator, denominator)\n * math.fraction({n: numerator, d: denominator})\n * math.fraction(matrix: Array | Matrix) Turn all matrix entries\n * into fractions\n *\n * Examples:\n *\n * math.fraction(1, 3)\n * math.fraction('2/3')\n * math.fraction({n: 2, d: 3})\n * math.fraction([0.2, 0.25, 1.25])\n *\n * See also:\n *\n * bignumber, number, string, unit\n *\n * @param {number | string | Fraction | BigNumber | Array | Matrix} [args]\n * Arguments specifying the numerator and denominator of\n * the fraction\n * @return {Fraction | Array | Matrix} Returns a fraction\n */\n return typed('fraction', {\n number: function (x) {\n if (!isFinite(x) || isNaN(x)) {\n throw new Error(x + ' cannot be represented as a fraction')\n }\n\n return new Fraction(x)\n },\n\n string: function (x) {\n return new Fraction(x)\n },\n\n 'number, number': function (numerator, denominator) {\n return new Fraction(numerator, denominator)\n },\n\n null: function (x) {\n return new Fraction(0)\n },\n\n BigNumber: function (x) {\n return new Fraction(x.toString())\n },\n\n Fraction: function (x) {\n return x // fractions are immutable\n },\n\n Object: function (x) {\n return new Fraction(x)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'matrix'\nconst dependencies = ['typed', 'Matrix', 'DenseMatrix', 'SparseMatrix']\n\nexport const createMatrix = /* #__PURE__ */ factory(name, dependencies, ({ typed, Matrix, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a Matrix. The function creates a new `math.Matrix` object from\n * an `Array`. A Matrix has utility functions to manipulate the data in the\n * matrix, like getting the size and getting or setting values in the matrix.\n * Supported storage formats are 'dense' and 'sparse'.\n *\n * Syntax:\n *\n * math.matrix() // creates an empty matrix using default storage format (dense).\n * math.matrix(data) // creates a matrix with initial data using default storage format (dense).\n * math.matrix('dense') // creates an empty matrix using the given storage format.\n * math.matrix(data, 'dense') // creates a matrix with initial data using the given storage format.\n * math.matrix(data, 'sparse') // creates a sparse matrix with initial data.\n * math.matrix(data, 'sparse', 'number') // creates a sparse matrix with initial data, number data type.\n *\n * Examples:\n *\n * let m = math.matrix([[1, 2], [3, 4]])\n * m.size() // Array [2, 2]\n * m.resize([3, 2], 5)\n * m.valueOf() // Array [[1, 2], [3, 4], [5, 5]]\n * m.get([1, 0]) // number 3\n *\n * See also:\n *\n * bignumber, boolean, complex, index, number, string, unit, sparse\n *\n * @param {Array | Matrix} [data] A multi dimensional array\n * @param {string} [format] The Matrix storage format\n *\n * @return {Matrix} The created matrix\n */\n return typed(name, {\n '': function () {\n return _create([])\n },\n\n string: function (format) {\n return _create([], format)\n },\n\n 'string, string': function (format, datatype) {\n return _create([], format, datatype)\n },\n\n Array: function (data) {\n return _create(data)\n },\n\n Matrix: function (data) {\n return _create(data, data.storage())\n },\n\n 'Array | Matrix, string': _create,\n\n 'Array | Matrix, string, string': _create\n })\n\n /**\n * Create a new Matrix with given storage format\n * @param {Array} data\n * @param {string} [format]\n * @param {string} [datatype]\n * @returns {Matrix} Returns a new Matrix\n * @private\n */\n function _create (data, format, datatype) {\n // get storage format constructor\n if (format === 'dense' || format === 'default' || format === undefined) {\n return new DenseMatrix(data, datatype)\n }\n\n if (format === 'sparse') {\n return new SparseMatrix(data, datatype)\n }\n\n throw new TypeError('Unknown matrix type ' + JSON.stringify(format) + '.')\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'splitUnit'\nconst dependencies = ['typed']\n\nexport const createSplitUnit = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Split a unit in an array of units whose sum is equal to the original unit.\n *\n * Syntax:\n *\n * splitUnit(unit: Unit, parts: Array.)\n *\n * Example:\n *\n * math.splitUnit(new Unit(1, 'm'), ['feet', 'inch'])\n * // [ 3 feet, 3.3700787401575 inch ]\n *\n * See also:\n *\n * unit\n *\n * @param {Array} [parts] An array of strings or valueless units.\n * @return {Array} An array of units.\n */\n return typed(name, {\n 'Unit, Array': function (unit, parts) {\n return unit.splitUnit(parts)\n }\n })\n})\n","import { isInteger, log2, log10, cbrt, expm1, sign, toFixed, log1p } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function absNumber (a) {\n return Math.abs(a)\n}\nabsNumber.signature = n1\n\nexport function addNumber (a, b) {\n return a + b\n}\naddNumber.signature = n2\n\nexport function subtractNumber (a, b) {\n return a - b\n}\nsubtractNumber.signature = n2\n\nexport function multiplyNumber (a, b) {\n return a * b\n}\nmultiplyNumber.signature = n2\n\nexport function divideNumber (a, b) {\n return a / b\n}\ndivideNumber.signature = n2\n\nexport function unaryMinusNumber (x) {\n return -x\n}\nunaryMinusNumber.signature = n1\n\nexport function unaryPlusNumber (x) {\n return x\n}\nunaryPlusNumber.signature = n1\n\nexport function cbrtNumber (x) {\n return cbrt(x)\n}\ncbrtNumber.signature = n1\n\nexport function ceilNumber (x) {\n return Math.ceil(x)\n}\nceilNumber.signature = n1\n\nexport function cubeNumber (x) {\n return x * x * x\n}\ncubeNumber.signature = n1\n\nexport function expNumber (x) {\n return Math.exp(x)\n}\nexpNumber.signature = n1\n\nexport function expm1Number (x) {\n return expm1(x)\n}\nexpm1Number.signature = n1\n\nexport function fixNumber (x) {\n return (x > 0) ? Math.floor(x) : Math.ceil(x)\n}\nfixNumber.signature = n1\n\nexport function floorNumber (x) {\n return Math.floor(x)\n}\nfloorNumber.signature = n1\n\n/**\n * Calculate gcd for numbers\n * @param {number} a\n * @param {number} b\n * @returns {number} Returns the greatest common denominator of a and b\n */\nexport function gcdNumber (a, b) {\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function gcd must be integer numbers')\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n let r\n while (b !== 0) {\n r = a % b\n a = b\n b = r\n }\n return (a < 0) ? -a : a\n}\ngcdNumber.signature = n2\n\n/**\n * Calculate lcm for two numbers\n * @param {number} a\n * @param {number} b\n * @returns {number} Returns the least common multiple of a and b\n */\nexport function lcmNumber (a, b) {\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function lcm must be integer numbers')\n }\n\n if (a === 0 || b === 0) {\n return 0\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n // evaluate lcm here inline to reduce overhead\n let t\n const prod = a * b\n while (b !== 0) {\n t = b\n b = a % t\n a = t\n }\n return Math.abs(prod / a)\n}\nlcmNumber.signature = n2\n\n/**\n * Calculate the logarithm of a value.\n * @param {number} x\n * @return {number}\n */\nexport function logNumber (x) {\n return Math.log(x)\n}\nlogNumber.signature = n1\n\n/**\n * Calculate the 10-base logarithm of a number\n * @param {number} x\n * @return {number}\n */\nexport function log10Number (x) {\n return log10(x)\n}\nlog10Number.signature = n1\n\n/**\n * Calculate the 2-base logarithm of a number\n * @param {number} x\n * @return {number}\n */\nexport function log2Number (x) {\n return log2(x)\n}\nlog2Number.signature = n1\n\n/**\n * Calculate the natural logarithm of a `number+1`\n * @param {number} x\n * @returns {number}\n */\nexport function log1pNumber (x) {\n return log1p(x)\n}\nlog1pNumber.signature = n1\n\n/**\n * Calculate the modulus of two numbers\n * @param {number} x\n * @param {number} y\n * @returns {number} res\n * @private\n */\nexport function modNumber (x, y) {\n if (y > 0) {\n // We don't use JavaScript's % operator here as this doesn't work\n // correctly for x < 0 and x === 0\n // see https://en.wikipedia.org/wiki/Modulo_operation\n return x - y * Math.floor(x / y)\n } else if (y === 0) {\n return x\n } else { // y < 0\n // TODO: implement mod for a negative divisor\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n}\nmodNumber.signature = n2\n\n/**\n * Calculate the nth root of a, solve x^root == a\n * http://rosettacode.org/wiki/Nth_root#JavaScript\n * @param {number} a\n * @param {number} root\n * @private\n */\nexport function nthRootNumber (a, root) {\n const inv = root < 0\n if (inv) {\n root = -root\n }\n\n if (root === 0) {\n throw new Error('Root must be non-zero')\n }\n if (a < 0 && (Math.abs(root) % 2 !== 1)) {\n throw new Error('Root must be odd when a is negative.')\n }\n\n // edge cases zero and infinity\n if (a === 0) {\n return inv ? Infinity : 0\n }\n if (!isFinite(a)) {\n return inv ? 0 : a\n }\n\n let x = Math.pow(Math.abs(a), 1 / root)\n // If a < 0, we require that root is an odd integer,\n // so (-1) ^ (1/root) = -1\n x = a < 0 ? -x : x\n return inv ? 1 / x : x\n\n // Very nice algorithm, but fails with nthRoot(-2, 3).\n // Newton's method has some well-known problems at times:\n // https://en.wikipedia.org/wiki/Newton%27s_method#Failure_analysis\n /*\n let x = 1 // Initial guess\n let xPrev = 1\n let i = 0\n const iMax = 10000\n do {\n const delta = (a / Math.pow(x, root - 1) - x) / root\n xPrev = x\n x = x + delta\n i++\n }\n while (xPrev !== x && i < iMax)\n\n if (xPrev !== x) {\n throw new Error('Function nthRoot failed to converge')\n }\n\n return inv ? 1 / x : x\n */\n}\nnthRootNumber.signature = n2\n\nexport function signNumber (x) {\n return sign(x)\n}\nsignNumber.signature = n1\n\nexport function sqrtNumber (x) {\n return Math.sqrt(x)\n}\nsqrtNumber.signature = n1\n\nexport function squareNumber (x) {\n return x * x\n}\nsquareNumber.signature = n1\n\n/**\n * Calculate xgcd for two numbers\n * @param {number} a\n * @param {number} b\n * @return {number} result\n * @private\n */\nexport function xgcdNumber (a, b) {\n // source: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm\n let t // used to swap two variables\n let q // quotient\n let r // remainder\n let x = 0\n let lastx = 1\n let y = 1\n let lasty = 0\n\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function xgcd must be integer numbers')\n }\n\n while (b) {\n q = Math.floor(a / b)\n r = a - q * b\n\n t = x\n x = lastx - q * x\n lastx = t\n\n t = y\n y = lasty - q * y\n lasty = t\n\n a = b\n b = r\n }\n\n let res\n if (a < 0) {\n res = [-a, -lastx, -lasty]\n } else {\n res = [a, a ? lastx : 0, lasty]\n }\n return res\n}\nxgcdNumber.signature = n2\n\n/**\n * Calculates the power of x to y, x^y, for two numbers.\n * @param {number} x\n * @param {number} y\n * @return {number} res\n */\nexport function powNumber (x, y) {\n // x^Infinity === 0 if -1 < x < 1\n // A real number 0 is returned instead of complex(0)\n if ((x * x < 1 && y === Infinity) ||\n (x * x > 1 && y === -Infinity)) {\n return 0\n }\n\n return Math.pow(x, y)\n}\npowNumber.signature = n2\n\n/**\n * round a number to the given number of decimals, or to zero if decimals is\n * not provided\n * @param {number} value\n * @param {number} decimals number of decimals, between 0 and 15 (0 by default)\n * @return {number} roundedValue\n */\nexport function roundNumber (value, decimals = 0) {\n return parseFloat(toFixed(value, decimals))\n}\nroundNumber.signature = n2\n\n/**\n * Calculate the norm of a number, the absolute value.\n * @param {number} x\n * @return {number}\n */\nexport function normNumber (x) {\n return Math.abs(x)\n}\nnormNumber.signature = n1\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { unaryMinusNumber } from '../../plain/number/index.js'\n\nconst name = 'unaryMinus'\nconst dependencies = ['typed']\n\nexport const createUnaryMinus = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Inverse the sign of a value, apply a unary minus operation.\n *\n * For matrices, the function is evaluated element wise. Boolean values and\n * strings will be converted to a number. For complex numbers, both real and\n * complex value are inverted.\n *\n * Syntax:\n *\n * math.unaryMinus(x)\n *\n * Examples:\n *\n * math.unaryMinus(3.5) // returns -3.5\n * math.unaryMinus(-4.2) // returns 4.2\n *\n * See also:\n *\n * add, subtract, unaryPlus\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Number to be inverted.\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Returns the value with inverted sign.\n */\n return typed(name, {\n number: unaryMinusNumber,\n\n Complex: function (x) {\n return x.neg()\n },\n\n BigNumber: function (x) {\n return x.neg()\n },\n\n Fraction: function (x) {\n return x.neg()\n },\n\n Unit: function (x) {\n const res = x.clone()\n res.value = this(x.value)\n return res\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since unaryMinus(0) = 0\n return deepMap(x, this, true)\n }\n\n // TODO: add support for string\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { unaryPlusNumber } from '../../plain/number/index.js'\n\nconst name = 'unaryPlus'\nconst dependencies = ['typed', 'config', 'BigNumber']\n\nexport const createUnaryPlus = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, BigNumber }) => {\n /**\n * Unary plus operation.\n * Boolean values and strings will be converted to a number, numeric values will be returned as is.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.unaryPlus(x)\n *\n * Examples:\n *\n * math.unaryPlus(3.5) // returns 3.5\n * math.unaryPlus(1) // returns 1\n *\n * See also:\n *\n * unaryMinus, add, subtract\n *\n * @param {number | BigNumber | Fraction | string | Complex | Unit | Array | Matrix} x\n * Input value\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Returns the input value when numeric, converts to a number when input is non-numeric.\n */\n return typed(name, {\n number: unaryPlusNumber,\n\n Complex: function (x) {\n return x // complex numbers are immutable\n },\n\n BigNumber: function (x) {\n return x // bignumbers are immutable\n },\n\n Fraction: function (x) {\n return x // fractions are immutable\n },\n\n Unit: function (x) {\n return x.clone()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since unaryPlus(0) = 0\n return deepMap(x, this, true)\n },\n\n 'boolean | string': function (x) {\n // convert to a number or bignumber\n return (config.number === 'BigNumber') ? new BigNumber(+x) : +x\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { absNumber } from '../../plain/number/index.js'\n\nconst name = 'abs'\nconst dependencies = ['typed']\n\nexport const createAbs = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the absolute value of a number. For matrices, the function is\n * evaluated element wise.\n *\n * Syntax:\n *\n * math.abs(x)\n *\n * Examples:\n *\n * math.abs(3.5) // returns number 3.5\n * math.abs(-4.2) // returns number 4.2\n *\n * math.abs([3, -5, -1, 0, 2]) // returns Array [3, 5, 1, 0, 2]\n *\n * See also:\n *\n * sign\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * A number or matrix for which to get the absolute value\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}\n * Absolute value of `x`\n */\n return typed(name, {\n number: absNumber,\n\n Complex: function (x) {\n return x.abs()\n },\n\n BigNumber: function (x) {\n return x.abs()\n },\n\n Fraction: function (x) {\n return x.abs()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since abs(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.abs()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { arraySize } from '../../utils/array.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { IndexError } from '../../error/IndexError.js'\n\nconst name = 'apply'\nconst dependencies = ['typed', 'isInteger']\n\nexport const createApply = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger }) => {\n /**\n * Apply a function that maps an array to a scalar\n * along a given axis of a matrix or array.\n * Returns a new matrix or array with one less dimension than the input.\n *\n * Syntax:\n *\n * math.apply(A, dim, callback)\n *\n * Where:\n *\n * - `dim: number` is a zero-based dimension over which to concatenate the matrices.\n *\n * Examples:\n *\n * const A = [[1, 2], [3, 4]]\n * const sum = math.sum\n *\n * math.apply(A, 0, sum) // returns [4, 6]\n * math.apply(A, 1, sum) // returns [3, 7]\n *\n * See also:\n *\n * map, filter, forEach\n *\n * @param {Array | Matrix} array The input Matrix\n * @param {number} dim The dimension along which the callback is applied\n * @param {Function} callback The callback function that is applied. This Function\n * should take an array or 1-d matrix as an input and\n * return a number.\n * @return {Array | Matrix} res The residual matrix with the function applied over some dimension.\n */\n return typed(name, {\n 'Array | Matrix, number | BigNumber, function': function (mat, dim, callback) {\n if (!isInteger(dim)) {\n throw new TypeError('Integer number expected for dimension')\n }\n\n const size = Array.isArray(mat) ? arraySize(mat) : mat.size()\n if (dim < 0 || (dim >= size.length)) {\n throw new IndexError(dim, size.length)\n }\n\n if (isMatrix(mat)) {\n return mat.create(_apply(mat.valueOf(), dim, callback))\n } else {\n return _apply(mat, dim, callback)\n }\n }\n })\n})\n\n/**\n * Recursively reduce a matrix\n * @param {Array} mat\n * @param {number} dim\n * @param {Function} callback\n * @returns {Array} ret\n * @private\n */\nfunction _apply (mat, dim, callback) {\n let i, ret, tran\n\n if (dim <= 0) {\n if (!Array.isArray(mat[0])) {\n return callback(mat)\n } else {\n tran = _switch(mat)\n ret = []\n for (i = 0; i < tran.length; i++) {\n ret[i] = _apply(tran[i], dim - 1, callback)\n }\n return ret\n }\n } else {\n ret = []\n for (i = 0; i < mat.length; i++) {\n ret[i] = _apply(mat[i], dim - 1, callback)\n }\n return ret\n }\n}\n\n/**\n * Transpose a matrix\n * @param {Array} mat\n * @returns {Array} ret\n * @private\n */\nfunction _switch (mat) {\n const I = mat.length\n const J = mat[0].length\n let i, j\n const ret = []\n for (j = 0; j < J; j++) {\n const tmp = []\n for (i = 0; i < I; i++) {\n tmp.push(mat[i][j])\n }\n ret.push(tmp)\n }\n return ret\n}\n","import { factory } from '../../utils/factory.js'\nimport { addNumber } from '../../plain/number/index.js'\n\nconst name = 'addScalar'\nconst dependencies = ['typed']\n\nexport const createAddScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Add two scalar values, `x + y`.\n * This function is meant for internal use: it is used by the public function\n * `add`\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x First value to add\n * @param {number | BigNumber | Fraction | Complex} y Second value to add\n * @return {number | BigNumber | Fraction | Complex | Unit} Sum of `x` and `y`\n * @private\n */\n return typed(name, {\n\n 'number, number': addNumber,\n\n 'Complex, Complex': function (x, y) {\n return x.add(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.plus(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.add(y)\n },\n\n 'Unit, Unit': function (x, y) {\n if (x.value === null || x.value === undefined) throw new Error('Parameter x contains a unit with undefined value')\n if (y.value === null || y.value === undefined) throw new Error('Parameter y contains a unit with undefined value')\n if (!x.equalBase(y)) throw new Error('Units do not match')\n\n const res = x.clone()\n res.value = this(res.value, y.value)\n res.fixPrefix = false\n return res\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isBigNumber, isComplex, isFraction } from '../../utils/is.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cbrtNumber } from '../../plain/number/index.js'\n\nconst name = 'cbrt'\nconst dependencies = [\n 'config',\n 'typed',\n 'isNegative',\n 'unaryMinus',\n 'matrix',\n 'Complex',\n 'BigNumber',\n 'Fraction'\n]\n\nexport const createCbrt = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, isNegative, unaryMinus, matrix, Complex, BigNumber, Fraction }) => {\n /**\n * Calculate the cubic root of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cbrt(x)\n * math.cbrt(x, allRoots)\n *\n * Examples:\n *\n * math.cbrt(27) // returns 3\n * math.cube(3) // returns 27\n * math.cbrt(-64) // returns -4\n * math.cbrt(math.unit('27 m^3')) // returns Unit 3 m\n * math.cbrt([27, 64, 125]) // returns [3, 4, 5]\n *\n * const x = math.complex('8i')\n * math.cbrt(x) // returns Complex 1.7320508075689 + i\n * math.cbrt(x, true) // returns Matrix [\n * // 1.7320508075689 + i\n * // -1.7320508075689 + i\n * // -2i\n * // ]\n *\n * See also:\n *\n * square, sqrt, cube\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x\n * Value for which to calculate the cubic root.\n * @param {boolean} [allRoots] Optional, false by default. Only applicable\n * when `x` is a number or complex number. If true, all complex\n * roots are returned, if false (default) the principal root is\n * returned.\n * @return {number | BigNumber | Complex | Unit | Array | Matrix}\n * Returns the cubic root of `x`\n */\n return typed(name, {\n number: cbrtNumber,\n // note: signature 'number, boolean' is also supported,\n // created by typed as it knows how to convert number to Complex\n\n Complex: _cbrtComplex,\n\n 'Complex, boolean': _cbrtComplex,\n\n BigNumber: function (x) {\n return x.cbrt()\n },\n\n Unit: _cbrtUnit,\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since cbrt(0) = 0\n return deepMap(x, this, true)\n }\n })\n\n /**\n * Calculate the cubic root for a complex number\n * @param {Complex} x\n * @param {boolean} [allRoots] If true, the function will return an array\n * with all three roots. If false or undefined,\n * the principal root is returned.\n * @returns {Complex | Array. | Matrix.} Returns the cubic root(s) of x\n * @private\n */\n function _cbrtComplex (x, allRoots) {\n // https://www.wikiwand.com/en/Cube_root#/Complex_numbers\n\n const arg3 = x.arg() / 3\n const abs = x.abs()\n\n // principal root:\n const principal = new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3).exp())\n\n if (allRoots) {\n const all = [\n principal,\n new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 + Math.PI * 2 / 3).exp()),\n new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 - Math.PI * 2 / 3).exp())\n ]\n\n return (config.matrix === 'Array') ? all : matrix(all)\n } else {\n return principal\n }\n }\n\n /**\n * Calculate the cubic root for a Unit\n * @param {Unit} x\n * @return {Unit} Returns the cubic root of x\n * @private\n */\n function _cbrtUnit (x) {\n if (x.value && isComplex(x.value)) {\n let result = x.clone()\n result.value = 1.0\n result = result.pow(1.0 / 3) // Compute the units\n result.value = _cbrtComplex(x.value) // Compute the value\n return result\n } else {\n const negate = isNegative(x.value)\n if (negate) {\n x.value = unaryMinus(x.value)\n }\n\n // TODO: create a helper function for this\n let third\n if (isBigNumber(x.value)) {\n third = new BigNumber(1).div(3)\n } else if (isFraction(x.value)) {\n third = new Fraction(1, 3)\n } else {\n third = 1 / 3\n }\n\n const result = x.pow(third)\n\n if (negate) {\n result.value = unaryMinus(result.value)\n }\n\n return result\n }\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm11'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm11 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked NZ times (number of nonzero items in S).\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm11 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // initialize ptr\n cptr[j] = cindex.length\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = aindex[k]\n // invoke callback\n const v = inverse ? cf(b, avalues[k]) : cf(avalues[k], b)\n // check value is zero\n if (!eq(v, zero)) {\n // push index & value\n cindex.push(i)\n cvalues.push(v)\n }\n }\n }\n // update ptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return s.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { clone } from '../../../utils/object.js'\n\nconst name = 'algorithm14'\nconst dependencies = ['typed']\n\nexport const createAlgorithm14 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over DenseMatrix items and invokes the callback function f(Aij..z, b).\n * Callback function invoked MxN times.\n *\n * C(i,j,...z) = f(Aij..z, b)\n *\n * @param {Matrix} a The DenseMatrix instance (A)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij..z,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Aij..z)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97659042\n */\n return function algorithm14 (a, b, callback, inverse) {\n // a arrays\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // populate cdata, iterate through dimensions\n const cdata = asize.length > 0 ? _iterate(cf, 0, asize, asize[0], adata, b, inverse) : []\n\n // c matrix\n return a.createDenseMatrix({\n data: cdata,\n size: clone(asize),\n datatype: dt\n })\n }\n\n // recursive function\n function _iterate (f, level, s, n, av, bv, inverse) {\n // initialize array for this level\n const cv = []\n // check we reach the last level\n if (level === s.length - 1) {\n // loop arrays in last level\n for (let i = 0; i < n; i++) {\n // invoke callback and store value\n cv[i] = inverse ? f(bv, av[i]) : f(av[i], bv)\n }\n } else {\n // iterate current level\n for (let j = 0; j < n; j++) {\n // iterate next level\n cv[j] = _iterate(f, level + 1, s, s[level + 1], av[j], bv, inverse)\n }\n }\n return cv\n }\n})\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { ceilNumber } from '../../plain/number/index.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'ceil'\nconst dependencies = ['typed', 'config', 'round', 'matrix', 'equalScalar']\n\nexport const createCeil = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, round, matrix, equalScalar }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards plus infinity\n * If `x` is complex, both real and imaginary part are rounded towards plus infinity.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.ceil(x)\n * math.ceil(x, n)\n *\n * Examples:\n *\n * math.ceil(3.2) // returns number 4\n * math.ceil(3.8) // returns number 4\n * math.ceil(-4.2) // returns number -4\n * math.ceil(-4.7) // returns number -4\n *\n * math.ceil(3.212, 2) // returns number 3.22\n * math.ceil(3.288, 2) // returns number 3.29\n * math.ceil(-4.212, 2) // returns number -4.21\n * math.ceil(-4.782, 2) // returns number -4.78\n *\n * const c = math.complex(3.24, -2.71)\n * math.ceil(c) // returns Complex 4 - 2i\n * math.ceil(c, 1) // returns Complex 3.3 - 2.7i\n *\n * math.ceil([3.2, 3.8, -4.7]) // returns Array [4, 4, -4]\n * math.ceil([3.21, 3.82, -4.71], 1) // returns Array [3.3, 3.9, -4.7]\n *\n * See also:\n *\n * floor, fix, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('ceil', {\n number: function (x) {\n if (nearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return ceilNumber(x)\n }\n },\n\n 'number, number': function (x, n) {\n if (nearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n let [number, exponent] = `${x}e`.split('e')\n const result = Math.ceil(Number(`${number}e${Number(exponent) + n}`));\n [number, exponent] = `${result}e`.split('e')\n return Number(`${number}e${Number(exponent) - n}`)\n }\n },\n\n Complex: function (x) {\n return x.ceil()\n },\n\n 'Complex, number': function (x, n) {\n return x.ceil(n)\n },\n\n BigNumber: function (x) {\n if (bigNearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return x.ceil()\n }\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (bigNearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n return x.toDecimalPlaces(n.toNumber(), Decimal.ROUND_CEIL)\n }\n },\n\n Fraction: function (x) {\n return x.ceil()\n },\n\n 'Fraction, number': function (x, n) {\n return x.ceil(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number': function (x, n) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cubeNumber } from '../../plain/number/index.js'\n\nconst name = 'cube'\nconst dependencies = ['typed']\n\nexport const createCube = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the cube of a value, `x * x * x`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cube(x)\n *\n * Examples:\n *\n * math.cube(2) // returns number 8\n * math.pow(2, 3) // returns number 8\n * math.cube(4) // returns number 64\n * 4 * 4 * 4 // returns number 64\n *\n * math.cube([1, 2, 3, 4]) // returns Array [1, 8, 27, 64]\n *\n * See also:\n *\n * multiply, square, pow, cbrt\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x Number for which to calculate the cube\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} Cube of x\n */\n return typed(name, {\n number: cubeNumber,\n\n Complex: function (x) {\n return x.mul(x).mul(x) // Is faster than pow(x, 3)\n },\n\n BigNumber: function (x) {\n return x.times(x).times(x)\n },\n\n Fraction: function (x) {\n return x.pow(3) // Is faster than mul()mul()mul()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since cube(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.pow(3)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { expNumber } from '../../plain/number/index.js'\n\nconst name = 'exp'\nconst dependencies = ['typed']\n\nexport const createExp = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the exponent of a value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.exp(x)\n *\n * Examples:\n *\n * math.exp(2) // returns number 7.3890560989306495\n * math.pow(math.e, 2) // returns number 7.3890560989306495\n * math.log(math.exp(2)) // returns number 2\n *\n * math.exp([1, 2, 3])\n * // returns Array [\n * // 2.718281828459045,\n * // 7.3890560989306495,\n * // 20.085536923187668\n * // ]\n *\n * See also:\n *\n * expm1, log, pow\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x A number or matrix to exponentiate\n * @return {number | BigNumber | Complex | Array | Matrix} Exponent of `x`\n */\n return typed(name, {\n number: expNumber,\n\n Complex: function (x) {\n return x.exp()\n },\n\n BigNumber: function (x) {\n return x.exp()\n },\n\n 'Array | Matrix': function (x) {\n // TODO: exp(sparse) should return a dense matrix since exp(0)==1\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { expm1Number } from '../../plain/number/index.js'\n\nconst name = 'expm1'\nconst dependencies = ['typed', 'Complex']\n\nexport const createExpm1 = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex }) => {\n /**\n * Calculate the value of subtracting 1 from the exponential value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.expm1(x)\n *\n * Examples:\n *\n * math.expm1(2) // returns number 6.38905609893065\n * math.pow(math.e, 2) - 1 // returns number 6.3890560989306495\n * math.log(math.expm1(2) + 1) // returns number 2\n *\n * math.expm1([1, 2, 3])\n * // returns Array [\n * // 1.718281828459045,\n * // 6.3890560989306495,\n * // 19.085536923187668\n * // ]\n *\n * See also:\n *\n * exp, log, pow\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x A number or matrix to apply expm1\n * @return {number | BigNumber | Complex | Array | Matrix} Exponent of `x`\n */\n return typed(name, {\n number: expm1Number,\n\n Complex: function (x) {\n const r = Math.exp(x.re)\n return new Complex(\n r * Math.cos(x.im) - 1,\n r * Math.sin(x.im)\n )\n },\n\n BigNumber: function (x) {\n return x.exp().minus(1)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'fix'\nconst dependencies = ['typed', 'Complex', 'matrix', 'ceil', 'floor']\n\nexport const createFix = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex, matrix, ceil, floor }) => {\n const algorithm14 = createAlgorithm14({ typed })\n /**\n * Round a value towards zero.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.fix(x)\n *\n * Examples:\n *\n * math.fix(3.2) // returns number 3\n * math.fix(3.8) // returns number 3\n * math.fix(-4.2) // returns number -4\n * math.fix(-4.7) // returns number -4\n *\n * math.fix(3.12, 1) // returns number 3.1\n * math.fix(3.18, 1) // returns number 3.1\n * math.fix(-4.12, 1) // returns number -4.1\n * math.fix(-4.17, 1) // returns number -4.1\n *\n * const c = math.complex(3.22, -2.78)\n * math.fix(c) // returns Complex 3 - 2i\n * math.fix(c, 1) // returns Complex 3.2 - 2.7i\n *\n * math.fix([3.2, 3.8, -4.7]) // returns Array [3, 3, -4]\n * math.fix([3.2, 3.8, -4.7], 1) // returns Array [3.2, 3.8, -4.7]\n *\n * See also:\n *\n * ceil, floor, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('fix', {\n number: function (x) {\n return (x > 0) ? floor(x) : ceil(x)\n },\n\n 'number, number | BigNumber': function (x, n) {\n return (x > 0) ? floor(x, n) : ceil(x, n)\n },\n\n Complex: function (x) {\n return new Complex(\n (x.re > 0) ? Math.floor(x.re) : Math.ceil(x.re),\n (x.im > 0) ? Math.floor(x.im) : Math.ceil(x.im)\n )\n },\n\n 'Complex, number | BigNumber': function (x, n) {\n return new Complex(\n (x.re > 0) ? floor(x.re, n) : ceil(x.re, n),\n (x.im > 0) ? floor(x.im, n) : ceil(x.im, n)\n )\n },\n\n BigNumber: function (x) {\n return x.isNegative() ? ceil(x) : floor(x)\n },\n\n 'BigNumber, number | BigNumber': function (x, n) {\n return x.isNegative() ? ceil(x, n) : floor(x, n)\n },\n\n Fraction: function (x) {\n return x.s < 0 ? x.ceil() : x.floor()\n },\n\n 'Fraction, number | BigNumber': function (x, n) {\n return x.s < 0 ? x.ceil(n) : x.floor(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since fix(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number | BigNumber': function (x, n) {\n // deep map collection, skip zeros since fix(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'floor'\nconst dependencies = ['typed', 'config', 'round', 'matrix', 'equalScalar']\n\nexport const createFloor = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, round, matrix, equalScalar }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards minus infinity.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.floor(x)\n * math.floor(x, n)\n *\n * Examples:\n *\n * math.floor(3.2) // returns number 3\n * math.floor(3.8) // returns number 3\n * math.floor(-4.2) // returns number -5\n * math.floor(-4.7) // returns number -5\n *\n * math.floor(3.212, 2) // returns number 3.21\n * math.floor(3.288, 2) // returns number 3.28\n * math.floor(-4.212, 2) // returns number -4.22\n * math.floor(-4.782, 2) // returns number -4.79\n *\n * const c = math.complex(3.24, -2.71)\n * math.floor(c) // returns Complex 3 - 3i\n * math.floor(c, 1) // returns Complex 3.2 - 2.8i\n *\n * math.floor([3.2, 3.8, -4.7]) // returns Array [3, 3, -5]\n * math.floor([3.21, 3.82, -4.71], 1) // returns Array [3.2, 3.8, -4.8]\n *\n * See also:\n *\n * ceil, fix, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('floor', {\n number: function (x) {\n if (nearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return Math.floor(x)\n }\n },\n\n 'number, number': function (x, n) {\n if (nearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n let [number, exponent] = `${x}e`.split('e')\n const result = Math.floor(Number(`${number}e${Number(exponent) + n}`));\n [number, exponent] = `${result}e`.split('e')\n return Number(`${number}e${Number(exponent) - n}`)\n }\n },\n\n Complex: function (x) {\n return x.floor()\n },\n\n 'Complex, number': function (x, n) {\n return x.floor(n)\n },\n\n BigNumber: function (x) {\n if (bigNearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return x.floor()\n }\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (bigNearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n return x.toDecimalPlaces(n.toNumber(), Decimal.ROUND_FLOOR)\n }\n },\n\n Fraction: function (x) {\n return x.floor()\n },\n\n 'Fraction, number': function (x, n) {\n return x.floor(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since floor(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number': function (x, n) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm01'\nconst dependencies = ['typed']\n\nexport const createAlgorithm01 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over SparseMatrix nonzero items and invokes the callback function f(Dij, Sij).\n * Callback function invoked NNZ times (number of nonzero items in SparseMatrix).\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ Dij ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (S)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm1 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // process data types\n const dt = typeof adt === 'string' && adt === bdt ? adt : undefined\n // callback function\n const cf = dt ? typed.find(callback, [dt, dt]) : callback\n\n // vars\n let i, j\n\n // result (DenseMatrix)\n const cdata = []\n // initialize c\n for (i = 0; i < rows; i++) { cdata[i] = [] }\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns in b\n for (j = 0; j < columns; j++) {\n // column mark\n const mark = j + 1\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // update workspace\n x[i] = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n // mark i as updated\n w[i] = mark\n }\n // loop rows\n for (i = 0; i < rows; i++) {\n // check row is in workspace\n if (w[i] === mark) {\n // c[i][j] was already calculated\n cdata[i][j] = x[i]\n } else {\n // item does not exist in S\n cdata[i][j] = adata[i][j]\n }\n }\n }\n\n // return dense matrix\n return denseMatrix.createDenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm04'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm04 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤ A(i,j) ; A(i,j) !== 0\n * └ B(i,j) ; B(i,j) !== 0\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm04 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspace\n const xa = avalues && bvalues ? [] : undefined\n const xb = avalues && bvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // vars\n let i, j, k, k0, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop A(:,j)\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // update c\n cindex.push(i)\n // update workspace\n wa[i] = mark\n // check we need to process values\n if (xa) { xa[i] = avalues[k] }\n }\n // loop B(:,j)\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // check row exists in A\n if (wa[i] === mark) {\n // update record in xa @ i\n if (xa) {\n // invoke callback\n const v = cf(xa[i], bvalues[k])\n // check for zero\n if (!eq(v, zero)) {\n // update workspace\n xa[i] = v\n } else {\n // remove mark (index will be removed later)\n wa[i] = null\n }\n }\n } else {\n // update c\n cindex.push(i)\n // update workspace\n wb[i] = mark\n // check we need to process values\n if (xb) { xb[i] = bvalues[k] }\n }\n }\n // check we need to process values (non pattern matrix)\n if (xa && xb) {\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // check workspace has value @ i\n if (wa[i] === mark) {\n // push value (Aij != 0 || (Aij != 0 && Bij != 0))\n cvalues[k] = xa[i]\n // increment pointer\n k++\n } else if (wb[i] === mark) {\n // push value (bij != 0)\n cvalues[k] = xb[i]\n // increment pointer\n k++\n } else {\n // remove index @ k\n cindex.splice(k, 1)\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm10'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm10 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked NZ times (number of nonzero items in S).\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ b ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm10 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cdata = []\n\n // workspaces\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const r = aindex[k]\n // update workspace\n x[r] = avalues[k]\n w[r] = mark\n }\n // loop rows\n for (let i = 0; i < rows; i++) {\n // initialize C on first column\n if (j === 0) {\n // create row array\n cdata[i] = []\n }\n // check sparse matrix has a value @ i,j\n if (w[i] === mark) {\n // invoke callback, update C\n cdata[i][j] = inverse ? cf(b, x[i]) : cf(x[i], b)\n } else {\n // dense matrix value @ i, j\n cdata[i][j] = b\n }\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm13'\nconst dependencies = ['typed']\n\nexport const createAlgorithm13 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over DenseMatrix items and invokes the callback function f(Aij..z, Bij..z).\n * Callback function invoked MxN times.\n *\n * C(i,j,...z) = f(Aij..z, Bij..z)\n *\n * @param {Matrix} a The DenseMatrix instance (A)\n * @param {Matrix} b The DenseMatrix instance (B)\n * @param {Function} callback The f(Aij..z,Bij..z) operation to invoke\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97658658\n */\n return function algorithm13 (a, b, callback) {\n // a arrays\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b arrays\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // c arrays\n const csize = []\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // validate each one of the dimension sizes\n for (let s = 0; s < asize.length; s++) {\n // must match\n if (asize[s] !== bsize[s]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n // update dimension in c\n csize[s] = asize[s]\n }\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // populate cdata, iterate through dimensions\n const cdata = csize.length > 0 ? _iterate(cf, 0, csize, csize[0], adata, bdata) : []\n\n // c matrix\n return a.createDenseMatrix({\n data: cdata,\n size: csize,\n datatype: dt\n })\n }\n\n // recursive function\n function _iterate (f, level, s, n, av, bv) {\n // initialize array for this level\n const cv = []\n // check we reach the last level\n if (level === s.length - 1) {\n // loop arrays in last level\n for (let i = 0; i < n; i++) {\n // invoke callback and store value\n cv[i] = f(av[i], bv[i])\n }\n } else {\n // iterate current level\n for (let j = 0; j < n; j++) {\n // iterate next level\n cv[j] = _iterate(f, level + 1, s, s[level + 1], av[j], bv[j])\n }\n }\n return cv\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { gcdNumber } from '../../plain/number/index.js'\n\nconst name = 'gcd'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createGcd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the greatest common divisor for two or more values or arrays.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.gcd(a, b)\n * math.gcd(a, b, c, ...)\n *\n * Examples:\n *\n * math.gcd(8, 12) // returns 4\n * math.gcd(-4, 6) // returns 2\n * math.gcd(25, 15, -10) // returns 5\n *\n * math.gcd([8, -4], [12, 6]) // returns [4, 2]\n *\n * See also:\n *\n * lcm, xgcd\n *\n * @param {... number | BigNumber | Fraction | Array | Matrix} args Two or more integer numbers\n * @return {number | BigNumber | Fraction | Array | Matrix} The greatest common divisor\n */\n return typed(name, {\n\n 'number, number': gcdNumber,\n\n 'BigNumber, BigNumber': _gcdBigNumber,\n\n 'Fraction, Fraction': function (x, y) {\n return x.gcd(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm10(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n },\n\n // TODO: need a smarter notation here\n 'Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber': function (a, b, args) {\n let res = this(a, b)\n for (let i = 0; i < args.length; i++) {\n res = this(res, args[i])\n }\n return res\n }\n })\n\n /**\n * Calculate gcd for BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @returns {BigNumber} Returns greatest common denominator of a and b\n * @private\n */\n function _gcdBigNumber (a, b) {\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function gcd must be integer numbers')\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n const zero = new BigNumber(0)\n while (!b.isZero()) {\n const r = a.mod(b)\n a = b\n b = r\n }\n return a.lt(zero) ? a.neg() : a\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm02'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm02 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix nonzero items and invokes the callback function f(Dij, Sij).\n * Callback function invoked NNZ times (number of nonzero items in SparseMatrix).\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (S)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm02 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result (SparseMatrix)\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // loop columns in b\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = bindex[k]\n // update C(i,j)\n const cij = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n // check for nonzero\n if (!eq(cij, zero)) {\n // push i & v\n cindex.push(i)\n cvalues.push(cij)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return sparseMatrix.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\nimport { scatter } from '../../../utils/collection.js'\n\nconst name = 'algorithm06'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm06 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked (Anz U Bnz) times, where Anz and Bnz are the nonzero elements in both matrices.\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm06 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const x = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const w = []\n // marks indicating value in a given row has been updated\n const u = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // scatter the values of A(:,j) into workspace\n scatter(a, j, w, x, u, mark, cindex, cf)\n // scatter the values of B(:,j) into workspace\n scatter(b, j, w, x, u, mark, cindex, cf)\n // check we need to process values (non pattern matrix)\n if (x) {\n // initialize first index in j\n let k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n const i = cindex[k]\n // check function was invoked on current row (Aij !=0 && Bij != 0)\n if (u[i] === mark) {\n // value @ i\n const v = x[i]\n // check for zero value\n if (!eq(v, zero)) {\n // push value\n cvalues.push(v)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n } else {\n // initialize first index in j\n let p = cptr[j]\n // loop index in j\n while (p < cindex.length) {\n // row\n const r = cindex[p]\n // check function was invoked on current row (Aij !=0 && Bij != 0)\n if (u[r] !== mark) {\n // remove value @ i, do not increment pointer\n cindex.splice(p, 1)\n } else {\n // increment pointer\n p++\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { lcmNumber } from '../../plain/number/index.js'\n\nconst name = 'lcm'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar'\n]\n\nexport const createLcm = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the least common multiple for two or more values or arrays.\n *\n * lcm is defined as:\n *\n * lcm(a, b) = abs(a * b) / gcd(a, b)\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.lcm(a, b)\n * math.lcm(a, b, c, ...)\n *\n * Examples:\n *\n * math.lcm(4, 6) // returns 12\n * math.lcm(6, 21) // returns 42\n * math.lcm(6, 21, 5) // returns 210\n *\n * math.lcm([4, 6], [6, 21]) // returns [12, 42]\n *\n * See also:\n *\n * gcd, xgcd\n *\n * @param {... number | BigNumber | Array | Matrix} args Two or more integer numbers\n * @return {number | BigNumber | Array | Matrix} The least common multiple\n */\n return typed(name, {\n 'number, number': lcmNumber,\n\n 'BigNumber, BigNumber': _lcmBigNumber,\n\n 'Fraction, Fraction': function (x, y) {\n return x.lcm(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n return algorithm11(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n },\n\n // TODO: need a smarter notation here\n 'Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber': function (a, b, args) {\n let res = this(a, b)\n for (let i = 0; i < args.length; i++) {\n res = this(res, args[i])\n }\n return res\n }\n })\n\n /**\n * Calculate lcm for two BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @returns {BigNumber} Returns the least common multiple of a and b\n * @private\n */\n function _lcmBigNumber (a, b) {\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function lcm must be integer numbers')\n }\n\n if (a.isZero()) {\n return a\n }\n if (b.isZero()) {\n return b\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n // evaluate lcm here inline to reduce overhead\n const prod = a.times(b)\n while (!b.isZero()) {\n const t = b\n b = a.mod(t)\n a = t\n }\n return prod.div(a).abs()\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log10Number } from '../../plain/number/index.js'\n\nconst name = 'log10'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createLog10 = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the 10-base logarithm of a value. This is the same as calculating `log(x, 10)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log10(x)\n *\n * Examples:\n *\n * math.log10(0.00001) // returns -5\n * math.log10(10000) // returns 4\n * math.log(10000) / math.log(10) // returns 4\n * math.pow(10, 4) // returns 10000\n *\n * See also:\n *\n * exp, log, log1p, log2\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the 10-base logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return log10Number(x)\n } else {\n // negative value -> complex value computation\n return new Complex(x, 0).log().div(Math.LN10)\n }\n },\n\n Complex: function (x) {\n return new Complex(x).log().div(Math.LN10)\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.log()\n } else {\n // downgrade to number, return Complex valued result\n return new Complex(x.toNumber(), 0).log().div(Math.LN10)\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log2Number } from '../../plain/number/index.js'\n\nconst name = 'log2'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createLog2 = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log2(x)\n *\n * Examples:\n *\n * math.log2(0.03125) // returns -5\n * math.log2(16) // returns 4\n * math.log2(16) / math.log2(2) // returns 4\n * math.pow(2, 4) // returns 16\n *\n * See also:\n *\n * exp, log, log1p, log10\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the 2-base logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return log2Number(x)\n } else {\n // negative value -> complex value computation\n return _log2Complex(new Complex(x, 0))\n }\n },\n\n Complex: _log2Complex,\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.log(2)\n } else {\n // downgrade to number, return Complex valued result\n return _log2Complex(new Complex(x.toNumber(), 0))\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n\n /**\n * Calculate log2 for a complex value\n * @param {Complex} x\n * @returns {Complex}\n * @private\n */\n function _log2Complex (x) {\n const newX = Math.sqrt(x.re * x.re + x.im * x.im)\n return new Complex(\n (Math.log2) ? Math.log2(newX) : Math.log(newX) / Math.LN2,\n Math.atan2(x.im, x.re) / Math.LN2\n )\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm03'\nconst dependencies = ['typed']\n\nexport const createAlgorithm03 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over SparseMatrix items and invokes the callback function f(Dij, Sij).\n * Callback function invoked M*N times.\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ f(Dij, 0) ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (C)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm03 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result (DenseMatrix)\n const cdata = []\n\n // initialize dense matrix\n for (let z = 0; z < rows; z++) {\n // initialize row\n cdata[z] = []\n }\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns in b\n for (let j = 0; j < columns; j++) {\n // column mark\n const mark = j + 1\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = bindex[k]\n // update workspace\n x[i] = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n w[i] = mark\n }\n // process workspace\n for (let y = 0; y < rows; y++) {\n // check we have a calculated value for current row\n if (w[y] === mark) {\n // use calculated value\n cdata[y][j] = x[y]\n } else {\n // calculate value\n cdata[y][j] = inverse ? cf(zero, adata[y][j]) : cf(adata[y][j], zero)\n }\n }\n }\n\n // return dense matrix\n return denseMatrix.createDenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm05'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm05 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 || B(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm05 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const xa = cvalues ? [] : undefined\n const xb = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // vars\n let i, j, k, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop values A(:,j)\n for (k = aptr[j], k1 = aptr[j + 1]; k < k1; k++) {\n // row\n i = aindex[k]\n // push index\n cindex.push(i)\n // update workspace\n wa[i] = mark\n // check we need to process values\n if (xa) { xa[i] = avalues[k] }\n }\n // loop values B(:,j)\n for (k = bptr[j], k1 = bptr[j + 1]; k < k1; k++) {\n // row\n i = bindex[k]\n // check row existed in A\n if (wa[i] !== mark) {\n // push index\n cindex.push(i)\n }\n // update workspace\n wb[i] = mark\n // check we need to process values\n if (xb) { xb[i] = bvalues[k] }\n }\n // check we need to process values (non pattern matrix)\n if (cvalues) {\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // marks\n const wai = wa[i]\n const wbi = wb[i]\n // check Aij or Bij are nonzero\n if (wai === mark || wbi === mark) {\n // matrix values @ i,j\n const va = wai === mark ? xa[i] : zero\n const vb = wbi === mark ? xb[i] : zero\n // Cij\n const vc = cf(va, vb)\n // check for zero\n if (!eq(vc, zero)) {\n // push value\n cvalues.push(vc)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm12'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm12 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked MxN times.\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ f(0, b) ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm12 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cdata = []\n\n // workspaces\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const r = aindex[k]\n // update workspace\n x[r] = avalues[k]\n w[r] = mark\n }\n // loop rows\n for (let i = 0; i < rows; i++) {\n // initialize C on first column\n if (j === 0) {\n // create row array\n cdata[i] = []\n }\n // check sparse matrix has a value @ i,j\n if (w[i] === mark) {\n // invoke callback, update C\n cdata[i][j] = inverse ? cf(b, x[i]) : cf(x[i], b)\n } else {\n // dense matrix value @ i, j\n cdata[i][j] = inverse ? cf(b, 0) : cf(0, b)\n }\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { modNumber } from '../../plain/number/index.js'\n\nconst name = 'mod'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createMod = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculates the modulus, the remainder of an integer division.\n *\n * For matrices, the function is evaluated element wise.\n *\n * The modulus is defined as:\n *\n * x - y * floor(x / y)\n *\n * See https://en.wikipedia.org/wiki/Modulo_operation.\n *\n * Syntax:\n *\n * math.mod(x, y)\n *\n * Examples:\n *\n * math.mod(8, 3) // returns 2\n * math.mod(11, 2) // returns 1\n *\n * function isOdd(x) {\n * return math.mod(x, 2) != 0\n * }\n *\n * isOdd(2) // returns false\n * isOdd(3) // returns true\n *\n * See also:\n *\n * divide\n *\n * @param {number | BigNumber | Fraction | Array | Matrix} x Dividend\n * @param {number | BigNumber | Fraction | Array | Matrix} y Divisor\n * @return {number | BigNumber | Fraction | Array | Matrix} Returns the remainder of `x` divided by `y`.\n */\n return typed(name, {\n\n 'number, number': modNumber,\n\n 'BigNumber, BigNumber': function (x, y) {\n if (y.isNeg()) {\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n return y.isZero() ? x : x.mod(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n if (y.compare(0) < 0) {\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n // Workaround suggested in Fraction.js library to calculate correct modulo for negative dividend\n return x.compare(0) >= 0 ? x.mod(y) : x.mod(y).add(y).mod(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { multiplyNumber } from '../../plain/number/index.js'\n\nconst name = 'multiplyScalar'\nconst dependencies = ['typed']\n\nexport const createMultiplyScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Multiply two scalar values, `x * y`.\n * This function is meant for internal use: it is used by the public function\n * `multiply`\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x First value to multiply\n * @param {number | BigNumber | Fraction | Complex} y Second value to multiply\n * @return {number | BigNumber | Fraction | Complex | Unit} Multiplication of `x` and `y`\n * @private\n */\n return typed('multiplyScalar', {\n\n 'number, number': multiplyNumber,\n\n 'Complex, Complex': function (x, y) {\n return x.mul(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.times(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.mul(y)\n },\n\n 'number | Fraction | BigNumber | Complex, Unit': function (x, y) {\n const res = y.clone()\n res.value = (res.value === null) ? res._normalize(x) : this(res.value, x)\n return res\n },\n\n 'Unit, number | Fraction | BigNumber | Complex': function (x, y) {\n const res = x.clone()\n res.value = (res.value === null) ? res._normalize(y) : this(res.value, y)\n return res\n },\n\n 'Unit, Unit': function (x, y) {\n return x.multiply(y)\n }\n\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { extend } from '../../utils/object.js'\nimport { arraySize } from '../../utils/array.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'multiply'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'addScalar',\n 'multiplyScalar',\n 'equalScalar',\n 'dot'\n]\n\nexport const createMultiply = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, addScalar, multiplyScalar, equalScalar, dot }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n function _validateMatrixDimensions (size1, size2) {\n // check left operand dimensions\n switch (size1.length) {\n case 1:\n // check size2\n switch (size2.length) {\n case 1:\n // Vector x Vector\n if (size1[0] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Vectors must have the same length')\n }\n break\n case 2:\n // Vector x Matrix\n if (size1[0] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Vector length (' + size1[0] + ') must match Matrix rows (' + size2[0] + ')')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)')\n }\n break\n case 2:\n // check size2\n switch (size2.length) {\n case 1:\n // Matrix x Vector\n if (size1[1] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Matrix columns (' + size1[1] + ') must match Vector length (' + size2[0] + ')')\n }\n break\n case 2:\n // Matrix x Matrix\n if (size1[1] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Matrix A columns (' + size1[1] + ') must match Matrix B rows (' + size2[0] + ')')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix A has ' + size1.length + ' dimensions)')\n }\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (N)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {number} Scalar value\n */\n function _multiplyVectorVector (a, b, n) {\n // check empty vector\n if (n === 0) { throw new Error('Cannot multiply two empty vectors') }\n return dot(a, b)\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (M)\n * @param {Matrix} b Matrix (MxN)\n *\n * @return {Matrix} Dense Vector (N)\n */\n function _multiplyVectorMatrix (a, b) {\n // process storage\n if (b.storage() !== 'dense') {\n throw new Error('Support for SparseMatrix not implemented')\n }\n return _multiplyVectorDenseMatrix(a, b)\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (M)\n * @param {Matrix} b Dense Matrix (MxN)\n *\n * @return {Matrix} Dense Vector (N)\n */\n function _multiplyVectorDenseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // rows & columns\n const alength = asize[0]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix columns\n for (let j = 0; j < bcolumns; j++) {\n // sum (do not initialize it with zero)\n let sum = mf(adata[0], bdata[0][j])\n // loop vector\n for (let i = 1; i < alength; i++) {\n // multiply & accumulate\n sum = af(sum, mf(adata[i], bdata[i][j]))\n }\n c[j] = sum\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [bcolumns],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Matrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} Dense Vector (M)\n */\n const _multiplyMatrixVector = typed('_multiplyMatrixVector', {\n 'DenseMatrix, any': _multiplyDenseMatrixVector,\n 'SparseMatrix, any': _multiplySparseMatrixVector\n })\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Matrix (MxN)\n * @param {Matrix} b Matrix (NxC)\n *\n * @return {Matrix} Matrix (MxC)\n */\n const _multiplyMatrixMatrix = typed('_multiplyMatrixMatrix', {\n 'DenseMatrix, DenseMatrix': _multiplyDenseMatrixDenseMatrix,\n 'DenseMatrix, SparseMatrix': _multiplyDenseMatrixSparseMatrix,\n 'SparseMatrix, DenseMatrix': _multiplySparseMatrixDenseMatrix,\n 'SparseMatrix, SparseMatrix': _multiplySparseMatrixSparseMatrix\n })\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} Dense Vector (M)\n */\n function _multiplyDenseMatrixVector (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = asize[0]\n const acolumns = asize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix a rows\n for (let i = 0; i < arows; i++) {\n // current row\n const row = adata[i]\n // sum (do not initialize it with zero)\n let sum = mf(row[0], bdata[0])\n // loop matrix a columns\n for (let j = 1; j < acolumns; j++) {\n // multiply & accumulate\n sum = af(sum, mf(row[j], bdata[j]))\n }\n c[i] = sum\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [arows],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b DenseMatrix (NxC)\n *\n * @return {Matrix} DenseMatrix (MxC)\n */\n function _multiplyDenseMatrixDenseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // rows & columns\n const arows = asize[0]\n const acolumns = asize[1]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix a rows\n for (let i = 0; i < arows; i++) {\n // current row\n const row = adata[i]\n // initialize row array\n c[i] = []\n // loop matrix b columns\n for (let j = 0; j < bcolumns; j++) {\n // sum (avoid initializing sum to zero)\n let sum = mf(row[0], bdata[0][j])\n // loop matrix a columns\n for (let x = 1; x < acolumns; x++) {\n // multiply & accumulate\n sum = af(sum, mf(row[x], bdata[x][j]))\n }\n c[i][j] = sum\n }\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [arows, bcolumns],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b SparseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplyDenseMatrixSparseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b sparse\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n // validate b matrix\n if (!bvalues) { throw new Error('Cannot multiply Dense Matrix times Pattern only Matrix') }\n // rows & columns\n const arows = asize[0]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n // c matrix\n const c = b.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // indeces in column jb\n const kb0 = bptr[jb]\n const kb1 = bptr[jb + 1]\n // do not process column jb if no data exists\n if (kb1 > kb0) {\n // last row mark processed\n let last = 0\n // loop a rows\n for (let i = 0; i < arows; i++) {\n // column mark\n const mark = i + 1\n // C[i, jb]\n let cij\n // values in b column j\n for (let kb = kb0; kb < kb1; kb++) {\n // row\n const ib = bindex[kb]\n // check value has been initialized\n if (last !== mark) {\n // first value in column jb\n cij = mf(adata[i][ib], bvalues[kb])\n // update mark\n last = mark\n } else {\n // accumulate value\n cij = af(cij, mf(adata[i][ib], bvalues[kb]))\n }\n }\n // check column has been processed and value != 0\n if (last === mark && !eq(cij, zero)) {\n // push row & value\n cindex.push(i)\n cvalues.push(cij)\n }\n }\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} SparseMatrix (M, 1)\n */\n function _multiplySparseMatrixVector (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // validate a matrix\n if (!avalues) { throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix') }\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = a._size[0]\n const brows = b._size[0]\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // workspace\n const x = []\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n\n // update ptr\n cptr[0] = 0\n // rows in b\n for (let ib = 0; ib < brows; ib++) {\n // b[ib]\n const vbi = bdata[ib]\n // check b[ib] != 0, avoid loops\n if (!eq(vbi, zero)) {\n // A values & index in ib column\n for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // a row\n const ia = aindex[ka]\n // check value exists in current j\n if (!w[ia]) {\n // ia is new entry in j\n w[ia] = true\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(vbi, avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(vbi, avalues[ka]))\n }\n }\n }\n }\n // copy values from x to column jb of c\n for (let p1 = cindex.length, p = 0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n // update ptr\n cptr[1] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, 1],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b DenseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplySparseMatrixDenseMatrix (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // validate a matrix\n if (!avalues) { throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix') }\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = a._size[0]\n const brows = b._size[0]\n const bcolumns = b._size[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n // c matrix\n const c = a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // workspace\n const x = []\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // mark in workspace for current column\n const mark = jb + 1\n // rows in jb\n for (let ib = 0; ib < brows; ib++) {\n // b[ib, jb]\n const vbij = bdata[ib][jb]\n // check b[ib, jb] != 0, avoid loops\n if (!eq(vbij, zero)) {\n // A values & index in ib column\n for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // a row\n const ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(vbij, avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(vbij, avalues[ka]))\n }\n }\n }\n }\n // copy values from x to column jb of c\n for (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b SparseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplySparseMatrixSparseMatrix (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // b sparse\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bdt = b._datatype\n\n // rows & columns\n const arows = a._size[0]\n const bcolumns = b._size[1]\n // flag indicating both matrices (a & b) contain data\n const values = avalues && bvalues\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const cvalues = values ? [] : undefined\n const cindex = []\n const cptr = []\n // c matrix\n const c = a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // workspace\n const x = values ? [] : undefined\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n // variables\n let ka, ka0, ka1, kb, kb0, kb1, ia, ib\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // mark in workspace for current column\n const mark = jb + 1\n // B values & index in j\n for (kb0 = bptr[jb], kb1 = bptr[jb + 1], kb = kb0; kb < kb1; kb++) {\n // b row\n ib = bindex[kb]\n // check we need to process values\n if (values) {\n // loop values in a[:,ib]\n for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // row\n ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(bvalues[kb], avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(bvalues[kb], avalues[ka]))\n }\n }\n } else {\n // loop values in a[:,ib]\n for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // row\n ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n }\n }\n }\n }\n // check we need to process matrix values (pattern matrix)\n if (values) {\n // copy values from x to column jb of c\n for (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * Multiply two or more values, `x * y`.\n * For matrices, the matrix product is calculated.\n *\n * Syntax:\n *\n * math.multiply(x, y)\n * math.multiply(x, y, z, ...)\n *\n * Examples:\n *\n * math.multiply(4, 5.2) // returns number 20.8\n * math.multiply(2, 3, 4) // returns number 24\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(4, 1)\n * math.multiply(a, b) // returns Complex 5 + 14i\n *\n * const c = [[1, 2], [4, 3]]\n * const d = [[1, 2, 3], [3, -4, 7]]\n * math.multiply(c, d) // returns Array [[7, -6, 17], [13, -4, 33]]\n *\n * const e = math.unit('2.1 km')\n * math.multiply(3, e) // returns Unit 6.3 km\n *\n * See also:\n *\n * divide, prod, cross, dot\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to multiply\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to multiply\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`\n */\n return typed(name, extend({\n // we extend the signatures of multiplyScalar with signatures dealing with matrices\n\n 'Array, Array': function (x, y) {\n // check dimensions\n _validateMatrixDimensions(arraySize(x), arraySize(y))\n\n // use dense matrix implementation\n const m = this(matrix(x), matrix(y))\n // return array or scalar\n return isMatrix(m) ? m.valueOf() : m\n },\n\n 'Matrix, Matrix': function (x, y) {\n // dimensions\n const xsize = x.size()\n const ysize = y.size()\n\n // check dimensions\n _validateMatrixDimensions(xsize, ysize)\n\n // process dimensions\n if (xsize.length === 1) {\n // process y dimensions\n if (ysize.length === 1) {\n // Vector * Vector\n return _multiplyVectorVector(x, y, xsize[0])\n }\n // Vector * Matrix\n return _multiplyVectorMatrix(x, y)\n }\n // process y dimensions\n if (ysize.length === 1) {\n // Matrix * Vector\n return _multiplyMatrixVector(x, y)\n }\n // Matrix * Matrix\n return _multiplyMatrixMatrix(x, y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use Matrix * Matrix implementation\n return this(x, matrix(y))\n },\n\n 'Array, Matrix': function (x, y) {\n // use Matrix * Matrix implementation\n return this(matrix(x, y.storage()), y)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, multiplyScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, multiplyScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, multiplyScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, multiplyScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, multiplyScalar, true).valueOf()\n },\n\n 'any, any': multiplyScalar,\n\n 'any, any, ...any': function (x, y, rest) {\n let result = this(x, y)\n\n for (let i = 0; i < rest.length; i++) {\n result = this(result, rest[i])\n }\n\n return result\n }\n }, multiplyScalar.signatures))\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { nthRootNumber } from '../../plain/number/index.js'\n\nconst name = 'nthRoot'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber'\n]\n\nexport const createNthRoot = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the nth root of a value.\n * The principal nth root of a positive real number A, is the positive real\n * solution of the equation\n *\n * x^root = A\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.nthRoot(a)\n * math.nthRoot(a, root)\n *\n * Examples:\n *\n * math.nthRoot(9, 2) // returns 3, as 3^2 == 9\n * math.sqrt(9) // returns 3, as 3^2 == 9\n * math.nthRoot(64, 3) // returns 4, as 4^3 == 64\n *\n * See also:\n *\n * sqrt, pow\n *\n * @param {number | BigNumber | Array | Matrix | Complex} a\n * Value for which to calculate the nth root\n * @param {number | BigNumber} [root=2] The root.\n * @return {number | Complex | Array | Matrix} Returns the nth root of `a`\n */\n const complexErr = ('' +\n 'Complex number not supported in function nthRoot. ' +\n 'Use nthRoots instead.'\n )\n return typed(name, {\n\n number: function (x) {\n return nthRootNumber(x, 2)\n },\n\n 'number, number': nthRootNumber,\n\n BigNumber: function (x) {\n return _bigNthRoot(x, new BigNumber(2))\n },\n Complex: function (x) {\n throw new Error(complexErr)\n },\n 'Complex, number': function (x, y) {\n throw new Error(complexErr)\n },\n 'BigNumber, BigNumber': _bigNthRoot,\n\n 'Array | Matrix': function (x) {\n return this(x, 2)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // sparse + sparse\n return algorithm06(x, y, this)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // dense + sparse\n return algorithm01(x, y, this, false)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // sparse - scalar\n return algorithm11(y, x, this, true)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n\n /**\n * Calculate the nth root of a for BigNumbers, solve x^root == a\n * https://rosettacode.org/wiki/Nth_root#JavaScript\n * @param {BigNumber} a\n * @param {BigNumber} root\n * @private\n */\n function _bigNthRoot (a, root) {\n const precision = BigNumber.precision\n const Big = BigNumber.clone({ precision: precision + 2 })\n const zero = new BigNumber(0)\n\n const one = new Big(1)\n const inv = root.isNegative()\n if (inv) {\n root = root.neg()\n }\n\n if (root.isZero()) {\n throw new Error('Root must be non-zero')\n }\n if (a.isNegative() && !root.abs().mod(2).equals(1)) {\n throw new Error('Root must be odd when a is negative.')\n }\n\n // edge cases zero and infinity\n if (a.isZero()) {\n return inv ? new Big(Infinity) : 0\n }\n if (!a.isFinite()) {\n return inv ? zero : a\n }\n\n let x = a.abs().pow(one.div(root))\n // If a < 0, we require that root is an odd integer,\n // so (-1) ^ (1/root) = -1\n x = a.isNeg() ? x.neg() : x\n return new BigNumber((inv ? one.div(x) : x).toPrecision(precision))\n }\n})\n\nexport const createNthRootNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, {\n number: nthRootNumber,\n 'number, number': nthRootNumber\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { signNumber } from '../../plain/number/index.js'\n\nconst name = 'sign'\nconst dependencies = ['typed', 'BigNumber', 'Fraction', 'complex']\n\nexport const createSign = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber, complex, Fraction }) => {\n /**\n * Compute the sign of a value. The sign of a value x is:\n *\n * - 1 when x > 0\n * - -1 when x < 0\n * - 0 when x == 0\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sign(x)\n *\n * Examples:\n *\n * math.sign(3.5) // returns 1\n * math.sign(-4.2) // returns -1\n * math.sign(0) // returns 0\n *\n * math.sign([3, 5, -2, 0, 2]) // returns [1, 1, -1, 0, 1]\n *\n * See also:\n *\n * abs\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * The number for which to determine the sign\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}e\n * The sign of `x`\n */\n return typed(name, {\n number: signNumber,\n\n Complex: function (x) {\n return x.im === 0 ? complex(signNumber(x.re)) : x.sign()\n },\n\n BigNumber: function (x) {\n return new BigNumber(x.cmp(0))\n },\n\n Fraction: function (x) {\n return new Fraction(x.s, 1)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sign(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return this(x.value)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'sqrt'\nconst dependencies = ['config', 'typed', 'Complex']\n\nexport const createSqrt = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, Complex }) => {\n /**\n * Calculate the square root of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sqrt(x)\n *\n * Examples:\n *\n * math.sqrt(25) // returns 5\n * math.square(5) // returns 25\n * math.sqrt(-4) // returns Complex 2i\n *\n * See also:\n *\n * square, multiply, cube, cbrt, sqrtm\n *\n * @param {number | BigNumber | Complex | Array | Matrix | Unit} x\n * Value for which to calculate the square root.\n * @return {number | BigNumber | Complex | Array | Matrix | Unit}\n * Returns the square root of `x`\n */\n return typed('sqrt', {\n number: _sqrtNumber,\n\n Complex: function (x) {\n return x.sqrt()\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.sqrt()\n } else {\n // negative value -> downgrade to number to do complex value computation\n return _sqrtNumber(x.toNumber())\n }\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sqrt(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n // Someday will work for complex units when they are implemented\n return x.pow(0.5)\n }\n\n })\n\n /**\n * Calculate sqrt for a number\n * @param {number} x\n * @returns {number | Complex} Returns the square root of x\n * @private\n */\n function _sqrtNumber (x) {\n if (isNaN(x)) {\n return NaN\n } else if (x >= 0 || config.predictable) {\n return Math.sqrt(x)\n } else {\n return new Complex(x, 0).sqrt()\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { squareNumber } from '../../plain/number/index.js'\n\nconst name = 'square'\nconst dependencies = ['typed']\n\nexport const createSquare = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the square of a value, `x * x`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.square(x)\n *\n * Examples:\n *\n * math.square(2) // returns number 4\n * math.square(3) // returns number 9\n * math.pow(3, 2) // returns number 9\n * math.multiply(3, 3) // returns number 9\n *\n * math.square([1, 2, 3, 4]) // returns Array [1, 4, 9, 16]\n *\n * See also:\n *\n * multiply, cube, sqrt, pow\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * Number for which to calculate the square\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}\n * Squared value\n */\n return typed(name, {\n number: squareNumber,\n\n Complex: function (x) {\n return x.mul(x)\n },\n\n BigNumber: function (x) {\n return x.times(x)\n },\n\n Fraction: function (x) {\n return x.mul(x)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since square(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.pow(2)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'subtract'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'addScalar',\n 'unaryMinus',\n 'DenseMatrix'\n]\n\nexport const createSubtract = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, addScalar, unaryMinus, DenseMatrix }) => {\n // TODO: split function subtract in two: subtract and subtractScalar\n\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Subtract two values, `x - y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.subtract(x, y)\n *\n * Examples:\n *\n * math.subtract(5.3, 2) // returns number 3.3\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(4, 1)\n * math.subtract(a, b) // returns Complex -2 + 2i\n *\n * math.subtract([5, 7, 4], 4) // returns Array [1, 3, 0]\n *\n * const c = math.unit('2.1 km')\n * const d = math.unit('500m')\n * math.subtract(c, d) // returns Unit 1.6 km\n *\n * See also:\n *\n * add\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x\n * Initial value\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y\n * Value to subtract from `x`\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Subtraction of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': function (x, y) {\n return x - y\n },\n\n 'Complex, Complex': function (x, y) {\n return x.sub(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.minus(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.sub(y)\n },\n\n 'Unit, Unit': function (x, y) {\n if (x.value === null) {\n throw new Error('Parameter x contains a unit with undefined value')\n }\n\n if (y.value === null) {\n throw new Error('Parameter y contains a unit with undefined value')\n }\n\n if (!x.equalBase(y)) {\n throw new Error('Units do not match')\n }\n\n const res = x.clone()\n res.value = this(res.value, y.value)\n res.fixPrefix = false\n\n return res\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, unaryMinus(y), addScalar)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\n/**\n * Check whether matrix x and y have the same number of dimensions.\n * Throws a DimensionError when dimensions are not equal\n * @param {Matrix} x\n * @param {Matrix} y\n */\nfunction checkEqualDimensions (x, y) {\n const xsize = x.size()\n const ysize = y.size()\n\n if (xsize.length !== ysize.length) {\n throw new DimensionError(xsize.length, ysize.length)\n }\n}\n","import { factory } from '../../utils/factory.js'\nimport { xgcdNumber } from '../../plain/number/index.js'\n\nconst name = 'xgcd'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createXgcd = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Calculate the extended greatest common divisor for two values.\n * See https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.\n *\n * Syntax:\n *\n * math.xgcd(a, b)\n *\n * Examples:\n *\n * math.xgcd(8, 12) // returns [4, -1, 1]\n * math.gcd(8, 12) // returns 4\n * math.xgcd(36163, 21199) // returns [1247, -7, 12]\n *\n * See also:\n *\n * gcd, lcm\n *\n * @param {number | BigNumber} a An integer number\n * @param {number | BigNumber} b An integer number\n * @return {Array} Returns an array containing 3 integers `[div, m, n]`\n * where `div = gcd(a, b)` and `a*m + b*n = div`\n */\n return typed(name, {\n 'number, number': function (a, b) {\n const res = xgcdNumber(a, b)\n\n return (config.matrix === 'Array')\n ? res\n : matrix(res)\n },\n 'BigNumber, BigNumber': _xgcdBigNumber\n // TODO: implement support for Fraction\n })\n\n /**\n * Calculate xgcd for two BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @return {BigNumber[]} result\n * @private\n */\n function _xgcdBigNumber (a, b) {\n // source: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm\n let // used to swap two variables\n t\n\n let // quotient\n q\n\n let // remainder\n r\n\n const zero = new BigNumber(0)\n const one = new BigNumber(1)\n let x = zero\n let lastx = one\n let y = one\n let lasty = zero\n\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function xgcd must be integer numbers')\n }\n\n while (!b.isZero()) {\n q = a.div(b).floor()\n r = a.mod(b)\n\n t = x\n x = lastx.minus(q.times(x))\n lastx = t\n\n t = y\n y = lasty.minus(q.times(y))\n lasty = t\n\n a = b\n b = r\n }\n\n let res\n if (a.lt(zero)) {\n res = [a.neg(), lastx.neg(), lasty.neg()]\n } else {\n res = [a, !a.isZero() ? lastx : 0, lasty]\n }\n return (config.matrix === 'Array') ? res : matrix(res)\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm09'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm09 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and invokes the callback function f(Aij, Bij).\n * Callback function invoked NZA times, number of nonzero elements in A.\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm09 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const x = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const w = []\n\n // vars\n let i, j, k, k0, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // column mark\n const mark = j + 1\n // check we need to process values\n if (x) {\n // loop B(:,j)\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // update workspace\n w[i] = mark\n x[i] = bvalues[k]\n }\n }\n // loop A(:,j)\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check we need to process values\n if (x) {\n // b value @ i,j\n const vb = w[i] === mark ? x[i] : zero\n // invoke f\n const vc = cf(avalues[k], vb)\n // check zero value\n if (!eq(vc, zero)) {\n // push index\n cindex.push(i)\n // push value\n cvalues.push(vc)\n }\n } else {\n // push index\n cindex.push(i)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm09 } from '../../type/matrix/utils/algorithm09.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotMultiply'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'multiplyScalar'\n]\n\nexport const createDotMultiply = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, multiplyScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm09 = createAlgorithm09({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Multiply two matrices element wise. The function accepts both matrices and\n * scalar values.\n *\n * Syntax:\n *\n * math.dotMultiply(x, y)\n *\n * Examples:\n *\n * math.dotMultiply(2, 4) // returns 8\n *\n * a = [[9, 5], [6, 1]]\n * b = [[3, 2], [5, 2]]\n *\n * math.dotMultiply(a, b) // returns [[27, 10], [30, 2]]\n * math.multiply(a, b) // returns [[52, 28], [23, 14]]\n *\n * See also:\n *\n * multiply, divide, dotDivide\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Left hand value\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Right hand value\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`\n */\n return typed(name, {\n\n 'any, any': multiplyScalar,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm09(x, y, multiplyScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, multiplyScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, multiplyScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, multiplyScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, multiplyScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, multiplyScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, multiplyScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, multiplyScalar, true).valueOf()\n }\n })\n})\n","/**\n * Bitwise and for Bignumbers\n *\n * Special Cases:\n * N & n = N\n * n & 0 = 0\n * n & -1 = n\n * n & n = n\n * I & I = I\n * -I & -I = -I\n * I & -I = 0\n * I & n = n\n * I & -n = I\n * -I & n = 0\n * -I & -n = -I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` & `y`, is fully precise\n * @private\n */\nexport function bitAndBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitAnd')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n\n if (x.isZero() || y.eq(-1) || x.eq(y)) {\n return x\n }\n if (y.isZero() || x.eq(-1)) {\n return y\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if (!x.isFinite() && !y.isFinite()) {\n if (x.isNegative() === y.isNegative()) {\n return x\n }\n return new BigNumber(0)\n }\n if (!x.isFinite()) {\n if (y.isNegative()) {\n return x\n }\n if (x.isNegative()) {\n return new BigNumber(0)\n }\n return y\n }\n if (!y.isFinite()) {\n if (x.isNegative()) {\n return y\n }\n if (y.isNegative()) {\n return new BigNumber(0)\n }\n return x\n }\n }\n return bitwise(x, y, function (a, b) { return a & b })\n}\n\n/**\n * Bitwise not\n * @param {BigNumber} x\n * @return {BigNumber} Result of ~`x`, fully precise\n *\n */\nexport function bitNotBigNumber (x) {\n if (x.isFinite() && !x.isInteger()) {\n throw new Error('Integer expected in function bitNot')\n }\n\n const BigNumber = x.constructor\n const prevPrec = BigNumber.precision\n BigNumber.config({ precision: 1E9 })\n\n const result = x.plus(new BigNumber(1))\n result.s = -result.s || null\n\n BigNumber.config({ precision: prevPrec })\n return result\n}\n\n/**\n * Bitwise OR for BigNumbers\n *\n * Special Cases:\n * N | n = N\n * n | 0 = n\n * n | -1 = -1\n * n | n = n\n * I | I = I\n * -I | -I = -I\n * I | -n = -1\n * I | -I = -1\n * I | n = I\n * -I | n = -I\n * -I | -n = -n\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` | `y`, fully precise\n */\nexport function bitOrBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitOr')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n\n const negOne = new BigNumber(-1)\n if (x.isZero() || y.eq(negOne) || x.eq(y)) {\n return y\n }\n if (y.isZero() || x.eq(negOne)) {\n return x\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if ((!x.isFinite() && !x.isNegative() && y.isNegative()) ||\n (x.isNegative() && !y.isNegative() && !y.isFinite())) {\n return negOne\n }\n if (x.isNegative() && y.isNegative()) {\n return x.isFinite() ? x : y\n }\n return x.isFinite() ? y : x\n }\n\n return bitwise(x, y, function (a, b) { return a | b })\n}\n\n/**\n * Applies bitwise function to numbers\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @param {function (a, b)} func\n * @return {BigNumber}\n */\nexport function bitwise (x, y, func) {\n const BigNumber = x.constructor\n\n let xBits, yBits\n const xSign = +(x.s < 0)\n const ySign = +(y.s < 0)\n if (xSign) {\n xBits = decCoefficientToBinaryString(bitNotBigNumber(x))\n for (let i = 0; i < xBits.length; ++i) {\n xBits[i] ^= 1\n }\n } else {\n xBits = decCoefficientToBinaryString(x)\n }\n if (ySign) {\n yBits = decCoefficientToBinaryString(bitNotBigNumber(y))\n for (let i = 0; i < yBits.length; ++i) {\n yBits[i] ^= 1\n }\n } else {\n yBits = decCoefficientToBinaryString(y)\n }\n\n let minBits, maxBits, minSign\n if (xBits.length <= yBits.length) {\n minBits = xBits\n maxBits = yBits\n minSign = xSign\n } else {\n minBits = yBits\n maxBits = xBits\n minSign = ySign\n }\n\n let shortLen = minBits.length\n let longLen = maxBits.length\n const expFuncVal = func(xSign, ySign) ^ 1\n let outVal = new BigNumber(expFuncVal ^ 1)\n let twoPower = new BigNumber(1)\n const two = new BigNumber(2)\n\n const prevPrec = BigNumber.precision\n BigNumber.config({ precision: 1E9 })\n\n while (shortLen > 0) {\n if (func(minBits[--shortLen], maxBits[--longLen]) === expFuncVal) {\n outVal = outVal.plus(twoPower)\n }\n twoPower = twoPower.times(two)\n }\n while (longLen > 0) {\n if (func(minSign, maxBits[--longLen]) === expFuncVal) {\n outVal = outVal.plus(twoPower)\n }\n twoPower = twoPower.times(two)\n }\n\n BigNumber.config({ precision: prevPrec })\n\n if (expFuncVal === 0) {\n outVal.s = -outVal.s\n }\n return outVal\n}\n\n/* Extracted from decimal.js, and edited to specialize. */\nfunction decCoefficientToBinaryString (x) {\n // Convert to string\n const a = x.d // array with digits\n let r = a[0] + ''\n\n for (let i = 1; i < a.length; ++i) {\n let s = a[i] + ''\n for (let z = 7 - s.length; z--;) {\n s = '0' + s\n }\n\n r += s\n }\n\n let j = r.length\n while (r.charAt(j) === '0') {\n j--\n }\n\n let xe = x.e\n let str = r.slice(0, j + 1 || 1)\n const strL = str.length\n if (xe > 0) {\n if (++xe > strL) {\n // Append zeros.\n xe -= strL\n while (xe--) {\n str += '0'\n }\n } else if (xe < strL) {\n str = str.slice(0, xe) + '.' + str.slice(xe)\n }\n }\n\n // Convert from base 10 (decimal) to base 2\n const arr = [0]\n for (let i = 0; i < str.length;) {\n let arrL = arr.length\n while (arrL--) {\n arr[arrL] *= 10\n }\n\n arr[0] += parseInt(str.charAt(i++)) // convert to int\n for (let j = 0; j < arr.length; ++j) {\n if (arr[j] > 1) {\n if (arr[j + 1] === null || arr[j + 1] === undefined) {\n arr[j + 1] = 0\n }\n\n arr[j + 1] += arr[j] >> 1\n arr[j] &= 1\n }\n }\n }\n\n return arr.reverse()\n}\n\n/**\n * Bitwise XOR for BigNumbers\n *\n * Special Cases:\n * N ^ n = N\n * n ^ 0 = n\n * n ^ n = 0\n * n ^ -1 = ~n\n * I ^ n = I\n * I ^ -n = -I\n * I ^ -I = -1\n * -I ^ n = -I\n * -I ^ -n = I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` ^ `y`, fully precise\n *\n */\nexport function bitXor (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitXor')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n if (x.isZero()) {\n return y\n }\n if (y.isZero()) {\n return x\n }\n\n if (x.eq(y)) {\n return new BigNumber(0)\n }\n\n const negOne = new BigNumber(-1)\n if (x.eq(negOne)) {\n return bitNotBigNumber(y)\n }\n if (y.eq(negOne)) {\n return bitNotBigNumber(x)\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if (!x.isFinite() && !y.isFinite()) {\n return negOne\n }\n return new BigNumber(x.isNegative() === y.isNegative()\n ? Infinity\n : -Infinity)\n }\n return bitwise(x, y, function (a, b) { return a ^ b })\n}\n\n/**\n * Bitwise left shift\n *\n * Special Cases:\n * n << -n = N\n * n << N = N\n * N << n = N\n * n << 0 = n\n * 0 << n = 0\n * I << I = N\n * I << n = I\n * n << I = I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` << `y`\n *\n */\nexport function leftShiftBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function leftShift')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN() || (y.isNegative() && !y.isZero())) {\n return new BigNumber(NaN)\n }\n if (x.isZero() || y.isZero()) {\n return x\n }\n if (!x.isFinite() && !y.isFinite()) {\n return new BigNumber(NaN)\n }\n\n // Math.pow(2, y) is fully precise for y < 55, and fast\n if (y.lt(55)) {\n return x.times(Math.pow(2, y.toNumber()) + '')\n }\n return x.times(new BigNumber(2).pow(y))\n}\n\n/*\n * Special Cases:\n * n >> -n = N\n * n >> N = N\n * N >> n = N\n * I >> I = N\n * n >> 0 = n\n * I >> n = I\n * -I >> n = -I\n * -I >> I = -I\n * n >> I = I\n * -n >> I = -1\n * 0 >> n = 0\n *\n * @param {BigNumber} value\n * @param {BigNumber} value\n * @return {BigNumber} Result of `x` >> `y`\n *\n */\nexport function rightArithShiftBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function rightArithShift')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN() || (y.isNegative() && !y.isZero())) {\n return new BigNumber(NaN)\n }\n if (x.isZero() || y.isZero()) {\n return x\n }\n if (!y.isFinite()) {\n if (x.isNegative()) {\n return new BigNumber(-1)\n }\n if (!x.isFinite()) {\n return new BigNumber(NaN)\n }\n return new BigNumber(0)\n }\n\n // Math.pow(2, y) is fully precise for y < 55, and fast\n if (y.lt(55)) {\n return x.div(Math.pow(2, y.toNumber()) + '').floor()\n }\n return x.div(new BigNumber(2).pow(y)).floor()\n}\n","import { isInteger } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function bitAndNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitAnd')\n }\n\n return x & y\n}\nbitAndNumber.signature = n2\n\nexport function bitNotNumber (x) {\n if (!isInteger(x)) {\n throw new Error('Integer expected in function bitNot')\n }\n\n return ~x\n}\nbitNotNumber.signature = n1\n\nexport function bitOrNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitOr')\n }\n\n return x | y\n}\nbitOrNumber.signature = n2\n\nexport function bitXorNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitXor')\n }\n\n return x ^ y\n}\nbitXorNumber.signature = n2\n\nexport function leftShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function leftShift')\n }\n\n return x << y\n}\nleftShiftNumber.signature = n2\n\nexport function rightArithShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function rightArithShift')\n }\n\n return x >> y\n}\nrightArithShiftNumber.signature = n2\n\nexport function rightLogShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function rightLogShift')\n }\n\n return x >>> y\n}\nrightLogShiftNumber.signature = n2\n","import { bitAndBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitAndNumber } from '../../plain/number/index.js'\n\nconst name = 'bitAnd'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar'\n]\n\nexport const createBitAnd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise AND two values, `x & y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.bitAnd(x, y)\n *\n * Examples:\n *\n * math.bitAnd(53, 131) // returns number 1\n *\n * math.bitAnd([1, 12, 31], 42) // returns Array [0, 8, 10]\n *\n * See also:\n *\n * bitNot, bitOr, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to and\n * @param {number | BigNumber | Array | Matrix} y Second value to and\n * @return {number | BigNumber | Array | Matrix} AND of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitAndNumber,\n\n 'BigNumber, BigNumber': bitAndBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { bitNotBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitNotNumber } from '../../plain/number/index.js'\n\nconst name = 'bitNot'\nconst dependencies = ['typed']\n\nexport const createBitNot = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Bitwise NOT value, `~x`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.bitNot(x)\n *\n * Examples:\n *\n * math.bitNot(1) // returns number -2\n *\n * math.bitNot([2, -3, 4]) // returns Array [-3, 2, 5]\n *\n * See also:\n *\n * bitAnd, bitOr, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to not\n * @return {number | BigNumber | Array | Matrix} NOT of `x`\n */\n return typed(name, {\n number: bitNotNumber,\n\n BigNumber: bitNotBigNumber,\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { bitOrBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { bitOrNumber } from '../../plain/number/index.js'\n\nconst name = 'bitOr'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createBitOr = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise OR two values, `x | y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the lowest print base.\n *\n * Syntax:\n *\n * math.bitOr(x, y)\n *\n * Examples:\n *\n * math.bitOr(1, 2) // returns number 3\n *\n * math.bitOr([1, 2, 3], 4) // returns Array [5, 6, 7]\n *\n * See also:\n *\n * bitAnd, bitNot, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to or\n * @param {number | BigNumber | Array | Matrix} y Second value to or\n * @return {number | BigNumber | Array | Matrix} OR of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitOrNumber,\n\n 'BigNumber, BigNumber': bitOrBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm07'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm07 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B items (zero and nonzero) and invokes the callback function f(Aij, Bij).\n * Callback function invoked MxN times.\n *\n * C(i,j) = f(Aij, Bij)\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm07 (a, b, callback) {\n // sparse matrix arrays\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // vars\n let i, j\n\n // result arrays\n const cdata = []\n // initialize c\n for (i = 0; i < rows; i++) { cdata[i] = [] }\n\n // workspaces\n const xa = []\n const xb = []\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // scatter the values of A(:,j) into workspace\n _scatter(a, j, wa, xa, mark)\n // scatter the values of B(:,j) into workspace\n _scatter(b, j, wb, xb, mark)\n // loop rows\n for (i = 0; i < rows; i++) {\n // matrix values @ i,j\n const va = wa[i] === mark ? xa[i] : zero\n const vb = wb[i] === mark ? xb[i] : zero\n // invoke callback\n cdata[i][j] = cf(va, vb)\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n\n function _scatter (m, j, w, x, mark) {\n // a arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // loop values in column j\n for (let k = ptr[j], k1 = ptr[j + 1]; k < k1; k++) {\n // row\n const i = index[k]\n // update workspace\n w[i] = mark\n x[i] = values[k]\n }\n }\n})\n","import { bitXor as bigBitXor } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitXorNumber } from '../../plain/number/index.js'\n\nconst name = 'bitXor'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createBitXor = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise XOR two values, `x ^ y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.bitXor(x, y)\n *\n * Examples:\n *\n * math.bitXor(1, 2) // returns number 3\n *\n * math.bitXor([2, 3, 4], 4) // returns Array [6, 7, 0]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to xor\n * @param {number | BigNumber | Array | Matrix} y Second value to xor\n * @return {number | BigNumber | Array | Matrix} XOR of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitXorNumber,\n\n 'BigNumber, BigNumber': bigBitXor,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'arg'\nconst dependencies = ['typed']\n\nexport const createArg = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the argument of a complex value.\n * For a complex number `a + bi`, the argument is computed as `atan2(b, a)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.arg(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 2)\n * math.arg(a) / math.pi // returns number 0.25\n *\n * const b = math.complex('2 + 3i')\n * math.arg(b) // returns number 0.982793723247329\n * math.atan2(3, 2) // returns number 0.982793723247329\n *\n * See also:\n *\n * re, im, conj, abs\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The argument of x\n */\n return typed(name, {\n number: function (x) {\n return Math.atan2(0, x)\n },\n\n BigNumber: function (x) {\n return x.constructor.atan2(0, x)\n },\n\n Complex: function (x) {\n return x.arg()\n },\n\n // TODO: implement BigNumber support for function arg\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'conj'\nconst dependencies = ['typed']\n\nexport const createConj = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the complex conjugate of a complex value.\n * If `x = a+bi`, the complex conjugate of `x` is `a - bi`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.conj(x)\n *\n * Examples:\n *\n * math.conj(math.complex('2 + 3i')) // returns Complex 2 - 3i\n * math.conj(math.complex('2 - 3i')) // returns Complex 2 + 3i\n * math.conj(math.complex('-5.2i')) // returns Complex 5.2i\n *\n * See also:\n *\n * re, im, arg, abs\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Complex | Array | Matrix}\n * The complex conjugate of x\n */\n return typed(name, {\n number: function (x) {\n return x\n },\n\n BigNumber: function (x) {\n return x\n },\n\n Complex: function (x) {\n return x.conjugate()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'im'\nconst dependencies = ['typed']\n\nexport const createIm = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Get the imaginary part of a complex number.\n * For a complex number `a + bi`, the function returns `b`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.im(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 3)\n * math.re(a) // returns number 2\n * math.im(a) // returns number 3\n *\n * math.re(math.complex('-5.2i')) // returns number -5.2\n * math.re(math.complex(2.4)) // returns number 0\n *\n * See also:\n *\n * re, conj, abs, arg\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The imaginary part of x\n */\n return typed(name, {\n number: function (x) {\n return 0\n },\n\n BigNumber: function (x) {\n return x.mul(0)\n },\n\n Complex: function (x) {\n return x.im\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 're'\nconst dependencies = ['typed']\n\nexport const createRe = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Get the real part of a complex number.\n * For a complex number `a + bi`, the function returns `a`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.re(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 3)\n * math.re(a) // returns number 2\n * math.im(a) // returns number 3\n *\n * math.re(math.complex('-5.2i')) // returns number 0\n * math.re(math.complex(2.4)) // returns number 2.4\n *\n * See also:\n *\n * im, conj, abs, arg\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The real part of x\n */\n return typed(name, {\n number: function (x) {\n return x\n },\n\n BigNumber: function (x) {\n return x\n },\n\n Complex: function (x) {\n return x.re\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","const n1 = 'number'\nconst n2 = 'number, number'\n\nexport function notNumber (x) {\n return !x\n}\nnotNumber.signature = n1\n\nexport function orNumber (x, y) {\n return !!(x || y)\n}\norNumber.signature = n2\n\nexport function xorNumber (x, y) {\n return !!x !== !!y\n}\nxorNumber.signature = n2\n\nexport function andNumber (x, y) {\n return !!(x && y)\n}\nandNumber.signature = n2\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { notNumber } from '../../plain/number/index.js'\n\nconst name = 'not'\nconst dependencies = ['typed']\n\nexport const createNot = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Logical `not`. Flips boolean value of a given parameter.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.not(x)\n *\n * Examples:\n *\n * math.not(2) // returns false\n * math.not(0) // returns true\n * math.not(true) // returns false\n *\n * a = [2, -7, 0]\n * math.not(a) // returns [false, false, true]\n *\n * See also:\n *\n * and, or, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @return {boolean | Array | Matrix}\n * Returns true when input is a zero or empty value.\n */\n return typed(name, {\n number: notNumber,\n\n Complex: function (x) {\n return x.re === 0 && x.im === 0\n },\n\n BigNumber: function (x) {\n return x.isZero() || x.isNaN()\n },\n\n Unit: function (x) {\n return x.value !== null ? this(x.value) : true\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { factory } from '../../utils/factory.js'\nimport { orNumber } from '../../plain/number/index.js'\n\nconst name = 'or'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createOr = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `or`. Test if at least one value is defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.or(x, y)\n *\n * Examples:\n *\n * math.or(2, 4) // returns true\n *\n * a = [2, 5, 0]\n * b = [0, 22, 0]\n * c = 0\n *\n * math.or(a, b) // returns [true, true, false]\n * math.or(b, c) // returns [false, true, false]\n *\n * See also:\n *\n * and, not, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when one of the inputs is defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': orNumber,\n\n 'Complex, Complex': function (x, y) {\n return (x.re !== 0 || x.im !== 0) || (y.re !== 0 || y.im !== 0)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return (!x.isZero() && !x.isNaN()) || (!y.isZero() && !y.isNaN())\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { factory } from '../../utils/factory.js'\nimport { xorNumber } from '../../plain/number/index.js'\n\nconst name = 'xor'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createXor = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `xor`. Test whether one and only one value is defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.xor(x, y)\n *\n * Examples:\n *\n * math.xor(2, 4) // returns false\n *\n * a = [2, 0, 0]\n * b = [2, 7, 0]\n * c = 0\n *\n * math.xor(a, b) // returns [false, true, false]\n * math.xor(a, c) // returns [true, false, false]\n *\n * See also:\n *\n * and, not, or\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when one and only one input is defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': xorNumber,\n\n 'Complex, Complex': function (x, y) {\n return ((x.re !== 0 || x.im !== 0) !== (y.re !== 0 || y.im !== 0))\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return ((!x.isZero() && !x.isNaN()) !== (!y.isZero() && !y.isNaN()))\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { isBigNumber, isMatrix, isNumber } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { arraySize } from '../../utils/array.js'\nimport { IndexError } from '../../error/IndexError.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'concat'\nconst dependencies = ['typed', 'matrix', 'isInteger']\n\nexport const createConcat = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, isInteger }) => {\n /**\n * Concatenate two or more matrices.\n *\n * Syntax:\n *\n * math.concat(A, B, C, ...)\n * math.concat(A, B, C, ..., dim)\n *\n * Where:\n *\n * - `dim: number` is a zero-based dimension over which to concatenate the matrices.\n * By default the last dimension of the matrices.\n *\n * Examples:\n *\n * const A = [[1, 2], [5, 6]]\n * const B = [[3, 4], [7, 8]]\n *\n * math.concat(A, B) // returns [[1, 2, 3, 4], [5, 6, 7, 8]]\n * math.concat(A, B, 0) // returns [[1, 2], [5, 6], [3, 4], [7, 8]]\n * math.concat('hello', ' ', 'world') // returns 'hello world'\n *\n * See also:\n *\n * size, squeeze, subset, transpose\n *\n * @param {... Array | Matrix} args Two or more matrices\n * @return {Array | Matrix} Concatenated matrix\n */\n return typed(name, {\n // TODO: change signature to '...Array | Matrix, dim?' when supported\n '...Array | Matrix | number | BigNumber': function (args) {\n let i\n const len = args.length\n let dim = -1 // zero-based dimension\n let prevDim\n let asMatrix = false\n const matrices = [] // contains multi dimensional arrays\n\n for (i = 0; i < len; i++) {\n const arg = args[i]\n\n // test whether we need to return a Matrix (if not we return an Array)\n if (isMatrix(arg)) {\n asMatrix = true\n }\n\n if (isNumber(arg) || isBigNumber(arg)) {\n if (i !== len - 1) {\n throw new Error('Dimension must be specified as last argument')\n }\n\n // last argument contains the dimension on which to concatenate\n prevDim = dim\n dim = arg.valueOf() // change BigNumber to number\n\n if (!isInteger(dim)) {\n throw new TypeError('Integer number expected for dimension')\n }\n\n if (dim < 0 || (i > 0 && dim > prevDim)) {\n // TODO: would be more clear when throwing a DimensionError here\n throw new IndexError(dim, prevDim + 1)\n }\n } else {\n // this is a matrix or array\n const m = clone(arg).valueOf()\n const size = arraySize(m)\n matrices[i] = m\n prevDim = dim\n dim = size.length - 1\n\n // verify whether each of the matrices has the same number of dimensions\n if (i > 0 && dim !== prevDim) {\n throw new DimensionError(prevDim + 1, dim + 1)\n }\n }\n }\n\n if (matrices.length === 0) {\n throw new SyntaxError('At least one matrix expected')\n }\n\n let res = matrices.shift()\n while (matrices.length) {\n res = _concat(res, matrices.shift(), dim, 0)\n }\n\n return asMatrix ? matrix(res) : res\n },\n\n '...string': function (args) {\n return args.join('')\n }\n })\n})\n\n/**\n * Recursively concatenate two matrices.\n * The contents of the matrices is not cloned.\n * @param {Array} a Multi dimensional array\n * @param {Array} b Multi dimensional array\n * @param {number} concatDim The dimension on which to concatenate (zero-based)\n * @param {number} dim The current dim (zero-based)\n * @return {Array} c The concatenated matrix\n * @private\n */\nfunction _concat (a, b, concatDim, dim) {\n if (dim < concatDim) {\n // recurse into next dimension\n if (a.length !== b.length) {\n throw new DimensionError(a.length, b.length)\n }\n\n const c = []\n for (let i = 0; i < a.length; i++) {\n c[i] = _concat(a[i], b[i], concatDim, dim + 1)\n }\n return c\n } else {\n // concatenate this dimension\n return a.concat(b)\n }\n}\n","import { factory } from '../../utils/factory.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\n\nconst name = 'column'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\nexport const createColumn = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n /**\n * Return a column from a Matrix.\n *\n * Syntax:\n *\n * math.column(value, index)\n *\n * Example:\n *\n * // get a column\n * const d = [[1, 2], [3, 4]]\n * math.column(d, 1) // returns [[2], [4]]\n *\n * See also:\n *\n * row\n *\n * @param {Array | Matrix } value An array or matrix\n * @param {number} column The index of the column\n * @return {Array | Matrix} The retrieved column\n */\n return typed(name, {\n 'Matrix, number': _column,\n\n 'Array, number': function (value, column) {\n return _column(matrix(clone(value)), column).valueOf()\n }\n })\n\n /**\n * Retrieve a column of a matrix\n * @param {Matrix } value A matrix\n * @param {number} column The index of the column\n * @return {Matrix} The retrieved column\n */\n function _column (value, column) {\n // check dimensions\n if (value.size().length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n\n validateIndex(column, value.size()[1])\n\n const rowRange = range(0, value.size()[0])\n const index = new Index(rowRange, column)\n return value.subset(index)\n }\n})\n","import { arraySize, squeeze } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'cross'\nconst dependencies = ['typed', 'matrix', 'subtract', 'multiply']\n\nexport const createCross = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, multiply }) => {\n /**\n * Calculate the cross product for two vectors in three dimensional space.\n * The cross product of `A = [a1, a2, a3]` and `B = [b1, b2, b3]` is defined\n * as:\n *\n * cross(A, B) = [\n * a2 * b3 - a3 * b2,\n * a3 * b1 - a1 * b3,\n * a1 * b2 - a2 * b1\n * ]\n *\n * If one of the input vectors has a dimension greater than 1, the output\n * vector will be a 1x3 (2-dimensional) matrix.\n *\n * Syntax:\n *\n * math.cross(x, y)\n *\n * Examples:\n *\n * math.cross([1, 1, 0], [0, 1, 1]) // Returns [1, -1, 1]\n * math.cross([3, -3, 1], [4, 9, 2]) // Returns [-15, -2, 39]\n * math.cross([2, 3, 4], [5, 6, 7]) // Returns [-3, 6, -3]\n * math.cross([[1, 2, 3]], [[4], [5], [6]]) // Returns [[-3, 6, -3]]\n *\n * See also:\n *\n * dot, multiply\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {Array | Matrix} Returns the cross product of `x` and `y`\n */\n return typed(name, {\n 'Matrix, Matrix': function (x, y) {\n return matrix(_cross(x.toArray(), y.toArray()))\n },\n\n 'Matrix, Array': function (x, y) {\n return matrix(_cross(x.toArray(), y))\n },\n\n 'Array, Matrix': function (x, y) {\n return matrix(_cross(x, y.toArray()))\n },\n\n 'Array, Array': _cross\n })\n\n /**\n * Calculate the cross product for two arrays\n * @param {Array} x First vector\n * @param {Array} y Second vector\n * @returns {Array} Returns the cross product of x and y\n * @private\n */\n function _cross (x, y) {\n const highestDimension = Math.max(arraySize(x).length, arraySize(y).length)\n\n x = squeeze(x)\n y = squeeze(y)\n\n const xSize = arraySize(x)\n const ySize = arraySize(y)\n\n if (xSize.length !== 1 || ySize.length !== 1 || xSize[0] !== 3 || ySize[0] !== 3) {\n throw new RangeError('Vectors with length 3 expected ' +\n '(Size A = [' + xSize.join(', ') + '], B = [' + ySize.join(', ') + '])')\n }\n\n const product = [\n subtract(multiply(x[1], y[2]), multiply(x[2], y[1])),\n subtract(multiply(x[2], y[0]), multiply(x[0], y[2])),\n subtract(multiply(x[0], y[1]), multiply(x[1], y[0]))\n ]\n\n if (highestDimension > 1) {\n return [product]\n } else {\n return product\n }\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { arraySize } from '../../utils/array.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'diag'\nconst dependencies = ['typed', 'matrix', 'DenseMatrix', 'SparseMatrix']\n\nexport const createDiag = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a diagonal matrix or retrieve the diagonal of a matrix\n *\n * When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.\n * When `x` is a two dimensional matrix, the matrixes `k`th diagonal will be returned as vector.\n * When k is positive, the values are placed on the super diagonal.\n * When k is negative, the values are placed on the sub diagonal.\n *\n * Syntax:\n *\n * math.diag(X)\n * math.diag(X, format)\n * math.diag(X, k)\n * math.diag(X, k, format)\n *\n * Examples:\n *\n * // create a diagonal matrix\n * math.diag([1, 2, 3]) // returns [[1, 0, 0], [0, 2, 0], [0, 0, 3]]\n * math.diag([1, 2, 3], 1) // returns [[0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]\n * math.diag([1, 2, 3], -1) // returns [[0, 0, 0], [1, 0, 0], [0, 2, 0], [0, 0, 3]]\n *\n * // retrieve the diagonal from a matrix\n * const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]\n * math.diag(a) // returns [1, 5, 9]\n *\n * See also:\n *\n * ones, zeros, identity\n *\n * @param {Matrix | Array} x A two dimensional matrix or a vector\n * @param {number | BigNumber} [k=0] The diagonal where the vector will be filled\n * in or retrieved.\n * @param {string} [format='dense'] The matrix storage format.\n *\n * @returns {Matrix | Array} Diagonal matrix from input vector, or diagonal from input matrix.\n */\n return typed(name, {\n // FIXME: simplify this huge amount of signatures as soon as typed-function supports optional arguments\n\n Array: function (x) {\n return _diag(x, 0, arraySize(x), null)\n },\n\n 'Array, number': function (x, k) {\n return _diag(x, k, arraySize(x), null)\n },\n\n 'Array, BigNumber': function (x, k) {\n return _diag(x, k.toNumber(), arraySize(x), null)\n },\n\n 'Array, string': function (x, format) {\n return _diag(x, 0, arraySize(x), format)\n },\n\n 'Array, number, string': function (x, k, format) {\n return _diag(x, k, arraySize(x), format)\n },\n\n 'Array, BigNumber, string': function (x, k, format) {\n return _diag(x, k.toNumber(), arraySize(x), format)\n },\n\n Matrix: function (x) {\n return _diag(x, 0, x.size(), x.storage())\n },\n\n 'Matrix, number': function (x, k) {\n return _diag(x, k, x.size(), x.storage())\n },\n\n 'Matrix, BigNumber': function (x, k) {\n return _diag(x, k.toNumber(), x.size(), x.storage())\n },\n\n 'Matrix, string': function (x, format) {\n return _diag(x, 0, x.size(), format)\n },\n\n 'Matrix, number, string': function (x, k, format) {\n return _diag(x, k, x.size(), format)\n },\n\n 'Matrix, BigNumber, string': function (x, k, format) {\n return _diag(x, k.toNumber(), x.size(), format)\n }\n })\n\n /**\n * Creeate diagonal matrix from a vector or vice versa\n * @param {Array | Matrix} x\n * @param {number} k\n * @param {string} format Storage format for matrix. If null,\n * an Array is returned\n * @returns {Array | Matrix}\n * @private\n */\n function _diag (x, k, size, format) {\n if (!isInteger(k)) {\n throw new TypeError('Second parameter in function diag must be an integer')\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // check dimensions\n switch (size.length) {\n case 1:\n return _createDiagonalMatrix(x, k, format, size[0], kSub, kSuper)\n case 2:\n return _getDiagonal(x, k, format, size, kSub, kSuper)\n }\n throw new RangeError('Matrix for function diag must be 2 dimensional')\n }\n\n function _createDiagonalMatrix (x, k, format, l, kSub, kSuper) {\n // matrix size\n const ms = [l + kSub, l + kSuper]\n\n if (format && format !== 'sparse' && format !== 'dense') {\n throw new TypeError(`Unknown matrix type ${format}\"`)\n }\n\n // create diagonal matrix\n const m = format === 'sparse'\n ? SparseMatrix.diagonal(ms, x, k)\n : DenseMatrix.diagonal(ms, x, k)\n // check we need to return a matrix\n return format !== null ? m : m.valueOf()\n }\n\n function _getDiagonal (x, k, format, s, kSub, kSuper) {\n // check x is a Matrix\n if (isMatrix(x)) {\n // get diagonal matrix\n const dm = x.diagonal(k)\n // check we need to return a matrix\n if (format !== null) {\n // check we need to change matrix format\n if (format !== dm.storage()) { return matrix(dm, format) }\n return dm\n }\n return dm.valueOf()\n }\n // vector size\n const n = Math.min(s[0] - kSub, s[1] - kSuper)\n // diagonal values\n const vector = []\n // loop diagonal\n for (let i = 0; i < n; i++) {\n vector[i] = x[i + kSub][i + kSuper]\n }\n // check we need to return a matrix\n return format !== null ? matrix(vector) : vector\n }\n})\n","// (c) 2018, Mariusz Nowak\n// SPDX-License-Identifier: ISC\n// Derived from https://github.com/medikoo/lru-queue\nexport function lruQueue (limit) {\n let size = 0\n let base = 1\n let queue = Object.create(null)\n let map = Object.create(null)\n let index = 0\n const del = function (id) {\n const oldIndex = map[id]\n if (!oldIndex) return\n delete queue[oldIndex]\n delete map[id]\n --size\n if (base !== oldIndex) return\n if (!size) {\n index = 0\n base = 1\n return\n }\n while (!hasOwnProperty.call(queue, ++base)) continue\n }\n limit = Math.abs(limit)\n return {\n hit: function (id) {\n const oldIndex = map[id]; const nuIndex = ++index\n queue[nuIndex] = id\n map[id] = nuIndex\n if (!oldIndex) {\n ++size\n if (size <= limit) return undefined\n id = queue[base]\n del(id)\n return id\n }\n delete queue[oldIndex]\n if (base !== oldIndex) return undefined\n while (!hasOwnProperty.call(queue, ++base)) continue\n return undefined\n },\n delete: del,\n clear: function () {\n size = index = 0\n base = 1\n queue = Object.create(null)\n map = Object.create(null)\n }\n }\n};\n","// function utils\n\nimport { lruQueue } from './lruQueue.js'\n\n/**\n * Memoize a given function by caching the computed result.\n * The cache of a memoized function can be cleared by deleting the `cache`\n * property of the function.\n *\n * @param {function} fn The function to be memoized.\n * Must be a pure function.\n * @param {Object} [options]\n * @param {function(args: Array): string} [options.hasher]\n * A custom hash builder. Is JSON.stringify by default.\n * @param {number | undefined} [options.limit]\n * Maximum number of values that may be cached. Undefined indicates\n * unlimited (default)\n * @return {function} Returns the memoized function\n */\nexport function memoize (fn, { hasher, limit } = {}) {\n limit = limit == null ? Number.POSITIVE_INFINITY : limit\n hasher = hasher == null ? JSON.stringify : hasher\n\n return function memoize () {\n if (typeof memoize.cache !== 'object') {\n memoize.cache = {\n values: new Map(),\n lru: lruQueue(limit || Number.POSITIVE_INFINITY)\n }\n }\n const args = []\n for (let i = 0; i < arguments.length; i++) {\n args[i] = arguments[i]\n }\n const hash = hasher(args)\n\n if (memoize.cache.values.has(hash)) {\n memoize.cache.lru.hit(hash)\n return memoize.cache.values.get(hash)\n }\n\n const newVal = fn.apply(fn, args)\n memoize.cache.values.set(hash, newVal)\n memoize.cache.values.delete(memoize.cache.lru.hit(hash))\n\n return newVal\n }\n}\n\n/**\n * Memoize a given function by caching all results and the arguments,\n * and comparing against the arguments of previous results before\n * executing again.\n * This is less performant than `memoize` which calculates a hash,\n * which is very fast to compare. Use `memoizeCompare` only when it is\n * not possible to create a unique serializable hash from the function\n * arguments.\n * The isEqual function must compare two sets of arguments\n * and return true when equal (can be a deep equality check for example).\n * @param {function} fn\n * @param {function(a: *, b: *) : boolean} isEqual\n * @returns {function}\n */\nexport function memoizeCompare (fn, isEqual) {\n const memoize = function memoize () {\n const args = []\n for (let i = 0; i < arguments.length; i++) {\n args[i] = arguments[i]\n }\n\n for (let c = 0; c < memoize.cache.length; c++) {\n const cached = memoize.cache[c]\n\n if (isEqual(args, cached.args)) {\n // TODO: move this cache entry to the top so recently used entries move up?\n return cached.res\n }\n }\n\n const res = fn.apply(fn, args)\n memoize.cache.unshift({ args, res })\n\n return res\n }\n\n memoize.cache = []\n\n return memoize\n}\n\n/**\n * Find the maximum number of arguments expected by a typed function.\n * @param {function} fn A typed function\n * @return {number} Returns the maximum number of expected arguments.\n * Returns -1 when no signatures where found on the function.\n */\nexport function maxArgumentCount (fn) {\n return Object.keys(fn.signatures || {})\n .reduce(function (args, signature) {\n const count = (signature.match(/,/g) || []).length + 1\n return Math.max(args, count)\n }, -1)\n}\n","import { filter, filterRegExp } from '../../utils/array.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'filter'\nconst dependencies = ['typed']\n\nexport const createFilter = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Filter the items in an array or one dimensional matrix.\n *\n * Syntax:\n *\n * math.filter(x, test)\n *\n * Examples:\n *\n * function isPositive (x) {\n * return x > 0\n * }\n * math.filter([6, -2, -1, 4, 3], isPositive) // returns [6, 4, 3]\n *\n * math.filter([\"23\", \"foo\", \"100\", \"55\", \"bar\"], /[0-9]+/) // returns [\"23\", \"100\", \"55\"]\n *\n * See also:\n *\n * forEach, map, sort\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to filter\n * @param {Function | RegExp} test\n * A function or regular expression to test items.\n * All entries for which `test` returns true are returned.\n * When `test` is a function, it is invoked with three parameters:\n * the value of the element, the index of the element, and the\n * matrix/array being traversed. The function must return a boolean.\n * @return {Matrix | Array} Returns the filtered matrix.\n */\n return typed('filter', {\n 'Array, function': _filterCallback,\n\n 'Matrix, function': function (x, test) {\n return x.create(_filterCallback(x.toArray(), test))\n },\n\n 'Array, RegExp': filterRegExp,\n\n 'Matrix, RegExp': function (x, test) {\n return x.create(filterRegExp(x.toArray(), test))\n }\n })\n})\n\n/**\n * Filter values in a callback given a callback function\n * @param {Array} x\n * @param {Function} callback\n * @return {Array} Returns the filtered array\n * @private\n */\nfunction _filterCallback (x, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n return filter(x, function (value, index, array) {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, [index])\n } else { // 3 or -1\n return callback(value, [index], array)\n }\n })\n}\n","import { clone } from '../../utils/object.js'\nimport { flatten as flattenArray } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'flatten'\nconst dependencies = ['typed', 'matrix']\n\nexport const createFlatten = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Flatten a multi dimensional matrix into a single dimensional matrix.\n *\n * Syntax:\n *\n * math.flatten(x)\n *\n * Examples:\n *\n * math.flatten([[1,2], [3,4]]) // returns [1, 2, 3, 4]\n *\n * See also:\n *\n * concat, resize, size, squeeze\n *\n * @param {Matrix | Array} x Matrix to be flattened\n * @return {Matrix | Array} Returns the flattened matrix\n */\n return typed(name, {\n Array: function (x) {\n return flattenArray(clone(x))\n },\n\n Matrix: function (x) {\n const flat = flattenArray(clone(x.toArray()))\n // TODO: return the same matrix type as x\n return matrix(flat)\n }\n })\n})\n","import { maxArgumentCount } from '../../utils/function.js'\nimport { forEach as forEachArray } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'forEach'\nconst dependencies = ['typed']\n\nexport const createForEach = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterate over all elements of a matrix/array, and executes the given callback function.\n *\n * Syntax:\n *\n * math.forEach(x, callback)\n *\n * Examples:\n *\n * math.forEach([1, 2, 3], function(value) {\n * console.log(value)\n * })\n * // outputs 1, 2, 3\n *\n * See also:\n *\n * filter, map, sort\n *\n * @param {Matrix | Array} x The matrix to iterate on.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix/array being traversed.\n */\n return typed(name, {\n 'Array, function': _forEach,\n\n 'Matrix, function': function (x, callback) {\n return x.forEach(callback)\n }\n })\n})\n\n/**\n * forEach for a multi dimensional array\n * @param {Array} array\n * @param {Function} callback\n * @private\n */\nfunction _forEach (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n forEachArray(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n recurse(child, index.concat(i))\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n callback(value)\n } else if (args === 2) {\n callback(value, index)\n } else { // 3 or -1\n callback(value, index, array)\n }\n }\n }\n recurse(array, [])\n}\n","import { factory } from '../../utils/factory.js'\nimport { getArrayDataType } from '../../utils/array.js'\nimport { typeOf } from '../../utils/is.js'\n\nconst name = 'getMatrixDataType'\nconst dependencies = ['typed']\n\nexport const createGetMatrixDataType = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Find the data type of all elements in a matrix or array,\n * for example 'number' if all items are a number and 'Complex' if all values\n * are complex numbers.\n * If a matrix contains more than one data type, it will return 'mixed'.\n *\n * Syntax:\n *\n * math.getMatrixDataType(x)\n *\n * Examples:\n *\n * const x = [ [1, 2, 3], [4, 5, 6] ]\n * const mixedX = [ [1, true], [2, 3] ]\n * const fractionX = [ [math.fraction(1, 3)], [math.fraction(1, 3] ]\n * const unitX = [ [math.unit('5cm')], [math.unit('5cm')] ]\n * const bigNumberX = [ [math.bignumber(1)], [math.bignumber(0)] ]\n * const sparse = math.sparse(x)\n * const dense = math.matrix(x)\n * math.getMatrixDataType(x) // returns 'number'\n * math.getMatrixDataType(sparse) // returns 'number'\n * math.getMatrixDataType(dense) // returns 'number'\n * math.getMatrixDataType(mixedX) // returns 'mixed'\n * math.getMatrixDataType(fractionX) // returns 'Fraction'\n * math.getMatrixDataType(unitX) // returns 'Unit'\n * math.getMatrixDataType(bigNumberX) // return 'BigNumber'\n *\n * See also:\n * SparseMatrix, DenseMatrix\n *\n * @param {...Matrix | Array} x The Matrix with values.\n *\n * @return {string} A string representation of the matrix type\n */\n return typed(name, {\n Array: function (x) {\n return getArrayDataType(x, typeOf)\n },\n Matrix: function (x) {\n return x.getDataType()\n }\n })\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { resize } from '../../utils/array.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'identity'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'BigNumber',\n 'DenseMatrix',\n 'SparseMatrix'\n]\n\nexport const createIdentity = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a 2-dimensional identity matrix with size m x n or n x n.\n * The matrix has ones on the diagonal and zeros elsewhere.\n *\n * Syntax:\n *\n * math.identity(n)\n * math.identity(n, format)\n * math.identity(m, n)\n * math.identity(m, n, format)\n * math.identity([m, n])\n * math.identity([m, n], format)\n *\n * Examples:\n *\n * math.identity(3) // returns [[1, 0, 0], [0, 1, 0], [0, 0, 1]]\n * math.identity(3, 2) // returns [[1, 0], [0, 1], [0, 0]]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.identity(math.size(A)) // returns [[1, 0, 0], [0, 1, 0]]\n *\n * See also:\n *\n * diag, ones, zeros, size, range\n *\n * @param {...number | Matrix | Array} size The size for the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Matrix | Array | number} A matrix with ones on the diagonal.\n */\n return typed(name, {\n '': function () {\n return (config.matrix === 'Matrix') ? matrix([]) : []\n },\n\n string: function (format) {\n return matrix(format)\n },\n\n 'number | BigNumber': function (rows) {\n return _identity(rows, rows, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber, string': function (rows, format) {\n return _identity(rows, rows, format)\n },\n\n 'number | BigNumber, number | BigNumber': function (rows, cols) {\n return _identity(rows, cols, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber, number | BigNumber, string': function (rows, cols, format) {\n return _identity(rows, cols, format)\n },\n\n Array: function (size) {\n return _identityVector(size)\n },\n\n 'Array, string': function (size, format) {\n return _identityVector(size, format)\n },\n\n Matrix: function (size) {\n return _identityVector(size.valueOf(), size.storage())\n },\n\n 'Matrix, string': function (size, format) {\n return _identityVector(size.valueOf(), format)\n }\n })\n\n function _identityVector (size, format) {\n switch (size.length) {\n case 0: return format ? matrix(format) : []\n case 1: return _identity(size[0], size[0], format)\n case 2: return _identity(size[0], size[1], format)\n default: throw new Error('Vector containing two values expected')\n }\n }\n\n /**\n * Create an identity matrix\n * @param {number | BigNumber} rows\n * @param {number | BigNumber} cols\n * @param {string} [format]\n * @returns {Matrix}\n * @private\n */\n function _identity (rows, cols, format) {\n // BigNumber constructor with the right precision\n const Big = (isBigNumber(rows) || isBigNumber(cols))\n ? BigNumber\n : null\n\n if (isBigNumber(rows)) rows = rows.toNumber()\n if (isBigNumber(cols)) cols = cols.toNumber()\n\n if (!isInteger(rows) || rows < 1) {\n throw new Error('Parameters in function identity must be positive integers')\n }\n if (!isInteger(cols) || cols < 1) {\n throw new Error('Parameters in function identity must be positive integers')\n }\n\n const one = Big ? new BigNumber(1) : 1\n const defaultValue = Big ? new Big(0) : 0\n const size = [rows, cols]\n\n // check we need to return a matrix\n if (format) {\n // create diagonal matrix (use optimized implementation for storage format)\n if (format === 'sparse') {\n return SparseMatrix.diagonal(size, one, 0, defaultValue)\n }\n if (format === 'dense') {\n return DenseMatrix.diagonal(size, one, 0, defaultValue)\n }\n throw new TypeError(`Unknown matrix type \"${format}\"`)\n }\n\n // create and resize array\n const res = resize([], size, defaultValue)\n // fill in ones on the diagonal\n const minimum = rows < cols ? rows : cols\n // fill diagonal\n for (let d = 0; d < minimum; d++) {\n res[d][d] = one\n }\n return res\n }\n})\n","import { arraySize as size } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'kron'\nconst dependencies = ['typed', 'matrix', 'multiplyScalar']\n\nexport const createKron = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, multiplyScalar }) => {\n /**\n * Calculates the kronecker product of 2 matrices or vectors.\n *\n * NOTE: If a one dimensional vector / matrix is given, it will be\n * wrapped so its two dimensions.\n * See the examples.\n *\n * Syntax:\n *\n * math.kron(x, y)\n *\n * Examples:\n *\n * math.kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])\n * // returns [ [ 1, 2, 0, 0 ], [ 3, 4, 0, 0 ], [ 0, 0, 1, 2 ], [ 0, 0, 3, 4 ] ]\n *\n * math.kron([1,1], [2,3,4])\n * // returns [ [ 2, 3, 4, 2, 3, 4 ] ]\n *\n * See also:\n *\n * multiply, dot, cross\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {Array | Matrix} Returns the kronecker product of `x` and `y`\n */\n return typed(name, {\n 'Matrix, Matrix': function (x, y) {\n return matrix(_kron(x.toArray(), y.toArray()))\n },\n\n 'Matrix, Array': function (x, y) {\n return matrix(_kron(x.toArray(), y))\n },\n\n 'Array, Matrix': function (x, y) {\n return matrix(_kron(x, y.toArray()))\n },\n\n 'Array, Array': _kron\n })\n\n /**\n * Calculate the kronecker product of two matrices / vectors\n * @param {Array} a First vector\n * @param {Array} b Second vector\n * @returns {Array} Returns the kronecker product of x and y\n * @private\n */\n function _kron (a, b) {\n // Deal with the dimensions of the matricies.\n if (size(a).length === 1) {\n // Wrap it in a 2D Matrix\n a = [a]\n }\n if (size(b).length === 1) {\n // Wrap it in a 2D Matrix\n b = [b]\n }\n if (size(a).length > 2 || size(b).length > 2) {\n throw new RangeError('Vectors with dimensions greater then 2 are not supported expected ' +\n '(Size x = ' + JSON.stringify(a.length) + ', y = ' + JSON.stringify(b.length) + ')')\n }\n const t = []\n let r = []\n\n return a.map(function (a) {\n return b.map(function (b) {\n r = []\n t.push(r)\n return a.map(function (y) {\n return b.map(function (x) {\n return r.push(multiplyScalar(y, x))\n })\n })\n })\n }) && t\n }\n})\n","import { maxArgumentCount } from '../../utils/function.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'map'\nconst dependencies = ['typed']\n\nexport const createMap = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a new matrix or array with the results of the callback function executed on\n * each entry of the matrix/array.\n *\n * Syntax:\n *\n * math.map(x, callback)\n *\n * Examples:\n *\n * math.map([1, 2, 3], function(value) {\n * return value * value\n * }) // returns [1, 4, 9]\n *\n * See also:\n *\n * filter, forEach, sort\n *\n * @param {Matrix | Array} x The matrix to iterate on.\n * @param {Function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the matrix being traversed.\n * @return {Matrix | array} Transformed map of x\n */\n return typed(name, {\n 'Array, function': _map,\n\n 'Matrix, function': function (x, callback) {\n return x.map(callback)\n }\n })\n})\n\n/**\n * Map for a multi dimensional array\n * @param {Array} array\n * @param {Function} callback\n * @return {Array}\n * @private\n */\nfunction _map (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n return value.map(function (child, i) {\n // we create a copy of the index array and append the new index value\n return recurse(child, index.concat(i))\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, index)\n } else { // 3 or -1\n return callback(value, index, array)\n }\n }\n }\n\n return recurse(array, [])\n}\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'diff'\nconst dependencies = ['typed', 'matrix', 'subtract', 'number']\n\nexport const createDiff = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, number }) => {\n /**\n * Create a new matrix or array of the difference between elements of the given array\n * The optional dim parameter lets you specify the dimension to evaluate the difference of\n * If no dimension parameter is passed it is assumed as dimension 0\n *\n * Dimension is zero-based in javascript and one-based in the parser and can be a number or bignumber\n * Arrays must be 'rectangular' meaning arrays like [1, 2]\n * If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays\n *\n * Syntax:\n *\n * math.diff(arr)\n * math.diff(arr, dim)\n *\n * Examples:\n *\n * const arr = [1, 2, 4, 7, 0]\n * math.diff(arr) // returns [1, 2, 3, -7] (no dimension passed so 0 is assumed)\n * math.diff(math.matrix(arr)) // returns math.matrix([1, 2, 3, -7])\n *\n * const arr = [[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [9, 8, 7, 6, 4]]\n * math.diff(arr) // returns [[0, 0, 0, 0, 0], [8, 6, 4, 2, -1]]\n * math.diff(arr, 0) // returns [[0, 0, 0, 0, 0], [8, 6, 4, 2, -1]]\n * math.diff(arr, 1) // returns [[1, 1, 1, 1], [1, 1, 1, 1], [-1, -1, -1, -2]]\n * math.diff(arr, math.bignumber(1)) // returns [[1, 1, 1, 1], [1, 1, 1, 1], [-1, -1, -1, -2]]\n *\n * math.diff(arr, 2) // throws RangeError as arr is 2 dimensional not 3\n * math.diff(arr, -1) // throws RangeError as negative dimensions are not allowed\n *\n * // These will all produce the same result\n * math.diff([[1, 2], [3, 4]])\n * math.diff([math.matrix([1, 2]), math.matrix([3, 4])])\n * math.diff([[1, 2], math.matrix([3, 4])])\n * math.diff([math.matrix([1, 2]), [3, 4]])\n * // They do not produce the same result as math.diff(math.matrix([[1, 2], [3, 4]])) as this returns a matrix\n *\n * See Also:\n *\n * sum\n * subtract\n * partitionSelect\n *\n * @param {Array | Matrix} arr An array or matrix\n * @param {number} dim Dimension\n * @return {Array | Matrix} Difference between array elements in given dimension\n */\n return typed(name, {\n 'Array | Matrix': function (arr) { // No dimension specified => assume dimension 0\n if (isMatrix(arr)) {\n return matrix(_diff(arr.toArray()))\n } else {\n return _diff(arr)\n }\n },\n 'Array | Matrix, number': function (arr, dim) {\n if (!isInteger(dim)) throw new RangeError('Dimension must be a whole number')\n if (isMatrix(arr)) {\n return matrix(_recursive(arr.toArray(), dim))\n } else {\n return _recursive(arr, dim)\n }\n },\n 'Array | Matrix, BigNumber': function (arr, dim) {\n return this(arr, number(dim))\n }\n })\n\n /**\n * Recursively find the correct dimension in the array/matrix\n * Then Apply _diff to that dimension\n *\n * @param {Array} arr The array\n * @param {number} dim Dimension\n * @return {Array} resulting array\n */\n function _recursive (arr, dim) {\n if (isMatrix(arr)) {\n arr = arr.toArray() // Makes sure arrays like [ matrix([0, 1]), matrix([1, 0]) ] are processed properly\n }\n if (!Array.isArray(arr)) {\n throw RangeError('Array/Matrix does not have that many dimensions')\n }\n if (dim > 0) {\n const result = []\n arr.forEach(element => {\n result.push(_recursive(element, dim - 1))\n })\n return result\n } else if (dim === 0) {\n return _diff(arr)\n } else {\n throw RangeError('Cannot have negative dimension')\n }\n }\n\n /**\n * Difference between elements in the array\n *\n * @param {Array} arr An array\n * @return {Array} resulting array\n */\n function _diff (arr) {\n const result = []\n const size = arr.length\n if (size < 2) {\n return arr\n }\n for (let i = 1; i < size; i++) {\n result.push(_ElementDiff(arr[i - 1], arr[i]))\n }\n return result\n }\n\n /**\n * Difference between 2 objects\n *\n * @param {Object} obj1 First object\n * @param {Object} obj2 Second object\n * @return {Array} resulting array\n */\n function _ElementDiff (obj1, obj2) {\n // Convert matrices to arrays\n if (isMatrix(obj1)) obj1 = obj1.toArray()\n if (isMatrix(obj2)) obj2 = obj2.toArray()\n\n const obj1IsArray = Array.isArray(obj1)\n const obj2IsArray = Array.isArray(obj2)\n if (obj1IsArray && obj2IsArray) {\n return _ArrayDiff(obj1, obj2)\n }\n if (!obj1IsArray && !obj2IsArray) {\n return subtract(obj2, obj1) // Difference is (second - first) NOT (first - second)\n }\n throw TypeError('Cannot calculate difference between 1 array and 1 non-array')\n }\n\n /**\n * Difference of elements in 2 arrays\n *\n * @param {Array} arr1 Array 1\n * @param {Array} arr2 Array 2\n * @return {Array} resulting array\n */\n function _ArrayDiff (arr1, arr2) {\n if (arr1.length !== arr2.length) {\n throw RangeError('Not all sub-arrays have the same length')\n }\n const result = []\n const size = arr1.length\n for (let i = 0; i < size; i++) {\n result.push(_ElementDiff(arr1[i], arr2[i]))\n }\n return result\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { resize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ones'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createOnes = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Create a matrix filled with ones. The created matrix can have one or\n * multiple dimensions.\n *\n * Syntax:\n *\n * math.ones(m)\n * math.ones(m, format)\n * math.ones(m, n)\n * math.ones(m, n, format)\n * math.ones([m, n])\n * math.ones([m, n], format)\n * math.ones([m, n, p, ...])\n * math.ones([m, n, p, ...], format)\n *\n * Examples:\n *\n * math.ones(3) // returns [1, 1, 1]\n * math.ones(3, 2) // returns [[1, 1], [1, 1], [1, 1]]\n * math.ones(3, 2, 'dense') // returns Dense Matrix [[1, 1], [1, 1], [1, 1]]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.ones(math.size(A)) // returns [[1, 1, 1], [1, 1, 1]]\n *\n * See also:\n *\n * zeros, identity, size, range\n *\n * @param {...number | Array} size The size of each dimension of the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Array | Matrix | number} A matrix filled with ones\n */\n return typed('ones', {\n '': function () {\n return (config.matrix === 'Array')\n ? _ones([])\n : _ones([], 'default')\n },\n\n // math.ones(m, n, p, ..., format)\n // TODO: more accurate signature '...number | BigNumber, string' as soon as typed-function supports this\n '...number | BigNumber | string': function (size) {\n const last = size[size.length - 1]\n if (typeof last === 'string') {\n const format = size.pop()\n return _ones(size, format)\n } else if (config.matrix === 'Array') {\n return _ones(size)\n } else {\n return _ones(size, 'default')\n }\n },\n\n Array: _ones,\n\n Matrix: function (size) {\n const format = size.storage()\n return _ones(size.valueOf(), format)\n },\n\n 'Array | Matrix, string': function (size, format) {\n return _ones(size.valueOf(), format)\n }\n })\n\n /**\n * Create an Array or Matrix with ones\n * @param {Array} size\n * @param {string} [format='default']\n * @return {Array | Matrix}\n * @private\n */\n function _ones (size, format) {\n const hasBigNumbers = _normalize(size)\n const defaultValue = hasBigNumbers ? new BigNumber(1) : 1\n _validate(size)\n\n if (format) {\n // return a matrix\n const m = matrix(format)\n if (size.length > 0) {\n return m.resize(size, defaultValue)\n }\n return m\n } else {\n // return an Array\n const arr = []\n if (size.length > 0) {\n return resize(arr, size, defaultValue)\n }\n return arr\n }\n }\n\n // replace BigNumbers with numbers, returns true if size contained BigNumbers\n function _normalize (size) {\n let hasBigNumbers = false\n size.forEach(function (value, index, arr) {\n if (isBigNumber(value)) {\n hasBigNumbers = true\n arr[index] = value.toNumber()\n }\n })\n return hasBigNumbers\n }\n\n // validate arguments\n function _validate (size) {\n size.forEach(function (value) {\n if (typeof value !== 'number' || !isInteger(value) || value < 0) {\n throw new Error('Parameters in function ones must be positive integers')\n }\n })\n }\n})\n","\nexport function noBignumber () {\n throw new Error('No \"bignumber\" implementation available')\n}\n\nexport function noFraction () {\n throw new Error('No \"fraction\" implementation available')\n}\n\nexport function noMatrix () {\n throw new Error('No \"matrix\" implementation available')\n}\n\nexport function noIndex () {\n throw new Error('No \"index\" implementation available')\n}\n\nexport function noSubset () {\n throw new Error('No \"matrix\" implementation available')\n}\n","import { factory } from '../../utils/factory.js'\nimport { noBignumber, noMatrix } from '../../utils/noop.js'\n\nconst name = 'range'\nconst dependencies = ['typed', 'config', '?matrix', '?bignumber', 'smaller', 'smallerEq', 'larger', 'largerEq']\n\nexport const createRange = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq }) => {\n /**\n * Create an array from a range.\n * By default, the range end is excluded. This can be customized by providing\n * an extra parameter `includeEnd`.\n *\n * Syntax:\n *\n * math.range(str [, includeEnd]) // Create a range from a string,\n * // where the string contains the\n * // start, optional step, and end,\n * // separated by a colon.\n * math.range(start, end [, includeEnd]) // Create a range with start and\n * // end and a step size of 1.\n * math.range(start, end, step [, includeEnd]) // Create a range with start, step,\n * // and end.\n *\n * Where:\n *\n * - `str: string`\n * A string 'start:end' or 'start:step:end'\n * - `start: {number | BigNumber}`\n * Start of the range\n * - `end: number | BigNumber`\n * End of the range, excluded by default, included when parameter includeEnd=true\n * - `step: number | BigNumber`\n * Step size. Default value is 1.\n * - `includeEnd: boolean`\n * Option to specify whether to include the end or not. False by default.\n *\n * Examples:\n *\n * math.range(2, 6) // [2, 3, 4, 5]\n * math.range(2, -3, -1) // [2, 1, 0, -1, -2]\n * math.range('2:1:6') // [2, 3, 4, 5]\n * math.range(2, 6, true) // [2, 3, 4, 5, 6]\n *\n * See also:\n *\n * ones, zeros, size, subset\n *\n * @param {*} args Parameters describing the ranges `start`, `end`, and optional `step`.\n * @return {Array | Matrix} range\n */\n return typed(name, {\n // TODO: simplify signatures when typed-function supports default values and optional arguments\n\n // TODO: a number or boolean should not be converted to string here\n string: _strRange,\n 'string, boolean': _strRange,\n\n 'number, number': function (start, end) {\n return _out(_rangeEx(start, end, 1))\n },\n 'number, number, number': function (start, end, step) {\n return _out(_rangeEx(start, end, step))\n },\n 'number, number, boolean': function (start, end, includeEnd) {\n return includeEnd\n ? _out(_rangeInc(start, end, 1))\n : _out(_rangeEx(start, end, 1))\n },\n 'number, number, number, boolean': function (start, end, step, includeEnd) {\n return includeEnd\n ? _out(_rangeInc(start, end, step))\n : _out(_rangeEx(start, end, step))\n },\n\n 'BigNumber, BigNumber': function (start, end) {\n const BigNumber = start.constructor\n\n return _out(_bigRangeEx(start, end, new BigNumber(1)))\n },\n 'BigNumber, BigNumber, BigNumber': function (start, end, step) {\n return _out(_bigRangeEx(start, end, step))\n },\n 'BigNumber, BigNumber, boolean': function (start, end, includeEnd) {\n const BigNumber = start.constructor\n\n return includeEnd\n ? _out(_bigRangeInc(start, end, new BigNumber(1)))\n : _out(_bigRangeEx(start, end, new BigNumber(1)))\n },\n 'BigNumber, BigNumber, BigNumber, boolean': function (start, end, step, includeEnd) {\n return includeEnd\n ? _out(_bigRangeInc(start, end, step))\n : _out(_bigRangeEx(start, end, step))\n }\n\n })\n\n function _out (arr) {\n if (config.matrix === 'Matrix') {\n return matrix ? matrix(arr) : noMatrix()\n }\n\n return arr\n }\n\n function _strRange (str, includeEnd) {\n const r = _parse(str)\n if (!r) {\n throw new SyntaxError('String \"' + str + '\" is no valid range')\n }\n\n let fn\n if (config.number === 'BigNumber') {\n if (bignumber === undefined) {\n noBignumber()\n }\n\n fn = includeEnd ? _bigRangeInc : _bigRangeEx\n return _out(fn(\n bignumber(r.start),\n bignumber(r.end),\n bignumber(r.step)))\n } else {\n fn = includeEnd ? _rangeInc : _rangeEx\n return _out(fn(r.start, r.end, r.step))\n }\n }\n\n /**\n * Create a range with numbers. End is excluded\n * @param {number} start\n * @param {number} end\n * @param {number} step\n * @returns {Array} range\n * @private\n */\n function _rangeEx (start, end, step) {\n const array = []\n let x = start\n if (step > 0) {\n while (smaller(x, end)) {\n array.push(x)\n x += step\n }\n } else if (step < 0) {\n while (larger(x, end)) {\n array.push(x)\n x += step\n }\n }\n\n return array\n }\n\n /**\n * Create a range with numbers. End is included\n * @param {number} start\n * @param {number} end\n * @param {number} step\n * @returns {Array} range\n * @private\n */\n function _rangeInc (start, end, step) {\n const array = []\n let x = start\n if (step > 0) {\n while (smallerEq(x, end)) {\n array.push(x)\n x += step\n }\n } else if (step < 0) {\n while (largerEq(x, end)) {\n array.push(x)\n x += step\n }\n }\n\n return array\n }\n\n /**\n * Create a range with big numbers. End is excluded\n * @param {BigNumber} start\n * @param {BigNumber} end\n * @param {BigNumber} step\n * @returns {Array} range\n * @private\n */\n function _bigRangeEx (start, end, step) {\n const zero = bignumber(0)\n const array = []\n let x = start\n if (step.gt(zero)) {\n while (smaller(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n } else if (step.lt(zero)) {\n while (larger(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n }\n\n return array\n }\n\n /**\n * Create a range with big numbers. End is included\n * @param {BigNumber} start\n * @param {BigNumber} end\n * @param {BigNumber} step\n * @returns {Array} range\n * @private\n */\n function _bigRangeInc (start, end, step) {\n const zero = bignumber(0)\n const array = []\n let x = start\n if (step.gt(zero)) {\n while (smallerEq(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n } else if (step.lt(zero)) {\n while (largerEq(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n }\n\n return array\n }\n\n /**\n * Parse a string into a range,\n * The string contains the start, optional step, and end, separated by a colon.\n * If the string does not contain a valid range, null is returned.\n * For example str='0:2:11'.\n * @param {string} str\n * @return {{start: number, end: number, step: number} | null} range Object containing properties start, end, step\n * @private\n */\n function _parse (str) {\n const args = str.split(':')\n\n // number\n const nums = args.map(function (arg) {\n // use Number and not parseFloat as Number returns NaN on invalid garbage in the string\n return Number(arg)\n })\n\n const invalid = nums.some(function (num) {\n return isNaN(num)\n })\n if (invalid) {\n return null\n }\n\n switch (nums.length) {\n case 2:\n return {\n start: nums[0],\n end: nums[1],\n step: 1\n }\n\n case 3:\n return {\n start: nums[0],\n end: nums[2],\n step: nums[1]\n }\n\n default:\n return null\n }\n }\n})\n","import { reshape as arrayReshape } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'reshape'\nconst dependencies = ['typed', 'isInteger', 'matrix']\n\nexport const createReshape = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger, matrix }) => {\n /**\n * Reshape a multi dimensional array to fit the specified dimensions\n *\n * Syntax:\n *\n * math.reshape(x, sizes)\n *\n * Examples:\n *\n * math.reshape([1, 2, 3, 4, 5, 6], [2, 3])\n * // returns Array [[1, 2, 3], [4, 5, 6]]\n *\n * math.reshape([[1, 2], [3, 4]], [1, 4])\n * // returns Array [[1, 2, 3, 4]]\n *\n * math.reshape([[1, 2], [3, 4]], [4])\n * // returns Array [1, 2, 3, 4]\n *\n * const x = math.matrix([1, 2, 3, 4, 5, 6, 7, 8])\n * math.reshape(x, [2, 2, 2])\n * // returns Matrix [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]\n *\n * See also:\n *\n * size, squeeze, resize\n *\n * @param {Array | Matrix | *} x Matrix to be reshaped\n * @param {number[]} sizes One dimensional array with integral sizes for\n * each dimension\n *\n * @return {* | Array | Matrix} A reshaped clone of matrix `x`\n *\n * @throws {TypeError} If `sizes` does not contain solely integers\n * @throws {DimensionError} If the product of the new dimension sizes does\n * not equal that of the old ones\n */\n return typed(name, {\n\n 'Matrix, Array': function (x, sizes) {\n if (x.reshape) {\n return x.reshape(sizes)\n } else {\n return matrix(arrayReshape(x.valueOf(), sizes))\n }\n },\n\n 'Array, Array': function (x, sizes) {\n sizes.forEach(function (size) {\n if (!isInteger(size)) {\n throw new TypeError('Invalid size for dimension: ' + size)\n }\n })\n return arrayReshape(x, sizes)\n }\n\n })\n})\n","/**\n * Create a syntax error with the message:\n * 'Wrong number of arguments in function ( provided, - expected)'\n * @param {string} fn Function name\n * @param {number} count Actual argument count\n * @param {number} min Minimum required argument count\n * @param {number} [max] Maximum required argument count\n * @extends Error\n */\nexport function ArgumentsError (fn, count, min, max) {\n if (!(this instanceof ArgumentsError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.fn = fn\n this.count = count\n this.min = min\n this.max = max\n\n this.message = 'Wrong number of arguments in function ' + fn +\n ' (' + count + ' provided, ' +\n min + ((max !== undefined && max !== null) ? ('-' + max) : '') + ' expected)'\n\n this.stack = (new Error()).stack\n}\n\nArgumentsError.prototype = new Error()\nArgumentsError.prototype.constructor = Error\nArgumentsError.prototype.name = 'ArgumentsError'\nArgumentsError.prototype.isArgumentsError = true\n","import { isBigNumber, isMatrix } from '../../utils/is.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { ArgumentsError } from '../../error/ArgumentsError.js'\nimport { isInteger } from '../../utils/number.js'\nimport { format } from '../../utils/string.js'\nimport { clone } from '../../utils/object.js'\nimport { resize as arrayResize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'resize'\nconst dependencies = ['config', 'matrix']\n\nexport const createResize = /* #__PURE__ */ factory(name, dependencies, ({ config, matrix }) => {\n /**\n * Resize a matrix\n *\n * Syntax:\n *\n * math.resize(x, size)\n * math.resize(x, size, defaultValue)\n *\n * Examples:\n *\n * math.resize([1, 2, 3, 4, 5], [3]) // returns Array [1, 2, 3]\n * math.resize([1, 2, 3], [5], 0) // returns Array [1, 2, 3, 0, 0]\n * math.resize(2, [2, 3], 0) // returns Matrix [[2, 0, 0], [0, 0, 0]]\n * math.resize(\"hello\", [8], \"!\") // returns string 'hello!!!'\n *\n * See also:\n *\n * size, squeeze, subset, reshape\n *\n * @param {Array | Matrix | *} x Matrix to be resized\n * @param {Array | Matrix} size One dimensional array with numbers\n * @param {number | string} [defaultValue=0] Zero by default, except in\n * case of a string, in that case\n * defaultValue = ' '\n * @return {* | Array | Matrix} A resized clone of matrix `x`\n */\n // TODO: rework resize to a typed-function\n return function resize (x, size, defaultValue) {\n if (arguments.length !== 2 && arguments.length !== 3) {\n throw new ArgumentsError('resize', arguments.length, 2, 3)\n }\n\n if (isMatrix(size)) {\n size = size.valueOf() // get Array\n }\n\n if (isBigNumber(size[0])) {\n // convert bignumbers to numbers\n size = size.map(function (value) {\n return !isBigNumber(value) ? value : value.toNumber()\n })\n }\n\n // check x is a Matrix\n if (isMatrix(x)) {\n // use optimized matrix implementation, return copy\n return x.resize(size, defaultValue, true)\n }\n\n if (typeof x === 'string') {\n // resize string\n return _resizeString(x, size, defaultValue)\n }\n\n // check result should be a matrix\n const asMatrix = Array.isArray(x) ? false : (config.matrix !== 'Array')\n\n if (size.length === 0) {\n // output a scalar\n while (Array.isArray(x)) {\n x = x[0]\n }\n\n return clone(x)\n } else {\n // output an array/matrix\n if (!Array.isArray(x)) {\n x = [x]\n }\n x = clone(x)\n\n const res = arrayResize(x, size, defaultValue)\n return asMatrix ? matrix(res) : res\n }\n }\n\n /**\n * Resize a string\n * @param {string} str\n * @param {number[]} size\n * @param {string} [defaultChar=' ']\n * @private\n */\n function _resizeString (str, size, defaultChar) {\n if (defaultChar !== undefined) {\n if (typeof defaultChar !== 'string' || defaultChar.length !== 1) {\n throw new TypeError('Single character expected as defaultValue')\n }\n } else {\n defaultChar = ' '\n }\n\n if (size.length !== 1) {\n throw new DimensionError(size.length, 1)\n }\n const len = size[0]\n if (typeof len !== 'number' || !isInteger(len)) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n\n if (str.length > len) {\n return str.substring(0, len)\n } else if (str.length < len) {\n let res = str\n for (let i = 0, ii = len - str.length; i < ii; i++) {\n res += defaultChar\n }\n return res\n } else {\n return str\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { arraySize } from '../../utils/array.js'\n\nconst name = 'rotate'\nconst dependencies = [\n 'typed',\n 'multiply',\n 'rotationMatrix'\n]\n\nexport const createRotate = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed, multiply, rotationMatrix\n }) => {\n /**\n * Rotate a vector of size 1x2 counter-clockwise by a given angle\n * Rotate a vector of size 1x3 counter-clockwise by a given angle around the given axis\n *\n * Syntax:\n *\n * math.rotate(w, theta)\n * math.rotate(w, theta, v)\n *\n * Examples:\n *\n * math.rotate([11, 12], math.pi / 2) // returns matrix([-12, 11])\n * math.rotate(matrix([11, 12]), math.pi / 2) // returns matrix([-12, 11])\n *\n * math.rotate([1, 0, 0], unit('90deg'), [0, 0, 1]) // returns matrix([0, 1, 0])\n * math.rotate(matrix([1, 0, 0]), unit('90deg'), [0, 0, 1]) // returns matrix([0, 1, 0])\n *\n * math.rotate([1, 0], math.complex(1 + i)) // returns matrix([cos(1 + i) - sin(1 + i), sin(1 + i) + cos(1 + i)])\n *\n * See also:\n *\n * matrix, rotationMatrix\n *\n * @param {Array | Matrix} w Vector to rotate\n * @param {number | BigNumber | Complex | Unit} theta Rotation angle\n * @param {Array | Matrix} [v] Rotation axis\n * @return {Array | Matrix} Multiplication of the rotation matrix and w\n */\n return typed(name, {\n 'Array , number | BigNumber | Complex | Unit': function (w, theta) {\n _validateSize(w, 2)\n const matrixRes = multiply(rotationMatrix(theta), w)\n return matrixRes.toArray()\n },\n\n 'Matrix , number | BigNumber | Complex | Unit': function (w, theta) {\n _validateSize(w, 2)\n return multiply(rotationMatrix(theta), w)\n },\n\n 'Array, number | BigNumber | Complex | Unit, Array | Matrix': function (w, theta, v) {\n _validateSize(w, 3)\n const matrixRes = multiply(rotationMatrix(theta, v), w)\n return matrixRes\n },\n\n 'Matrix, number | BigNumber | Complex | Unit, Array | Matrix': function (w, theta, v) {\n _validateSize(w, 3)\n return multiply(rotationMatrix(theta, v), w)\n }\n })\n\n function _validateSize (v, expectedSize) {\n const actualSize = Array.isArray(v) ? arraySize(v) : v.size()\n if (actualSize.length > 2) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n if (actualSize.length === 2 && actualSize[1] !== 1) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n if (actualSize[0] !== expectedSize) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'rotationMatrix'\nconst dependencies = [\n 'typed',\n 'config',\n 'multiplyScalar',\n 'addScalar',\n 'unaryMinus',\n 'norm',\n 'matrix',\n 'BigNumber',\n 'DenseMatrix',\n 'SparseMatrix',\n 'cos',\n 'sin'\n]\n\nexport const createRotationMatrix = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed, config, multiplyScalar,\n addScalar, unaryMinus, norm, BigNumber,\n matrix, DenseMatrix, SparseMatrix, cos, sin\n }) => {\n /**\n * Create a 2-dimensional counter-clockwise rotation matrix (2x2) for a given angle (expressed in radians).\n * Create a 2-dimensional counter-clockwise rotation matrix (3x3) by a given angle (expressed in radians) around a given axis (1x3).\n *\n * Syntax:\n *\n * math.rotationMatrix(theta)\n * math.rotationMatrix(theta, format)\n * math.rotationMatrix(theta, [v])\n * math.rotationMatrix(theta, [v], format)\n *\n * Examples:\n *\n * math.rotationMatrix(math.pi / 2) // returns [[0, -1], [1, 0]]\n * math.rotationMatrix(math.bignumber(1)) // returns [[bignumber(cos(1)), bignumber(-sin(1))], [bignumber(sin(1)), bignumber(cos(1))]]\n * math.rotationMatrix(math.complex(1 + i)) // returns [[cos(1 + i), -sin(1 + i)], [sin(1 + i), cos(1 + i)]]\n * math.rotationMatrix(math.unit('1rad')) // returns [[cos(1), -sin(1)], [sin(1), cos(1)]]\n *\n * math.rotationMatrix(math.pi / 2, [0, 1, 0]) // returns [[0, 0, 1], [0, 1, 0], [-1, 0, 0]]\n * math.rotationMatrix(math.pi / 2, matrix([0, 1, 0])) // returns matrix([[0, 0, 1], [0, 1, 0], [-1, 0, 0]])\n *\n *\n * See also:\n *\n * matrix, cos, sin\n *\n *\n * @param {number | BigNumber | Complex | Unit} theta Rotation angle\n * @param {Array | Matrix} [v] Rotation axis\n * @param {string} [format] Result Matrix storage format\n * @return {Array | Matrix} Rotation matrix\n */\n\n return typed(name, {\n '': function () {\n return (config.matrix === 'Matrix') ? matrix([]) : []\n },\n\n string: function (format) {\n return matrix(format)\n },\n\n 'number | BigNumber | Complex | Unit': function (theta) {\n return _rotationMatrix2x2(theta, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber | Complex | Unit, string': function (theta, format) {\n return _rotationMatrix2x2(theta, format)\n },\n\n 'number | BigNumber | Complex | Unit, Array': function (theta, v) {\n const matrixV = matrix(v)\n _validateVector(matrixV)\n return _rotationMatrix3x3(theta, matrixV, undefined)\n },\n\n 'number | BigNumber | Complex | Unit, Matrix': function (theta, v) {\n _validateVector(v)\n const storageType = v.storage() || (config.matrix === 'Matrix' ? 'dense' : undefined)\n return _rotationMatrix3x3(theta, v, storageType)\n },\n\n 'number | BigNumber | Complex | Unit, Array, string': function (theta, v, format) {\n const matrixV = matrix(v)\n _validateVector(matrixV)\n return _rotationMatrix3x3(theta, matrixV, format)\n },\n\n 'number | BigNumber | Complex | Unit, Matrix, string': function (theta, v, format) {\n _validateVector(v)\n return _rotationMatrix3x3(theta, v, format)\n }\n\n })\n\n /**\n * Returns 2x2 matrix of 2D rotation of angle theta\n *\n * @param {number | BigNumber | Complex | Unit} theta The rotation angle\n * @param {string} format The result Matrix storage format\n * @returns {Matrix}\n * @private\n */\n function _rotationMatrix2x2 (theta, format) {\n const Big = isBigNumber(theta)\n\n const minusOne = Big ? new BigNumber(-1) : -1\n const cosTheta = cos(theta)\n const sinTheta = sin(theta)\n const data = [[cosTheta, multiplyScalar(minusOne, sinTheta)], [sinTheta, cosTheta]]\n\n return _convertToFormat(data, format)\n }\n\n function _validateVector (v) {\n const size = v.size()\n if (size.length < 1 || size[0] !== 3) {\n throw new RangeError('Vector must be of dimensions 1x3')\n }\n }\n\n function _mul (array) {\n return array.reduce((p, curr) => multiplyScalar(p, curr))\n }\n\n function _convertToFormat (data, format) {\n if (format) {\n if (format === 'sparse') {\n return new SparseMatrix(data)\n }\n if (format === 'dense') {\n return new DenseMatrix(data)\n }\n throw new TypeError(`Unknown matrix type \"${format}\"`)\n }\n return data\n }\n\n /**\n * Returns a 3x3 matrix of rotation of angle theta around vector v\n *\n * @param {number | BigNumber | Complex | Unit} theta The rotation angle\n * @param {Matrix} v The rotation axis vector\n * @param {string} format The storage format of the resulting matrix\n * @returns {Matrix}\n * @private\n */\n function _rotationMatrix3x3 (theta, v, format) {\n const normV = norm(v)\n if (normV === 0) {\n throw new RangeError('Rotation around zero vector')\n }\n\n const Big = isBigNumber(theta) ? BigNumber : null\n\n const one = Big ? new Big(1) : 1\n const minusOne = Big ? new Big(-1) : -1\n const vx = Big ? new Big(v.get([0]) / normV) : v.get([0]) / normV\n const vy = Big ? new Big(v.get([1]) / normV) : v.get([1]) / normV\n const vz = Big ? new Big(v.get([2]) / normV) : v.get([2]) / normV\n const c = cos(theta)\n const oneMinusC = addScalar(one, unaryMinus(c))\n const s = sin(theta)\n\n const r11 = addScalar(c, _mul([vx, vx, oneMinusC]))\n const r12 = addScalar(_mul([vx, vy, oneMinusC]), _mul([minusOne, vz, s]))\n const r13 = addScalar(_mul([vx, vz, oneMinusC]), _mul([vy, s]))\n\n const r21 = addScalar(_mul([vx, vy, oneMinusC]), _mul([vz, s]))\n const r22 = addScalar(c, _mul([vy, vy, oneMinusC]))\n const r23 = addScalar(_mul([vy, vz, oneMinusC]), _mul([minusOne, vx, s]))\n\n const r31 = addScalar(_mul([vx, vz, oneMinusC]), _mul([minusOne, vy, s]))\n const r32 = addScalar(_mul([vy, vz, oneMinusC]), _mul([vx, s]))\n const r33 = addScalar(c, _mul([vz, vz, oneMinusC]))\n\n const data = [[r11, r12, r13], [r21, r22, r23], [r31, r32, r33]]\n\n return _convertToFormat(data, format)\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\n\nconst name = 'row'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\nexport const createRow = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n /**\n * Return a row from a Matrix.\n *\n * Syntax:\n *\n * math.row(value, index)\n *\n * Example:\n *\n * // get a row\n * const d = [[1, 2], [3, 4]]\n * math.row(d, 1) // returns [[3, 4]]\n *\n * See also:\n *\n * column\n *\n * @param {Array | Matrix } value An array or matrix\n * @param {number} row The index of the row\n * @return {Array | Matrix} The retrieved row\n */\n return typed(name, {\n 'Matrix, number': _row,\n\n 'Array, number': function (value, row) {\n return _row(matrix(clone(value)), row).valueOf()\n }\n })\n\n /**\n * Retrieve a row of a matrix\n * @param {Matrix } value A matrix\n * @param {number} row The index of the row\n * @return {Matrix} The retrieved row\n */\n function _row (value, row) {\n // check dimensions\n if (value.size().length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n\n validateIndex(row, value.size()[0])\n\n const columnRange = range(0, value.size()[1])\n const index = new Index(row, columnRange)\n return value.subset(index)\n }\n})\n","import { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { noMatrix } from '../../utils/noop.js'\n\nconst name = 'size'\nconst dependencies = ['typed', 'config', '?matrix']\n\nexport const createSize = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix }) => {\n /**\n * Calculate the size of a matrix or scalar.\n *\n * Syntax:\n *\n * math.size(x)\n *\n * Examples:\n *\n * math.size(2.3) // returns []\n * math.size('hello world') // returns [11]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.size(A) // returns [2, 3]\n * math.size(math.range(1,6)) // returns [5]\n *\n * See also:\n *\n * resize, squeeze, subset\n *\n * @param {boolean | number | Complex | Unit | string | Array | Matrix} x A matrix\n * @return {Array | Matrix} A vector with size of `x`.\n */\n return typed(name, {\n Matrix: function (x) {\n return x.create(x.size())\n },\n\n Array: arraySize,\n\n string: function (x) {\n return (config.matrix === 'Array') ? [x.length] : matrix([x.length])\n },\n\n 'number | Complex | BigNumber | Unit | boolean | null': function (x) {\n // scalar\n return (config.matrix === 'Array')\n ? []\n : matrix ? matrix([]) : noMatrix()\n }\n })\n})\n","import { clone } from '../../utils/object.js'\nimport { squeeze as arraySqueeze } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'squeeze'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSqueeze = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.\n *\n * Syntax:\n *\n * math.squeeze(x)\n *\n * Examples:\n *\n * math.squeeze([3]) // returns 3\n * math.squeeze([[3]]) // returns 3\n *\n * const A = math.zeros(3, 1) // returns [[0], [0], [0]] (size 3x1)\n * math.squeeze(A) // returns [0, 0, 0] (size 3)\n *\n * const B = math.zeros(1, 3) // returns [[0, 0, 0]] (size 1x3)\n * math.squeeze(B) // returns [0, 0, 0] (size 3)\n *\n * // only inner and outer dimensions are removed\n * const C = math.zeros(2, 1, 3) // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)\n * math.squeeze(C) // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)\n *\n * See also:\n *\n * subset\n *\n * @param {Matrix | Array} x Matrix to be squeezed\n * @return {Matrix | Array} Squeezed matrix\n */\n return typed(name, {\n Array: function (x) {\n return arraySqueeze(clone(x))\n },\n\n Matrix: function (x) {\n const res = arraySqueeze(x.toArray())\n // FIXME: return the same type of matrix as the input\n return Array.isArray(res) ? matrix(res) : res\n },\n\n any: function (x) {\n // scalar\n return clone(x)\n }\n })\n})\n","import { hasOwnProperty } from './object.js'\n\n/**\n * Get a property of a plain object\n * Throws an error in case the object is not a plain object or the\n * property is not defined on the object itself\n * @param {Object} object\n * @param {string} prop\n * @return {*} Returns the property value when safe\n */\nfunction getSafeProperty (object, prop) {\n // only allow getting safe properties of a plain object\n if (isPlainObject(object) && isSafeProperty(object, prop)) {\n return object[prop]\n }\n\n if (typeof object[prop] === 'function' && isSafeMethod(object, prop)) {\n throw new Error('Cannot access method \"' + prop + '\" as a property')\n }\n\n throw new Error('No access to property \"' + prop + '\"')\n}\n\n/**\n * Set a property on a plain object.\n * Throws an error in case the object is not a plain object or the\n * property would override an inherited property like .constructor or .toString\n * @param {Object} object\n * @param {string} prop\n * @param {*} value\n * @return {*} Returns the value\n */\n// TODO: merge this function into access.js?\nfunction setSafeProperty (object, prop, value) {\n // only allow setting safe properties of a plain object\n if (isPlainObject(object) && isSafeProperty(object, prop)) {\n object[prop] = value\n return value\n }\n\n throw new Error('No access to property \"' + prop + '\"')\n}\n\n/**\n * Test whether a property is safe to use for an object.\n * For example .toString and .constructor are not safe\n * @param {string} prop\n * @return {boolean} Returns true when safe\n */\nfunction isSafeProperty (object, prop) {\n if (!object || typeof object !== 'object') {\n return false\n }\n // SAFE: whitelisted\n // e.g length\n if (hasOwnProperty(safeNativeProperties, prop)) {\n return true\n }\n // UNSAFE: inherited from Object prototype\n // e.g constructor\n if (prop in Object.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Object.prototype is a root object\n return false\n }\n // UNSAFE: inherited from Function prototype\n // e.g call, apply\n if (prop in Function.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Function.prototype is a root object\n return false\n }\n return true\n}\n\n/**\n * Validate whether a method is safe.\n * Throws an error when that's not the case.\n * @param {Object} object\n * @param {string} method\n */\n// TODO: merge this function into assign.js?\nfunction validateSafeMethod (object, method) {\n if (!isSafeMethod(object, method)) {\n throw new Error('No access to method \"' + method + '\"')\n }\n}\n\n/**\n * Check whether a method is safe.\n * Throws an error when that's not the case (for example for `constructor`).\n * @param {Object} object\n * @param {string} method\n * @return {boolean} Returns true when safe, false otherwise\n */\nfunction isSafeMethod (object, method) {\n if (object === null || object === undefined || typeof object[method] !== 'function') {\n return false\n }\n // UNSAFE: ghosted\n // e.g overridden toString\n // Note that IE10 doesn't support __proto__ and we can't do this check there.\n if (hasOwnProperty(object, method) &&\n (Object.getPrototypeOf && (method in Object.getPrototypeOf(object)))) {\n return false\n }\n // SAFE: whitelisted\n // e.g toString\n if (hasOwnProperty(safeNativeMethods, method)) {\n return true\n }\n // UNSAFE: inherited from Object prototype\n // e.g constructor\n if (method in Object.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Object.prototype is a root object\n return false\n }\n // UNSAFE: inherited from Function prototype\n // e.g call, apply\n if (method in Function.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Function.prototype is a root object\n return false\n }\n return true\n}\n\nfunction isPlainObject (object) {\n return typeof object === 'object' && object && object.constructor === Object\n}\n\nconst safeNativeProperties = {\n length: true,\n name: true\n}\n\nconst safeNativeMethods = {\n toString: true,\n valueOf: true,\n toLocaleString: true\n}\n\nexport { getSafeProperty }\nexport { setSafeProperty }\nexport { isSafeProperty }\nexport { validateSafeMethod }\nexport { isSafeMethod }\nexport { isPlainObject }\n","import { isIndex } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\nimport { getSafeProperty, setSafeProperty } from '../../utils/customs.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'subset'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSubset = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Get or set a subset of a matrix or string.\n *\n * Syntax:\n * math.subset(value, index) // retrieve a subset\n * math.subset(value, index, replacement [, defaultValue]) // replace a subset\n *\n * Examples:\n *\n * // get a subset\n * const d = [[1, 2], [3, 4]]\n * math.subset(d, math.index(1, 0)) // returns 3\n * math.subset(d, math.index([0, 1], 1)) // returns [[2], [4]]\n *\n * // replace a subset\n * const e = []\n * const f = math.subset(e, math.index(0, [0, 2]), [5, 6]) // f = [[5, 6]]\n * const g = math.subset(f, math.index(1, 1), 7, 0) // g = [[5, 6], [0, 7]]\n *\n * See also:\n *\n * size, resize, squeeze, index\n *\n * @param {Array | Matrix | string} matrix An array, matrix, or string\n * @param {Index} index An index containing ranges for each\n * dimension\n * @param {*} [replacement] An array, matrix, or scalar.\n * If provided, the subset is replaced with replacement.\n * If not provided, the subset is returned\n * @param {*} [defaultValue=undefined] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * math.matrix elements will be left undefined.\n * @return {Array | Matrix | string} Either the retrieved subset or the updated matrix.\n */\n return typed(name, {\n // get subset\n 'Array, Index': function (value, index) {\n const m = matrix(value)\n const subset = m.subset(index) // returns a Matrix\n return index.isScalar()\n ? subset\n : subset.valueOf() // return an Array (like the input)\n },\n\n 'Matrix, Index': function (value, index) {\n return value.subset(index)\n },\n\n 'Object, Index': _getObjectProperty,\n\n 'string, Index': _getSubstring,\n\n // set subset\n 'Array, Index, any': function (value, index, replacement) {\n return matrix(clone(value))\n .subset(index, replacement, undefined)\n .valueOf()\n },\n\n 'Array, Index, any, any': function (value, index, replacement, defaultValue) {\n return matrix(clone(value))\n .subset(index, replacement, defaultValue)\n .valueOf()\n },\n\n 'Matrix, Index, any': function (value, index, replacement) {\n return value.clone().subset(index, replacement)\n },\n\n 'Matrix, Index, any, any': function (value, index, replacement, defaultValue) {\n return value.clone().subset(index, replacement, defaultValue)\n },\n\n 'string, Index, string': _setSubstring,\n 'string, Index, string, string': _setSubstring,\n 'Object, Index, any': _setObjectProperty\n })\n})\n\n/**\n * Retrieve a subset of a string\n * @param {string} str string from which to get a substring\n * @param {Index} index An index containing ranges for each dimension\n * @returns {string} substring\n * @private\n */\nfunction _getSubstring (str, index) {\n if (!isIndex(index)) {\n // TODO: better error message\n throw new TypeError('Index expected')\n }\n if (index.size().length !== 1) {\n throw new DimensionError(index.size().length, 1)\n }\n\n // validate whether the range is out of range\n const strLen = str.length\n validateIndex(index.min()[0], strLen)\n validateIndex(index.max()[0], strLen)\n\n const range = index.dimension(0)\n\n let substr = ''\n range.forEach(function (v) {\n substr += str.charAt(v)\n })\n\n return substr\n}\n\n/**\n * Replace a substring in a string\n * @param {string} str string to be replaced\n * @param {Index} index An index containing ranges for each dimension\n * @param {string} replacement Replacement string\n * @param {string} [defaultValue] Default value to be uses when resizing\n * the string. is ' ' by default\n * @returns {string} result\n * @private\n */\nfunction _setSubstring (str, index, replacement, defaultValue) {\n if (!index || index.isIndex !== true) {\n // TODO: better error message\n throw new TypeError('Index expected')\n }\n if (index.size().length !== 1) {\n throw new DimensionError(index.size().length, 1)\n }\n if (defaultValue !== undefined) {\n if (typeof defaultValue !== 'string' || defaultValue.length !== 1) {\n throw new TypeError('Single character expected as defaultValue')\n }\n } else {\n defaultValue = ' '\n }\n\n const range = index.dimension(0)\n const len = range.size()[0]\n\n if (len !== replacement.length) {\n throw new DimensionError(range.size()[0], replacement.length)\n }\n\n // validate whether the range is out of range\n const strLen = str.length\n validateIndex(index.min()[0])\n validateIndex(index.max()[0])\n\n // copy the string into an array with characters\n const chars = []\n for (let i = 0; i < strLen; i++) {\n chars[i] = str.charAt(i)\n }\n\n range.forEach(function (v, i) {\n chars[v] = replacement.charAt(i[0])\n })\n\n // initialize undefined characters with a space\n if (chars.length > strLen) {\n for (let i = strLen - 1, len = chars.length; i < len; i++) {\n if (!chars[i]) {\n chars[i] = defaultValue\n }\n }\n }\n\n return chars.join('')\n}\n\n/**\n * Retrieve a property from an object\n * @param {Object} object\n * @param {Index} index\n * @return {*} Returns the value of the property\n * @private\n */\nfunction _getObjectProperty (object, index) {\n if (index.size().length !== 1) {\n throw new DimensionError(index.size(), 1)\n }\n\n const key = index.dimension(0)\n if (typeof key !== 'string') {\n throw new TypeError('String expected as index to retrieve an object property')\n }\n\n return getSafeProperty(object, key)\n}\n\n/**\n * Set a property on an object\n * @param {Object} object\n * @param {Index} index\n * @param {*} replacement\n * @return {*} Returns the updated object\n * @private\n */\nfunction _setObjectProperty (object, index, replacement) {\n if (index.size().length !== 1) {\n throw new DimensionError(index.size(), 1)\n }\n\n const key = index.dimension(0)\n if (typeof key !== 'string') {\n throw new TypeError('String expected as index to retrieve an object property')\n }\n\n // clone the object, and apply the property to the clone\n const updated = clone(object)\n setSafeProperty(updated, key, replacement)\n\n return updated\n}\n","import { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'transpose'\nconst dependencies = ['typed', 'matrix']\n\nexport const createTranspose = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Transpose a matrix. All values of the matrix are reflected over its\n * main diagonal. Only applicable to two dimensional matrices containing\n * a vector (i.e. having size `[1,n]` or `[n,1]`). One dimensional\n * vectors and scalars return the input unchanged.\n *\n * Syntax:\n *\n * math.transpose(x)\n *\n * Examples:\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.transpose(A) // returns [[1, 4], [2, 5], [3, 6]]\n *\n * See also:\n *\n * diag, inv, subset, squeeze\n *\n * @param {Array | Matrix} x Matrix to be transposed\n * @return {Array | Matrix} The transposed matrix\n */\n return typed('transpose', {\n\n Array: function (x) {\n // use dense matrix implementation\n return this(matrix(x)).valueOf()\n },\n\n Matrix: function (x) {\n // matrix size\n const size = x.size()\n\n // result\n let c\n\n // process dimensions\n switch (size.length) {\n case 1:\n // vector\n c = x.clone()\n break\n\n case 2:\n {\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // check columns\n if (columns === 0) {\n // throw exception\n throw new RangeError('Cannot transpose a 2D matrix with no columns (size: ' + format(size) + ')')\n }\n\n // process storage format\n switch (x.storage()) {\n case 'dense':\n c = _denseTranspose(x, rows, columns)\n break\n case 'sparse':\n c = _sparseTranspose(x, rows, columns)\n break\n }\n }\n break\n\n default:\n // multi dimensional\n throw new RangeError('Matrix must be a vector or two dimensional (size: ' + format(this._size) + ')')\n }\n return c\n },\n\n // scalars\n any: function (x) {\n return clone(x)\n }\n })\n\n function _denseTranspose (m, rows, columns) {\n // matrix array\n const data = m._data\n // transposed matrix data\n const transposed = []\n let transposedRow\n // loop columns\n for (let j = 0; j < columns; j++) {\n // initialize row\n transposedRow = transposed[j] = []\n // loop rows\n for (let i = 0; i < rows; i++) {\n // set data\n transposedRow[i] = clone(data[i][j])\n }\n }\n // return matrix\n return m.createDenseMatrix({\n data: transposed,\n size: [columns, rows],\n datatype: m._datatype\n })\n }\n\n function _sparseTranspose (m, rows, columns) {\n // matrix arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // result matrices\n const cvalues = values ? [] : undefined\n const cindex = []\n const cptr = []\n // row counts\n const w = []\n for (let x = 0; x < rows; x++) { w[x] = 0 }\n // vars\n let p, l, j\n // loop values in matrix\n for (p = 0, l = index.length; p < l; p++) {\n // number of values in row\n w[index[p]]++\n }\n // cumulative sum\n let sum = 0\n // initialize cptr with the cummulative sum of row counts\n for (let i = 0; i < rows; i++) {\n // update cptr\n cptr.push(sum)\n // update sum\n sum += w[i]\n // update w\n w[i] = cptr[i]\n }\n // update cptr\n cptr.push(sum)\n // loop columns\n for (j = 0; j < columns; j++) {\n // values & index in column\n for (let k0 = ptr[j], k1 = ptr[j + 1], k = k0; k < k1; k++) {\n // C values & index\n const q = w[index[k]]++\n // C[j, i] = A[i, j]\n cindex[q] = j\n // check we need to process values (pattern matrix)\n if (values) { cvalues[q] = clone(values[k]) }\n }\n }\n // return matrix\n return m.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [columns, rows],\n datatype: m._datatype\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'ctranspose'\nconst dependencies = ['typed', 'transpose', 'conj']\n\nexport const createCtranspose = /* #__PURE__ */ factory(name, dependencies, ({ typed, transpose, conj }) => {\n /**\n * Transpose and complex conjugate a matrix. All values of the matrix are\n * reflected over its main diagonal and then the complex conjugate is\n * taken. This is equivalent to complex conjugation for scalars and\n * vectors.\n *\n * Syntax:\n *\n * math.ctranspose(x)\n *\n * Examples:\n *\n * const A = [[1, 2, 3], [4, 5, math.complex(6,7)]]\n * math.ctranspose(A) // returns [[1, 4], [2, 5], [3, {re:6,im:7}]]\n *\n * See also:\n *\n * transpose, diag, inv, subset, squeeze\n *\n * @param {Array | Matrix} x Matrix to be ctransposed\n * @return {Array | Matrix} The ctransposed matrix\n */\n return typed(name, {\n any: function (x) {\n return conj(transpose(x))\n }\n })\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { resize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'zeros'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createZeros = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Create a matrix filled with zeros. The created matrix can have one or\n * multiple dimensions.\n *\n * Syntax:\n *\n * math.zeros(m)\n * math.zeros(m, format)\n * math.zeros(m, n)\n * math.zeros(m, n, format)\n * math.zeros([m, n])\n * math.zeros([m, n], format)\n *\n * Examples:\n *\n * math.zeros(3) // returns [0, 0, 0]\n * math.zeros(3, 2) // returns [[0, 0], [0, 0], [0, 0]]\n * math.zeros(3, 'dense') // returns [0, 0, 0]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.zeros(math.size(A)) // returns [[0, 0, 0], [0, 0, 0]]\n *\n * See also:\n *\n * ones, identity, size, range\n *\n * @param {...number | Array} size The size of each dimension of the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Array | Matrix} A matrix filled with zeros\n */\n return typed(name, {\n '': function () {\n return (config.matrix === 'Array')\n ? _zeros([])\n : _zeros([], 'default')\n },\n\n // math.zeros(m, n, p, ..., format)\n // TODO: more accurate signature '...number | BigNumber, string' as soon as typed-function supports this\n '...number | BigNumber | string': function (size) {\n const last = size[size.length - 1]\n if (typeof last === 'string') {\n const format = size.pop()\n return _zeros(size, format)\n } else if (config.matrix === 'Array') {\n return _zeros(size)\n } else {\n return _zeros(size, 'default')\n }\n },\n\n Array: _zeros,\n\n Matrix: function (size) {\n const format = size.storage()\n return _zeros(size.valueOf(), format)\n },\n\n 'Array | Matrix, string': function (size, format) {\n return _zeros(size.valueOf(), format)\n }\n })\n\n /**\n * Create an Array or Matrix with zeros\n * @param {Array} size\n * @param {string} [format='default']\n * @return {Array | Matrix}\n * @private\n */\n function _zeros (size, format) {\n const hasBigNumbers = _normalize(size)\n const defaultValue = hasBigNumbers ? new BigNumber(0) : 0\n _validate(size)\n\n if (format) {\n // return a matrix\n const m = matrix(format)\n if (size.length > 0) {\n return m.resize(size, defaultValue)\n }\n return m\n } else {\n // return an Array\n const arr = []\n if (size.length > 0) {\n return resize(arr, size, defaultValue)\n }\n return arr\n }\n }\n\n // replace BigNumbers with numbers, returns true if size contained BigNumbers\n function _normalize (size) {\n let hasBigNumbers = false\n size.forEach(function (value, index, arr) {\n if (isBigNumber(value)) {\n hasBigNumbers = true\n arr[index] = value.toNumber()\n }\n })\n return hasBigNumbers\n }\n\n // validate arguments\n function _validate (size) {\n size.forEach(function (value) {\n if (typeof value !== 'number' || !isInteger(value) || value < 0) {\n throw new Error('Parameters in function zeros must be positive integers')\n }\n })\n }\n})\n\n// TODO: zeros contains almost the same code as ones. Reuse this?\n","/* eslint-disable no-loss-of-precision */\n\nimport { deepMap } from '../../utils/collection.js'\nimport { sign } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'erf'\nconst dependencies = [\n 'typed'\n]\n\nexport const createErf = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the erf function of a value using a rational Chebyshev\n * approximations for different intervals of x.\n *\n * This is a translation of W. J. Cody's Fortran implementation from 1987\n * ( https://www.netlib.org/specfun/erf ). See the AMS publication\n * \"Rational Chebyshev Approximations for the Error Function\" by W. J. Cody\n * for an explanation of this process.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.erf(x)\n *\n * Examples:\n *\n * math.erf(0.2) // returns 0.22270258921047847\n * math.erf(-0.5) // returns -0.5204998778130465\n * math.erf(4) // returns 0.9999999845827421\n *\n * @param {number | Array | Matrix} x A real number\n * @return {number | Array | Matrix} The erf of `x`\n */\n return typed('name', {\n number: function (x) {\n const y = Math.abs(x)\n\n if (y >= MAX_NUM) {\n return sign(x)\n }\n if (y <= THRESH) {\n return sign(x) * erf1(y)\n }\n if (y <= 4.0) {\n return sign(x) * (1 - erfc2(y))\n }\n return sign(x) * (1 - erfc3(y))\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n\n // TODO: For complex numbers, use the approximation for the Faddeeva function\n // from \"More Efficient Computation of the Complex Error Function\" (AMS)\n\n })\n\n /**\n * Approximates the error function erf() for x <= 0.46875 using this function:\n * n\n * erf(x) = x * sum (p_j * x^(2j)) / (q_j * x^(2j))\n * j=0\n */\n function erf1 (y) {\n const ysq = y * y\n let xnum = P[0][4] * ysq\n let xden = ysq\n let i\n\n for (i = 0; i < 3; i += 1) {\n xnum = (xnum + P[0][i]) * ysq\n xden = (xden + Q[0][i]) * ysq\n }\n return y * (xnum + P[0][3]) / (xden + Q[0][3])\n }\n\n /**\n * Approximates the complement of the error function erfc() for\n * 0.46875 <= x <= 4.0 using this function:\n * n\n * erfc(x) = e^(-x^2) * sum (p_j * x^j) / (q_j * x^j)\n * j=0\n */\n function erfc2 (y) {\n let xnum = P[1][8] * y\n let xden = y\n let i\n\n for (i = 0; i < 7; i += 1) {\n xnum = (xnum + P[1][i]) * y\n xden = (xden + Q[1][i]) * y\n }\n const result = (xnum + P[1][7]) / (xden + Q[1][7])\n const ysq = parseInt(y * 16) / 16\n const del = (y - ysq) * (y + ysq)\n return Math.exp(-ysq * ysq) * Math.exp(-del) * result\n }\n\n /**\n * Approximates the complement of the error function erfc() for x > 4.0 using\n * this function:\n *\n * erfc(x) = (e^(-x^2) / x) * [ 1/sqrt(pi) +\n * n\n * 1/(x^2) * sum (p_j * x^(-2j)) / (q_j * x^(-2j)) ]\n * j=0\n */\n function erfc3 (y) {\n let ysq = 1 / (y * y)\n let xnum = P[2][5] * ysq\n let xden = ysq\n let i\n\n for (i = 0; i < 4; i += 1) {\n xnum = (xnum + P[2][i]) * ysq\n xden = (xden + Q[2][i]) * ysq\n }\n let result = ysq * (xnum + P[2][4]) / (xden + Q[2][4])\n result = (SQRPI - result) / y\n ysq = parseInt(y * 16) / 16\n const del = (y - ysq) * (y + ysq)\n return Math.exp(-ysq * ysq) * Math.exp(-del) * result\n }\n})\n\n/**\n * Upper bound for the first approximation interval, 0 <= x <= THRESH\n * @constant\n */\nconst THRESH = 0.46875\n\n/**\n * Constant used by W. J. Cody's Fortran77 implementation to denote sqrt(pi)\n * @constant\n */\nconst SQRPI = 5.6418958354775628695e-1\n\n/**\n * Coefficients for each term of the numerator sum (p_j) for each approximation\n * interval (see W. J. Cody's paper for more details)\n * @constant\n */\nconst P = [[\n 3.16112374387056560e00, 1.13864154151050156e02,\n 3.77485237685302021e02, 3.20937758913846947e03,\n 1.85777706184603153e-1\n], [\n 5.64188496988670089e-1, 8.88314979438837594e00,\n 6.61191906371416295e01, 2.98635138197400131e02,\n 8.81952221241769090e02, 1.71204761263407058e03,\n 2.05107837782607147e03, 1.23033935479799725e03,\n 2.15311535474403846e-8\n], [\n 3.05326634961232344e-1, 3.60344899949804439e-1,\n 1.25781726111229246e-1, 1.60837851487422766e-2,\n 6.58749161529837803e-4, 1.63153871373020978e-2\n]]\n\n/**\n * Coefficients for each term of the denominator sum (q_j) for each approximation\n * interval (see W. J. Cody's paper for more details)\n * @constant\n */\nconst Q = [[\n 2.36012909523441209e01, 2.44024637934444173e02,\n 1.28261652607737228e03, 2.84423683343917062e03\n], [\n 1.57449261107098347e01, 1.17693950891312499e02,\n 5.37181101862009858e02, 1.62138957456669019e03,\n 3.29079923573345963e03, 4.36261909014324716e03,\n 3.43936767414372164e03, 1.23033935480374942e03\n], [\n 2.56852019228982242e00, 1.87295284992346047e00,\n 5.27905102951428412e-1, 6.05183413124413191e-2,\n 2.33520497626869185e-3\n]]\n\n/**\n * Maximum/minimum safe numbers to input to erf() (in ES6+, this number is\n * Number.[MAX|MIN]_SAFE_INTEGER). erf() for all numbers beyond this limit will\n * return 1\n */\nconst MAX_NUM = Math.pow(2, 53)\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'mode'\nconst dependencies = ['typed', 'isNaN', 'isNumeric']\n\nexport const createMode = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNaN, isNumeric }) => {\n /**\n * Computes the mode of a set of numbers or a list with values(numbers or characters).\n * If there are more than one modes, it returns a list of those values.\n *\n * Syntax:\n *\n * math.mode(a, b, c, ...)\n * math.mode(A)\n *\n * Examples:\n *\n * math.mode(2, 1, 4, 3, 1) // returns [1]\n * math.mode([1, 2.7, 3.2, 4, 2.7]) // returns [2.7]\n * math.mode(1, 4, 6, 1, 6) // returns [1, 6]\n * math.mode('a','a','b','c') // returns [\"a\"]\n * math.mode(1, 1.5, 'abc') // returns [1, 1.5, \"abc\"]\n *\n * See also:\n *\n * median,\n * mean\n *\n * @param {... *} args A single matrix\n * @return {*} The mode of all values\n */\n return typed(name, {\n 'Array | Matrix': _mode,\n\n '...': function (args) {\n return _mode(args)\n }\n })\n\n /**\n * Calculates the mode in an 1-dimensional array\n * @param {Array} values\n * @return {Array} mode\n * @private\n */\n function _mode (values) {\n values = flatten(values.valueOf())\n const num = values.length\n if (num === 0) {\n throw new Error('Cannot calculate mode of an empty array')\n }\n\n const count = {}\n let mode = []\n let max = 0\n for (let i = 0; i < values.length; i++) {\n const value = values[i]\n\n if (isNumeric(value) && isNaN(value)) {\n throw new Error('Cannot calculate mode of an array containing NaN values')\n }\n\n if (!(value in count)) {\n count[value] = 0\n }\n\n count[value]++\n\n if (count[value] === max) {\n mode.push(value)\n } else if (count[value] > max) {\n max = count[value]\n mode = [value]\n }\n }\n return mode\n }\n})\n","import { typeOf } from '../../../utils/is.js'\n\n/**\n * Improve error messages for statistics functions. Errors are typically\n * thrown in an internally used function like larger, causing the error\n * not to mention the function (like max) which is actually used by the user.\n *\n * @param {Error} err\n * @param {String} fnName\n * @param {*} [value]\n * @return {Error}\n */\nexport function improveErrorMessage (err, fnName, value) {\n // TODO: add information with the index (also needs transform in expression parser)\n let details\n\n if (String(err).indexOf('Unexpected type') !== -1) {\n details = arguments.length > 2\n ? ' (type: ' + typeOf(value) + ', value: ' + JSON.stringify(value) + ')'\n : ' (type: ' + err.data.actual + ')'\n\n return new TypeError('Cannot calculate ' + fnName + ', unexpected type of argument' + details)\n }\n\n if (String(err).indexOf('complex numbers') !== -1) {\n details = arguments.length > 2\n ? ' (type: ' + typeOf(value) + ', value: ' + JSON.stringify(value) + ')'\n : ''\n\n return new TypeError('Cannot calculate ' + fnName + ', no ordering relation is defined for complex numbers' + details)\n }\n\n return err\n}\n","import { deepForEach } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'prod'\nconst dependencies = ['typed', 'config', 'multiplyScalar', 'numeric']\n\nexport const createProd = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, multiplyScalar, numeric }) => {\n /**\n * Compute the product of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the sum of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.prod(a, b, c, ...)\n * math.prod(A)\n *\n * Examples:\n *\n * math.multiply(2, 3) // returns 6\n * math.prod(2, 3) // returns 6\n * math.prod(2, 3, 4) // returns 24\n * math.prod([2, 3, 4]) // returns 24\n * math.prod([[2, 5], [4, 3]]) // returns 120\n *\n * See also:\n *\n * mean, median, min, max, sum, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The product of all values\n */\n return typed(name, {\n // prod([a, b, c, d, ...])\n 'Array | Matrix': _prod,\n\n // prod([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n // TODO: implement prod(A, dim)\n throw new Error('prod(A, dim) is not yet supported')\n // return reduce(arguments[0], arguments[1], math.prod)\n },\n\n // prod(a, b, c, d, ...)\n '...': function (args) {\n return _prod(args)\n }\n })\n\n /**\n * Recursively calculate the product of an n-dimensional array\n * @param {Array} array\n * @return {number} prod\n * @private\n */\n function _prod (array) {\n let prod\n\n deepForEach(array, function (value) {\n try {\n prod = (prod === undefined) ? value : multiplyScalar(prod, value)\n } catch (err) {\n throw improveErrorMessage(err, 'prod', value)\n }\n })\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof prod === 'string') {\n prod = numeric(prod, config.number)\n }\n\n if (prod === undefined) {\n throw new Error('Cannot calculate prod of an empty array')\n }\n\n return prod\n }\n})\n","import { format as formatString } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'format'\nconst dependencies = ['typed']\n\nexport const createFormat = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Format a value of any type into a string.\n *\n * Syntax:\n *\n * math.format(value)\n * math.format(value, options)\n * math.format(value, precision)\n * math.format(value, callback)\n *\n * Where:\n *\n * - `value: *`\n * The value to be formatted\n * - `options: Object`\n * An object with formatting options. Available options:\n * - `notation: string`\n * Number notation. Choose from:\n * - 'fixed'\n * Always use regular number notation.\n * For example '123.40' and '14000000'\n * - 'exponential'\n * Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * - 'engineering'\n * Always use engineering notation: always have exponential notation,\n * and select the exponent to be a multiple of 3.\n * For example '123.4e+0' and '14.0e+6'\n * - 'auto' (default)\n * Regular number notation for numbers having an absolute value between\n * `lower` and `upper` bounds, and uses exponential notation elsewhere.\n * Lower bound is included, upper bound is excluded.\n * For example '123.4' and '1.4e7'.\n * - `precision: number`\n * A number between 0 and 16 to round the digits of the number. In case\n * of notations 'exponential', 'engineering', and 'auto', `precision`\n * defines the total number of significant digits returned.\n * In case of notation 'fixed', `precision` defines the number of\n * significant digits after the decimal point.\n * `precision` is undefined by default.\n * - `lowerExp: number`\n * Exponent determining the lower boundary for formatting a value with\n * an exponent when `notation='auto`. Default value is `-3`.\n * - `upperExp: number`\n * Exponent determining the upper boundary for formatting a value with\n * an exponent when `notation='auto`. Default value is `5`.\n * - `fraction: string`. Available values: 'ratio' (default) or 'decimal'.\n * For example `format(fraction(1, 3))` will output '1/3' when 'ratio' is\n * configured, and will output `0.(3)` when 'decimal' is configured.\n * - `callback: function`\n * A custom formatting function, invoked for all numeric elements in `value`,\n * for example all elements of a matrix, or the real and imaginary\n * parts of a complex number. This callback can be used to override the\n * built-in numeric notation with any type of formatting. Function `callback`\n * is called with `value` as parameter and must return a string.\n *\n * When `value` is an Object:\n *\n * - When the object contains a property `format` being a function, this function\n * is invoked as `value.format(options)` and the result is returned.\n * - When the object has its own `toString` method, this method is invoked\n * and the result is returned.\n * - In other cases the function will loop over all object properties and\n * return JSON object notation like '{\"a\": 2, \"b\": 3}'.\n *\n * When value is a function:\n *\n * - When the function has a property `syntax`, it returns this\n * syntax description.\n * - In other cases, a string `'function'` is returned.\n *\n * Examples:\n *\n * math.format(6.4) // returns '6.4'\n * math.format(1240000) // returns '1.24e6'\n * math.format(1/3) // returns '0.3333333333333333'\n * math.format(1/3, 3) // returns '0.333'\n * math.format(21385, 2) // returns '21000'\n * math.format(12e8, {notation: 'fixed'}) // returns '1200000000'\n * math.format(2.3, {notation: 'fixed', precision: 4}) // returns '2.3000'\n * math.format(52.8, {notation: 'exponential'}) // returns '5.28e+1'\n * math.format(12400,{notation: 'engineering'}) // returns '12.400e+3'\n * math.format(2000, {lowerExp: -2, upperExp: 2}) // returns '2e+3'\n *\n * function formatCurrency(value) {\n * // return currency notation with two digits:\n * return '$' + value.toFixed(2)\n *\n * // you could also use math.format inside the callback:\n * // return '$' + math.format(value, {notation: 'fixed', precision: 2})\n * }\n * math.format([2.1, 3, 0.016], formatCurrency} // returns '[$2.10, $3.00, $0.02]'\n *\n * See also:\n *\n * print\n *\n * @param {*} value Value to be stringified\n * @param {Object | Function | number} [options] Formatting options\n * @return {string} The formatted value\n */\n return typed(name, {\n any: formatString,\n 'any, Object | function | number': formatString\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\n\nfunction baseFormatter (base) {\n const prefixes = { 2: '0b', 8: '0o', 16: '0x' }\n const prefix = prefixes[base]\n return function (n) {\n if (n > 2 ** 31 - 1 || n < -(2 ** 31)) {\n throw new Error('Value must be in range [-2^31, 2^31-1]')\n }\n if (!isInteger(n)) {\n throw new Error('Value must be an integer')\n }\n if (n < 0) {\n n = n + 2 ** 32\n }\n return `${prefix}${n.toString(base)}`\n }\n}\n\nconst dependencies = ['typed']\n\nexport function createBaseFormatterFactory (name, base) {\n return factory(name, dependencies, ({ typed }) => {\n return typed(name, {\n number: baseFormatter(base)\n })\n })\n}\n","import { createBaseFormatterFactory } from './baseUtils.js'\n\n/**\n * Format a number as binary.\n *\n * Syntax:\n *\n * math.bin(value)\n *\n * Examples:\n *\n * //the following outputs \"0b10\"\n * math.bin(2)\n *\n * See also:\n *\n * oct\n * hex\n *\n * @param {number} value Value to be stringified\n * @return {string} The formatted value\n */\nexport const createBin = createBaseFormatterFactory('bin', 2)\n","import { createBaseFormatterFactory } from './baseUtils.js'\n\n/**\n * Format a number as octal.\n *\n * Syntax:\n *\n * math.oct(value)\n *\n * Examples:\n *\n * //the following outputs \"0o70\"\n * math.oct(56)\n *\n * See also:\n *\n * bin\n * hex\n *\n * @param {number} value Value to be stringified\n * @return {string} The formatted value\n */\n\nexport const createOct = createBaseFormatterFactory('oct', 8)\n","import { createBaseFormatterFactory } from './baseUtils.js'\n\n/**\n * Format a number as hexadecimal.\n *\n * Syntax:\n *\n * math.hex(value)\n *\n * Examples:\n *\n * //the following outputs \"0xF0\"\n * math.hex(240)\n *\n * See also:\n *\n * oct\n * bin\n *\n * @param {number} value Value to be stringified\n * @return {string} The formatted value\n */\nexport const createHex = createBaseFormatterFactory('hex', 16)\n","import { format } from '../../utils/string.js'\nimport { isString } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'print'\nconst dependencies = ['typed']\n\nexport const createPrint = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Interpolate values into a string template.\n *\n * Syntax:\n *\n * math.print(template, values)\n * math.print(template, values, precision)\n * math.print(template, values, options)\n *\n * Example usage:\n *\n * // the following outputs: 'Lucy is 5 years old'\n * math.print('Lucy is $age years old', {age: 5})\n *\n * // the following outputs: 'The value of pi is 3.141592654'\n * math.print('The value of pi is $pi', {pi: math.pi}, 10)\n *\n * // the following outputs: 'hello Mary! The date is 2013-03-23'\n * math.print('Hello $user.name! The date is $date', {\n * user: {\n * name: 'Mary',\n * },\n * date: new Date(2013, 2, 23).toISOString().substring(0, 10)\n * })\n *\n * // the following outputs: 'My favorite fruits are apples and bananas !'\n * math.print('My favorite fruits are $0 and $1 !', [\n * 'apples',\n * 'bananas'\n * ])\n *\n * See also:\n *\n * format\n *\n * @param {string} template A string containing variable placeholders.\n * @param {Object | Array | Matrix} values An object or array containing variables\n * which will be filled in in the template.\n * @param {number | Object} [options] Formatting options,\n * or the number of digits to format numbers.\n * See function math.format for a description\n * of all options.\n * @return {string} Interpolated string\n */\n return typed(name, {\n // note: Matrix will be converted automatically to an Array\n 'string, Object | Array': _print,\n 'string, Object | Array, number | Object': _print\n })\n})\n\n/**\n * Interpolate values into a string template.\n * @param {string} template\n * @param {Object} values\n * @param {number | Object} [options]\n * @returns {string} Interpolated string\n * @private\n */\nfunction _print (template, values, options) {\n return template.replace(/\\$([\\w.]+)/g, function (original, key) {\n const keys = key.split('.')\n let value = values[keys.shift()]\n while (keys.length && value !== undefined) {\n const k = keys.shift()\n value = k ? value[k] : value + '.'\n }\n\n if (value !== undefined) {\n if (!isString(value)) {\n return format(value, options)\n } else {\n return value\n }\n }\n\n return original\n }\n )\n}\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'to'\nconst dependencies = [\n 'typed',\n 'matrix'\n]\n\nexport const createTo = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Change the unit of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.to(x, unit)\n *\n * Examples:\n *\n * math.to(math.unit('2 inch'), 'cm') // returns Unit 5.08 cm\n * math.to(math.unit('2 inch'), math.unit(null, 'cm')) // returns Unit 5.08 cm\n * math.to(math.unit(16, 'bytes'), 'bits') // returns Unit 128 bits\n *\n * See also:\n *\n * unit\n *\n * @param {Unit | Array | Matrix} x The unit to be converted.\n * @param {Unit | Array | Matrix} unit New unit. Can be a string like \"cm\"\n * or a unit without value.\n * @return {Unit | Array | Matrix} value with changed, fixed unit.\n */\n return typed(name, {\n 'Unit, Unit | string': function (x, unit) {\n return x.to(unit)\n },\n\n 'Matrix, Matrix': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'Matrix, any': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm14(x, y, this, false)\n },\n\n 'any, Matrix': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isPrime'\nconst dependencies = ['typed']\n\nexport const createIsPrime = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is prime: has no divisors other than itself and one.\n * The function supports type `number`, `bignumber`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isPrime(x)\n *\n * Examples:\n *\n * math.isPrime(3) // returns true\n * math.isPrime(-2) // returns false\n * math.isPrime(0) // returns false\n * math.isPrime(-0) // returns false\n * math.isPrime(0.5) // returns false\n * math.isPrime('2') // returns true\n * math.isPrime([2, 17, 100]) // returns [true, true, false]\n *\n * See also:\n *\n * isNumeric, isZero, isNegative, isInteger\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: function (x) {\n if (x * 0 !== 0) {\n return false\n }\n if (x <= 3) {\n return x > 1\n }\n if (x % 2 === 0 || x % 3 === 0) {\n return false\n }\n for (let i = 5; i * i <= x; i += 6) {\n if (x % i === 0 || x % (i + 2) === 0) {\n return false\n }\n }\n return true\n },\n\n BigNumber: function (n) {\n if (n.toNumber() * 0 !== 0) {\n return false\n }\n if (n.lte(3)) return n.gt(1)\n if (n.mod(2).eq(0) || n.mod(3).eq(0)) return false\n\n for (let i = 5; n.gte(i * i); i += 6) {\n if (n.mod(i).eq(0) || n.mod(i + 2).eq(0)) {\n return false\n }\n }\n\n return true\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { noBignumber, noFraction } from '../../utils/noop.js'\n\nconst name = 'numeric'\nconst dependencies = ['number', '?bignumber', '?fraction']\n\nexport const createNumeric = /* #__PURE__ */ factory(name, dependencies, ({ number, bignumber, fraction }) => {\n const validInputTypes = {\n string: true,\n number: true,\n BigNumber: true,\n Fraction: true\n }\n\n // Load the conversion functions for each output type\n const validOutputTypes = {\n number: (x) => number(x),\n BigNumber: bignumber\n ? (x) => bignumber(x)\n : noBignumber,\n Fraction: fraction\n ? (x) => fraction(x)\n : noFraction\n }\n\n /**\n * Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.\n *\n * Syntax:\n *\n * math.numeric(x)\n *\n * Examples:\n *\n * math.numeric('4') // returns number 4\n * math.numeric('4', 'number') // returns number 4\n * math.numeric('4', 'BigNumber') // returns BigNumber 4\n * math.numeric('4', 'Fraction') // returns Fraction 4\n * math.numeric(4, 'Fraction') // returns Fraction 4\n * math.numeric(math.fraction(2, 5), 'number') // returns number 0.4\n *\n * See also:\n *\n * number, fraction, bignumber, string, format\n *\n * @param {string | number | BigNumber | Fraction } value\n * A numeric value or a string containing a numeric value\n * @param {string} outputType\n * Desired numeric output type.\n * Available values: 'number', 'BigNumber', or 'Fraction'\n * @return {number | BigNumber | Fraction}\n * Returns an instance of the numeric in the requested type\n */\n return function numeric (value, outputType) {\n const inputType = typeOf(value)\n\n if (!(inputType in validInputTypes)) {\n throw new TypeError('Cannot convert ' + value + ' of type \"' + inputType + '\"; valid input types are ' + Object.keys(validInputTypes).join(', '))\n }\n if (!(outputType in validOutputTypes)) {\n throw new TypeError('Cannot convert ' + value + ' to type \"' + outputType + '\"; valid output types are ' + Object.keys(validOutputTypes).join(', '))\n }\n\n if (outputType === inputType) {\n return value\n } else {\n return validOutputTypes[outputType](value)\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { typeOf } from '../../utils/is.js'\n\nconst name = 'divideScalar'\nconst dependencies = ['typed', 'numeric']\n\nexport const createDivideScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed, numeric }) => {\n /**\n * Divide two scalar values, `x / y`.\n * This function is meant for internal use: it is used by the public functions\n * `divide` and `inv`.\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x Numerator\n * @param {number | BigNumber | Fraction | Complex} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit} Quotient, `x / y`\n * @private\n */\n return typed(name, {\n 'number, number': function (x, y) {\n return x / y\n },\n\n 'Complex, Complex': function (x, y) {\n return x.div(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.div(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.div(y)\n },\n\n 'Unit, number | Fraction | BigNumber': function (x, y) {\n const res = x.clone()\n // TODO: move the divide function to Unit.js, it uses internals of Unit\n const one = numeric(1, typeOf(y))\n res.value = this(((res.value === null) ? res._normalize(one) : res.value), y)\n return res\n },\n\n 'number | Fraction | BigNumber, Unit': function (x, y) {\n let res = y.clone()\n res = res.pow(-1)\n // TODO: move the divide function to Unit.js, it uses internals of Unit\n const one = numeric(1, typeOf(x))\n res.value = this(x, ((y.value === null) ? y._normalize(one) : y.value))\n return res\n },\n\n 'Unit, Unit': function (x, y) {\n return x.divide(y)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { arraySize as size } from '../../utils/array.js'\nimport { powNumber } from '../../plain/number/index.js'\n\nconst name = 'pow'\nconst dependencies = [\n 'typed',\n 'config',\n 'identity',\n 'multiply',\n 'matrix',\n 'fraction',\n 'number',\n 'Complex'\n]\n\nexport const createPow = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, identity, multiply, matrix, number, fraction, Complex }) => {\n /**\n * Calculates the power of x to y, `x ^ y`.\n * Matrix exponentiation is supported for square matrices `x`, and positive\n * integer exponents `y`.\n *\n * For cubic roots of negative numbers, the function returns the principal\n * root by default. In order to let the function return the real root,\n * math.js can be configured with `math.config({predictable: true})`.\n * To retrieve all cubic roots of a value, use `math.cbrt(x, true)`.\n *\n * Syntax:\n *\n * math.pow(x, y)\n *\n * Examples:\n *\n * math.pow(2, 3) // returns number 8\n *\n * const a = math.complex(2, 3)\n * math.pow(a, 2) // returns Complex -5 + 12i\n *\n * const b = [[1, 2], [4, 3]]\n * math.pow(b, 2) // returns Array [[9, 8], [16, 17]]\n *\n * See also:\n *\n * multiply, sqrt, cbrt, nthRoot\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x The base\n * @param {number | BigNumber | Complex} y The exponent\n * @return {number | BigNumber | Complex | Array | Matrix} The value of `x` to the power `y`\n */\n return typed(name, {\n 'number, number': _pow,\n\n 'Complex, Complex': function (x, y) {\n return x.pow(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n if (y.isInteger() || x >= 0 || config.predictable) {\n return x.pow(y)\n } else {\n return new Complex(x.toNumber(), 0).pow(y.toNumber(), 0)\n }\n },\n\n 'Fraction, Fraction': function (x, y) {\n if (y.d !== 1) {\n if (config.predictable) {\n throw new Error('Function pow does not support non-integer exponents for fractions.')\n } else {\n return _pow(x.valueOf(), y.valueOf())\n }\n } else {\n return x.pow(y)\n }\n },\n\n 'Array, number': _powArray,\n\n 'Array, BigNumber': function (x, y) {\n return _powArray(x, y.toNumber())\n },\n\n 'Matrix, number': _powMatrix,\n\n 'Matrix, BigNumber': function (x, y) {\n return _powMatrix(x, y.toNumber())\n },\n\n 'Unit, number | BigNumber': function (x, y) {\n return x.pow(y)\n }\n\n })\n\n /**\n * Calculates the power of x to y, x^y, for two numbers.\n * @param {number} x\n * @param {number} y\n * @return {number | Complex} res\n * @private\n */\n function _pow (x, y) {\n // Alternatively could define a 'realmode' config option or something, but\n // 'predictable' will work for now\n if (config.predictable && !isInteger(y) && x < 0) {\n // Check to see if y can be represented as a fraction\n try {\n const yFrac = fraction(y)\n const yNum = number(yFrac)\n if (y === yNum || Math.abs((y - yNum) / y) < 1e-14) {\n if (yFrac.d % 2 === 1) {\n return (yFrac.n % 2 === 0 ? 1 : -1) * Math.pow(-x, y)\n }\n }\n } catch (ex) {\n // fraction() throws an error if y is Infinity, etc.\n }\n\n // Unable to express y as a fraction, so continue on\n }\n\n // **for predictable mode** x^Infinity === NaN if x < -1\n // N.B. this behavour is different from `Math.pow` which gives\n // (-2)^Infinity === Infinity\n if (config.predictable &&\n ((x < -1 && y === Infinity) ||\n (x > -1 && x < 0 && y === -Infinity))) {\n return NaN\n }\n\n if (isInteger(y) || x >= 0 || config.predictable) {\n return powNumber(x, y)\n } else {\n // TODO: the following infinity checks are duplicated from powNumber. Deduplicate this somehow\n\n // x^Infinity === 0 if -1 < x < 1\n // A real number 0 is returned instead of complex(0)\n if ((x * x < 1 && y === Infinity) ||\n (x * x > 1 && y === -Infinity)) {\n return 0\n }\n\n return new Complex(x, 0).pow(y, 0)\n }\n }\n\n /**\n * Calculate the power of a 2d array\n * @param {Array} x must be a 2 dimensional, square matrix\n * @param {number} y a positive, integer value\n * @returns {Array}\n * @private\n */\n function _powArray (x, y) {\n if (!isInteger(y) || y < 0) {\n throw new TypeError('For A^b, b must be a positive integer (value is ' + y + ')')\n }\n // verify that A is a 2 dimensional square matrix\n const s = size(x)\n if (s.length !== 2) {\n throw new Error('For A^b, A must be 2 dimensional (A has ' + s.length + ' dimensions)')\n }\n if (s[0] !== s[1]) {\n throw new Error('For A^b, A must be square (size is ' + s[0] + 'x' + s[1] + ')')\n }\n\n let res = identity(s[0]).valueOf()\n let px = x\n while (y >= 1) {\n if ((y & 1) === 1) {\n res = multiply(px, res)\n }\n y >>= 1\n px = multiply(px, px)\n }\n return res\n }\n\n /**\n * Calculate the power of a 2d matrix\n * @param {Matrix} x must be a 2 dimensional, square matrix\n * @param {number} y a positive, integer value\n * @returns {Matrix}\n * @private\n */\n function _powMatrix (x, y) {\n return matrix(_powArray(x.valueOf(), y))\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { isInteger } from '../../utils/number.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { roundNumber } from '../../plain/number/index.js'\n\nconst NO_INT = 'Number of decimals in function round must be an integer'\n\nconst name = 'round'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createRound = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, BigNumber, DenseMatrix }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards the nearest integer.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.round(x)\n * math.round(x, n)\n *\n * Examples:\n *\n * math.round(3.22) // returns number 3\n * math.round(3.82) // returns number 4\n * math.round(-4.2) // returns number -4\n * math.round(-4.7) // returns number -5\n * math.round(3.22, 1) // returns number 3.2\n * math.round(3.88, 1) // returns number 3.9\n * math.round(-4.21, 1) // returns number -4.2\n * math.round(-4.71, 1) // returns number -4.7\n * math.round(math.pi, 3) // returns number 3.142\n * math.round(123.45678, 2) // returns number 123.46\n *\n * const c = math.complex(3.2, -2.7)\n * math.round(c) // returns Complex 3 - 3i\n *\n * math.round([3.2, 3.8, -4.7]) // returns Array [3, 4, -5]\n *\n * See also:\n *\n * ceil, fix, floor\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed(name, {\n ...roundNumberSignatures,\n\n Complex: function (x) {\n return x.round()\n },\n\n 'Complex, number': function (x, n) {\n if (n % 1) { throw new TypeError(NO_INT) }\n\n return x.round(n)\n },\n\n 'Complex, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n const _n = n.toNumber()\n return x.round(_n)\n },\n\n 'number, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n return new BigNumber(x).toDecimalPlaces(n.toNumber())\n },\n\n BigNumber: function (x) {\n return x.toDecimalPlaces(0)\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n return x.toDecimalPlaces(n.toNumber())\n },\n\n Fraction: function (x) {\n return x.round()\n },\n\n 'Fraction, number': function (x, n) {\n if (n % 1) { throw new TypeError(NO_INT) }\n return x.round(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since round(0) = 0\n return deepMap(x, this, true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, SparseMatrix': function (x, y) {\n // check scalar is zero\n if (equalScalar(x, 0)) {\n // do not execute algorithm, result will be a zero matrix\n return zeros(y.size(), y.storage())\n }\n return algorithm12(y, x, this, true)\n },\n\n 'number | Complex | BigNumber, DenseMatrix': function (x, y) {\n // check scalar is zero\n if (equalScalar(x, 0)) {\n // do not execute algorithm, result will be a zero matrix\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nconst roundNumberSignatures = {\n number: roundNumber,\n\n 'number, number': function (x, n) {\n if (!isInteger(n)) { throw new TypeError(NO_INT) }\n if (n < 0 || n > 15) { throw new Error('Number of decimals in function round must be in te range of 0-15') }\n\n return roundNumber(x, n)\n }\n}\n\nexport const createRoundNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, roundNumberSignatures)\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { logNumber } from '../../plain/number/index.js'\n\nconst name = 'log'\nconst dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n\nexport const createLog = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n /**\n * Calculate the logarithm of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log(x)\n * math.log(x, base)\n *\n * Examples:\n *\n * math.log(3.5) // returns 1.252762968495368\n * math.exp(math.log(2.4)) // returns 2.4\n *\n * math.pow(10, 4) // returns 10000\n * math.log(10000, 10) // returns 4\n * math.log(10000) / math.log(10) // returns 4\n *\n * math.log(1024, 2) // returns 10\n * math.pow(2, 10) // returns 1024\n *\n * See also:\n *\n * exp, log2, log10, log1p\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @param {number | BigNumber | Complex} [base=e]\n * Optional base for the logarithm. If not provided, the natural\n * logarithm of `x` is calculated.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return logNumber(x)\n } else {\n // negative value -> complex value computation\n return new Complex(x, 0).log()\n }\n },\n\n Complex: function (x) {\n return x.log()\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.ln()\n } else {\n // downgrade to number, return Complex valued result\n return new Complex(x.toNumber(), 0).log()\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n 'any, any': function (x, base) {\n // calculate logarithm for a specified base, log(x, base)\n return divideScalar(this(x), this(base))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log1p as _log1p } from '../../utils/number.js'\n\nconst name = 'log1p'\nconst dependencies = ['typed', 'config', 'divideScalar', 'log', 'Complex']\n\nexport const createLog1p = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, log, Complex }) => {\n /**\n * Calculate the logarithm of a `value+1`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log1p(x)\n * math.log1p(x, base)\n *\n * Examples:\n *\n * math.log1p(2.5) // returns 1.252762968495368\n * math.exp(math.log1p(1.4)) // returns 2.4\n *\n * math.pow(10, 4) // returns 10000\n * math.log1p(9999, 10) // returns 4\n * math.log1p(9999) / math.log(10) // returns 4\n *\n * See also:\n *\n * exp, log, log2, log10\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm of `x+1`.\n * @param {number | BigNumber | Complex} [base=e]\n * Optional base for the logarithm. If not provided, the natural\n * logarithm of `x+1` is calculated.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the logarithm of `x+1`\n */\n return typed(name, {\n number: function (x) {\n if (x >= -1 || config.predictable) {\n return _log1p(x)\n } else {\n // negative value -> complex value computation\n return _log1pComplex(new Complex(x, 0))\n }\n },\n\n Complex: _log1pComplex,\n\n BigNumber: function (x) {\n const y = x.plus(1)\n if (!y.isNegative() || config.predictable) {\n return y.ln()\n } else {\n // downgrade to number, return Complex valued result\n return _log1pComplex(new Complex(x.toNumber(), 0))\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n 'any, any': function (x, base) {\n // calculate logarithm for a specified base, log1p(x, base)\n return divideScalar(this(x), log(base))\n }\n })\n\n /**\n * Calculate the natural logarithm of a complex number + 1\n * @param {Complex} x\n * @returns {Complex}\n * @private\n */\n function _log1pComplex (x) {\n const xRe1p = x.re + 1\n return new Complex(\n Math.log(Math.sqrt(xRe1p * xRe1p + x.im * x.im)),\n Math.atan2(x.im, xRe1p)\n )\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'nthRoots'\nconst dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n\nexport const createNthRoots = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n /**\n * Each function here returns a real multiple of i as a Complex value.\n * @param {number} val\n * @return {Complex} val, i*val, -val or -i*val for index 0, 1, 2, 3\n */\n // This is used to fix float artifacts for zero-valued components.\n const _calculateExactResult = [\n function realPos (val) { return new Complex(val, 0) },\n function imagPos (val) { return new Complex(0, val) },\n function realNeg (val) { return new Complex(-val, 0) },\n function imagNeg (val) { return new Complex(0, -val) }\n ]\n\n /**\n * Calculate the nth root of a Complex Number a using De Movire's Theorem.\n * @param {Complex} a\n * @param {number} root\n * @return {Array} array of n Complex Roots\n */\n function _nthComplexRoots (a, root) {\n if (root < 0) throw new Error('Root must be greater than zero')\n if (root === 0) throw new Error('Root must be non-zero')\n if (root % 1 !== 0) throw new Error('Root must be an integer')\n if (a === 0 || a.abs() === 0) return [new Complex(0, 0)]\n const aIsNumeric = typeof (a) === 'number'\n let offset\n // determine the offset (argument of a)/(pi/2)\n if (aIsNumeric || a.re === 0 || a.im === 0) {\n if (aIsNumeric) {\n offset = 2 * (+(a < 0)) // numeric value on the real axis\n } else if (a.im === 0) {\n offset = 2 * (+(a.re < 0)) // complex value on the real axis\n } else {\n offset = 2 * (+(a.im < 0)) + 1 // complex value on the imaginary axis\n }\n }\n const arg = a.arg()\n const abs = a.abs()\n const roots = []\n const r = Math.pow(abs, 1 / root)\n for (let k = 0; k < root; k++) {\n const halfPiFactor = (offset + 4 * k) / root\n /**\n * If (offset + 4*k)/root is an integral multiple of pi/2\n * then we can produce a more exact result.\n */\n if (halfPiFactor === Math.round(halfPiFactor)) {\n roots.push(_calculateExactResult[halfPiFactor % 4](r))\n continue\n }\n roots.push(new Complex({ r: r, phi: (arg + 2 * Math.PI * k) / root }))\n }\n return roots\n }\n\n /**\n * Calculate the nth roots of a value.\n * An nth root of a positive real number A,\n * is a positive real solution of the equation \"x^root = A\".\n * This function returns an array of complex values.\n *\n * Syntax:\n *\n * math.nthRoots(x)\n * math.nthRoots(x, root)\n *\n * Examples:\n *\n * math.nthRoots(1)\n * // returns [\n * // {re: 1, im: 0},\n * // {re: -1, im: 0}\n * // ]\n * nthRoots(1, 3)\n * // returns [\n * // { re: 1, im: 0 },\n * // { re: -0.4999999999999998, im: 0.8660254037844387 },\n * // { re: -0.5000000000000004, im: -0.8660254037844385 }\n * ]\n *\n * See also:\n *\n * nthRoot, pow, sqrt\n *\n * @param {number | BigNumber | Fraction | Complex} x Number to be rounded\n * @return {number | BigNumber | Fraction | Complex} Rounded value\n */\n return typed(name, {\n Complex: function (x) {\n return _nthComplexRoots(x, 2)\n },\n 'Complex, number': _nthComplexRoots\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotPow'\nconst dependencies = [\n 'typed',\n 'equalScalar',\n 'matrix',\n 'pow',\n 'DenseMatrix'\n]\n\nexport const createDotPow = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar, matrix, pow, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculates the power of x to y element wise.\n *\n * Syntax:\n *\n * math.dotPow(x, y)\n *\n * Examples:\n *\n * math.dotPow(2, 3) // returns number 8\n *\n * const a = [[1, 2], [4, 3]]\n * math.dotPow(a, 2) // returns Array [[1, 4], [16, 9]]\n * math.pow(a, 2) // returns Array [[9, 8], [16, 17]]\n *\n * See also:\n *\n * pow, sqrt, multiply\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x The base\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y The exponent\n * @return {number | BigNumber | Complex | Unit | Array | Matrix} The value of `x` to the power `y`\n */\n return typed(name, {\n\n 'any, any': pow,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, pow, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, pow, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, pow, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, pow)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotDivide'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'divideScalar',\n 'DenseMatrix'\n]\n\nexport const createDotDivide = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, divideScalar, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Divide two matrices element wise. The function accepts both matrices and\n * scalar values.\n *\n * Syntax:\n *\n * math.dotDivide(x, y)\n *\n * Examples:\n *\n * math.dotDivide(2, 4) // returns 0.5\n *\n * a = [[9, 5], [6, 1]]\n * b = [[3, 2], [5, 2]]\n *\n * math.dotDivide(a, b) // returns [[3, 2.5], [1.2, 0.5]]\n * math.divide(a, b) // returns [[1.75, 0.75], [-1.75, 2.25]]\n *\n * See also:\n *\n * divide, multiply, dotMultiply\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Numerator\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Quotient, `x ./ y`\n */\n return typed(name, {\n\n 'any, any': divideScalar,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, divideScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, divideScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, divideScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, divideScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, divideScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, divideScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, divideScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, divideScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, divideScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, divideScalar, true).valueOf()\n }\n })\n})\n","import { isArray, isMatrix, isDenseMatrix, isSparseMatrix } from '../../../../utils/is.js'\nimport { arraySize } from '../../../../utils/array.js'\nimport { format } from '../../../../utils/string.js'\n\nexport function createSolveValidation ({ DenseMatrix }) {\n /**\n * Validates matrix and column vector b for backward/forward substitution algorithms.\n *\n * @param {Matrix} m An N x N matrix\n * @param {Array | Matrix} b A column vector\n * @param {Boolean} copy Return a copy of vector b\n *\n * @return {DenseMatrix} Dense column vector b\n */\n return function solveValidation (m, b, copy) {\n const mSize = m.size()\n\n if (mSize.length !== 2) {\n throw new RangeError('Matrix must be two dimensional (size: ' + format(mSize) + ')')\n }\n\n const rows = mSize[0]\n const columns = mSize[1]\n\n if (rows !== columns) {\n throw new RangeError('Matrix must be square (size: ' + format(mSize) + ')')\n }\n\n let data = []\n\n if (isMatrix(b)) {\n const bSize = b.size()\n const bdata = b._data\n\n // 1-dim vector\n if (bSize.length === 1) {\n if (bSize[0] !== rows) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [bdata[i]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n\n // 2-dim column\n if (bSize.length === 2) {\n if (bSize[0] !== rows || bSize[1] !== 1) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n if (isDenseMatrix(b)) {\n if (copy) {\n data = []\n\n for (let i = 0; i < rows; i++) {\n data[i] = [bdata[i][0]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n\n return b\n }\n\n if (isSparseMatrix(b)) {\n for (let i = 0; i < rows; i++) { data[i] = [0] }\n\n const values = b._values\n const index = b._index\n const ptr = b._ptr\n\n for (let k1 = ptr[1], k = ptr[0]; k < k1; k++) {\n const i = index[k]\n data[i][0] = values[k]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n }\n\n throw new RangeError('Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.')\n }\n\n if (isArray(b)) {\n const bsize = arraySize(b)\n\n if (bsize.length === 1) {\n if (bsize[0] !== rows) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [b[i]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1]\n })\n }\n\n if (bsize.length === 2) {\n if (bsize[0] !== rows || bsize[1] !== 1) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [b[i][0]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1]\n })\n }\n\n throw new RangeError('Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.')\n }\n }\n}\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'lsolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createLsolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds one solution of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix. Throws an error if there's no solution.\n *\n * `L * x = b`\n *\n * Syntax:\n *\n * math.lsolve(L, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = lsolve(a, b) // [[-5.5], [20]]\n *\n * See also:\n *\n * lsolveAll, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} L A N x N matrix or array (L)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix | Array} A column vector with the linear system solution (x)\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseForwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseForwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const r = _denseForwardSubstitution(m, b)\n return r.valueOf()\n }\n })\n\n function _denseForwardSubstitution (m, b) {\n // validate matrix and vector, return copy of column vector b\n b = solveValidation(m, b, true)\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n // result\n const x = []\n\n const mdata = m._data\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n const bj = bdata[j][0] || 0\n let xj\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n const vjj = mdata[j][j]\n\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n xj = divideScalar(bj, vjj)\n\n // loop rows\n for (let i = j + 1; i < rows; i++) {\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))]\n }\n } else {\n // degenerate row, we can choose any value\n xj = 0\n }\n\n x[j] = [xj]\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n\n function _sparseForwardSubstitution (m, b) {\n // validate matrix and vector, return copy of column vector b\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // result\n const x = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n const bj = bdata[j][0] || 0\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n let vjj = 0\n // matrix values & indices (column j)\n const jValues = []\n const jIndices = []\n\n // first and last index in the column\n const firstIndex = ptr[j]\n const lastIndex = ptr[j + 1]\n\n // values in column, find value at [j, j]\n for (let k = firstIndex; k < lastIndex; k++) {\n const i = index[k]\n\n // check row (rows are not sorted!)\n if (i === j) {\n vjj = values[k]\n } else if (i > j) {\n // store lower triangular\n jValues.push(values[k])\n jIndices.push(i)\n }\n }\n\n // at this point we must have a value in vjj\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n const xj = divideScalar(bj, vjj)\n\n for (let k = 0, l = jIndices.length; k < l; k++) {\n const i = jIndices[k]\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, jValues[k]))]\n }\n\n x[j] = [xj]\n } else {\n // degenerate row, we can choose any value\n x[j] = [0]\n }\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'usolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createUsolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds one solution of a linear equation system by backward substitution. Matrix must be an upper triangular matrix. Throws an error if there's no solution.\n *\n * `U * x = b`\n *\n * Syntax:\n *\n * math.usolve(U, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = usolve(a, b) // [[8], [9]]\n *\n * See also:\n *\n * usolveAll, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} U A N x N matrix or array (U)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix | Array} A column vector with the linear system solution (x)\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseBackwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseBackwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const r = _denseBackwardSubstitution(m, b)\n return r.valueOf()\n }\n })\n\n function _denseBackwardSubstitution (m, b) {\n // make b into a column vector\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n // result\n const x = []\n\n const mdata = m._data\n // loop columns backwards\n for (let j = columns - 1; j >= 0; j--) {\n // b[j]\n const bj = bdata[j][0] || 0\n // x[j]\n let xj\n\n if (!equalScalar(bj, 0)) {\n // value at [j, j]\n const vjj = mdata[j][j]\n\n if (equalScalar(vjj, 0)) {\n // system cannot be solved\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n xj = divideScalar(bj, vjj)\n\n // loop rows\n for (let i = j - 1; i >= 0; i--) {\n // update copy of b\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))]\n }\n } else {\n // zero value at j\n xj = 0\n }\n // update x\n x[j] = [xj]\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n\n function _sparseBackwardSubstitution (m, b) {\n // make b into a column vector\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // result\n const x = []\n\n // loop columns backwards\n for (let j = columns - 1; j >= 0; j--) {\n const bj = bdata[j][0] || 0\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n let vjj = 0\n\n // upper triangular matrix values & index (column j)\n const jValues = []\n const jIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[j]\n const lastIndex = ptr[j + 1]\n\n // values in column, find value at [j, j], loop backwards\n for (let k = lastIndex - 1; k >= firstIndex; k--) {\n const i = index[k]\n\n // check row (rows are not sorted!)\n if (i === j) {\n vjj = values[k]\n } else if (i < j) {\n // store upper triangular\n jValues.push(values[k])\n jIndices.push(i)\n }\n }\n\n // at this point we must have a value in vjj\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n const xj = divideScalar(bj, vjj)\n\n for (let k = 0, lastIndex = jIndices.length; k < lastIndex; k++) {\n const i = jIndices[k]\n bdata[i] = [subtract(bdata[i][0], multiplyScalar(xj, jValues[k]))]\n }\n\n x[j] = [xj]\n } else {\n // degenerate row, we can choose any value\n x[j] = [0]\n }\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'lsolveAll'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createLsolveAll = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds all solutions of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix.\n *\n * `L * x = b`\n *\n * Syntax:\n *\n * math.lsolve(L, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = lsolve(a, b) // [ [[-5.5], [20]] ]\n *\n * See also:\n *\n * lsolve, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} L A N x N matrix or array (L)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix[] | Array[]} An array of affine-independent column vectors (x) that solve the linear system\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseForwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseForwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const R = _denseForwardSubstitution(m, b)\n return R.map(r => r.valueOf())\n }\n })\n\n function _denseForwardSubstitution (m, b_) {\n // the algorithm is derived from\n // https://www.overleaf.com/project/5e6c87c554a3190001a3fc93\n\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const M = m._data\n const rows = m._size[0]\n const columns = m._size[1]\n\n // loop columns\n for (let i = 0; i < columns; i++) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n if (!equalScalar(M[i][i], 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], M[i][i])\n\n for (let j = i + 1; j < columns; j++) {\n // b[j] -= b[i] * M[j,i]\n b[j] = subtract(b[j], multiplyScalar(b[i], M[j][i]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = i + 1; j < columns; j++) {\n bNew[j] = subtract(bNew[j], M[j][i])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n\n function _sparseForwardSubstitution (m, b_) {\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // loop columns\n for (let i = 0; i < columns; i++) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n // values & indices (column i)\n const iValues = []\n const iIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[i]\n const lastIndex = ptr[i + 1]\n\n // find the value at [i, i]\n let Mii = 0\n for (let j = firstIndex; j < lastIndex; j++) {\n const J = index[j]\n // check row\n if (J === i) {\n Mii = values[j]\n } else if (J > i) {\n // store lower triangular\n iValues.push(values[j])\n iIndices.push(J)\n }\n }\n\n if (!equalScalar(Mii, 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], Mii)\n\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n b[J] = subtract(b[J], multiplyScalar(b[i], iValues[j]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n bNew[J] = subtract(bNew[J], iValues[j])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'usolveAll'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createUsolveAll = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds all solutions of a linear equation system by backward substitution. Matrix must be an upper triangular matrix.\n *\n * `U * x = b`\n *\n * Syntax:\n *\n * math.usolve(U, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = usolve(a, b) // [ [[8], [9]] ]\n *\n * See also:\n *\n * usolve, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} U A N x N matrix or array (U)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix[] | Array[]} An array of affine-independent column vectors (x) that solve the linear system\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseBackwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseBackwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const R = _denseBackwardSubstitution(m, b)\n return R.map(r => r.valueOf())\n }\n })\n\n function _denseBackwardSubstitution (m, b_) {\n // the algorithm is derived from\n // https://www.overleaf.com/project/5e6c87c554a3190001a3fc93\n\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const M = m._data\n const rows = m._size[0]\n const columns = m._size[1]\n\n // loop columns backwards\n for (let i = columns - 1; i >= 0; i--) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n if (!equalScalar(M[i][i], 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], M[i][i])\n\n for (let j = i - 1; j >= 0; j--) {\n // b[j] -= b[i] * M[j,i]\n b[j] = subtract(b[j], multiplyScalar(b[i], M[j][i]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = i - 1; j >= 0; j--) {\n bNew[j] = subtract(bNew[j], M[j][i])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n\n function _sparseBackwardSubstitution (m, b_) {\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // loop columns backwards\n for (let i = columns - 1; i >= 0; i--) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n // values & indices (column i)\n const iValues = []\n const iIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[i]\n const lastIndex = ptr[i + 1]\n\n // find the value at [i, i]\n let Mii = 0\n for (let j = lastIndex - 1; j >= firstIndex; j--) {\n const J = index[j]\n // check row\n if (J === i) {\n Mii = values[j]\n } else if (J < i) {\n // store upper triangular\n iValues.push(values[j])\n iIndices.push(J)\n }\n }\n\n if (!equalScalar(Mii, 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], Mii)\n\n // loop upper triangular\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n b[J] = subtract(b[J], multiplyScalar(b[i], iValues[j]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n // loop upper triangular\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n bNew[J] = subtract(bNew[J], iValues[j])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm08'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm08 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤ A(i,j) ; A(i,j) !== 0\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm08 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues || !bvalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrices') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // vars\n let k, k0, k1, i\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop values in a\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // mark workspace\n w[i] = mark\n // set value\n x[i] = avalues[k]\n // add index\n cindex.push(i)\n }\n // loop values in b\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // check value exists in workspace\n if (w[i] === mark) {\n // evaluate callback\n x[i] = cf(x[i], bvalues[k])\n }\n }\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // value @ i\n const v = x[i]\n // check for zero value\n if (!eq(v, zero)) {\n // push value\n cvalues.push(v)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { leftShiftNumber } from '../../plain/number/index.js'\nimport { leftShiftBigNumber } from '../../utils/bignumber/bitwise.js'\n\nconst name = 'leftShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createLeftShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise left logical shift of a value x by y number of bits, `x << y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.leftShift(x, y)\n *\n * Examples:\n *\n * math.leftShift(1, 2) // returns number 4\n *\n * math.leftShift([1, 2, 3], 4) // returns Array [16, 32, 64]\n *\n * See also:\n *\n * leftShift, bitNot, bitOr, bitXor, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be shifted\n * @param {number | BigNumber} y Amount of shifts\n * @return {number | BigNumber | Array | Matrix} `x` shifted left `y` times\n */\n return typed(name, {\n\n 'number, number': leftShiftNumber,\n\n 'BigNumber, BigNumber': leftShiftBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { rightArithShiftBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { rightArithShiftNumber } from '../../plain/number/index.js'\n\nconst name = 'rightArithShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createRightArithShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise right arithmetic shift of a value x by y number of bits, `x >> y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.rightArithShift(x, y)\n *\n * Examples:\n *\n * math.rightArithShift(4, 2) // returns number 1\n *\n * math.rightArithShift([16, -32, 64], 4) // returns Array [1, -2, 3]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, bitXor, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be shifted\n * @param {number | BigNumber} y Amount of shifts\n * @return {number | BigNumber | Array | Matrix} `x` sign-filled shifted right `y` times\n */\n return typed(name, {\n\n 'number, number': rightArithShiftNumber,\n\n 'BigNumber, BigNumber': rightArithShiftBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { rightLogShiftNumber } from '../../plain/number/index.js'\n\nconst name = 'rightLogShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createRightLogShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise right logical shift of value x by y number of bits, `x >>> y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.rightLogShift(x, y)\n *\n * Examples:\n *\n * math.rightLogShift(4, 2) // returns number 1\n *\n * math.rightLogShift([16, -32, 64], 4) // returns Array [1, 2, 3]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, bitXor, leftShift, rightLogShift\n *\n * @param {number | Array | Matrix} x Value to be shifted\n * @param {number} y Amount of shifts\n * @return {number | Array | Matrix} `x` zero-filled shifted right `y` times\n */\n\n return typed(name, {\n\n 'number, number': rightLogShiftNumber,\n\n // 'BigNumber, BigNumber': ..., // TODO: implement BigNumber support for rightLogShift\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { factory } from '../../utils/factory.js'\nimport { andNumber } from '../../plain/number/index.js'\n\nconst name = 'and'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'not'\n]\n\nexport const createAnd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, not }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `and`. Test whether two values are both defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.and(x, y)\n *\n * Examples:\n *\n * math.and(2, 4) // returns true\n *\n * a = [2, 0, 0]\n * b = [3, 7, 0]\n * c = 0\n *\n * math.and(a, b) // returns [true, false, false]\n * math.and(a, c) // returns [false, false, false]\n *\n * See also:\n *\n * not, or, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when both inputs are defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': andNumber,\n\n 'Complex, Complex': function (x, y) {\n return (x.re !== 0 || x.im !== 0) && (y.re !== 0 || y.im !== 0)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return !x.isZero() && !y.isZero() && !x.isNaN() && !y.isNaN()\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n // check scalar\n if (not(y)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n // check scalar\n if (not(y)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n // check scalar\n if (not(x)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm11(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n // check scalar\n if (not(x)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\n\nconst name = 'compare'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'Fraction',\n 'DenseMatrix'\n]\n\nexport const createCompare = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, equalScalar, matrix, BigNumber, Fraction, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.\n *\n * x and y are considered equal when the relative difference between x and y\n * is smaller than the configured epsilon. The function cannot be used to\n * compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.compare(x, y)\n *\n * Examples:\n *\n * math.compare(6, 1) // returns 1\n * math.compare(2, 3) // returns -1\n * math.compare(7, 7) // returns 0\n * math.compare('10', '2') // returns 1\n * math.compare('1000', '1e3') // returns 0\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('40 mm')\n * math.compare(a, b) // returns 1\n *\n * math.compare(2, [1, 2, 3]) // returns [1, 0, -1]\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, larger, largerEq, compareNatural, compareText\n *\n * @param {number | BigNumber | Fraction | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | Unit | string | Array | Matrix} y Second value to compare\n * @return {number | BigNumber | Fraction | Array | Matrix} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x === y ? 0 : (x > y ? 1 : -1)\n },\n\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n ? 0\n : (x > y ? 1 : -1)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return bigNearlyEqual(x, y, config.epsilon)\n ? new BigNumber(0)\n : new BigNumber(x.cmp(y))\n },\n\n 'Fraction, Fraction': function (x, y) {\n return new Fraction(x.compare(y))\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createCompareNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n ? 0\n : (x > y ? 1 : -1)\n }\n })\n})\n","import naturalSort from 'javascript-natural-sort'\nimport { isDenseMatrix, isSparseMatrix, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'compareNatural'\nconst dependencies = [\n 'typed',\n 'compare'\n]\n\nexport const createCompareNatural = /* #__PURE__ */ factory(name, dependencies, ({ typed, compare }) => {\n const compareBooleans = compare.signatures['boolean,boolean']\n\n /**\n * Compare two values of any type in a deterministic, natural way.\n *\n * For numeric values, the function works the same as `math.compare`.\n * For types of values that can't be compared mathematically,\n * the function compares in a natural way.\n *\n * For numeric values, x and y are considered equal when the relative\n * difference between x and y is smaller than the configured epsilon.\n * The function cannot be used to compare values smaller than\n * approximately 2.22e-16.\n *\n * For Complex numbers, first the real parts are compared. If equal,\n * the imaginary parts are compared.\n *\n * Strings are compared with a natural sorting algorithm, which\n * orders strings in a \"logic\" way following some heuristics.\n * This differs from the function `compare`, which converts the string\n * into a numeric value and compares that. The function `compareText`\n * on the other hand compares text lexically.\n *\n * Arrays and Matrices are compared value by value until there is an\n * unequal pair of values encountered. Objects are compared by sorted\n * keys until the keys or their values are unequal.\n *\n * Syntax:\n *\n * math.compareNatural(x, y)\n *\n * Examples:\n *\n * math.compareNatural(6, 1) // returns 1\n * math.compareNatural(2, 3) // returns -1\n * math.compareNatural(7, 7) // returns 0\n *\n * math.compareNatural('10', '2') // returns 1\n * math.compareText('10', '2') // returns -1\n * math.compare('10', '2') // returns 1\n *\n * math.compareNatural('Answer: 10', 'Answer: 2') // returns 1\n * math.compareText('Answer: 10', 'Answer: 2') // returns -1\n * math.compare('Answer: 10', 'Answer: 2')\n * // Error: Cannot convert \"Answer: 10\" to a number\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('40 mm')\n * math.compareNatural(a, b) // returns 1\n *\n * const c = math.complex('2 + 3i')\n * const d = math.complex('2 + 4i')\n * math.compareNatural(c, d) // returns -1\n *\n * math.compareNatural([1, 2, 4], [1, 2, 3]) // returns 1\n * math.compareNatural([1, 2, 3], [1, 2]) // returns 1\n * math.compareNatural([1, 5], [1, 2, 3]) // returns 1\n * math.compareNatural([1, 2], [1, 2]) // returns 0\n *\n * math.compareNatural({a: 2}, {a: 4}) // returns -1\n *\n * See also:\n *\n * compare, compareText\n *\n * @param {*} x First value to compare\n * @param {*} y Second value to compare\n * @return {number} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n const typeX = typeOf(x)\n const typeY = typeOf(y)\n let c\n\n // numeric types\n if ((typeX === 'number' || typeX === 'BigNumber' || typeX === 'Fraction') &&\n (typeY === 'number' || typeY === 'BigNumber' || typeY === 'Fraction')) {\n c = compare(x, y)\n if (c.toString() !== '0') {\n // c can be number, BigNumber, or Fraction\n return c > 0 ? 1 : -1 // return a number\n } else {\n return naturalSort(typeX, typeY)\n }\n }\n\n // matrix types\n if (typeX === 'Array' || typeX === 'Matrix' ||\n typeY === 'Array' || typeY === 'Matrix') {\n c = compareMatricesAndArrays(this, x, y)\n if (c !== 0) {\n return c\n } else {\n return naturalSort(typeX, typeY)\n }\n }\n\n // in case of different types, order by name of type, i.e. 'BigNumber' < 'Complex'\n if (typeX !== typeY) {\n return naturalSort(typeX, typeY)\n }\n\n if (typeX === 'Complex') {\n return compareComplexNumbers(x, y)\n }\n\n if (typeX === 'Unit') {\n if (x.equalBase(y)) {\n return this(x.value, y.value)\n }\n\n // compare by units\n return compareArrays(this, x.formatUnits(), y.formatUnits())\n }\n\n if (typeX === 'boolean') {\n return compareBooleans(x, y)\n }\n\n if (typeX === 'string') {\n return naturalSort(x, y)\n }\n\n if (typeX === 'Object') {\n return compareObjects(this, x, y)\n }\n\n if (typeX === 'null') {\n return 0\n }\n\n if (typeX === 'undefined') {\n return 0\n }\n\n // this should not occur...\n throw new TypeError('Unsupported type of value \"' + typeX + '\"')\n }\n })\n\n /**\n * Compare mixed matrix/array types, by converting to same-shaped array.\n * This comparator is non-deterministic regarding input types.\n * @param {Array | SparseMatrix | DenseMatrix | *} x\n * @param {Array | SparseMatrix | DenseMatrix | *} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareMatricesAndArrays (compareNatural, x, y) {\n if (isSparseMatrix(x) && isSparseMatrix(y)) {\n return compareArrays(compareNatural, x.toJSON().values, y.toJSON().values)\n }\n if (isSparseMatrix(x)) {\n // note: convert to array is expensive\n return compareMatricesAndArrays(compareNatural, x.toArray(), y)\n }\n if (isSparseMatrix(y)) {\n // note: convert to array is expensive\n return compareMatricesAndArrays(compareNatural, x, y.toArray())\n }\n\n // convert DenseArray into Array\n if (isDenseMatrix(x)) {\n return compareMatricesAndArrays(compareNatural, x.toJSON().data, y)\n }\n if (isDenseMatrix(y)) {\n return compareMatricesAndArrays(compareNatural, x, y.toJSON().data)\n }\n\n // convert scalars to array\n if (!Array.isArray(x)) {\n return compareMatricesAndArrays(compareNatural, [x], y)\n }\n if (!Array.isArray(y)) {\n return compareMatricesAndArrays(compareNatural, x, [y])\n }\n\n return compareArrays(compareNatural, x, y)\n }\n\n /**\n * Compare two Arrays\n *\n * - First, compares value by value\n * - Next, if all corresponding values are equal,\n * look at the length: longest array will be considered largest\n *\n * @param {Array} x\n * @param {Array} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareArrays (compareNatural, x, y) {\n // compare each value\n for (let i = 0, ii = Math.min(x.length, y.length); i < ii; i++) {\n const v = compareNatural(x[i], y[i])\n if (v !== 0) {\n return v\n }\n }\n\n // compare the size of the arrays\n if (x.length > y.length) { return 1 }\n if (x.length < y.length) { return -1 }\n\n // both Arrays have equal size and content\n return 0\n }\n\n /**\n * Compare two objects\n *\n * - First, compare sorted property names\n * - Next, compare the property values\n *\n * @param {Object} x\n * @param {Object} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareObjects (compareNatural, x, y) {\n const keysX = Object.keys(x)\n const keysY = Object.keys(y)\n\n // compare keys\n keysX.sort(naturalSort)\n keysY.sort(naturalSort)\n const c = compareArrays(compareNatural, keysX, keysY)\n if (c !== 0) {\n return c\n }\n\n // compare values\n for (let i = 0; i < keysX.length; i++) {\n const v = compareNatural(x[keysX[i]], y[keysY[i]])\n if (v !== 0) {\n return v\n }\n }\n\n return 0\n }\n})\n\n/**\n * Compare two complex numbers, `x` and `y`:\n *\n * - First, compare the real values of `x` and `y`\n * - If equal, compare the imaginary values of `x` and `y`\n *\n * @params {Complex} x\n * @params {Complex} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\nfunction compareComplexNumbers (x, y) {\n if (x.re > y.re) { return 1 }\n if (x.re < y.re) { return -1 }\n\n if (x.im > y.im) { return 1 }\n if (x.im < y.im) { return -1 }\n\n return 0\n}\n","import { compareText as _compareText } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'compareText'\nconst dependencies = [\n 'typed',\n 'matrix'\n]\n\nexport const createCompareText = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Compare two strings lexically. Comparison is case sensitive.\n * Returns 1 when x > y, -1 when x < y, and 0 when x == y.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.compareText(x, y)\n *\n * Examples:\n *\n * math.compareText('B', 'A') // returns 1\n * math.compareText('2', '10') // returns 1\n * math.compare('2', '10') // returns -1\n * math.compareNatural('2', '10') // returns -1\n *\n * math.compareText('B', ['A', 'B', 'C']) // returns [1, 0, -1]\n *\n * See also:\n *\n * equal, equalText, compare, compareNatural\n *\n * @param {string | Array | DenseMatrix} x First string to compare\n * @param {string | Array | DenseMatrix} y Second string to compare\n * @return {number | Array | DenseMatrix} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n\n 'any, any': _compareText,\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, _compareText)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, _compareText, false)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, _compareText, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, _compareText, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, _compareText, true).valueOf()\n }\n })\n})\n\nexport const createCompareTextNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, {\n 'any, any': _compareText\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'equal'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createEqual = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether two values are equal.\n *\n * The function tests whether the relative difference between x and y is\n * smaller than the configured epsilon. The function cannot be used to\n * compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * In case of complex numbers, x.re must equal y.re, and x.im must equal y.im.\n *\n * Values `null` and `undefined` are compared strictly, thus `null` is only\n * equal to `null` and nothing else, and `undefined` is only equal to\n * `undefined` and nothing else. Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.equal(x, y)\n *\n * Examples:\n *\n * math.equal(2 + 2, 3) // returns false\n * math.equal(2 + 2, 4) // returns true\n *\n * const a = math.unit('50 cm')\n * const b = math.unit('5 m')\n * math.equal(a, b) // returns true\n *\n * const c = [2, 5, 1]\n * const d = [2, 7, 1]\n *\n * math.equal(c, d) // returns [true, false, true]\n * math.deepEqual(c, d) // returns false\n *\n * math.equal(\"1000\", \"1e3\") // returns true\n * math.equal(0, null) // returns false\n *\n * See also:\n *\n * unequal, smaller, smallerEq, larger, largerEq, compare, deepEqual, equalText\n *\n * @param {number | BigNumber | boolean | Complex | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | boolean | Complex | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the compared values are equal, else returns false\n */\n return typed(name, {\n\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y === null }\n if (y === null) { return x === null }\n if (x === undefined) { return y === undefined }\n if (y === undefined) { return x === undefined }\n\n return equalScalar(x, y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, equalScalar)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, equalScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, equalScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, equalScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, equalScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, equalScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, equalScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, equalScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, equalScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, equalScalar, true).valueOf()\n }\n })\n})\n\nexport const createEqualNumber = factory(name, ['typed', 'equalScalar'], ({ typed, equalScalar }) => {\n return typed(name, {\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y === null }\n if (y === null) { return x === null }\n if (x === undefined) { return y === undefined }\n if (y === undefined) { return x === undefined }\n\n return equalScalar(x, y)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'equalText'\nconst dependencies = [\n 'typed',\n 'compareText',\n 'isZero'\n]\n\nexport const createEqualText = /* #__PURE__ */ factory(name, dependencies, ({ typed, compareText, isZero }) => {\n /**\n * Check equality of two strings. Comparison is case sensitive.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.equalText(x, y)\n *\n * Examples:\n *\n * math.equalText('Hello', 'Hello') // returns true\n * math.equalText('a', 'A') // returns false\n * math.equal('2e3', '2000') // returns true\n * math.equalText('2e3', '2000') // returns false\n *\n * math.equalText('B', ['A', 'B', 'C']) // returns [false, true, false]\n *\n * See also:\n *\n * equal, compareText, compare, compareNatural\n *\n * @param {string | Array | DenseMatrix} x First string to compare\n * @param {string | Array | DenseMatrix} y Second string to compare\n * @return {number | Array | DenseMatrix} Returns true if the values are equal, and false if not.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n return isZero(compareText(x, y))\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'smaller'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createSmaller = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is smaller than y.\n *\n * The function returns true when x is smaller than y and the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.smaller(x, y)\n *\n * Examples:\n *\n * math.smaller(2, 3) // returns true\n * math.smaller(5, 2 * 2) // returns false\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('2 inch')\n * math.smaller(a, b) // returns true\n *\n * See also:\n *\n * equal, unequal, smallerEq, smaller, smallerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x < y\n },\n\n 'number, number': function (x, y) {\n return x < y && !nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.lt(y) && !bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) === -1\n },\n\n 'Complex, Complex': function (x, y) {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createSmallerNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x < y && !nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'smallerEq'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createSmallerEq = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is smaller or equal to y.\n *\n * The function returns true when x is smaller than y or the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.smallerEq(x, y)\n *\n * Examples:\n *\n * math.smaller(1 + 2, 3) // returns false\n * math.smallerEq(1 + 2, 3) // returns true\n *\n * See also:\n *\n * equal, unequal, smaller, larger, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x <= y\n },\n\n 'number, number': function (x, y) {\n return x <= y || nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.lte(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) !== 1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createSmallerEqNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x <= y || nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'larger'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createLarger = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is larger than y.\n *\n * The function returns true when x is larger than y and the relative\n * difference between x and y is larger than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.larger(x, y)\n *\n * Examples:\n *\n * math.larger(2, 3) // returns false\n * math.larger(5, 2 + 2) // returns true\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('2 inch')\n * math.larger(a, b) // returns false\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is larger than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x > y\n },\n\n 'number, number': function (x, y) {\n return x > y && !nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.gt(y) && !bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) === 1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createLargerNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x > y && !nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'largerEq'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createLargerEq = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is larger or equal to y.\n *\n * The function returns true when x is larger than y or the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.largerEq(x, y)\n *\n * Examples:\n *\n * math.larger(2, 1 + 1) // returns false\n * math.largerEq(2, 1 + 1) // returns true\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, larger, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is larger or equal to y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x >= y\n },\n\n 'number, number': function (x, y) {\n return x >= y || nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.gte(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) !== -1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createLargerEqNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x >= y || nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'deepEqual'\nconst dependencies = [\n 'typed',\n 'equal'\n]\n\nexport const createDeepEqual = /* #__PURE__ */ factory(name, dependencies, ({ typed, equal }) => {\n /**\n * Test element wise whether two matrices are equal.\n * The function accepts both matrices and scalar values.\n *\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.deepEqual(x, y)\n *\n * Examples:\n *\n * math.deepEqual(2, 4) // returns false\n *\n * a = [2, 5, 1]\n * b = [2, 7, 1]\n *\n * math.deepEqual(a, b) // returns false\n * math.equal(a, b) // returns [true, false, true]\n *\n * See also:\n *\n * equal, unequal\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First matrix to compare\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second matrix to compare\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Returns true when the input matrices have the same size and each of their elements is equal.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n return _deepEqual(x.valueOf(), y.valueOf())\n }\n })\n\n /**\n * Test whether two arrays have the same size and all elements are equal\n * @param {Array | *} x\n * @param {Array | *} y\n * @return {boolean} Returns true if both arrays are deep equal\n */\n function _deepEqual (x, y) {\n if (Array.isArray(x)) {\n if (Array.isArray(y)) {\n const len = x.length\n if (len !== y.length) {\n return false\n }\n\n for (let i = 0; i < len; i++) {\n if (!_deepEqual(x[i], y[i])) {\n return false\n }\n }\n\n return true\n } else {\n return false\n }\n } else {\n if (Array.isArray(y)) {\n return false\n } else {\n return equal(x, y)\n }\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'unequal'\nconst dependencies = [\n 'typed',\n 'config',\n 'equalScalar',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createUnequal = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, equalScalar, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether two values are unequal.\n *\n * The function tests whether the relative difference between x and y is\n * larger than the configured epsilon. The function cannot be used to compare\n * values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * In case of complex numbers, x.re must unequal y.re, or x.im must unequal y.im.\n * Strings are compared by their numerical value.\n *\n * Values `null` and `undefined` are compared strictly, thus `null` is unequal\n * with everything except `null`, and `undefined` is unequal with everything\n * except `undefined`.\n *\n * Syntax:\n *\n * math.unequal(x, y)\n *\n * Examples:\n *\n * math.unequal(2 + 2, 3) // returns true\n * math.unequal(2 + 2, 4) // returns false\n *\n * const a = math.unit('50 cm')\n * const b = math.unit('5 m')\n * math.unequal(a, b) // returns false\n *\n * const c = [2, 5, 1]\n * const d = [2, 7, 1]\n *\n * math.unequal(c, d) // returns [false, true, false]\n * math.deepEqual(c, d) // returns false\n *\n * math.unequal(0, null) // returns true\n * See also:\n *\n * equal, deepEqual, smaller, smallerEq, larger, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit | string | Array | Matrix | undefined} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit | string | Array | Matrix | undefined} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the compared values are unequal, else returns false\n */\n return typed('unequal', {\n\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y !== null }\n if (y === null) { return x !== null }\n if (x === undefined) { return y !== undefined }\n if (y === undefined) { return x !== undefined }\n\n return _unequal(x, y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, _unequal)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, _unequal, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, _unequal, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, _unequal)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, _unequal, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, _unequal, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, _unequal, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, _unequal, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, _unequal, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, _unequal, true).valueOf()\n }\n })\n\n function _unequal (x, y) {\n return !equalScalar(x, y)\n }\n})\n\nexport const createUnequalNumber = factory(name, ['typed', 'equalScalar'], ({ typed, equalScalar }) => {\n return typed(name, {\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y !== null }\n if (y === null) { return x !== null }\n if (x === undefined) { return y !== undefined }\n if (y === undefined) { return x !== undefined }\n\n return !equalScalar(x, y)\n }\n })\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'partitionSelect'\nconst dependencies = ['typed', 'isNumeric', 'isNaN', 'compare']\n\nexport const createPartitionSelect = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNumeric, isNaN, compare }) => {\n const asc = compare\n const desc = (a, b) => -compare(a, b)\n\n /**\n * Partition-based selection of an array or 1D matrix.\n * Will find the kth smallest value, and mutates the input array.\n * Uses Quickselect.\n *\n * Syntax:\n *\n * math.partitionSelect(x, k)\n * math.partitionSelect(x, k, compare)\n *\n * Examples:\n *\n * math.partitionSelect([5, 10, 1], 2) // returns 10\n * math.partitionSelect(['C', 'B', 'A', 'D'], 1) // returns 'B'\n *\n * function sortByLength (a, b) {\n * return a.length - b.length\n * }\n * math.partitionSelect(['Langdon', 'Tom', 'Sara'], 2, sortByLength) // returns 'Langdon'\n *\n * See also:\n *\n * sort\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to sort\n * @param {Number} k The kth smallest value to be retrieved zero-based index\n * @param {Function | 'asc' | 'desc'} [compare='asc']\n * An optional comparator function. The function is called as\n * `compare(a, b)`, and must return 1 when a > b, -1 when a < b,\n * and 0 when a == b.\n * @return {*} Returns the kth lowest value.\n */\n return typed(name, {\n 'Array | Matrix, number': function (x, k) {\n return _partitionSelect(x, k, asc)\n },\n\n 'Array | Matrix, number, string': function (x, k, compare) {\n if (compare === 'asc') {\n return _partitionSelect(x, k, asc)\n } else if (compare === 'desc') {\n return _partitionSelect(x, k, desc)\n } else {\n throw new Error('Compare string must be \"asc\" or \"desc\"')\n }\n },\n\n 'Array | Matrix, number, function': _partitionSelect\n })\n\n function _partitionSelect (x, k, compare) {\n if (!isInteger(k) || k < 0) {\n throw new Error('k must be a non-negative integer')\n }\n\n if (isMatrix(x)) {\n const size = x.size()\n if (size.length > 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n return quickSelect(x.valueOf(), k, compare)\n }\n\n if (Array.isArray(x)) {\n return quickSelect(x, k, compare)\n }\n }\n\n /**\n * Quickselect algorithm.\n * Code adapted from:\n * https://blog.teamleadnet.com/2012/07/quick-select-algorithm-find-kth-element.html\n *\n * @param {Array} arr\n * @param {Number} k\n * @param {Function} compare\n * @private\n */\n function quickSelect (arr, k, compare) {\n if (k >= arr.length) {\n throw new Error('k out of bounds')\n }\n\n // check for NaN values since these can cause an infinite while loop\n for (let i = 0; i < arr.length; i++) {\n if (isNumeric(arr[i]) && isNaN(arr[i])) {\n return arr[i] // return NaN\n }\n }\n\n let from = 0\n let to = arr.length - 1\n\n // if from == to we reached the kth element\n while (from < to) {\n let r = from\n let w = to\n const pivot = arr[Math.floor(Math.random() * (to - from + 1)) + from]\n\n // stop if the reader and writer meets\n while (r < w) {\n // arr[r] >= pivot\n if (compare(arr[r], pivot) >= 0) { // put the large values at the end\n const tmp = arr[w]\n arr[w] = arr[r]\n arr[r] = tmp\n --w\n } else { // the value is smaller than the pivot, skip\n ++r\n }\n }\n\n // if we stepped up (r++) we need to step one down (arr[r] > pivot)\n if (compare(arr[r], pivot) > 0) {\n --r\n }\n\n // the r pointer is on the end of the first k elements\n if (k <= r) {\n to = r\n } else {\n from = r + 1\n }\n }\n\n return arr[k]\n }\n})\n","import { arraySize as size } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'sort'\nconst dependencies = ['typed', 'matrix', 'compare', 'compareNatural']\n\nexport const createSort = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, compare, compareNatural }) => {\n const compareAsc = compare\n const compareDesc = (a, b) => -compare(a, b)\n\n /**\n * Sort the items in a matrix.\n *\n * Syntax:\n *\n * math.sort(x)\n * math.sort(x, compare)\n *\n * Examples:\n *\n * math.sort([5, 10, 1]) // returns [1, 5, 10]\n * math.sort(['C', 'B', 'A', 'D'], math.compareNatural)\n * // returns ['A', 'B', 'C', 'D']\n *\n * function sortByLength (a, b) {\n * return a.length - b.length\n * }\n * math.sort(['Langdon', 'Tom', 'Sara'], sortByLength)\n * // returns ['Tom', 'Sara', 'Langdon']\n *\n * See also:\n *\n * filter, forEach, map, compare, compareNatural\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to sort\n * @param {Function | 'asc' | 'desc' | 'natural'} [compare='asc']\n * An optional _comparator function or name. The function is called as\n * `compare(a, b)`, and must return 1 when a > b, -1 when a < b,\n * and 0 when a == b.\n * @return {Matrix | Array} Returns the sorted matrix.\n */\n return typed(name, {\n Array: function (x) {\n _arrayIsVector(x)\n return x.sort(compareAsc)\n },\n\n Matrix: function (x) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(compareAsc), x.storage())\n },\n\n 'Array, function': function (x, _comparator) {\n _arrayIsVector(x)\n return x.sort(_comparator)\n },\n\n 'Matrix, function': function (x, _comparator) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(_comparator), x.storage())\n },\n\n 'Array, string': function (x, order) {\n _arrayIsVector(x)\n return x.sort(_comparator(order))\n },\n\n 'Matrix, string': function (x, order) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(_comparator(order)), x.storage())\n }\n })\n\n /**\n * Get the comparator for given order ('asc', 'desc', 'natural')\n * @param {'asc' | 'desc' | 'natural'} order\n * @return {Function} Returns a _comparator function\n */\n function _comparator (order) {\n if (order === 'asc') {\n return compareAsc\n } else if (order === 'desc') {\n return compareDesc\n } else if (order === 'natural') {\n return compareNatural\n } else {\n throw new Error('String \"asc\", \"desc\", or \"natural\" expected')\n }\n }\n\n /**\n * Validate whether an array is one dimensional\n * Throws an error when this is not the case\n * @param {Array} array\n * @private\n */\n function _arrayIsVector (array) {\n if (size(array).length !== 1) {\n throw new Error('One dimensional array expected')\n }\n }\n\n /**\n * Validate whether a matrix is one dimensional\n * Throws an error when this is not the case\n * @param {Matrix} matrix\n * @private\n */\n function _matrixIsVector (matrix) {\n if (matrix.size().length !== 1) {\n throw new Error('One dimensional matrix expected')\n }\n }\n})\n","import { deepForEach, reduce, containsCollections } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'max'\nconst dependencies = ['typed', 'config', 'numeric', 'larger']\n\nexport const createMax = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, larger }) => {\n /**\n * Compute the maximum value of a matrix or a list with values.\n * In case of a multi dimensional array, the maximum of the flattened array\n * will be calculated. When `dim` is provided, the maximum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.max(a, b, c, ...)\n * math.max(A)\n * math.max(A, dim)\n *\n * Examples:\n *\n * math.max(2, 1, 4, 3) // returns 4\n * math.max([2, 1, 4, 3]) // returns 4\n *\n * // maximum over a specified dimension (zero-based)\n * math.max([[2, 5], [4, 3], [1, 7]], 0) // returns [4, 7]\n * math.max([[2, 5], [4, 3]], [1, 7], 1) // returns [5, 4, 7]\n *\n * math.max(2.7, 7.1, -4.5, 2.0, 4.1) // returns 7.1\n * math.min(2.7, 7.1, -4.5, 2.0, 4.1) // returns -4.5\n *\n * See also:\n *\n * mean, median, min, prod, std, sum, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The maximum value\n */\n return typed(name, {\n // max([a, b, c, d, ...])\n 'Array | Matrix': _max,\n\n // max([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return reduce(array, dim.valueOf(), _largest)\n },\n\n // max(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function max')\n }\n\n return _max(args)\n }\n })\n\n /**\n * Return the largest of two values\n * @param {*} x\n * @param {*} y\n * @returns {*} Returns x when x is largest, or y when y is largest\n * @private\n */\n function _largest (x, y) {\n try {\n return larger(x, y) ? x : y\n } catch (err) {\n throw improveErrorMessage(err, 'max', y)\n }\n }\n\n /**\n * Recursively calculate the maximum value in an n-dimensional array\n * @param {Array} array\n * @return {number} max\n * @private\n */\n function _max (array) {\n let res\n\n deepForEach(array, function (value) {\n try {\n if (isNaN(value) && typeof value === 'number') {\n res = NaN\n } else if (res === undefined || larger(value, res)) {\n res = value\n }\n } catch (err) {\n throw improveErrorMessage(err, 'max', value)\n }\n })\n\n if (res === undefined) {\n throw new Error('Cannot calculate max of an empty array')\n }\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof res === 'string') {\n res = numeric(res, config.number)\n }\n\n return res\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'min'\nconst dependencies = ['typed', 'config', 'numeric', 'smaller']\n\nexport const createMin = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, smaller }) => {\n /**\n * Compute the minimum value of a matrix or a list of values.\n * In case of a multi dimensional array, the minimum of the flattened array\n * will be calculated. When `dim` is provided, the minimum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.min(a, b, c, ...)\n * math.min(A)\n * math.min(A, dim)\n *\n * Examples:\n *\n * math.min(2, 1, 4, 3) // returns 1\n * math.min([2, 1, 4, 3]) // returns 1\n *\n * // minimum over a specified dimension (zero-based)\n * math.min([[2, 5], [4, 3], [1, 7]], 0) // returns [1, 3]\n * math.min([[2, 5], [4, 3], [1, 7]], 1) // returns [2, 3, 1]\n *\n * math.max(2.7, 7.1, -4.5, 2.0, 4.1) // returns 7.1\n * math.min(2.7, 7.1, -4.5, 2.0, 4.1) // returns -4.5\n *\n * See also:\n *\n * mean, median, max, prod, std, sum, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The minimum value\n */\n return typed(name, {\n // min([a, b, c, d, ...])\n 'Array | Matrix': _min,\n\n // min([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return reduce(array, dim.valueOf(), _smallest)\n },\n\n // min(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function min')\n }\n\n return _min(args)\n }\n })\n\n /**\n * Return the smallest of two values\n * @param {*} x\n * @param {*} y\n * @returns {*} Returns x when x is smallest, or y when y is smallest\n * @private\n */\n function _smallest (x, y) {\n try {\n return smaller(x, y) ? x : y\n } catch (err) {\n throw improveErrorMessage(err, 'min', y)\n }\n }\n\n /**\n * Recursively calculate the minimum value in an n-dimensional array\n * @param {Array} array\n * @return {number} min\n * @private\n */\n function _min (array) {\n let min\n\n deepForEach(array, function (value) {\n try {\n if (isNaN(value) && typeof value === 'number') {\n min = NaN\n } else if (min === undefined || smaller(value, min)) {\n min = value\n }\n } catch (err) {\n throw improveErrorMessage(err, 'min', value)\n }\n })\n\n if (min === undefined) {\n throw new Error('Cannot calculate min of an empty array')\n }\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof min === 'string') {\n min = numeric(min, config.number)\n }\n\n return min\n }\n})\n","import { isArray, isMatrix, isString, typeOf } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ImmutableDenseMatrix'\nconst dependencies = [\n 'smaller',\n 'DenseMatrix'\n]\n\nexport const createImmutableDenseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ smaller, DenseMatrix }) => {\n function ImmutableDenseMatrix (data, datatype) {\n if (!(this instanceof ImmutableDenseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data) || isArray(data)) {\n // use DenseMatrix implementation\n const matrix = new DenseMatrix(data, datatype)\n // internal structures\n this._data = matrix._data\n this._size = matrix._size\n this._datatype = matrix._datatype\n this._min = null\n this._max = null\n } else if (data && isArray(data.data) && isArray(data.size)) {\n // initialize fields from JSON representation\n this._data = data.data\n this._size = data.size\n this._datatype = data.datatype\n this._min = typeof data.min !== 'undefined' ? data.min : null\n this._max = typeof data.max !== 'undefined' ? data.max : null\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._data = []\n this._size = [0]\n this._datatype = datatype\n this._min = null\n this._max = null\n }\n }\n\n ImmutableDenseMatrix.prototype = new DenseMatrix()\n\n /**\n * Attach type information\n */\n ImmutableDenseMatrix.prototype.type = 'ImmutableDenseMatrix'\n ImmutableDenseMatrix.prototype.isImmutableDenseMatrix = true\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @param {Index} index\n * @param {Array | ImmutableDenseMatrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n ImmutableDenseMatrix.prototype.subset = function (index) {\n switch (arguments.length) {\n case 1:\n {\n // use base implementation\n const m = DenseMatrix.prototype.subset.call(this, index)\n // check result is a matrix\n if (isMatrix(m)) {\n // return immutable matrix\n return new ImmutableDenseMatrix({\n data: m._data,\n size: m._size,\n datatype: m._datatype\n })\n }\n return m\n }\n // intentional fall through\n case 2:\n case 3:\n throw new Error('Cannot invoke set subset on an Immutable Matrix instance')\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n /**\n * Replace a single element in the matrix.\n * @param {Number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {ImmutableDenseMatrix} self\n */\n ImmutableDenseMatrix.prototype.set = function () {\n throw new Error('Cannot invoke set on an Immutable Matrix instance')\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @param {Number[]} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n ImmutableDenseMatrix.prototype.resize = function () {\n throw new Error('Cannot invoke resize on an Immutable Matrix instance')\n }\n\n /**\n * Disallows reshaping in favor of immutability.\n *\n * @throws {Error} Operation not allowed\n */\n ImmutableDenseMatrix.prototype.reshape = function () {\n throw new Error('Cannot invoke reshape on an Immutable Matrix instance')\n }\n\n /**\n * Create a clone of the matrix\n * @return {ImmutableDenseMatrix} clone\n */\n ImmutableDenseMatrix.prototype.clone = function () {\n return new ImmutableDenseMatrix({\n data: clone(this._data),\n size: clone(this._size),\n datatype: this._datatype\n })\n }\n\n /**\n * Get a JSON representation of the matrix\n * @returns {Object}\n */\n ImmutableDenseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'ImmutableDenseMatrix',\n data: this._data,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Generate a matrix from a JSON object\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ImmutableDenseMatrix\", data: [], size: []}`,\n * where mathjs is optional\n * @returns {ImmutableDenseMatrix}\n */\n ImmutableDenseMatrix.fromJSON = function (json) {\n return new ImmutableDenseMatrix(json)\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @param {Number} i Matrix row index 1\n * @param {Number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n ImmutableDenseMatrix.prototype.swapRows = function () {\n throw new Error('Cannot invoke swapRows on an Immutable Matrix instance')\n }\n\n /**\n * Calculate the minimum value in the set\n * @return {Number | undefined} min\n */\n ImmutableDenseMatrix.prototype.min = function () {\n // check min has been calculated before\n if (this._min === null) {\n // minimum\n let m = null\n // compute min\n this.forEach(function (v) {\n if (m === null || smaller(v, m)) { m = v }\n })\n this._min = m !== null ? m : undefined\n }\n return this._min\n }\n\n /**\n * Calculate the maximum value in the set\n * @return {Number | undefined} max\n */\n ImmutableDenseMatrix.prototype.max = function () {\n // check max has been calculated before\n if (this._max === null) {\n // maximum\n let m = null\n // compute max\n this.forEach(function (v) {\n if (m === null || smaller(m, v)) { m = v }\n })\n this._max = m !== null ? m : undefined\n }\n return this._max\n }\n\n return ImmutableDenseMatrix\n}, { isClass: true })\n","import { isMatrix, isRange } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Index'\nconst dependencies = ['ImmutableDenseMatrix']\n\nexport const createIndexClass = /* #__PURE__ */ factory(name, dependencies, ({ ImmutableDenseMatrix }) => {\n /**\n * Create an index. An Index can store ranges and sets for multiple dimensions.\n * Matrix.get, Matrix.set, and math.subset accept an Index as input.\n *\n * Usage:\n * const index = new Index(range1, range2, matrix1, array1, ...)\n *\n * Where each parameter can be any of:\n * A number\n * A string (containing a name of an object property)\n * An instance of Range\n * An Array with the Set values\n * A Matrix with the Set values\n *\n * The parameters start, end, and step must be integer numbers.\n *\n * @class Index\n * @Constructor Index\n * @param {...*} ranges\n */\n function Index (ranges) {\n if (!(this instanceof Index)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this._dimensions = []\n this._isScalar = true\n\n for (let i = 0, ii = arguments.length; i < ii; i++) {\n const arg = arguments[i]\n\n if (isRange(arg)) {\n this._dimensions.push(arg)\n this._isScalar = false\n } else if (Array.isArray(arg) || isMatrix(arg)) {\n // create matrix\n const m = _createImmutableMatrix(arg.valueOf())\n this._dimensions.push(m)\n // size\n const size = m.size()\n // scalar\n if (size.length !== 1 || size[0] !== 1) {\n this._isScalar = false\n }\n } else if (typeof arg === 'number') {\n this._dimensions.push(_createImmutableMatrix([arg]))\n } else if (typeof arg === 'string') {\n // object property (arguments.count should be 1)\n this._dimensions.push(arg)\n } else {\n throw new TypeError('Dimension must be an Array, Matrix, number, string, or Range')\n }\n // TODO: implement support for wildcard '*'\n }\n }\n\n /**\n * Attach type information\n */\n Index.prototype.type = 'Index'\n Index.prototype.isIndex = true\n\n function _createImmutableMatrix (arg) {\n // loop array elements\n for (let i = 0, l = arg.length; i < l; i++) {\n if (typeof arg[i] !== 'number' || !isInteger(arg[i])) {\n throw new TypeError('Index parameters must be positive integer numbers')\n }\n }\n // create matrix\n return new ImmutableDenseMatrix(arg)\n }\n\n /**\n * Create a clone of the index\n * @memberof Index\n * @return {Index} clone\n */\n Index.prototype.clone = function () {\n const index = new Index()\n index._dimensions = clone(this._dimensions)\n index._isScalar = this._isScalar\n return index\n }\n\n /**\n * Create an index from an array with ranges/numbers\n * @memberof Index\n * @param {Array.} ranges\n * @return {Index} index\n * @private\n */\n Index.create = function (ranges) {\n const index = new Index()\n Index.apply(index, ranges)\n return index\n }\n\n /**\n * Retrieve the size of the index, the number of elements for each dimension.\n * @memberof Index\n * @returns {number[]} size\n */\n Index.prototype.size = function () {\n const size = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const d = this._dimensions[i]\n size[i] = (typeof d === 'string') ? 1 : d.size()[0]\n }\n\n return size\n }\n\n /**\n * Get the maximum value for each of the indexes ranges.\n * @memberof Index\n * @returns {number[]} max\n */\n Index.prototype.max = function () {\n const values = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const range = this._dimensions[i]\n values[i] = (typeof range === 'string') ? range : range.max()\n }\n\n return values\n }\n\n /**\n * Get the minimum value for each of the indexes ranges.\n * @memberof Index\n * @returns {number[]} min\n */\n Index.prototype.min = function () {\n const values = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const range = this._dimensions[i]\n values[i] = (typeof range === 'string') ? range : range.min()\n }\n\n return values\n }\n\n /**\n * Loop over each of the ranges of the index\n * @memberof Index\n * @param {Function} callback Called for each range with a Range as first\n * argument, the dimension as second, and the\n * index object as third.\n */\n Index.prototype.forEach = function (callback) {\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n callback(this._dimensions[i], i, this)\n }\n }\n\n /**\n * Retrieve the dimension for the given index\n * @memberof Index\n * @param {Number} dim Number of the dimension\n * @returns {Range | null} range\n */\n Index.prototype.dimension = function (dim) {\n return this._dimensions[dim] || null\n }\n\n /**\n * Test whether this index contains an object property\n * @returns {boolean} Returns true if the index is an object property\n */\n Index.prototype.isObjectProperty = function () {\n return this._dimensions.length === 1 && typeof this._dimensions[0] === 'string'\n }\n\n /**\n * Returns the object property name when the Index holds a single object property,\n * else returns null\n * @returns {string | null}\n */\n Index.prototype.getObjectProperty = function () {\n return this.isObjectProperty() ? this._dimensions[0] : null\n }\n\n /**\n * Test whether this index contains only a single value.\n *\n * This is the case when the index is created with only scalar values as ranges,\n * not for ranges resolving into a single value.\n * @memberof Index\n * @return {boolean} isScalar\n */\n Index.prototype.isScalar = function () {\n return this._isScalar\n }\n\n /**\n * Expand the Index into an array.\n * For example new Index([0,3], [2,7]) returns [[0,1,2], [2,3,4,5,6]]\n * @memberof Index\n * @returns {Array} array\n */\n Index.prototype.toArray = function () {\n const array = []\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const dimension = this._dimensions[i]\n array.push((typeof dimension === 'string') ? dimension : dimension.toArray())\n }\n return array\n }\n\n /**\n * Get the primitive value of the Index, a two dimensional array.\n * Equivalent to Index.toArray().\n * @memberof Index\n * @returns {Array} array\n */\n Index.prototype.valueOf = Index.prototype.toArray\n\n /**\n * Get the string representation of the index, for example '[2:6]' or '[0:2:10, 4:7, [1,2,3]]'\n * @memberof Index\n * @returns {String} str\n */\n Index.prototype.toString = function () {\n const strings = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const dimension = this._dimensions[i]\n if (typeof dimension === 'string') {\n strings.push(JSON.stringify(dimension))\n } else {\n strings.push(dimension.toString())\n }\n }\n\n return '[' + strings.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the Index\n * @memberof Index\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Index\", \"ranges\": [{\"mathjs\": \"Range\", start: 0, end: 10, step:1}, ...]}`\n */\n Index.prototype.toJSON = function () {\n return {\n mathjs: 'Index',\n dimensions: this._dimensions\n }\n }\n\n /**\n * Instantiate an Index from a JSON object\n * @memberof Index\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Index\", \"dimensions\": [{\"mathjs\": \"Range\", start: 0, end: 10, step:1}, ...]}`\n * @return {Index}\n */\n Index.fromJSON = function (json) {\n return Index.create(json.dimensions)\n }\n\n return Index\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'FibonacciHeap'\nconst dependencies = ['smaller', 'larger']\n\nexport const createFibonacciHeapClass = /* #__PURE__ */ factory(name, dependencies, ({ smaller, larger }) => {\n const oneOverLogPhi = 1.0 / Math.log((1.0 + Math.sqrt(5.0)) / 2.0)\n\n /**\n * Fibonacci Heap implementation, used interally for Matrix math.\n * @class FibonacciHeap\n * @constructor FibonacciHeap\n */\n function FibonacciHeap () {\n if (!(this instanceof FibonacciHeap)) { throw new SyntaxError('Constructor must be called with the new operator') }\n\n // initialize fields\n this._minimum = null\n this._size = 0\n }\n\n /**\n * Attach type information\n */\n FibonacciHeap.prototype.type = 'FibonacciHeap'\n FibonacciHeap.prototype.isFibonacciHeap = true\n\n /**\n * Inserts a new data element into the heap. No heap consolidation is\n * performed at this time, the new node is simply inserted into the root\n * list of this heap. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.insert = function (key, value) {\n // create node\n const node = {\n key: key,\n value: value,\n degree: 0\n }\n // check we have a node in the minimum\n if (this._minimum) {\n // minimum node\n const minimum = this._minimum\n // update left & right of node\n node.left = minimum\n node.right = minimum.right\n minimum.right = node\n node.right.left = node\n // update minimum node in heap if needed\n if (smaller(key, minimum.key)) {\n // node has a smaller key, use it as minimum\n this._minimum = node\n }\n } else {\n // set left & right\n node.left = node\n node.right = node\n // this is the first node\n this._minimum = node\n }\n // increment number of nodes in heap\n this._size++\n // return node\n return node\n }\n\n /**\n * Returns the number of nodes in heap. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.size = function () {\n return this._size\n }\n\n /**\n * Removes all elements from this heap.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.clear = function () {\n this._minimum = null\n this._size = 0\n }\n\n /**\n * Returns true if the heap is empty, otherwise false.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.isEmpty = function () {\n return this._size === 0\n }\n\n /**\n * Extracts the node with minimum key from heap. Amortized running\n * time: O(log n).\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.extractMinimum = function () {\n // node to remove\n const node = this._minimum\n // check we have a minimum\n if (node === null) { return node }\n // current minimum\n let minimum = this._minimum\n // get number of children\n let numberOfChildren = node.degree\n // pointer to the first child\n let x = node.child\n // for each child of node do...\n while (numberOfChildren > 0) {\n // store node in right side\n const tempRight = x.right\n // remove x from child list\n x.left.right = x.right\n x.right.left = x.left\n // add x to root list of heap\n x.left = minimum\n x.right = minimum.right\n minimum.right = x\n x.right.left = x\n // set Parent[x] to null\n x.parent = null\n x = tempRight\n numberOfChildren--\n }\n // remove node from root list of heap\n node.left.right = node.right\n node.right.left = node.left\n // update minimum\n if (node === node.right) {\n // empty\n minimum = null\n } else {\n // update minimum\n minimum = node.right\n // we need to update the pointer to the root with minimum key\n minimum = _findMinimumNode(minimum, this._size)\n }\n // decrement size of heap\n this._size--\n // update minimum\n this._minimum = minimum\n // return node\n return node\n }\n\n /**\n * Removes a node from the heap given the reference to the node. The trees\n * in the heap will be consolidated, if necessary. This operation may fail\n * to remove the correct element if there are nodes with key value -Infinity.\n * Running time: O(log n) amortized.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.remove = function (node) {\n // decrease key value\n this._minimum = _decreaseKey(this._minimum, node, -1)\n // remove the smallest\n this.extractMinimum()\n }\n\n /**\n * Decreases the key value for a heap node, given the new value to take on.\n * The structure of the heap may be changed and will not be consolidated.\n * Running time: O(1) amortized.\n * @memberof FibonacciHeap\n */\n function _decreaseKey (minimum, node, key) {\n // set node key\n node.key = key\n // get parent node\n const parent = node.parent\n if (parent && smaller(node.key, parent.key)) {\n // remove node from parent\n _cut(minimum, node, parent)\n // remove all nodes from parent to the root parent\n _cascadingCut(minimum, parent)\n }\n // update minimum node if needed\n if (smaller(node.key, minimum.key)) { minimum = node }\n // return minimum\n return minimum\n }\n\n /**\n * The reverse of the link operation: removes node from the child list of parent.\n * This method assumes that min is non-null. Running time: O(1).\n * @memberof FibonacciHeap\n */\n function _cut (minimum, node, parent) {\n // remove node from parent children and decrement Degree[parent]\n node.left.right = node.right\n node.right.left = node.left\n parent.degree--\n // reset y.child if necessary\n if (parent.child === node) { parent.child = node.right }\n // remove child if degree is 0\n if (parent.degree === 0) { parent.child = null }\n // add node to root list of heap\n node.left = minimum\n node.right = minimum.right\n minimum.right = node\n node.right.left = node\n // set parent[node] to null\n node.parent = null\n // set mark[node] to false\n node.mark = false\n }\n\n /**\n * Performs a cascading cut operation. This cuts node from its parent and then\n * does the same for its parent, and so on up the tree.\n * Running time: O(log n); O(1) excluding the recursion.\n * @memberof FibonacciHeap\n */\n function _cascadingCut (minimum, node) {\n // store parent node\n const parent = node.parent\n // if there's a parent...\n if (!parent) { return }\n // if node is unmarked, set it marked\n if (!node.mark) {\n node.mark = true\n } else {\n // it's marked, cut it from parent\n _cut(minimum, node, parent)\n // cut its parent as well\n _cascadingCut(parent)\n }\n }\n\n /**\n * Make the first node a child of the second one. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n const _linkNodes = function (node, parent) {\n // remove node from root list of heap\n node.left.right = node.right\n node.right.left = node.left\n // make node a Child of parent\n node.parent = parent\n if (!parent.child) {\n parent.child = node\n node.right = node\n node.left = node\n } else {\n node.left = parent.child\n node.right = parent.child.right\n parent.child.right = node\n node.right.left = node\n }\n // increase degree[parent]\n parent.degree++\n // set mark[node] false\n node.mark = false\n }\n\n function _findMinimumNode (minimum, size) {\n // to find trees of the same degree efficiently we use an array of length O(log n) in which we keep a pointer to one root of each degree\n const arraySize = Math.floor(Math.log(size) * oneOverLogPhi) + 1\n // create list with initial capacity\n const array = new Array(arraySize)\n // find the number of root nodes.\n let numRoots = 0\n let x = minimum\n if (x) {\n numRoots++\n x = x.right\n while (x !== minimum) {\n numRoots++\n x = x.right\n }\n }\n // vars\n let y\n // For each node in root list do...\n while (numRoots > 0) {\n // access this node's degree..\n let d = x.degree\n // get next node\n const next = x.right\n // check if there is a node already in array with the same degree\n while (true) {\n // get node with the same degree is any\n y = array[d]\n if (!y) { break }\n // make one node with the same degree a child of the other, do this based on the key value.\n if (larger(x.key, y.key)) {\n const temp = y\n y = x\n x = temp\n }\n // make y a child of x\n _linkNodes(y, x)\n // we have handled this degree, go to next one.\n array[d] = null\n d++\n }\n // save this node for later when we might encounter another of the same degree.\n array[d] = x\n // move forward through list.\n x = next\n numRoots--\n }\n // Set min to null (effectively losing the root list) and reconstruct the root list from the array entries in array[].\n minimum = null\n // loop nodes in array\n for (let i = 0; i < arraySize; i++) {\n // get current node\n y = array[i]\n if (!y) { continue }\n // check if we have a linked list\n if (minimum) {\n // First remove node from root list.\n y.left.right = y.right\n y.right.left = y.left\n // now add to root list, again.\n y.left = minimum\n y.right = minimum.right\n minimum.right = y\n y.right.left = y\n // check if this is a new min.\n if (smaller(y.key, minimum.key)) { minimum = y }\n } else { minimum = y }\n }\n return minimum\n }\n\n return FibonacciHeap\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'Spa'\nconst dependencies = ['addScalar', 'equalScalar', 'FibonacciHeap']\n\nexport const createSpaClass = /* #__PURE__ */ factory(name, dependencies, ({ addScalar, equalScalar, FibonacciHeap }) => {\n /**\n * An ordered Sparse Accumulator is a representation for a sparse vector that includes a dense array\n * of the vector elements and an ordered list of non-zero elements.\n */\n function Spa () {\n if (!(this instanceof Spa)) { throw new SyntaxError('Constructor must be called with the new operator') }\n\n // allocate vector, TODO use typed arrays\n this._values = []\n this._heap = new FibonacciHeap()\n }\n\n /**\n * Attach type information\n */\n Spa.prototype.type = 'Spa'\n Spa.prototype.isSpa = true\n\n /**\n * Set the value for index i.\n *\n * @param {number} i The index\n * @param {number | BigNumber | Complex} The value at index i\n */\n Spa.prototype.set = function (i, v) {\n // check we have a value @ i\n if (!this._values[i]) {\n // insert in heap\n const node = this._heap.insert(i, v)\n // set the value @ i\n this._values[i] = node\n } else {\n // update the value @ i\n this._values[i].value = v\n }\n }\n\n Spa.prototype.get = function (i) {\n const node = this._values[i]\n if (node) { return node.value }\n return 0\n }\n\n Spa.prototype.accumulate = function (i, v) {\n // node @ i\n let node = this._values[i]\n if (!node) {\n // insert in heap\n node = this._heap.insert(i, v)\n // initialize value\n this._values[i] = node\n } else {\n // accumulate value\n node.value = addScalar(node.value, v)\n }\n }\n\n Spa.prototype.forEach = function (from, to, callback) {\n // references\n const heap = this._heap\n const values = this._values\n // nodes\n const nodes = []\n // node with minimum key, save it\n let node = heap.extractMinimum()\n if (node) { nodes.push(node) }\n // extract nodes from heap (ordered)\n while (node && node.key <= to) {\n // check it is in range\n if (node.key >= from) {\n // check value is not zero\n if (!equalScalar(node.value, 0)) {\n // invoke callback\n callback(node.key, node.value, this)\n }\n }\n // extract next node, save it\n node = heap.extractMinimum()\n if (node) { nodes.push(node) }\n }\n // reinsert all nodes in heap\n for (let i = 0; i < nodes.length; i++) {\n // current node\n const n = nodes[i]\n // insert node in heap\n node = heap.insert(n.key, n.value)\n // update values\n values[node.key] = node\n }\n }\n\n Spa.prototype.swap = function (i, j) {\n // node @ i and j\n let nodei = this._values[i]\n let nodej = this._values[j]\n // check we need to insert indeces\n if (!nodei && nodej) {\n // insert in heap\n nodei = this._heap.insert(i, nodej.value)\n // remove from heap\n this._heap.remove(nodej)\n // set values\n this._values[i] = nodei\n this._values[j] = undefined\n } else if (nodei && !nodej) {\n // insert in heap\n nodej = this._heap.insert(j, nodei.value)\n // remove from heap\n this._heap.remove(nodei)\n // set values\n this._values[j] = nodej\n this._values[i] = undefined\n } else if (nodei && nodej) {\n // swap values\n const v = nodei.value\n nodei.value = nodej.value\n nodej.value = v\n }\n }\n\n return Spa\n}, { isClass: true })\n","import { memoize } from '../function.js'\n\n/**\n * Calculate BigNumber e\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns e\n */\nexport const createBigNumberE = memoize(function (BigNumber) {\n return new BigNumber(1).exp()\n}, { hasher })\n\n/**\n * Calculate BigNumber golden ratio, phi = (1+sqrt(5))/2\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns phi\n */\nexport const createBigNumberPhi = memoize(function (BigNumber) {\n return new BigNumber(1).plus(new BigNumber(5).sqrt()).div(2)\n}, { hasher })\n\n/**\n * Calculate BigNumber pi.\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns pi\n */\nexport const createBigNumberPi = memoize(function (BigNumber) {\n return BigNumber.acos(-1)\n}, { hasher })\n\n/**\n * Calculate BigNumber tau, tau = 2 * pi\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns tau\n */\nexport const createBigNumberTau = memoize(function (BigNumber) {\n return createBigNumberPi(BigNumber).times(2)\n}, { hasher })\n\n/**\n * Create a hash for a BigNumber constructor function. The created has is\n * the configured precision\n * @param {Array} args Supposed to contain a single entry with\n * a BigNumber constructor\n * @return {number} precision\n * @private\n */\nfunction hasher (args) {\n return args[0].precision\n}\n","import { isComplex, isUnit, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { memoize } from '../../utils/function.js'\nimport { endsWith } from '../../utils/string.js'\nimport { clone, hasOwnProperty } from '../../utils/object.js'\nimport { createBigNumberPi as createPi } from '../../utils/bignumber/constants.js'\n\nconst name = 'Unit'\nconst dependencies = [\n '?on',\n 'config',\n 'addScalar',\n 'subtract',\n 'multiplyScalar',\n 'divideScalar',\n 'pow',\n 'abs',\n 'fix',\n 'round',\n 'equal',\n 'isNumeric',\n 'format',\n 'number',\n 'Complex',\n 'BigNumber',\n 'Fraction'\n]\n\nexport const createUnitClass = /* #__PURE__ */ factory(name, dependencies, ({\n on,\n config,\n addScalar,\n subtract,\n multiplyScalar,\n divideScalar,\n pow,\n abs,\n fix,\n round,\n equal,\n isNumeric,\n format,\n number,\n Complex,\n BigNumber,\n Fraction\n}) => {\n const toNumber = number\n /**\n * A unit can be constructed in the following ways:\n *\n * const a = new Unit(value, name)\n * const b = new Unit(null, name)\n * const c = Unit.parse(str)\n *\n * Example usage:\n *\n * const a = new Unit(5, 'cm') // 50 mm\n * const b = Unit.parse('23 kg') // 23 kg\n * const c = math.in(a, new Unit(null, 'm') // 0.05 m\n * const d = new Unit(9.81, \"m/s^2\") // 9.81 m/s^2\n *\n * @class Unit\n * @constructor Unit\n * @param {number | BigNumber | Fraction | Complex | boolean} [value] A value like 5.2\n * @param {string} [name] A unit name like \"cm\" or \"inch\", or a derived unit of the form: \"u1[^ex1] [u2[^ex2] ...] [/ u3[^ex3] [u4[^ex4]]]\", such as \"kg m^2/s^2\", where each unit appearing after the forward slash is taken to be in the denominator. \"kg m^2 s^-2\" is a synonym and is also acceptable. Any of the units can include a prefix.\n */\n function Unit (value, name) {\n if (!(this instanceof Unit)) {\n throw new Error('Constructor must be called with the new operator')\n }\n\n if (!(value === null || value === undefined || isNumeric(value) || isComplex(value))) {\n throw new TypeError('First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined')\n }\n if (name !== undefined && (typeof name !== 'string' || name === '')) {\n throw new TypeError('Second parameter in Unit constructor must be a string')\n }\n\n if (name !== undefined) {\n const u = Unit.parse(name)\n this.units = u.units\n this.dimensions = u.dimensions\n } else {\n this.units = [\n {\n unit: UNIT_NONE,\n prefix: PREFIXES.NONE, // link to a list with supported prefixes\n power: 0\n }\n ]\n this.dimensions = []\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n this.dimensions[i] = 0\n }\n }\n\n this.value = (value !== undefined && value !== null) ? this._normalize(value) : null\n\n this.fixPrefix = false // if true, function format will not search for the\n // best prefix but leave it as initially provided.\n // fixPrefix is set true by the method Unit.to\n\n // The justification behind this is that if the constructor is explicitly called,\n // the caller wishes the units to be returned exactly as he supplied.\n this.skipAutomaticSimplification = true\n }\n\n /**\n * Attach type information\n */\n Unit.prototype.type = 'Unit'\n Unit.prototype.isUnit = true\n\n // private variables and functions for the Unit parser\n let text, index, c\n\n function skipWhitespace () {\n while (c === ' ' || c === '\\t') {\n next()\n }\n }\n\n function isDigitDot (c) {\n return ((c >= '0' && c <= '9') || c === '.')\n }\n\n function isDigit (c) {\n return ((c >= '0' && c <= '9'))\n }\n\n function next () {\n index++\n c = text.charAt(index)\n }\n\n function revert (oldIndex) {\n index = oldIndex\n c = text.charAt(index)\n }\n\n function parseNumber () {\n let number = ''\n const oldIndex = index\n\n if (c === '+') {\n next()\n } else if (c === '-') {\n number += c\n next()\n }\n\n if (!isDigitDot(c)) {\n // a + or - must be followed by a digit\n revert(oldIndex)\n return null\n }\n\n // get number, can have a single dot\n if (c === '.') {\n number += c\n next()\n if (!isDigit(c)) {\n // this is no legal number, it is just a dot\n revert(oldIndex)\n return null\n }\n } else {\n while (isDigit(c)) {\n number += c\n next()\n }\n if (c === '.') {\n number += c\n next()\n }\n }\n while (isDigit(c)) {\n number += c\n next()\n }\n\n // check for exponential notation like \"2.3e-4\" or \"1.23e50\"\n if (c === 'E' || c === 'e') {\n // The grammar branches here. This could either be part of an exponent or the start of a unit that begins with the letter e, such as \"4exabytes\"\n\n let tentativeNumber = ''\n const tentativeIndex = index\n\n tentativeNumber += c\n next()\n\n if (c === '+' || c === '-') {\n tentativeNumber += c\n next()\n }\n\n // Scientific notation MUST be followed by an exponent (otherwise we assume it is not scientific notation)\n if (!isDigit(c)) {\n // The e or E must belong to something else, so return the number without the e or E.\n revert(tentativeIndex)\n return number\n }\n\n // We can now safely say that this is scientific notation.\n number = number + tentativeNumber\n while (isDigit(c)) {\n number += c\n next()\n }\n }\n\n return number\n }\n\n function parseUnit () {\n let unitName = ''\n\n // Alphanumeric characters only; matches [a-zA-Z0-9]\n while (isDigit(c) || Unit.isValidAlpha(c)) {\n unitName += c\n next()\n }\n\n // Must begin with [a-zA-Z]\n const firstC = unitName.charAt(0)\n if (Unit.isValidAlpha(firstC)) {\n return unitName\n } else {\n return null\n }\n }\n\n function parseCharacter (toFind) {\n if (c === toFind) {\n next()\n return toFind\n } else {\n return null\n }\n }\n\n /**\n * Parse a string into a unit. The value of the unit is parsed as number,\n * BigNumber, or Fraction depending on the math.js config setting `number`.\n *\n * Throws an exception if the provided string does not contain a valid unit or\n * cannot be parsed.\n * @memberof Unit\n * @param {string} str A string like \"5.2 inch\", \"4e2 cm/s^2\"\n * @return {Unit} unit\n */\n Unit.parse = function (str, options) {\n options = options || {}\n text = str\n index = -1\n c = ''\n\n if (typeof text !== 'string') {\n throw new TypeError('Invalid argument in Unit.parse, string expected')\n }\n\n const unit = new Unit()\n unit.units = []\n\n let powerMultiplierCurrent = 1\n let expectingUnit = false\n\n // A unit should follow this pattern:\n // [number] ...[ [*/] unit[^number] ]\n // unit[^number] ... [ [*/] unit[^number] ]\n\n // Rules:\n // number is any floating point number.\n // unit is any alphanumeric string beginning with an alpha. Units with names like e3 should be avoided because they look like the exponent of a floating point number!\n // The string may optionally begin with a number.\n // Each unit may optionally be followed by ^number.\n // Whitespace or a forward slash is recommended between consecutive units, although the following technically is parseable:\n // 2m^2kg/s^2\n // it is not good form. If a unit starts with e, then it could be confused as a floating point number:\n // 4erg\n\n next()\n skipWhitespace()\n\n // Optional number at the start of the string\n const valueStr = parseNumber()\n let value = null\n if (valueStr) {\n if (config.number === 'BigNumber') {\n value = new BigNumber(valueStr)\n } else if (config.number === 'Fraction') {\n try {\n // not all numbers can be turned in Fractions, for example very small numbers not\n value = new Fraction(valueStr)\n } catch (err) {\n value = parseFloat(valueStr)\n }\n } else { // number\n value = parseFloat(valueStr)\n }\n\n skipWhitespace() // Whitespace is not required here\n\n // handle multiplication or division right after the value, like '1/s'\n if (parseCharacter('*')) {\n powerMultiplierCurrent = 1\n expectingUnit = true\n } else if (parseCharacter('/')) {\n powerMultiplierCurrent = -1\n expectingUnit = true\n }\n }\n\n // Stack to keep track of powerMultipliers applied to each parentheses group\n const powerMultiplierStack = []\n\n // Running product of all elements in powerMultiplierStack\n let powerMultiplierStackProduct = 1\n\n while (true) {\n skipWhitespace()\n\n // Check for and consume opening parentheses, pushing powerMultiplierCurrent to the stack\n // A '(' will always appear directly before a unit.\n while (c === '(') {\n powerMultiplierStack.push(powerMultiplierCurrent)\n powerMultiplierStackProduct *= powerMultiplierCurrent\n powerMultiplierCurrent = 1\n next()\n skipWhitespace()\n }\n\n // Is there something here?\n let uStr\n if (c) {\n const oldC = c\n uStr = parseUnit()\n if (uStr === null) {\n throw new SyntaxError('Unexpected \"' + oldC + '\" in \"' + text + '\" at index ' + index.toString())\n }\n } else {\n // End of input.\n break\n }\n\n // Verify the unit exists and get the prefix (if any)\n const res = _findUnit(uStr)\n if (res === null) {\n // Unit not found.\n throw new SyntaxError('Unit \"' + uStr + '\" not found.')\n }\n\n let power = powerMultiplierCurrent * powerMultiplierStackProduct\n // Is there a \"^ number\"?\n skipWhitespace()\n if (parseCharacter('^')) {\n skipWhitespace()\n const p = parseNumber()\n if (p === null) {\n // No valid number found for the power!\n throw new SyntaxError('In \"' + str + '\", \"^\" must be followed by a floating-point number')\n }\n power *= p\n }\n\n // Add the unit to the list\n unit.units.push({\n unit: res.unit,\n prefix: res.prefix,\n power: power\n })\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n unit.dimensions[i] += (res.unit.dimensions[i] || 0) * power\n }\n\n // Check for and consume closing parentheses, popping from the stack.\n // A ')' will always follow a unit.\n skipWhitespace()\n while (c === ')') {\n if (powerMultiplierStack.length === 0) {\n throw new SyntaxError('Unmatched \")\" in \"' + text + '\" at index ' + index.toString())\n }\n powerMultiplierStackProduct /= powerMultiplierStack.pop()\n next()\n skipWhitespace()\n }\n\n // \"*\" and \"/\" should mean we are expecting something to come next.\n // Is there a forward slash? If so, negate powerMultiplierCurrent. The next unit or paren group is in the denominator.\n expectingUnit = false\n\n if (parseCharacter('*')) {\n // explicit multiplication\n powerMultiplierCurrent = 1\n expectingUnit = true\n } else if (parseCharacter('/')) {\n // division\n powerMultiplierCurrent = -1\n expectingUnit = true\n } else {\n // implicit multiplication\n powerMultiplierCurrent = 1\n }\n\n // Replace the unit into the auto unit system\n if (res.unit.base) {\n const baseDim = res.unit.base.key\n UNIT_SYSTEMS.auto[baseDim] = {\n unit: res.unit,\n prefix: res.prefix\n }\n }\n }\n\n // Has the string been entirely consumed?\n skipWhitespace()\n if (c) {\n throw new SyntaxError('Could not parse: \"' + str + '\"')\n }\n\n // Is there a trailing slash?\n if (expectingUnit) {\n throw new SyntaxError('Trailing characters: \"' + str + '\"')\n }\n\n // Is the parentheses stack empty?\n if (powerMultiplierStack.length !== 0) {\n throw new SyntaxError('Unmatched \"(\" in \"' + text + '\"')\n }\n\n // Are there any units at all?\n if (unit.units.length === 0 && !options.allowNoUnits) {\n throw new SyntaxError('\"' + str + '\" contains no units')\n }\n\n unit.value = (value !== undefined) ? unit._normalize(value) : null\n return unit\n }\n\n /**\n * create a copy of this unit\n * @memberof Unit\n * @return {Unit} Returns a cloned version of the unit\n */\n Unit.prototype.clone = function () {\n const unit = new Unit()\n\n unit.fixPrefix = this.fixPrefix\n unit.skipAutomaticSimplification = this.skipAutomaticSimplification\n\n unit.value = clone(this.value)\n unit.dimensions = this.dimensions.slice(0)\n unit.units = []\n for (let i = 0; i < this.units.length; i++) {\n unit.units[i] = { }\n for (const p in this.units[i]) {\n if (hasOwnProperty(this.units[i], p)) {\n unit.units[i][p] = this.units[i][p]\n }\n }\n }\n\n return unit\n }\n\n /**\n * Return whether the unit is derived (such as m/s, or cm^2, but not N)\n * @memberof Unit\n * @return {boolean} True if the unit is derived\n */\n Unit.prototype._isDerived = function () {\n if (this.units.length === 0) {\n return false\n }\n return this.units.length > 1 || Math.abs(this.units[0].power - 1.0) > 1e-15\n }\n\n /**\n * Normalize a value, based on its currently set unit(s)\n * @memberof Unit\n * @param {number | BigNumber | Fraction | boolean} value\n * @return {number | BigNumber | Fraction | boolean} normalized value\n * @private\n */\n Unit.prototype._normalize = function (value) {\n let unitValue, unitOffset, unitPower, unitPrefixValue\n let convert\n\n if (value === null || value === undefined || this.units.length === 0) {\n return value\n } else if (this._isDerived()) {\n // This is a derived unit, so do not apply offsets.\n // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.\n let res = value\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n for (let i = 0; i < this.units.length; i++) {\n unitValue = convert(this.units[i].unit.value)\n unitPrefixValue = convert(this.units[i].prefix.value)\n unitPower = convert(this.units[i].power)\n res = multiplyScalar(res, pow(multiplyScalar(unitValue, unitPrefixValue), unitPower))\n }\n\n return res\n } else {\n // This is a single unit of power 1, like kg or degC\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n unitValue = convert(this.units[0].unit.value)\n unitOffset = convert(this.units[0].unit.offset)\n unitPrefixValue = convert(this.units[0].prefix.value)\n\n return multiplyScalar(addScalar(value, unitOffset), multiplyScalar(unitValue, unitPrefixValue))\n }\n }\n\n /**\n * Denormalize a value, based on its currently set unit(s)\n * @memberof Unit\n * @param {number} value\n * @param {number} [prefixValue] Optional prefix value to be used (ignored if this is a derived unit)\n * @return {number} denormalized value\n * @private\n */\n Unit.prototype._denormalize = function (value, prefixValue) {\n let unitValue, unitOffset, unitPower, unitPrefixValue\n let convert\n\n if (value === null || value === undefined || this.units.length === 0) {\n return value\n } else if (this._isDerived()) {\n // This is a derived unit, so do not apply offsets.\n // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.\n // Also, prefixValue is ignored--but we will still use the prefix value stored in each unit, since kg is usually preferable to g unless the user decides otherwise.\n let res = value\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n for (let i = 0; i < this.units.length; i++) {\n unitValue = convert(this.units[i].unit.value)\n unitPrefixValue = convert(this.units[i].prefix.value)\n unitPower = convert(this.units[i].power)\n res = divideScalar(res, pow(multiplyScalar(unitValue, unitPrefixValue), unitPower))\n }\n\n return res\n } else {\n // This is a single unit of power 1, like kg or degC\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n unitValue = convert(this.units[0].unit.value)\n unitPrefixValue = convert(this.units[0].prefix.value)\n unitOffset = convert(this.units[0].unit.offset)\n\n if (prefixValue === undefined || prefixValue === null) {\n return subtract(divideScalar(divideScalar(value, unitValue), unitPrefixValue), unitOffset)\n } else {\n return subtract(divideScalar(divideScalar(value, unitValue), prefixValue), unitOffset)\n }\n }\n }\n\n /**\n * Find a unit from a string\n * @memberof Unit\n * @param {string} str A string like 'cm' or 'inch'\n * @returns {Object | null} result When found, an object with fields unit and\n * prefix is returned. Else, null is returned.\n * @private\n */\n const _findUnit = memoize((str) => {\n // First, match units names exactly. For example, a user could define 'mm' as 10^-4 m, which is silly, but then we would want 'mm' to match the user-defined unit.\n if (hasOwnProperty(UNITS, str)) {\n const unit = UNITS[str]\n const prefix = unit.prefixes['']\n return {\n unit,\n prefix\n }\n }\n\n for (const name in UNITS) {\n if (hasOwnProperty(UNITS, name)) {\n if (endsWith(str, name)) {\n const unit = UNITS[name]\n const prefixLen = (str.length - name.length)\n const prefixName = str.substring(0, prefixLen)\n const prefix = hasOwnProperty(unit.prefixes, prefixName)\n ? unit.prefixes[prefixName]\n : undefined\n if (prefix !== undefined) {\n // store unit, prefix, and value\n return {\n unit,\n prefix\n }\n }\n }\n }\n }\n\n return null\n }, { hasher: (args) => args[0], limit: 100 })\n\n /**\n * Test if the given expression is a unit.\n * The unit can have a prefix but cannot have a value.\n * @memberof Unit\n * @param {string} name A string to be tested whether it is a value less unit.\n * The unit can have prefix, like \"cm\"\n * @return {boolean} true if the given string is a unit\n */\n Unit.isValuelessUnit = function (name) {\n return (_findUnit(name) !== null)\n }\n\n /**\n * check if this unit has given base unit\n * If this unit is a derived unit, this will ALWAYS return false, since by definition base units are not derived.\n * @memberof Unit\n * @param {BASE_UNITS | string | undefined} base\n */\n Unit.prototype.hasBase = function (base) {\n if (typeof (base) === 'string') {\n base = BASE_UNITS[base]\n }\n\n if (!base) { return false }\n\n // All dimensions must be the same\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n if (Math.abs((this.dimensions[i] || 0) - (base.dimensions[i] || 0)) > 1e-12) {\n return false\n }\n }\n return true\n }\n\n /**\n * Check if this unit has a base or bases equal to another base or bases\n * For derived units, the exponent on each base also must match\n * @memberof Unit\n * @param {Unit} other\n * @return {boolean} true if equal base\n */\n Unit.prototype.equalBase = function (other) {\n // All dimensions must be the same\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n if (Math.abs((this.dimensions[i] || 0) - (other.dimensions[i] || 0)) > 1e-12) {\n return false\n }\n }\n return true\n }\n\n /**\n * Check if this unit equals another unit\n * @memberof Unit\n * @param {Unit} other\n * @return {boolean} true if both units are equal\n */\n Unit.prototype.equals = function (other) {\n return (this.equalBase(other) && equal(this.value, other.value))\n }\n\n /**\n * Multiply this unit with another one\n * @memberof Unit\n * @param {Unit} other\n * @return {Unit} product of this unit and the other unit\n */\n Unit.prototype.multiply = function (other) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) + (other.dimensions[i] || 0)\n }\n\n // Append other's units list onto res\n for (let i = 0; i < other.units.length; i++) {\n // Make a shallow copy of every unit\n const inverted = {\n ...other.units[i]\n }\n res.units.push(inverted)\n }\n\n // If at least one operand has a value, then the result should also have a value\n if (this.value !== null || other.value !== null) {\n const valThis = this.value === null ? this._normalize(1) : this.value\n const valOther = other.value === null ? other._normalize(1) : other.value\n res.value = multiplyScalar(valThis, valOther)\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Divide this unit by another one\n * @memberof Unit\n * @param {Unit} other\n * @return {Unit} result of dividing this unit by the other unit\n */\n Unit.prototype.divide = function (other) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) - (other.dimensions[i] || 0)\n }\n\n // Invert and append other's units list onto res\n for (let i = 0; i < other.units.length; i++) {\n // Make a shallow copy of every unit\n const inverted = {\n ...other.units[i],\n power: -other.units[i].power\n }\n res.units.push(inverted)\n }\n\n // If at least one operand has a value, the result should have a value\n if (this.value !== null || other.value !== null) {\n const valThis = this.value === null ? this._normalize(1) : this.value\n const valOther = other.value === null ? other._normalize(1) : other.value\n res.value = divideScalar(valThis, valOther)\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Calculate the power of a unit\n * @memberof Unit\n * @param {number | Fraction | BigNumber} p\n * @returns {Unit} The result: this^p\n */\n Unit.prototype.pow = function (p) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) * p\n }\n\n // Adjust the power of each unit in the list\n for (let i = 0; i < res.units.length; i++) {\n res.units[i].power *= p\n }\n\n if (res.value !== null) {\n res.value = pow(res.value, p)\n\n // only allow numeric output, we don't want to return a Complex number\n // if (!isNumeric(res.value)) {\n // res.value = NaN\n // }\n // Update: Complex supported now\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Return the numeric value of this unit if it is dimensionless, has a value, and config.predictable == false; or the original unit otherwise\n * @param {Unit} unit\n * @returns {number | Fraction | BigNumber | Unit} The numeric value of the unit if conditions are met, or the original unit otherwise\n */\n function getNumericIfUnitless (unit) {\n if (unit.equalBase(BASE_UNITS.NONE) && unit.value !== null && !config.predictable) {\n return unit.value\n } else {\n return unit\n }\n }\n\n /**\n * Calculate the absolute value of a unit\n * @memberof Unit\n * @param {number | Fraction | BigNumber} x\n * @returns {Unit} The result: |x|, absolute value of x\n */\n Unit.prototype.abs = function () {\n // This gives correct, but unexpected, results for units with an offset.\n // For example, abs(-283.15 degC) = -263.15 degC !!!\n const ret = this.clone()\n ret.value = ret.value !== null ? abs(ret.value) : null\n\n for (const i in ret.units) {\n if (ret.units[i].unit.name === 'VA' || ret.units[i].unit.name === 'VAR') {\n ret.units[i].unit = UNITS.W\n }\n }\n\n return ret\n }\n\n /**\n * Convert the unit to a specific unit name.\n * @memberof Unit\n * @param {string | Unit} valuelessUnit A unit without value. Can have prefix, like \"cm\"\n * @returns {Unit} Returns a clone of the unit with a fixed prefix and unit.\n */\n Unit.prototype.to = function (valuelessUnit) {\n let other\n const value = this.value === null ? this._normalize(1) : this.value\n if (typeof valuelessUnit === 'string') {\n // other = new Unit(null, valuelessUnit)\n other = Unit.parse(valuelessUnit)\n if (!this.equalBase(other)) {\n throw new Error(`Units do not match ('${other.toString()}' != '${this.toString()}')`)\n }\n if (other.value !== null) {\n throw new Error('Cannot convert to a unit with a value')\n }\n\n other.value = clone(value)\n other.fixPrefix = true\n other.skipAutomaticSimplification = true\n return other\n } else if (isUnit(valuelessUnit)) {\n if (!this.equalBase(valuelessUnit)) {\n throw new Error(`Units do not match ('${valuelessUnit.toString()}' != '${this.toString()}')`)\n }\n if (valuelessUnit.value !== null) {\n throw new Error('Cannot convert to a unit with a value')\n }\n other = valuelessUnit.clone()\n other.value = clone(value)\n other.fixPrefix = true\n other.skipAutomaticSimplification = true\n return other\n } else {\n throw new Error('String or Unit expected as parameter')\n }\n }\n\n /**\n * Return the value of the unit when represented with given valueless unit\n * @memberof Unit\n * @param {string | Unit} valuelessUnit For example 'cm' or 'inch'\n * @return {number} Returns the unit value as number.\n */\n // TODO: deprecate Unit.toNumber? It's always better to use toNumeric\n Unit.prototype.toNumber = function (valuelessUnit) {\n return toNumber(this.toNumeric(valuelessUnit))\n }\n\n /**\n * Return the value of the unit in the original numeric type\n * @memberof Unit\n * @param {string | Unit} valuelessUnit For example 'cm' or 'inch'\n * @return {number | BigNumber | Fraction} Returns the unit value\n */\n Unit.prototype.toNumeric = function (valuelessUnit) {\n let other\n if (valuelessUnit) {\n // Allow getting the numeric value without converting to a different unit\n other = this.to(valuelessUnit)\n } else {\n other = this.clone()\n }\n\n if (other._isDerived() || other.units.length === 0) {\n return other._denormalize(other.value)\n } else {\n return other._denormalize(other.value, other.units[0].prefix.value)\n }\n }\n\n /**\n * Get a string representation of the unit.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.toString = function () {\n return this.format()\n }\n\n /**\n * Get a JSON representation of the unit\n * @memberof Unit\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Unit\", \"value\": 2, \"unit\": \"cm\", \"fixPrefix\": false}`\n */\n Unit.prototype.toJSON = function () {\n return {\n mathjs: 'Unit',\n value: this._denormalize(this.value),\n unit: this.formatUnits(),\n fixPrefix: this.fixPrefix\n }\n }\n\n /**\n * Instantiate a Unit from a JSON object\n * @memberof Unit\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Unit\", \"value\": 2, \"unit\": \"cm\", \"fixPrefix\": false}`\n * @return {Unit}\n */\n Unit.fromJSON = function (json) {\n const unit = new Unit(json.value, json.unit)\n unit.fixPrefix = json.fixPrefix || false\n return unit\n }\n\n /**\n * Returns the string representation of the unit.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.valueOf = Unit.prototype.toString\n\n /**\n * Simplify this Unit's unit list and return a new Unit with the simplified list.\n * The returned Unit will contain a list of the \"best\" units for formatting.\n */\n Unit.prototype.simplify = function () {\n const ret = this.clone()\n\n const proposedUnitList = []\n\n // Search for a matching base\n let matchingBase\n for (const key in currentUnitSystem) {\n if (hasOwnProperty(currentUnitSystem, key)) {\n if (ret.hasBase(BASE_UNITS[key])) {\n matchingBase = key\n break\n }\n }\n }\n\n if (matchingBase === 'NONE') {\n ret.units = []\n } else {\n let matchingUnit\n if (matchingBase) {\n // Does the unit system have a matching unit?\n if (hasOwnProperty(currentUnitSystem, matchingBase)) {\n matchingUnit = currentUnitSystem[matchingBase]\n }\n }\n if (matchingUnit) {\n ret.units = [{\n unit: matchingUnit.unit,\n prefix: matchingUnit.prefix,\n power: 1.0\n }]\n } else {\n // Multiple units or units with powers are formatted like this:\n // 5 (kg m^2) / (s^3 mol)\n // Build an representation from the base units of the current unit system\n let missingBaseDim = false\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n const baseDim = BASE_DIMENSIONS[i]\n if (Math.abs(ret.dimensions[i] || 0) > 1e-12) {\n if (hasOwnProperty(currentUnitSystem, baseDim)) {\n proposedUnitList.push({\n unit: currentUnitSystem[baseDim].unit,\n prefix: currentUnitSystem[baseDim].prefix,\n power: ret.dimensions[i] || 0\n })\n } else {\n missingBaseDim = true\n }\n }\n }\n\n // Is the proposed unit list \"simpler\" than the existing one?\n if (proposedUnitList.length < ret.units.length && !missingBaseDim) {\n // Replace this unit list with the proposed list\n ret.units = proposedUnitList\n }\n }\n }\n\n return ret\n }\n\n /**\n * Returns a new Unit in the SI system with the same value as this one\n */\n Unit.prototype.toSI = function () {\n const ret = this.clone()\n\n const proposedUnitList = []\n\n // Multiple units or units with powers are formatted like this:\n // 5 (kg m^2) / (s^3 mol)\n // Build an representation from the base units of the SI unit system\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n const baseDim = BASE_DIMENSIONS[i]\n if (Math.abs(ret.dimensions[i] || 0) > 1e-12) {\n if (hasOwnProperty(UNIT_SYSTEMS.si, baseDim)) {\n proposedUnitList.push({\n unit: UNIT_SYSTEMS.si[baseDim].unit,\n prefix: UNIT_SYSTEMS.si[baseDim].prefix,\n power: ret.dimensions[i] || 0\n })\n } else {\n throw new Error('Cannot express custom unit ' + baseDim + ' in SI units')\n }\n }\n }\n\n // Replace this unit list with the proposed list\n ret.units = proposedUnitList\n\n ret.fixPrefix = true\n ret.skipAutomaticSimplification = true\n\n return ret\n }\n\n /**\n * Get a string representation of the units of this Unit, without the value. The unit list is formatted as-is without first being simplified.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.formatUnits = function () {\n let strNum = ''\n let strDen = ''\n let nNum = 0\n let nDen = 0\n\n for (let i = 0; i < this.units.length; i++) {\n if (this.units[i].power > 0) {\n nNum++\n strNum += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n if (Math.abs(this.units[i].power - 1.0) > 1e-15) {\n strNum += '^' + this.units[i].power\n }\n } else if (this.units[i].power < 0) {\n nDen++\n }\n }\n\n if (nDen > 0) {\n for (let i = 0; i < this.units.length; i++) {\n if (this.units[i].power < 0) {\n if (nNum > 0) {\n strDen += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n if (Math.abs(this.units[i].power + 1.0) > 1e-15) {\n strDen += '^' + (-this.units[i].power)\n }\n } else {\n strDen += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n strDen += '^' + (this.units[i].power)\n }\n }\n }\n }\n // Remove leading \" \"\n strNum = strNum.substr(1)\n strDen = strDen.substr(1)\n\n // Add parans for better copy/paste back into evaluate, for example, or for better pretty print formatting\n if (nNum > 1 && nDen > 0) {\n strNum = '(' + strNum + ')'\n }\n if (nDen > 1 && nNum > 0) {\n strDen = '(' + strDen + ')'\n }\n\n let str = strNum\n if (nNum > 0 && nDen > 0) {\n str += ' / '\n }\n str += strDen\n\n return str\n }\n\n /**\n * Get a string representation of the Unit, with optional formatting options.\n * @memberof Unit\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string}\n */\n Unit.prototype.format = function (options) {\n // Simplfy the unit list, unless it is valueless or was created directly in the\n // constructor or as the result of to or toSI\n const simp = this.skipAutomaticSimplification || this.value === null\n ? this.clone()\n : this.simplify()\n\n // Apply some custom logic for handling VA and VAR. The goal is to express the value of the unit as a real value, if possible. Otherwise, use a real-valued unit instead of a complex-valued one.\n let isImaginary = false\n if (typeof (simp.value) !== 'undefined' && simp.value !== null && isComplex(simp.value)) {\n // TODO: Make this better, for example, use relative magnitude of re and im rather than absolute\n isImaginary = Math.abs(simp.value.re) < 1e-14\n }\n\n for (const i in simp.units) {\n if (hasOwnProperty(simp.units, i)) {\n if (simp.units[i].unit) {\n if (simp.units[i].unit.name === 'VA' && isImaginary) {\n simp.units[i].unit = UNITS.VAR\n } else if (simp.units[i].unit.name === 'VAR' && !isImaginary) {\n simp.units[i].unit = UNITS.VA\n }\n }\n }\n }\n\n // Now apply the best prefix\n // Units must have only one unit and not have the fixPrefix flag set\n if (simp.units.length === 1 && !simp.fixPrefix) {\n // Units must have integer powers, otherwise the prefix will change the\n // outputted value by not-an-integer-power-of-ten\n if (Math.abs(simp.units[0].power - Math.round(simp.units[0].power)) < 1e-14) {\n // Apply the best prefix\n simp.units[0].prefix = simp._bestPrefix()\n }\n }\n\n const value = simp._denormalize(simp.value)\n let str = (simp.value !== null) ? format(value, options || {}) : ''\n const unitStr = simp.formatUnits()\n if (simp.value && isComplex(simp.value)) {\n str = '(' + str + ')' // Surround complex values with ( ) to enable better parsing\n }\n if (unitStr.length > 0 && str.length > 0) {\n str += ' '\n }\n str += unitStr\n\n return str\n }\n\n /**\n * Calculate the best prefix using current value.\n * @memberof Unit\n * @returns {Object} prefix\n * @private\n */\n Unit.prototype._bestPrefix = function () {\n if (this.units.length !== 1) {\n throw new Error('Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!')\n }\n if (Math.abs(this.units[0].power - Math.round(this.units[0].power)) >= 1e-14) {\n throw new Error('Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!')\n }\n\n // find the best prefix value (resulting in the value of which\n // the absolute value of the log10 is closest to zero,\n // though with a little offset of 1.2 for nicer values: you get a\n // sequence 1mm 100mm 500mm 0.6m 1m 10m 100m 500m 0.6km 1km ...\n\n // Note: the units value can be any numeric type, but to find the best\n // prefix it's enough to work with limited precision of a regular number\n // Update: using mathjs abs since we also allow complex numbers\n const absValue = this.value !== null ? abs(this.value) : 0\n const absUnitValue = abs(this.units[0].unit.value)\n let bestPrefix = this.units[0].prefix\n if (absValue === 0) {\n return bestPrefix\n }\n const power = this.units[0].power\n let bestDiff = Math.log(absValue / Math.pow(bestPrefix.value * absUnitValue, power)) / Math.LN10 - 1.2\n if (bestDiff > -2.200001 && bestDiff < 1.800001) return bestPrefix // Allow the original prefix\n bestDiff = Math.abs(bestDiff)\n const prefixes = this.units[0].unit.prefixes\n for (const p in prefixes) {\n if (hasOwnProperty(prefixes, p)) {\n const prefix = prefixes[p]\n if (prefix.scientific) {\n const diff = Math.abs(\n Math.log(absValue / Math.pow(prefix.value * absUnitValue, power)) / Math.LN10 - 1.2)\n\n if (diff < bestDiff ||\n (diff === bestDiff && prefix.name.length < bestPrefix.name.length)) {\n // choose the prefix with the smallest diff, or if equal, choose the one\n // with the shortest name (can happen with SHORTLONG for example)\n bestPrefix = prefix\n bestDiff = diff\n }\n }\n }\n }\n\n return bestPrefix\n }\n\n /**\n * Returns an array of units whose sum is equal to this unit\n * @memberof Unit\n * @param {Array} [parts] An array of strings or valueless units.\n *\n * Example:\n *\n * const u = new Unit(1, 'm')\n * u.splitUnit(['feet', 'inch'])\n * [ 3 feet, 3.3700787401575 inch ]\n *\n * @return {Array} An array of units.\n */\n Unit.prototype.splitUnit = function (parts) {\n let x = this.clone()\n const ret = []\n for (let i = 0; i < parts.length; i++) {\n // Convert x to the requested unit\n x = x.to(parts[i])\n if (i === parts.length - 1) break\n\n // Get the numeric value of this unit\n const xNumeric = x.toNumeric()\n\n // Check to see if xNumeric is nearly equal to an integer,\n // since fix can incorrectly round down if there is round-off error\n const xRounded = round(xNumeric)\n let xFixed\n const isNearlyEqual = equal(xRounded, xNumeric)\n if (isNearlyEqual) {\n xFixed = xRounded\n } else {\n xFixed = fix(x.toNumeric())\n }\n\n const y = new Unit(xFixed, parts[i].toString())\n ret.push(y)\n x = subtract(x, y)\n }\n\n // This little bit fixes a bug where the remainder should be 0 but is a little bit off.\n // But instead of comparing x, the remainder, with zero--we will compare the sum of\n // all the parts so far with the original value. If they are nearly equal,\n // we set the remainder to 0.\n let testSum = 0\n for (let i = 0; i < ret.length; i++) {\n testSum = addScalar(testSum, ret[i].value)\n }\n if (equal(testSum, this.value)) {\n x.value = 0\n }\n\n ret.push(x)\n\n return ret\n }\n\n const PREFIXES = {\n NONE: {\n '': { name: '', value: 1, scientific: true }\n },\n SHORT: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e1, scientific: false },\n h: { name: 'h', value: 1e2, scientific: false },\n k: { name: 'k', value: 1e3, scientific: true },\n M: { name: 'M', value: 1e6, scientific: true },\n G: { name: 'G', value: 1e9, scientific: true },\n T: { name: 'T', value: 1e12, scientific: true },\n P: { name: 'P', value: 1e15, scientific: true },\n E: { name: 'E', value: 1e18, scientific: true },\n Z: { name: 'Z', value: 1e21, scientific: true },\n Y: { name: 'Y', value: 1e24, scientific: true },\n\n d: { name: 'd', value: 1e-1, scientific: false },\n c: { name: 'c', value: 1e-2, scientific: false },\n m: { name: 'm', value: 1e-3, scientific: true },\n u: { name: 'u', value: 1e-6, scientific: true },\n n: { name: 'n', value: 1e-9, scientific: true },\n p: { name: 'p', value: 1e-12, scientific: true },\n f: { name: 'f', value: 1e-15, scientific: true },\n a: { name: 'a', value: 1e-18, scientific: true },\n z: { name: 'z', value: 1e-21, scientific: true },\n y: { name: 'y', value: 1e-24, scientific: true }\n },\n LONG: {\n '': { name: '', value: 1, scientific: true },\n\n deca: { name: 'deca', value: 1e1, scientific: false },\n hecto: { name: 'hecto', value: 1e2, scientific: false },\n kilo: { name: 'kilo', value: 1e3, scientific: true },\n mega: { name: 'mega', value: 1e6, scientific: true },\n giga: { name: 'giga', value: 1e9, scientific: true },\n tera: { name: 'tera', value: 1e12, scientific: true },\n peta: { name: 'peta', value: 1e15, scientific: true },\n exa: { name: 'exa', value: 1e18, scientific: true },\n zetta: { name: 'zetta', value: 1e21, scientific: true },\n yotta: { name: 'yotta', value: 1e24, scientific: true },\n\n deci: { name: 'deci', value: 1e-1, scientific: false },\n centi: { name: 'centi', value: 1e-2, scientific: false },\n milli: { name: 'milli', value: 1e-3, scientific: true },\n micro: { name: 'micro', value: 1e-6, scientific: true },\n nano: { name: 'nano', value: 1e-9, scientific: true },\n pico: { name: 'pico', value: 1e-12, scientific: true },\n femto: { name: 'femto', value: 1e-15, scientific: true },\n atto: { name: 'atto', value: 1e-18, scientific: true },\n zepto: { name: 'zepto', value: 1e-21, scientific: true },\n yocto: { name: 'yocto', value: 1e-24, scientific: true }\n },\n SQUARED: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e2, scientific: false },\n h: { name: 'h', value: 1e4, scientific: false },\n k: { name: 'k', value: 1e6, scientific: true },\n M: { name: 'M', value: 1e12, scientific: true },\n G: { name: 'G', value: 1e18, scientific: true },\n T: { name: 'T', value: 1e24, scientific: true },\n P: { name: 'P', value: 1e30, scientific: true },\n E: { name: 'E', value: 1e36, scientific: true },\n Z: { name: 'Z', value: 1e42, scientific: true },\n Y: { name: 'Y', value: 1e48, scientific: true },\n\n d: { name: 'd', value: 1e-2, scientific: false },\n c: { name: 'c', value: 1e-4, scientific: false },\n m: { name: 'm', value: 1e-6, scientific: true },\n u: { name: 'u', value: 1e-12, scientific: true },\n n: { name: 'n', value: 1e-18, scientific: true },\n p: { name: 'p', value: 1e-24, scientific: true },\n f: { name: 'f', value: 1e-30, scientific: true },\n a: { name: 'a', value: 1e-36, scientific: true },\n z: { name: 'z', value: 1e-42, scientific: true },\n y: { name: 'y', value: 1e-48, scientific: true }\n },\n CUBIC: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e3, scientific: false },\n h: { name: 'h', value: 1e6, scientific: false },\n k: { name: 'k', value: 1e9, scientific: true },\n M: { name: 'M', value: 1e18, scientific: true },\n G: { name: 'G', value: 1e27, scientific: true },\n T: { name: 'T', value: 1e36, scientific: true },\n P: { name: 'P', value: 1e45, scientific: true },\n E: { name: 'E', value: 1e54, scientific: true },\n Z: { name: 'Z', value: 1e63, scientific: true },\n Y: { name: 'Y', value: 1e72, scientific: true },\n\n d: { name: 'd', value: 1e-3, scientific: false },\n c: { name: 'c', value: 1e-6, scientific: false },\n m: { name: 'm', value: 1e-9, scientific: true },\n u: { name: 'u', value: 1e-18, scientific: true },\n n: { name: 'n', value: 1e-27, scientific: true },\n p: { name: 'p', value: 1e-36, scientific: true },\n f: { name: 'f', value: 1e-45, scientific: true },\n a: { name: 'a', value: 1e-54, scientific: true },\n z: { name: 'z', value: 1e-63, scientific: true },\n y: { name: 'y', value: 1e-72, scientific: true }\n },\n BINARY_SHORT_SI: {\n '': { name: '', value: 1, scientific: true },\n k: { name: 'k', value: 1e3, scientific: true },\n M: { name: 'M', value: 1e6, scientific: true },\n G: { name: 'G', value: 1e9, scientific: true },\n T: { name: 'T', value: 1e12, scientific: true },\n P: { name: 'P', value: 1e15, scientific: true },\n E: { name: 'E', value: 1e18, scientific: true },\n Z: { name: 'Z', value: 1e21, scientific: true },\n Y: { name: 'Y', value: 1e24, scientific: true }\n },\n BINARY_SHORT_IEC: {\n '': { name: '', value: 1, scientific: true },\n Ki: { name: 'Ki', value: 1024, scientific: true },\n Mi: { name: 'Mi', value: Math.pow(1024, 2), scientific: true },\n Gi: { name: 'Gi', value: Math.pow(1024, 3), scientific: true },\n Ti: { name: 'Ti', value: Math.pow(1024, 4), scientific: true },\n Pi: { name: 'Pi', value: Math.pow(1024, 5), scientific: true },\n Ei: { name: 'Ei', value: Math.pow(1024, 6), scientific: true },\n Zi: { name: 'Zi', value: Math.pow(1024, 7), scientific: true },\n Yi: { name: 'Yi', value: Math.pow(1024, 8), scientific: true }\n },\n BINARY_LONG_SI: {\n '': { name: '', value: 1, scientific: true },\n kilo: { name: 'kilo', value: 1e3, scientific: true },\n mega: { name: 'mega', value: 1e6, scientific: true },\n giga: { name: 'giga', value: 1e9, scientific: true },\n tera: { name: 'tera', value: 1e12, scientific: true },\n peta: { name: 'peta', value: 1e15, scientific: true },\n exa: { name: 'exa', value: 1e18, scientific: true },\n zetta: { name: 'zetta', value: 1e21, scientific: true },\n yotta: { name: 'yotta', value: 1e24, scientific: true }\n },\n BINARY_LONG_IEC: {\n '': { name: '', value: 1, scientific: true },\n kibi: { name: 'kibi', value: 1024, scientific: true },\n mebi: { name: 'mebi', value: Math.pow(1024, 2), scientific: true },\n gibi: { name: 'gibi', value: Math.pow(1024, 3), scientific: true },\n tebi: { name: 'tebi', value: Math.pow(1024, 4), scientific: true },\n pebi: { name: 'pebi', value: Math.pow(1024, 5), scientific: true },\n exi: { name: 'exi', value: Math.pow(1024, 6), scientific: true },\n zebi: { name: 'zebi', value: Math.pow(1024, 7), scientific: true },\n yobi: { name: 'yobi', value: Math.pow(1024, 8), scientific: true }\n },\n BTU: {\n '': { name: '', value: 1, scientific: true },\n MM: { name: 'MM', value: 1e6, scientific: true }\n }\n }\n\n PREFIXES.SHORTLONG = Object.assign({}, PREFIXES.SHORT, PREFIXES.LONG)\n PREFIXES.BINARY_SHORT = Object.assign({}, PREFIXES.BINARY_SHORT_SI, PREFIXES.BINARY_SHORT_IEC)\n PREFIXES.BINARY_LONG = Object.assign({}, PREFIXES.BINARY_LONG_SI, PREFIXES.BINARY_LONG_IEC)\n\n /* Internally, each unit is represented by a value and a dimension array. The elements of the dimensions array have the following meaning:\n * Index Dimension\n * ----- ---------\n * 0 Length\n * 1 Mass\n * 2 Time\n * 3 Current\n * 4 Temperature\n * 5 Luminous intensity\n * 6 Amount of substance\n * 7 Angle\n * 8 Bit (digital)\n * For example, the unit \"298.15 K\" is a pure temperature and would have a value of 298.15 and a dimension array of [0, 0, 0, 0, 1, 0, 0, 0, 0]. The unit \"1 cal / (gm °C)\" can be written in terms of the 9 fundamental dimensions as [length^2] / ([time^2] * [temperature]), and would a value of (after conversion to SI) 4184.0 and a dimensions array of [2, 0, -2, 0, -1, 0, 0, 0, 0].\n *\n */\n\n const BASE_DIMENSIONS = ['MASS', 'LENGTH', 'TIME', 'CURRENT', 'TEMPERATURE', 'LUMINOUS_INTENSITY', 'AMOUNT_OF_SUBSTANCE', 'ANGLE', 'BIT']\n\n const BASE_UNITS = {\n NONE: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 0]\n },\n MASS: {\n dimensions: [1, 0, 0, 0, 0, 0, 0, 0, 0]\n },\n LENGTH: {\n dimensions: [0, 1, 0, 0, 0, 0, 0, 0, 0]\n },\n TIME: {\n dimensions: [0, 0, 1, 0, 0, 0, 0, 0, 0]\n },\n CURRENT: {\n dimensions: [0, 0, 0, 1, 0, 0, 0, 0, 0]\n },\n TEMPERATURE: {\n dimensions: [0, 0, 0, 0, 1, 0, 0, 0, 0]\n },\n LUMINOUS_INTENSITY: {\n dimensions: [0, 0, 0, 0, 0, 1, 0, 0, 0]\n },\n AMOUNT_OF_SUBSTANCE: {\n dimensions: [0, 0, 0, 0, 0, 0, 1, 0, 0]\n },\n\n FORCE: {\n dimensions: [1, 1, -2, 0, 0, 0, 0, 0, 0]\n },\n SURFACE: {\n dimensions: [0, 2, 0, 0, 0, 0, 0, 0, 0]\n },\n VOLUME: {\n dimensions: [0, 3, 0, 0, 0, 0, 0, 0, 0]\n },\n ENERGY: {\n dimensions: [1, 2, -2, 0, 0, 0, 0, 0, 0]\n },\n POWER: {\n dimensions: [1, 2, -3, 0, 0, 0, 0, 0, 0]\n },\n PRESSURE: {\n dimensions: [1, -1, -2, 0, 0, 0, 0, 0, 0]\n },\n\n ELECTRIC_CHARGE: {\n dimensions: [0, 0, 1, 1, 0, 0, 0, 0, 0]\n },\n ELECTRIC_CAPACITANCE: {\n dimensions: [-1, -2, 4, 2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_POTENTIAL: {\n dimensions: [1, 2, -3, -1, 0, 0, 0, 0, 0]\n },\n ELECTRIC_RESISTANCE: {\n dimensions: [1, 2, -3, -2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_INDUCTANCE: {\n dimensions: [1, 2, -2, -2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_CONDUCTANCE: {\n dimensions: [-1, -2, 3, 2, 0, 0, 0, 0, 0]\n },\n MAGNETIC_FLUX: {\n dimensions: [1, 2, -2, -1, 0, 0, 0, 0, 0]\n },\n MAGNETIC_FLUX_DENSITY: {\n dimensions: [1, 0, -2, -1, 0, 0, 0, 0, 0]\n },\n\n FREQUENCY: {\n dimensions: [0, 0, -1, 0, 0, 0, 0, 0, 0]\n },\n ANGLE: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 1, 0]\n },\n BIT: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 1]\n }\n }\n\n for (const key in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, key)) {\n BASE_UNITS[key].key = key\n }\n }\n\n const BASE_UNIT_NONE = {}\n\n const UNIT_NONE = { name: '', base: BASE_UNIT_NONE, value: 1, offset: 0, dimensions: BASE_DIMENSIONS.map(x => 0) }\n\n const UNITS = {\n // length\n meter: {\n name: 'meter',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n inch: {\n name: 'inch',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0254,\n offset: 0\n },\n foot: {\n name: 'foot',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.3048,\n offset: 0\n },\n yard: {\n name: 'yard',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.9144,\n offset: 0\n },\n mile: {\n name: 'mile',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1609.344,\n offset: 0\n },\n link: {\n name: 'link',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.201168,\n offset: 0\n },\n rod: {\n name: 'rod',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 5.0292,\n offset: 0\n },\n chain: {\n name: 'chain',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 20.1168,\n offset: 0\n },\n angstrom: {\n name: 'angstrom',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1e-10,\n offset: 0\n },\n\n m: {\n name: 'm',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n in: {\n name: 'in',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0254,\n offset: 0\n },\n ft: {\n name: 'ft',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.3048,\n offset: 0\n },\n yd: {\n name: 'yd',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.9144,\n offset: 0\n },\n mi: {\n name: 'mi',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1609.344,\n offset: 0\n },\n li: {\n name: 'li',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.201168,\n offset: 0\n },\n rd: {\n name: 'rd',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 5.029210,\n offset: 0\n },\n ch: {\n name: 'ch',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 20.1168,\n offset: 0\n },\n mil: {\n name: 'mil',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0000254,\n offset: 0\n }, // 1/1000 inch\n\n // Surface\n m2: {\n name: 'm2',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.SQUARED,\n value: 1,\n offset: 0\n },\n sqin: {\n name: 'sqin',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.00064516,\n offset: 0\n }, // 645.16 mm2\n sqft: {\n name: 'sqft',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.09290304,\n offset: 0\n }, // 0.09290304 m2\n sqyd: {\n name: 'sqyd',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.83612736,\n offset: 0\n }, // 0.83612736 m2\n sqmi: {\n name: 'sqmi',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 2589988.110336,\n offset: 0\n }, // 2.589988110336 km2\n sqrd: {\n name: 'sqrd',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 25.29295,\n offset: 0\n }, // 25.29295 m2\n sqch: {\n name: 'sqch',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 404.6873,\n offset: 0\n }, // 404.6873 m2\n sqmil: {\n name: 'sqmil',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 6.4516e-10,\n offset: 0\n }, // 6.4516 * 10^-10 m2\n acre: {\n name: 'acre',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 4046.86,\n offset: 0\n }, // 4046.86 m2\n hectare: {\n name: 'hectare',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 10000,\n offset: 0\n }, // 10000 m2\n\n // Volume\n m3: {\n name: 'm3',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.CUBIC,\n value: 1,\n offset: 0\n },\n L: {\n name: 'L',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n }, // litre\n l: {\n name: 'l',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n }, // litre\n litre: {\n name: 'litre',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.LONG,\n value: 0.001,\n offset: 0\n },\n cuin: {\n name: 'cuin',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 1.6387064e-5,\n offset: 0\n }, // 1.6387064e-5 m3\n cuft: {\n name: 'cuft',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.028316846592,\n offset: 0\n }, // 28.316 846 592 L\n cuyd: {\n name: 'cuyd',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.764554857984,\n offset: 0\n }, // 764.554 857 984 L\n teaspoon: {\n name: 'teaspoon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.000005,\n offset: 0\n }, // 5 mL\n tablespoon: {\n name: 'tablespoon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.000015,\n offset: 0\n }, // 15 mL\n // {name: 'cup', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000240, offset: 0}, // 240 mL // not possible, we have already another cup\n drop: {\n name: 'drop',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 5e-8,\n offset: 0\n }, // 0.05 mL = 5e-8 m3\n gtt: {\n name: 'gtt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 5e-8,\n offset: 0\n }, // 0.05 mL = 5e-8 m3\n\n // Liquid volume\n minim: {\n name: 'minim',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00000006161152,\n offset: 0\n }, // 0.06161152 mL\n fluiddram: {\n name: 'fluiddram',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0000036966911,\n offset: 0\n }, // 3.696691 mL\n fluidounce: {\n name: 'fluidounce',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00002957353,\n offset: 0\n }, // 29.57353 mL\n gill: {\n name: 'gill',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0001182941,\n offset: 0\n }, // 118.2941 mL\n cc: {\n name: 'cc',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 1e-6,\n offset: 0\n }, // 1e-6 L\n cup: {\n name: 'cup',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0002365882,\n offset: 0\n }, // 236.5882 mL\n pint: {\n name: 'pint',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0004731765,\n offset: 0\n }, // 473.1765 mL\n quart: {\n name: 'quart',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0009463529,\n offset: 0\n }, // 946.3529 mL\n gallon: {\n name: 'gallon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.003785412,\n offset: 0\n }, // 3.785412 L\n beerbarrel: {\n name: 'beerbarrel',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1173478,\n offset: 0\n }, // 117.3478 L\n oilbarrel: {\n name: 'oilbarrel',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1589873,\n offset: 0\n }, // 158.9873 L\n hogshead: {\n name: 'hogshead',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.2384810,\n offset: 0\n }, // 238.4810 L\n\n // {name: 'min', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00000006161152, offset: 0}, // 0.06161152 mL // min is already in use as minute\n fldr: {\n name: 'fldr',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0000036966911,\n offset: 0\n }, // 3.696691 mL\n floz: {\n name: 'floz',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00002957353,\n offset: 0\n }, // 29.57353 mL\n gi: {\n name: 'gi',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0001182941,\n offset: 0\n }, // 118.2941 mL\n cp: {\n name: 'cp',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0002365882,\n offset: 0\n }, // 236.5882 mL\n pt: {\n name: 'pt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0004731765,\n offset: 0\n }, // 473.1765 mL\n qt: {\n name: 'qt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0009463529,\n offset: 0\n }, // 946.3529 mL\n gal: {\n name: 'gal',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.003785412,\n offset: 0\n }, // 3.785412 L\n bbl: {\n name: 'bbl',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1173478,\n offset: 0\n }, // 117.3478 L\n obl: {\n name: 'obl',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1589873,\n offset: 0\n }, // 158.9873 L\n // {name: 'hogshead', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.2384810, offset: 0}, // 238.4810 L // TODO: hh?\n\n // Mass\n g: {\n name: 'g',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n },\n gram: {\n name: 'gram',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.LONG,\n value: 0.001,\n offset: 0\n },\n\n ton: {\n name: 'ton',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 907.18474,\n offset: 0\n },\n t: {\n name: 't',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 1000,\n offset: 0\n },\n tonne: {\n name: 'tonne',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.LONG,\n value: 1000,\n offset: 0\n },\n\n grain: {\n name: 'grain',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 64.79891e-6,\n offset: 0\n },\n dram: {\n name: 'dram',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 1.7718451953125e-3,\n offset: 0\n },\n ounce: {\n name: 'ounce',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 28.349523125e-3,\n offset: 0\n },\n poundmass: {\n name: 'poundmass',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 453.59237e-3,\n offset: 0\n },\n hundredweight: {\n name: 'hundredweight',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 45.359237,\n offset: 0\n },\n stick: {\n name: 'stick',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 115e-3,\n offset: 0\n },\n stone: {\n name: 'stone',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 6.35029318,\n offset: 0\n },\n\n gr: {\n name: 'gr',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 64.79891e-6,\n offset: 0\n },\n dr: {\n name: 'dr',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 1.7718451953125e-3,\n offset: 0\n },\n oz: {\n name: 'oz',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 28.349523125e-3,\n offset: 0\n },\n lbm: {\n name: 'lbm',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 453.59237e-3,\n offset: 0\n },\n cwt: {\n name: 'cwt',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 45.359237,\n offset: 0\n },\n\n // Time\n s: {\n name: 's',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n min: {\n name: 'min',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 60,\n offset: 0\n },\n h: {\n name: 'h',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3600,\n offset: 0\n },\n second: {\n name: 'second',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n sec: {\n name: 'sec',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n minute: {\n name: 'minute',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 60,\n offset: 0\n },\n hour: {\n name: 'hour',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3600,\n offset: 0\n },\n day: {\n name: 'day',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 86400,\n offset: 0\n },\n week: {\n name: 'week',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 7 * 86400,\n offset: 0\n },\n month: {\n name: 'month',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 2629800, // 1/12th of Julian year\n offset: 0\n },\n year: {\n name: 'year',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 31557600, // Julian year\n offset: 0\n },\n decade: {\n name: 'decade',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 315576000, // Julian decade\n offset: 0\n },\n century: {\n name: 'century',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3155760000, // Julian century\n offset: 0\n },\n millennium: {\n name: 'millennium',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 31557600000, // Julian millennium\n offset: 0\n },\n\n // Frequency\n hertz: {\n name: 'Hertz',\n base: BASE_UNITS.FREQUENCY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0,\n reciprocal: true\n },\n Hz: {\n name: 'Hz',\n base: BASE_UNITS.FREQUENCY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0,\n reciprocal: true\n },\n\n // Angle\n rad: {\n name: 'rad',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n radian: {\n name: 'radian',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n // deg = rad / (2*pi) * 360 = rad / 0.017453292519943295769236907684888\n deg: {\n name: 'deg',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n degree: {\n name: 'degree',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // grad = rad / (2*pi) * 400 = rad / 0.015707963267948966192313216916399\n grad: {\n name: 'grad',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n gradian: {\n name: 'gradian',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // cycle = rad / (2*pi) = rad / 6.2831853071795864769252867665793\n cycle: {\n name: 'cycle',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // arcsec = rad / (3600 * (360 / 2 * pi)) = rad / 0.0000048481368110953599358991410235795\n arcsec: {\n name: 'arcsec',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // arcmin = rad / (60 * (360 / 2 * pi)) = rad / 0.00029088820866572159615394846141477\n arcmin: {\n name: 'arcmin',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n\n // Electric current\n A: {\n name: 'A',\n base: BASE_UNITS.CURRENT,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n ampere: {\n name: 'ampere',\n base: BASE_UNITS.CURRENT,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n\n // Temperature\n // K(C) = °C + 273.15\n // K(F) = (°F + 459.67) / 1.8\n // K(R) = °R / 1.8\n K: {\n name: 'K',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 0\n },\n degC: {\n name: 'degC',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 273.15\n },\n degF: {\n name: 'degF',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 459.67\n },\n degR: {\n name: 'degR',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 0\n },\n kelvin: {\n name: 'kelvin',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 0\n },\n celsius: {\n name: 'celsius',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 273.15\n },\n fahrenheit: {\n name: 'fahrenheit',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 459.67\n },\n rankine: {\n name: 'rankine',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 0\n },\n\n // amount of substance\n mol: {\n name: 'mol',\n base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n mole: {\n name: 'mole',\n base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n\n // luminous intensity\n cd: {\n name: 'cd',\n base: BASE_UNITS.LUMINOUS_INTENSITY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n candela: {\n name: 'candela',\n base: BASE_UNITS.LUMINOUS_INTENSITY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n // TODO: units STERADIAN\n // {name: 'sr', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},\n // {name: 'steradian', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},\n\n // Force\n N: {\n name: 'N',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n newton: {\n name: 'newton',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n dyn: {\n name: 'dyn',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.SHORT,\n value: 0.00001,\n offset: 0\n },\n dyne: {\n name: 'dyne',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 0.00001,\n offset: 0\n },\n lbf: {\n name: 'lbf',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 4.4482216152605,\n offset: 0\n },\n poundforce: {\n name: 'poundforce',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 4.4482216152605,\n offset: 0\n },\n kip: {\n name: 'kip',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 4448.2216,\n offset: 0\n },\n kilogramforce: {\n name: 'kilogramforce',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 9.80665,\n offset: 0\n },\n\n // Energy\n J: {\n name: 'J',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n joule: {\n name: 'joule',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n erg: {\n name: 'erg',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.NONE,\n value: 1e-7,\n offset: 0\n },\n Wh: {\n name: 'Wh',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 3600,\n offset: 0\n },\n BTU: {\n name: 'BTU',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.BTU,\n value: 1055.05585262,\n offset: 0\n },\n eV: {\n name: 'eV',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1.602176565e-19,\n offset: 0\n },\n electronvolt: {\n name: 'electronvolt',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.LONG,\n value: 1.602176565e-19,\n offset: 0\n },\n\n // Power\n W: {\n name: 'W',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n watt: {\n name: 'watt',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n hp: {\n name: 'hp',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.NONE,\n value: 745.6998715386,\n offset: 0\n },\n\n // Electrical power units\n VAR: {\n name: 'VAR',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: Complex.I,\n offset: 0\n },\n\n VA: {\n name: 'VA',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n\n // Pressure\n Pa: {\n name: 'Pa',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n psi: {\n name: 'psi',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 6894.75729276459,\n offset: 0\n },\n atm: {\n name: 'atm',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 101325,\n offset: 0\n },\n bar: {\n name: 'bar',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.SHORTLONG,\n value: 100000,\n offset: 0\n },\n torr: {\n name: 'torr',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 133.322,\n offset: 0\n },\n mmHg: {\n name: 'mmHg',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 133.322,\n offset: 0\n },\n mmH2O: {\n name: 'mmH2O',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 9.80665,\n offset: 0\n },\n cmH2O: {\n name: 'cmH2O',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 98.0665,\n offset: 0\n },\n\n // Electric charge\n coulomb: {\n name: 'coulomb',\n base: BASE_UNITS.ELECTRIC_CHARGE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n C: {\n name: 'C',\n base: BASE_UNITS.ELECTRIC_CHARGE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric capacitance\n farad: {\n name: 'farad',\n base: BASE_UNITS.ELECTRIC_CAPACITANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n F: {\n name: 'F',\n base: BASE_UNITS.ELECTRIC_CAPACITANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric potential\n volt: {\n name: 'volt',\n base: BASE_UNITS.ELECTRIC_POTENTIAL,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n V: {\n name: 'V',\n base: BASE_UNITS.ELECTRIC_POTENTIAL,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric resistance\n ohm: {\n name: 'ohm',\n base: BASE_UNITS.ELECTRIC_RESISTANCE,\n prefixes: PREFIXES.SHORTLONG, // Both Mohm and megaohm are acceptable\n value: 1,\n offset: 0\n },\n /*\n * Unicode breaks in browsers if charset is not specified\n Ω: {\n name: 'Ω',\n base: BASE_UNITS.ELECTRIC_RESISTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n */\n // Electric inductance\n henry: {\n name: 'henry',\n base: BASE_UNITS.ELECTRIC_INDUCTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n H: {\n name: 'H',\n base: BASE_UNITS.ELECTRIC_INDUCTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric conductance\n siemens: {\n name: 'siemens',\n base: BASE_UNITS.ELECTRIC_CONDUCTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n S: {\n name: 'S',\n base: BASE_UNITS.ELECTRIC_CONDUCTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Magnetic flux\n weber: {\n name: 'weber',\n base: BASE_UNITS.MAGNETIC_FLUX,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n Wb: {\n name: 'Wb',\n base: BASE_UNITS.MAGNETIC_FLUX,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Magnetic flux density\n tesla: {\n name: 'tesla',\n base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n T: {\n name: 'T',\n base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n\n // Binary\n b: {\n name: 'b',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_SHORT,\n value: 1,\n offset: 0\n },\n bits: {\n name: 'bits',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_LONG,\n value: 1,\n offset: 0\n },\n B: {\n name: 'B',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_SHORT,\n value: 8,\n offset: 0\n },\n bytes: {\n name: 'bytes',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_LONG,\n value: 8,\n offset: 0\n }\n }\n\n // aliases (formerly plurals)\n const ALIASES = {\n meters: 'meter',\n inches: 'inch',\n feet: 'foot',\n yards: 'yard',\n miles: 'mile',\n links: 'link',\n rods: 'rod',\n chains: 'chain',\n angstroms: 'angstrom',\n\n lt: 'l',\n litres: 'litre',\n liter: 'litre',\n liters: 'litre',\n teaspoons: 'teaspoon',\n tablespoons: 'tablespoon',\n minims: 'minim',\n fluiddrams: 'fluiddram',\n fluidounces: 'fluidounce',\n gills: 'gill',\n cups: 'cup',\n pints: 'pint',\n quarts: 'quart',\n gallons: 'gallon',\n beerbarrels: 'beerbarrel',\n oilbarrels: 'oilbarrel',\n hogsheads: 'hogshead',\n gtts: 'gtt',\n\n grams: 'gram',\n tons: 'ton',\n tonnes: 'tonne',\n grains: 'grain',\n drams: 'dram',\n ounces: 'ounce',\n poundmasses: 'poundmass',\n hundredweights: 'hundredweight',\n sticks: 'stick',\n lb: 'lbm',\n lbs: 'lbm',\n\n kips: 'kip',\n kgf: 'kilogramforce',\n\n acres: 'acre',\n hectares: 'hectare',\n sqfeet: 'sqft',\n sqyard: 'sqyd',\n sqmile: 'sqmi',\n sqmiles: 'sqmi',\n\n mmhg: 'mmHg',\n mmh2o: 'mmH2O',\n cmh2o: 'cmH2O',\n\n seconds: 'second',\n secs: 'second',\n minutes: 'minute',\n mins: 'minute',\n hours: 'hour',\n hr: 'hour',\n hrs: 'hour',\n days: 'day',\n weeks: 'week',\n months: 'month',\n years: 'year',\n decades: 'decade',\n centuries: 'century',\n millennia: 'millennium',\n\n hertz: 'hertz',\n\n radians: 'radian',\n degrees: 'degree',\n gradians: 'gradian',\n cycles: 'cycle',\n arcsecond: 'arcsec',\n arcseconds: 'arcsec',\n arcminute: 'arcmin',\n arcminutes: 'arcmin',\n\n BTUs: 'BTU',\n watts: 'watt',\n joules: 'joule',\n\n amperes: 'ampere',\n coulombs: 'coulomb',\n volts: 'volt',\n ohms: 'ohm',\n farads: 'farad',\n webers: 'weber',\n teslas: 'tesla',\n electronvolts: 'electronvolt',\n moles: 'mole',\n\n bit: 'bits',\n byte: 'bytes'\n }\n\n /**\n * Calculate the values for the angle units.\n * Value is calculated as number or BigNumber depending on the configuration\n * @param {{number: 'number' | 'BigNumber'}} config\n */\n function calculateAngleValues (config) {\n if (config.number === 'BigNumber') {\n const pi = createPi(BigNumber)\n UNITS.rad.value = new BigNumber(1)\n UNITS.deg.value = pi.div(180) // 2 * pi / 360\n UNITS.grad.value = pi.div(200) // 2 * pi / 400\n UNITS.cycle.value = pi.times(2) // 2 * pi\n UNITS.arcsec.value = pi.div(648000) // 2 * pi / 360 / 3600\n UNITS.arcmin.value = pi.div(10800) // 2 * pi / 360 / 60\n } else { // number\n UNITS.rad.value = 1\n UNITS.deg.value = Math.PI / 180 // 2 * pi / 360\n UNITS.grad.value = Math.PI / 200 // 2 * pi / 400\n UNITS.cycle.value = Math.PI * 2 // 2 * pi\n UNITS.arcsec.value = Math.PI / 648000 // 2 * pi / 360 / 3600\n UNITS.arcmin.value = Math.PI / 10800 // 2 * pi / 360 / 60\n }\n\n // copy to the full names of the angles\n UNITS.radian.value = UNITS.rad.value\n UNITS.degree.value = UNITS.deg.value\n UNITS.gradian.value = UNITS.grad.value\n }\n\n // apply the angle values now\n calculateAngleValues(config)\n\n if (on) {\n // recalculate the values on change of configuration\n on('config', function (curr, prev) {\n if (curr.number !== prev.number) {\n calculateAngleValues(curr)\n }\n })\n }\n\n /**\n * A unit system is a set of dimensionally independent base units plus a set of derived units, formed by multiplication and division of the base units, that are by convention used with the unit system.\n * A user perhaps could issue a command to select a preferred unit system, or use the default (see below).\n * Auto unit system: The default unit system is updated on the fly anytime a unit is parsed. The corresponding unit in the default unit system is updated, so that answers are given in the same units the user supplies.\n */\n const UNIT_SYSTEMS = {\n si: {\n // Base units\n NONE: { unit: UNIT_NONE, prefix: PREFIXES.NONE[''] },\n LENGTH: { unit: UNITS.m, prefix: PREFIXES.SHORT[''] },\n MASS: { unit: UNITS.g, prefix: PREFIXES.SHORT.k },\n TIME: { unit: UNITS.s, prefix: PREFIXES.SHORT[''] },\n CURRENT: { unit: UNITS.A, prefix: PREFIXES.SHORT[''] },\n TEMPERATURE: { unit: UNITS.K, prefix: PREFIXES.SHORT[''] },\n LUMINOUS_INTENSITY: { unit: UNITS.cd, prefix: PREFIXES.SHORT[''] },\n AMOUNT_OF_SUBSTANCE: { unit: UNITS.mol, prefix: PREFIXES.SHORT[''] },\n ANGLE: { unit: UNITS.rad, prefix: PREFIXES.SHORT[''] },\n BIT: { unit: UNITS.bits, prefix: PREFIXES.SHORT[''] },\n\n // Derived units\n FORCE: { unit: UNITS.N, prefix: PREFIXES.SHORT[''] },\n ENERGY: { unit: UNITS.J, prefix: PREFIXES.SHORT[''] },\n POWER: { unit: UNITS.W, prefix: PREFIXES.SHORT[''] },\n PRESSURE: { unit: UNITS.Pa, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CHARGE: { unit: UNITS.C, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CAPACITANCE: { unit: UNITS.F, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_POTENTIAL: { unit: UNITS.V, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_RESISTANCE: { unit: UNITS.ohm, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_INDUCTANCE: { unit: UNITS.H, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CONDUCTANCE: { unit: UNITS.S, prefix: PREFIXES.SHORT[''] },\n MAGNETIC_FLUX: { unit: UNITS.Wb, prefix: PREFIXES.SHORT[''] },\n MAGNETIC_FLUX_DENSITY: { unit: UNITS.T, prefix: PREFIXES.SHORT[''] },\n FREQUENCY: { unit: UNITS.Hz, prefix: PREFIXES.SHORT[''] }\n }\n }\n\n // Clone to create the other unit systems\n UNIT_SYSTEMS.cgs = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n UNIT_SYSTEMS.cgs.LENGTH = { unit: UNITS.m, prefix: PREFIXES.SHORT.c }\n UNIT_SYSTEMS.cgs.MASS = { unit: UNITS.g, prefix: PREFIXES.SHORT[''] }\n UNIT_SYSTEMS.cgs.FORCE = { unit: UNITS.dyn, prefix: PREFIXES.SHORT[''] }\n UNIT_SYSTEMS.cgs.ENERGY = { unit: UNITS.erg, prefix: PREFIXES.NONE[''] }\n // there are wholly 4 unique cgs systems for electricity and magnetism,\n // so let's not worry about it unless somebody complains\n\n UNIT_SYSTEMS.us = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n UNIT_SYSTEMS.us.LENGTH = { unit: UNITS.ft, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.MASS = { unit: UNITS.lbm, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.TEMPERATURE = { unit: UNITS.degF, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.FORCE = { unit: UNITS.lbf, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.ENERGY = { unit: UNITS.BTU, prefix: PREFIXES.BTU[''] }\n UNIT_SYSTEMS.us.POWER = { unit: UNITS.hp, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.PRESSURE = { unit: UNITS.psi, prefix: PREFIXES.NONE[''] }\n\n // Add additional unit systems here.\n\n // Choose a unit system to seed the auto unit system.\n UNIT_SYSTEMS.auto = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n\n // Set the current unit system\n let currentUnitSystem = UNIT_SYSTEMS.auto\n\n /**\n * Set a unit system for formatting derived units.\n * @param {string} [name] The name of the unit system.\n */\n Unit.setUnitSystem = function (name) {\n if (hasOwnProperty(UNIT_SYSTEMS, name)) {\n currentUnitSystem = UNIT_SYSTEMS[name]\n } else {\n throw new Error('Unit system ' + name + ' does not exist. Choices are: ' + Object.keys(UNIT_SYSTEMS).join(', '))\n }\n }\n\n /**\n * Return the current unit system.\n * @return {string} The current unit system.\n */\n Unit.getUnitSystem = function () {\n for (const key in UNIT_SYSTEMS) {\n if (hasOwnProperty(UNIT_SYSTEMS, key)) {\n if (UNIT_SYSTEMS[key] === currentUnitSystem) {\n return key\n }\n }\n }\n }\n\n /**\n * Converters to convert from number to an other numeric type like BigNumber\n * or Fraction\n */\n Unit.typeConverters = {\n BigNumber: function (x) {\n return new BigNumber(x + '') // stringify to prevent constructor error\n },\n\n Fraction: function (x) {\n return new Fraction(x)\n },\n\n Complex: function (x) {\n return x\n },\n\n number: function (x) {\n return x\n }\n }\n\n /**\n * Retrieve the right convertor function corresponding with the type\n * of provided exampleValue.\n *\n * @param {string} type A string 'number', 'BigNumber', or 'Fraction'\n * In case of an unknown type,\n * @return {Function}\n */\n Unit._getNumberConverter = function (type) {\n if (!Unit.typeConverters[type]) {\n throw new TypeError('Unsupported type \"' + type + '\"')\n }\n\n return Unit.typeConverters[type]\n }\n\n // Add dimensions to each built-in unit\n for (const key in UNITS) {\n if (hasOwnProperty(UNITS, key)) {\n const unit = UNITS[key]\n unit.dimensions = unit.base.dimensions\n }\n }\n\n // Create aliases\n for (const name in ALIASES) {\n if (hasOwnProperty(ALIASES, name)) {\n const unit = UNITS[ALIASES[name]]\n const alias = {}\n for (const key in unit) {\n if (hasOwnProperty(unit, key)) {\n alias[key] = unit[key]\n }\n }\n alias.name = name\n UNITS[name] = alias\n }\n }\n\n /**\n * Checks if a character is a valid latin letter (upper or lower case).\n * Note that this function can be overridden, for example to allow support of other alphabets.\n * @param {string} c Tested character\n */\n Unit.isValidAlpha = function isValidAlpha (c) {\n return /^[a-zA-Z]$/.test(c)\n }\n\n function assertUnitNameIsValid (name) {\n for (let i = 0; i < name.length; i++) {\n c = name.charAt(i)\n\n if (i === 0 && !Unit.isValidAlpha(c)) { throw new Error('Invalid unit name (must begin with alpha character): \"' + name + '\"') }\n\n if (i > 0 && !(Unit.isValidAlpha(c) ||\n isDigit(c))) { throw new Error('Invalid unit name (only alphanumeric characters are allowed): \"' + name + '\"') }\n }\n }\n\n /**\n * Wrapper around createUnitSingle.\n * Example:\n * createUnit({\n * foo: { },\n * bar: {\n * definition: 'kg/foo',\n * aliases: ['ba', 'barr', 'bars'],\n * offset: 200\n * },\n * baz: '4 bar'\n * },\n * {\n * override: true\n * })\n * @param {object} obj Object map. Each key becomes a unit which is defined by its value.\n * @param {object} options\n */\n Unit.createUnit = function (obj, options) {\n if (typeof (obj) !== 'object') {\n throw new TypeError(\"createUnit expects first parameter to be of type 'Object'\")\n }\n\n // Remove all units and aliases we are overriding\n if (options && options.override) {\n for (const key in obj) {\n if (hasOwnProperty(obj, key)) {\n Unit.deleteUnit(key)\n }\n if (obj[key].aliases) {\n for (let i = 0; i < obj[key].aliases.length; i++) {\n Unit.deleteUnit(obj[key].aliases[i])\n }\n }\n }\n }\n\n // TODO: traverse multiple times until all units have been added\n let lastUnit\n for (const key in obj) {\n if (hasOwnProperty(obj, key)) {\n lastUnit = Unit.createUnitSingle(key, obj[key])\n }\n }\n return lastUnit\n }\n\n /**\n * Create a user-defined unit and register it with the Unit type.\n * Example:\n * createUnitSingle('knot', '0.514444444 m/s')\n * createUnitSingle('acre', new Unit(43560, 'ft^2'))\n *\n * @param {string} name The name of the new unit. Must be unique. Example: 'knot'\n * @param {string, Unit, Object} definition Definition of the unit in terms\n * of existing units. For example, '0.514444444 m / s'. Can be a Unit, a string,\n * or an Object. If an Object, may have the following properties:\n * - definition {string|Unit} The definition of this unit.\n * - prefixes {string} \"none\", \"short\", \"long\", \"binary_short\", or \"binary_long\".\n * The default is \"none\".\n * - aliases {Array} Array of strings. Example: ['knots', 'kt', 'kts']\n * - offset {Numeric} An offset to apply when converting from the unit. For\n * example, the offset for celsius is 273.15 and the offset for farhenheit\n * is 459.67. Default is 0.\n * - baseName {string} If the unit's dimension does not match that of any other\n * base unit, the name of the newly create base unit. Otherwise, this property\n * has no effect.\n *\n * @param {Object} options (optional) An object containing any of the following\n * properties:\n * - override {boolean} Whether this unit should be allowed to override existing\n * units.\n *\n * @return {Unit}\n */\n Unit.createUnitSingle = function (name, obj, options) {\n if (typeof (obj) === 'undefined' || obj === null) {\n obj = {}\n }\n\n if (typeof (name) !== 'string') {\n throw new TypeError(\"createUnitSingle expects first parameter to be of type 'string'\")\n }\n\n // Check collisions with existing units\n if (hasOwnProperty(UNITS, name)) {\n throw new Error('Cannot create unit \"' + name + '\": a unit with that name already exists')\n }\n\n // TODO: Validate name for collisions with other built-in functions (like abs or cos, for example), and for acceptable variable names. For example, '42' is probably not a valid unit. Nor is '%', since it is also an operator.\n\n assertUnitNameIsValid(name)\n\n let defUnit = null // The Unit from which the new unit will be created.\n let aliases = []\n let offset = 0\n let definition\n let prefixes\n let baseName\n if (obj && obj.type === 'Unit') {\n defUnit = obj.clone()\n } else if (typeof (obj) === 'string') {\n if (obj !== '') {\n definition = obj\n }\n } else if (typeof (obj) === 'object') {\n definition = obj.definition\n prefixes = obj.prefixes\n offset = obj.offset\n baseName = obj.baseName\n if (obj.aliases) {\n aliases = obj.aliases.valueOf() // aliases could be a Matrix, so convert to Array\n }\n } else {\n throw new TypeError('Cannot create unit \"' + name + '\" from \"' + obj.toString() + '\": expecting \"string\" or \"Unit\" or \"Object\"')\n }\n\n if (aliases) {\n for (let i = 0; i < aliases.length; i++) {\n if (hasOwnProperty(UNITS, aliases[i])) {\n throw new Error('Cannot create alias \"' + aliases[i] + '\": a unit with that name already exists')\n }\n }\n }\n\n if (definition && typeof (definition) === 'string' && !defUnit) {\n try {\n defUnit = Unit.parse(definition, { allowNoUnits: true })\n } catch (ex) {\n ex.message = 'Could not create unit \"' + name + '\" from \"' + definition + '\": ' + ex.message\n throw (ex)\n }\n } else if (definition && definition.type === 'Unit') {\n defUnit = definition.clone()\n }\n\n aliases = aliases || []\n offset = offset || 0\n if (prefixes && prefixes.toUpperCase) { prefixes = PREFIXES[prefixes.toUpperCase()] || PREFIXES.NONE } else { prefixes = PREFIXES.NONE }\n\n // If defUnit is null, it is because the user did not\n // specify a defintion. So create a new base dimension.\n let newUnit = {}\n if (!defUnit) {\n // Add a new base dimension\n baseName = baseName || name + '_STUFF' // foo --> foo_STUFF, or the essence of foo\n if (BASE_DIMENSIONS.indexOf(baseName) >= 0) {\n throw new Error('Cannot create new base unit \"' + name + '\": a base unit with that name already exists (and cannot be overridden)')\n }\n BASE_DIMENSIONS.push(baseName)\n\n // Push 0 onto existing base units\n for (const b in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, b)) {\n BASE_UNITS[b].dimensions[BASE_DIMENSIONS.length - 1] = 0\n }\n }\n\n // Add the new base unit\n const newBaseUnit = { dimensions: [] }\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n newBaseUnit.dimensions[i] = 0\n }\n newBaseUnit.dimensions[BASE_DIMENSIONS.length - 1] = 1\n newBaseUnit.key = baseName\n BASE_UNITS[baseName] = newBaseUnit\n\n newUnit = {\n name: name,\n value: 1,\n dimensions: BASE_UNITS[baseName].dimensions.slice(0),\n prefixes: prefixes,\n offset: offset,\n base: BASE_UNITS[baseName]\n }\n\n currentUnitSystem[baseName] = {\n unit: newUnit,\n prefix: PREFIXES.NONE['']\n }\n } else {\n newUnit = {\n name: name,\n value: defUnit.value,\n dimensions: defUnit.dimensions.slice(0),\n prefixes: prefixes,\n offset: offset\n }\n\n // Create a new base if no matching base exists\n let anyMatch = false\n for (const i in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, i)) {\n let match = true\n for (let j = 0; j < BASE_DIMENSIONS.length; j++) {\n if (Math.abs((newUnit.dimensions[j] || 0) - (BASE_UNITS[i].dimensions[j] || 0)) > 1e-12) {\n match = false\n break\n }\n }\n if (match) {\n anyMatch = true\n newUnit.base = BASE_UNITS[i]\n break\n }\n }\n }\n if (!anyMatch) {\n baseName = baseName || name + '_STUFF' // foo --> foo_STUFF, or the essence of foo\n // Add the new base unit\n const newBaseUnit = { dimensions: defUnit.dimensions.slice(0) }\n newBaseUnit.key = baseName\n BASE_UNITS[baseName] = newBaseUnit\n\n currentUnitSystem[baseName] = {\n unit: newUnit,\n prefix: PREFIXES.NONE['']\n }\n\n newUnit.base = BASE_UNITS[baseName]\n }\n }\n\n Unit.UNITS[name] = newUnit\n\n for (let i = 0; i < aliases.length; i++) {\n const aliasName = aliases[i]\n const alias = {}\n for (const key in newUnit) {\n if (hasOwnProperty(newUnit, key)) {\n alias[key] = newUnit[key]\n }\n }\n alias.name = aliasName\n Unit.UNITS[aliasName] = alias\n }\n // delete the memoization cache, since adding a new unit to the array\n // invalidates all old results\n delete _findUnit.cache\n\n return new Unit(null, name)\n }\n\n Unit.deleteUnit = function (name) {\n delete Unit.UNITS[name]\n }\n\n // expose arrays with prefixes, dimensions, units, systems\n Unit.PREFIXES = PREFIXES\n Unit.BASE_DIMENSIONS = BASE_DIMENSIONS\n Unit.BASE_UNITS = BASE_UNITS\n Unit.UNIT_SYSTEMS = UNIT_SYSTEMS\n Unit.UNITS = UNITS\n\n return Unit\n}, { isClass: true })\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'unit'\nconst dependencies = ['typed', 'Unit']\n\n// This function is named createUnitFunction to prevent a naming conflict with createUnit\nexport const createUnitFunction = /* #__PURE__ */ factory(name, dependencies, ({ typed, Unit }) => {\n /**\n * Create a unit. Depending on the passed arguments, the function\n * will create and return a new math.Unit object.\n * When a matrix is provided, all elements will be converted to units.\n *\n * Syntax:\n *\n * math.unit(unit : string)\n * math.unit(value : number, unit : string)\n *\n * Examples:\n *\n * const a = math.unit(5, 'cm') // returns Unit 50 mm\n * const b = math.unit('23 kg') // returns Unit 23 kg\n * a.to('m') // returns Unit 0.05 m\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, number, string, createUnit\n *\n * @param {* | Array | Matrix} args A number and unit.\n * @return {Unit | Array | Matrix} The created unit\n */\n\n return typed(name, {\n Unit: function (x) {\n return x.clone()\n },\n\n string: function (x) {\n if (Unit.isValuelessUnit(x)) {\n return new Unit(null, x) // a pure unit\n }\n\n return Unit.parse(x, { allowNoUnits: true }) // a unit with value, like '5cm'\n },\n\n 'number | BigNumber | Fraction | Complex, string': function (value, unit) {\n return new Unit(value, unit)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'sparse'\nconst dependencies = ['typed', 'SparseMatrix']\n\nexport const createSparse = /* #__PURE__ */ factory(name, dependencies, ({ typed, SparseMatrix }) => {\n /**\n * Create a Sparse Matrix. The function creates a new `math.Matrix` object from\n * an `Array`. A Matrix has utility functions to manipulate the data in the\n * matrix, like getting the size and getting or setting values in the matrix.\n *\n * Syntax:\n *\n * math.sparse() // creates an empty sparse matrix.\n * math.sparse(data) // creates a sparse matrix with initial data.\n * math.sparse(data, 'number') // creates a sparse matrix with initial data, number datatype.\n *\n * Examples:\n *\n * let m = math.sparse([[1, 2], [3, 4]])\n * m.size() // Array [2, 2]\n * m.resize([3, 2], 5)\n * m.valueOf() // Array [[1, 2], [3, 4], [5, 5]]\n * m.get([1, 0]) // number 3\n *\n * See also:\n *\n * bignumber, boolean, complex, index, number, string, unit, matrix\n *\n * @param {Array | Matrix} [data] A two dimensional array\n *\n * @return {Matrix} The created matrix\n */\n return typed(name, {\n '': function () {\n return new SparseMatrix([])\n },\n\n string: function (datatype) {\n return new SparseMatrix([], datatype)\n },\n\n 'Array | Matrix': function (data) {\n return new SparseMatrix(data)\n },\n\n 'Array | Matrix, string': function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'createUnit'\nconst dependencies = ['typed', 'Unit']\n\nexport const createCreateUnit = /* #__PURE__ */ factory(name, dependencies, ({ typed, Unit }) => {\n /**\n * Create a user-defined unit and register it with the Unit type.\n *\n * Syntax:\n *\n * math.createUnit({\n * baseUnit1: {\n * aliases: [string, ...]\n * prefixes: object\n * },\n * unit2: {\n * definition: string,\n * aliases: [string, ...]\n * prefixes: object,\n * offset: number\n * },\n * unit3: string // Shortcut\n * })\n *\n * // Another shortcut:\n * math.createUnit(string, unit : string, [object])\n *\n * Examples:\n *\n * math.createUnit('foo')\n * math.createUnit('knot', {definition: '0.514444444 m/s', aliases: ['knots', 'kt', 'kts']})\n * math.createUnit('mph', '1 mile/hour')\n *\n * @param {string} name The name of the new unit. Must be unique. Example: 'knot'\n * @param {string, Unit} definition Definition of the unit in terms of existing units. For example, '0.514444444 m / s'.\n * @param {Object} options (optional) An object containing any of the following properties:\n * - `prefixes {string}` \"none\", \"short\", \"long\", \"binary_short\", or \"binary_long\". The default is \"none\".\n * - `aliases {Array}` Array of strings. Example: ['knots', 'kt', 'kts']\n * - `offset {Numeric}` An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.\n *\n * See also:\n *\n * unit\n *\n * @return {Unit} The new unit\n */\n return typed(name, {\n\n // General function signature. First parameter is an object where each property is the definition of a new unit. The object keys are the unit names and the values are the definitions. The values can be objects, strings, or Units. If a property is an empty object or an empty string, a new base unit is created. The second parameter is the options.\n 'Object, Object': function (obj, options) {\n return Unit.createUnit(obj, options)\n },\n\n // Same as above but without the options.\n Object: function (obj) {\n return Unit.createUnit(obj, {})\n },\n\n // Shortcut method for creating one unit.\n 'string, Unit | string | Object, Object': function (name, def, options) {\n const obj = {}\n obj[name] = def\n return Unit.createUnit(obj, options)\n },\n\n // Same as above but without the options.\n 'string, Unit | string | Object': function (name, def) {\n const obj = {}\n obj[name] = def\n return Unit.createUnit(obj, {})\n },\n\n // Without a definition, creates a base unit.\n string: function (name) {\n const obj = {}\n obj[name] = {}\n return Unit.createUnit(obj, {})\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'acos'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAcos = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the inverse cosine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acos(x)\n *\n * Examples:\n *\n * math.acos(0.5) // returns number 1.0471975511965979\n * math.acos(math.cos(1.5)) // returns number 1.5\n *\n * math.acos(2) // returns Complex 0 + 1.3169578969248166 i\n *\n * See also:\n *\n * cos, atan, asin\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc cosine of x\n */\n return typed(name, {\n number: function (x) {\n if ((x >= -1 && x <= 1) || config.predictable) {\n return Math.acos(x)\n } else {\n return new Complex(x, 0).acos()\n }\n },\n\n Complex: function (x) {\n return x.acos()\n },\n\n BigNumber: function (x) {\n return x.acos()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { acosh, asinh, atanh, cosh, sign, sinh, tanh } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function acosNumber (x) {\n return Math.acos(x)\n}\nacosNumber.signature = n1\n\nexport function acoshNumber (x) {\n return acosh(x)\n}\nacoshNumber.signature = n1\n\nexport function acotNumber (x) {\n return Math.atan(1 / x)\n}\nacotNumber.signature = n1\n\nexport function acothNumber (x) {\n return isFinite(x)\n ? (Math.log((x + 1) / x) + Math.log(x / (x - 1))) / 2\n : 0\n}\nacothNumber.signature = n1\n\nexport function acscNumber (x) {\n return Math.asin(1 / x)\n}\nacscNumber.signature = n1\n\nexport function acschNumber (x) {\n const xInv = 1 / x\n return Math.log(xInv + Math.sqrt(xInv * xInv + 1))\n}\nacschNumber.signature = n1\n\nexport function asecNumber (x) {\n return Math.acos(1 / x)\n}\nasecNumber.signature = n1\n\nexport function asechNumber (x) {\n const xInv = 1 / x\n const ret = Math.sqrt(xInv * xInv - 1)\n return Math.log(ret + xInv)\n}\nasechNumber.signature = n1\n\nexport function asinNumber (x) {\n return Math.asin(x)\n}\nasinNumber.signature = n1\n\nexport function asinhNumber (x) {\n return asinh(x)\n}\nasinhNumber.signature = n1\n\nexport function atanNumber (x) {\n return Math.atan(x)\n}\natanNumber.signature = n1\n\nexport function atan2Number (y, x) {\n return Math.atan2(y, x)\n}\natan2Number.signature = n2\n\nexport function atanhNumber (x) {\n return atanh(x)\n}\natanhNumber.signature = n1\n\nexport function cosNumber (x) {\n return Math.cos(x)\n}\ncosNumber.signature = n1\n\nexport function coshNumber (x) {\n return cosh(x)\n}\ncoshNumber.signature = n1\n\nexport function cotNumber (x) {\n return 1 / Math.tan(x)\n}\ncotNumber.signature = n1\n\nexport function cothNumber (x) {\n const e = Math.exp(2 * x)\n return (e + 1) / (e - 1)\n}\ncothNumber.signature = n1\n\nexport function cscNumber (x) {\n return 1 / Math.sin(x)\n}\ncscNumber.signature = n1\n\nexport function cschNumber (x) {\n // consider values close to zero (+/-)\n if (x === 0) {\n return Number.POSITIVE_INFINITY\n } else {\n return Math.abs(2 / (Math.exp(x) - Math.exp(-x))) * sign(x)\n }\n}\ncschNumber.signature = n1\n\nexport function secNumber (x) {\n return 1 / Math.cos(x)\n}\nsecNumber.signature = n1\n\nexport function sechNumber (x) {\n return 2 / (Math.exp(x) + Math.exp(-x))\n}\nsechNumber.signature = n1\n\nexport function sinNumber (x) {\n return Math.sin(x)\n}\nsinNumber.signature = n1\n\nexport function sinhNumber (x) {\n return sinh(x)\n}\nsinhNumber.signature = n1\n\nexport function tanNumber (x) {\n return Math.tan(x)\n}\ntanNumber.signature = n1\n\nexport function tanhNumber (x) {\n return tanh(x)\n}\ntanhNumber.signature = n1\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acoshNumber } from '../../plain/number/index.js'\n\nconst name = 'acosh'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAcosh = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the hyperbolic arccos of a value,\n * defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acosh(x)\n *\n * Examples:\n *\n * math.acosh(1.5) // returns 0.9624236501192069\n *\n * See also:\n *\n * cosh, asinh, atanh\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccosine of x\n */\n return typed(name, {\n number: function (x) {\n if (x >= 1 || config.predictable) {\n return acoshNumber(x)\n }\n if (x <= -1) {\n return new Complex(Math.log(Math.sqrt(x * x - 1) - x), Math.PI)\n }\n return new Complex(x, 0).acosh()\n },\n\n Complex: function (x) {\n return x.acosh()\n },\n\n BigNumber: function (x) {\n return x.acosh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acotNumber } from '../../plain/number/index.js'\n\nconst name = 'acot'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createAcot = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the inverse cotangent of a value, defined as `acot(x) = atan(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acot(x)\n *\n * Examples:\n *\n * math.acot(0.5) // returns number 0.4636476090008061\n * math.acot(math.cot(1.5)) // returns number 1.5\n *\n * math.acot(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * cot, atan\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc cotangent of x\n */\n return typed(name, {\n number: acotNumber,\n\n Complex: function (x) {\n return x.acot()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).atan()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acothNumber } from '../../plain/number/index.js'\n\nconst name = 'acoth'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAcoth = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the hyperbolic arccotangent of a value,\n * defined as `acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acoth(x)\n *\n * Examples:\n *\n * math.acoth(0.5) // returns 0.8047189562170503\n *\n * See also:\n *\n * acsch, asech\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccotangent of x\n */\n return typed(name, {\n number: function (x) {\n if (x >= 1 || x <= -1 || config.predictable) {\n return acothNumber(x)\n }\n return new Complex(x, 0).acoth()\n },\n\n Complex: function (x) {\n return x.acoth()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).atanh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acscNumber } from '../../plain/number/index.js'\n\nconst name = 'acsc'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAcsc = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the inverse cosecant of a value, defined as `acsc(x) = asin(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acsc(x)\n *\n * Examples:\n *\n * math.acsc(0.5) // returns number 0.5235987755982989\n * math.acsc(math.csc(1.5)) // returns number ~1.5\n *\n * math.acsc(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * csc, asin, asec\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc cosecant of x\n */\n return typed(name, {\n number: function (x) {\n if (x <= -1 || x >= 1 || config.predictable) {\n return acscNumber(x)\n }\n return new Complex(x, 0).acsc()\n },\n\n Complex: function (x) {\n return x.acsc()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).asin()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acschNumber } from '../../plain/number/index.js'\n\nconst name = 'acsch'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createAcsch = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic arccosecant of a value,\n * defined as `acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acsch(x)\n *\n * Examples:\n *\n * math.acsch(0.5) // returns 1.4436354751788103\n *\n * See also:\n *\n * asech, acoth\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccosecant of x\n */\n return typed(name, {\n number: acschNumber,\n\n Complex: function (x) {\n return x.acsch()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).asinh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asecNumber } from '../../plain/number/index.js'\n\nconst name = 'asec'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAsec = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the inverse secant of a value. Defined as `asec(x) = acos(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asec(x)\n *\n * Examples:\n *\n * math.asec(0.5) // returns 1.0471975511965979\n * math.asec(math.sec(1.5)) // returns 1.5\n *\n * math.asec(2) // returns 0 + 1.3169578969248166 i\n *\n * See also:\n *\n * acos, acot, acsc\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc secant of x\n */\n return typed(name, {\n number: function (x) {\n if (x <= -1 || x >= 1 || config.predictable) {\n return asecNumber(x)\n }\n return new Complex(x, 0).asec()\n },\n\n Complex: function (x) {\n return x.asec()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).acos()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asechNumber } from '../../plain/number/index.js'\n\nconst name = 'asech'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAsech = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the hyperbolic arcsecant of a value,\n * defined as `asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asech(x)\n *\n * Examples:\n *\n * math.asech(0.5) // returns 1.3169578969248166\n *\n * See also:\n *\n * acsch, acoth\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arcsecant of x\n */\n return typed(name, {\n number: function (x) {\n if ((x <= 1 && x >= -1) || config.predictable) {\n const xInv = 1 / x\n if (xInv > 0 || config.predictable) {\n return asechNumber(x)\n }\n\n const ret = Math.sqrt(xInv * xInv - 1)\n return new Complex(Math.log(ret - xInv), Math.PI)\n }\n\n return new Complex(x, 0).asech()\n },\n\n Complex: function (x) {\n return x.asech()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).acosh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'asin'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAsin = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the inverse sine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asin(x)\n *\n * Examples:\n *\n * math.asin(0.5) // returns number 0.5235987755982989\n * math.asin(math.sin(1.5)) // returns number ~1.5\n *\n * math.asin(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * sin, atan, acos\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc sine of x\n */\n return typed(name, {\n number: function (x) {\n if ((x >= -1 && x <= 1) || config.predictable) {\n return Math.asin(x)\n } else {\n return new Complex(x, 0).asin()\n }\n },\n\n Complex: function (x) {\n return x.asin()\n },\n\n BigNumber: function (x) {\n return x.asin()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since asin(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asinhNumber } from '../../plain/number/index.js'\n\nconst name = 'asinh'\nconst dependencies = ['typed']\n\nexport const createAsinh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic arcsine of a value,\n * defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asinh(x)\n *\n * Examples:\n *\n * math.asinh(0.5) // returns 0.48121182505960347\n *\n * See also:\n *\n * acosh, atanh\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arcsine of x\n */\n return typed('asinh', {\n number: asinhNumber,\n\n Complex: function (x) {\n return x.asinh()\n },\n\n BigNumber: function (x) {\n return x.asinh()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since asinh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'atan'\nconst dependencies = ['typed']\n\nexport const createAtan = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the inverse tangent of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atan(x)\n *\n * Examples:\n *\n * math.atan(0.5) // returns number 0.4636476090008061\n * math.atan(math.tan(1.5)) // returns number 1.5\n *\n * math.atan(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * tan, asin, acos\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc tangent of x\n */\n return typed('atan', {\n number: function (x) {\n return Math.atan(x)\n },\n\n Complex: function (x) {\n return x.atan()\n },\n\n BigNumber: function (x) {\n return x.atan()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since atan(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm09 } from '../../type/matrix/utils/algorithm09.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'atan2'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createAtan2 = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm09 = createAlgorithm09({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the inverse tangent function with two arguments, y/x.\n * By providing two arguments, the right quadrant of the computed angle can be\n * determined.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atan2(y, x)\n *\n * Examples:\n *\n * math.atan2(2, 2) / math.pi // returns number 0.25\n *\n * const angle = math.unit(60, 'deg') // returns Unit 60 deg\n * const x = math.cos(angle)\n * const y = math.sin(angle)\n *\n * math.atan(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * tan, atan, sin, cos\n *\n * @param {number | Array | Matrix} y Second dimension\n * @param {number | Array | Matrix} x First dimension\n * @return {number | Array | Matrix} Four-quadrant inverse tangent\n */\n return typed(name, {\n\n 'number, number': Math.atan2,\n\n // Complex numbers doesn't seem to have a reasonable implementation of\n // atan2(). Even Matlab removed the support, after they only calculated\n // the atan only on base of the real part of the numbers and ignored the imaginary.\n\n 'BigNumber, BigNumber': function (y, x) {\n return BigNumber.atan2(y, x)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm09(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n // mind the order of y and x!\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // mind the order of y and x\n return algorithm12(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // mind the order of y and x\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { atanhNumber } from '../../plain/number/index.js'\n\nconst name = 'atanh'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAtanh = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the hyperbolic arctangent of a value,\n * defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atanh(x)\n *\n * Examples:\n *\n * math.atanh(0.5) // returns 0.5493061443340549\n *\n * See also:\n *\n * acosh, asinh\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arctangent of x\n */\n return typed(name, {\n number: function (x) {\n if ((x <= 1 && x >= -1) || config.predictable) {\n return atanhNumber(x)\n }\n return new Complex(x, 0).atanh()\n },\n\n Complex: function (x) {\n return x.atanh()\n },\n\n BigNumber: function (x) {\n return x.atanh()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since atanh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'cos'\nconst dependencies = ['typed']\n\nexport const createCos = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the cosine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cos(x)\n *\n * Examples:\n *\n * math.cos(2) // returns number -0.4161468365471422\n * math.cos(math.pi / 4) // returns number 0.7071067811865475\n * math.cos(math.unit(180, 'deg')) // returns number -1\n * math.cos(math.unit(60, 'deg')) // returns number 0.5\n *\n * const angle = 0.2\n * math.pow(math.sin(angle), 2) + math.pow(math.cos(angle), 2) // returns number ~1\n *\n * See also:\n *\n * cos, tan\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Cosine of x\n */\n return typed(name, {\n number: Math.cos,\n\n Complex: function (x) {\n return x.cos()\n },\n\n BigNumber: function (x) {\n return x.cos()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cos is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cosh as coshNumber } from '../../utils/number.js'\n\nconst name = 'cosh'\nconst dependencies = ['typed']\n\nexport const createCosh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic cosine of a value,\n * defined as `cosh(x) = 1/2 * (exp(x) + exp(-x))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cosh(x)\n *\n * Examples:\n *\n * math.cosh(0.5) // returns number 1.1276259652063807\n *\n * See also:\n *\n * sinh, tanh\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic cosine of x\n */\n return typed(name, {\n number: coshNumber,\n\n Complex: function (x) {\n return x.cosh()\n },\n\n BigNumber: function (x) {\n return x.cosh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cosh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cotNumber } from '../../plain/number/index.js'\n\nconst name = 'cot'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCot = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the cotangent of a value. Defined as `cot(x) = 1 / tan(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cot(x)\n *\n * Examples:\n *\n * math.cot(2) // returns number -0.45765755436028577\n * 1 / math.tan(2) // returns number -0.45765755436028577\n *\n * See also:\n *\n * tan, sec, csc\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Cotangent of x\n */\n return typed(name, {\n number: cotNumber,\n\n Complex: function (x) {\n return x.cot()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.tan())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cot is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cothNumber } from '../../plain/number/index.js'\n\nconst name = 'coth'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCoth = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic cotangent of a value,\n * defined as `coth(x) = 1 / tanh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.coth(x)\n *\n * Examples:\n *\n * // coth(x) = 1 / tanh(x)\n * math.coth(2) // returns 1.0373147207275482\n * 1 / math.tanh(2) // returns 1.0373147207275482\n *\n * See also:\n *\n * sinh, tanh, cosh\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic cotangent of x\n */\n return typed(name, {\n number: cothNumber,\n\n Complex: function (x) {\n return x.coth()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.tanh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function coth is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cscNumber } from '../../plain/number/index.js'\n\nconst name = 'csc'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCsc = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the cosecant of a value, defined as `csc(x) = 1/sin(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.csc(x)\n *\n * Examples:\n *\n * math.csc(2) // returns number 1.099750170294617\n * 1 / math.sin(2) // returns number 1.099750170294617\n *\n * See also:\n *\n * sin, sec, cot\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Cosecant of x\n */\n return typed(name, {\n number: cscNumber,\n\n Complex: function (x) {\n return x.csc()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.sin())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function csc is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cschNumber } from '../../plain/number/index.js'\n\nconst name = 'csch'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCsch = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic cosecant of a value,\n * defined as `csch(x) = 1 / sinh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.csch(x)\n *\n * Examples:\n *\n * // csch(x) = 1/ sinh(x)\n * math.csch(0.5) // returns 1.9190347513349437\n * 1 / math.sinh(0.5) // returns 1.9190347513349437\n *\n * See also:\n *\n * sinh, sech, coth\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic cosecant of x\n */\n return typed(name, {\n number: cschNumber,\n\n Complex: function (x) {\n return x.csch()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.sinh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function csch is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { secNumber } from '../../plain/number/index.js'\n\nconst name = 'sec'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createSec = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the secant of a value, defined as `sec(x) = 1/cos(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sec(x)\n *\n * Examples:\n *\n * math.sec(2) // returns number -2.4029979617223822\n * 1 / math.cos(2) // returns number -2.4029979617223822\n *\n * See also:\n *\n * cos, csc, cot\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Secant of x\n */\n return typed(name, {\n number: secNumber,\n\n Complex: function (x) {\n return x.sec()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.cos())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sec is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { sechNumber } from '../../plain/number/index.js'\n\nconst name = 'sech'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createSech = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic secant of a value,\n * defined as `sech(x) = 1 / cosh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sech(x)\n *\n * Examples:\n *\n * // sech(x) = 1/ cosh(x)\n * math.sech(0.5) // returns 0.886818883970074\n * 1 / math.cosh(0.5) // returns 0.886818883970074\n *\n * See also:\n *\n * cosh, csch, coth\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic secant of x\n */\n return typed(name, {\n number: sechNumber,\n\n Complex: function (x) {\n return x.sech()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.cosh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sech is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'sin'\nconst dependencies = ['typed']\n\nexport const createSin = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the sine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sin(x)\n *\n * Examples:\n *\n * math.sin(2) // returns number 0.9092974268256813\n * math.sin(math.pi / 4) // returns number 0.7071067811865475\n * math.sin(math.unit(90, 'deg')) // returns number 1\n * math.sin(math.unit(30, 'deg')) // returns number 0.5\n *\n * const angle = 0.2\n * math.pow(math.sin(angle), 2) + math.pow(math.cos(angle), 2) // returns number ~1\n *\n * See also:\n *\n * cos, tan\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Sine of x\n */\n return typed(name, {\n number: Math.sin,\n\n Complex: function (x) {\n return x.sin()\n },\n\n BigNumber: function (x) {\n return x.sin()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sin is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sin(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { sinhNumber } from '../../plain/number/index.js'\n\nconst name = 'sinh'\nconst dependencies = ['typed']\n\nexport const createSinh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic sine of a value,\n * defined as `sinh(x) = 1/2 * (exp(x) - exp(-x))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sinh(x)\n *\n * Examples:\n *\n * math.sinh(0.5) // returns number 0.5210953054937474\n *\n * See also:\n *\n * cosh, tanh\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic sine of x\n */\n return typed(name, {\n number: sinhNumber,\n\n Complex: function (x) {\n return x.sinh()\n },\n\n BigNumber: function (x) {\n return x.sinh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sinh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sinh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'tan'\nconst dependencies = ['typed']\n\nexport const createTan = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the tangent of a value. `tan(x)` is equal to `sin(x) / cos(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.tan(x)\n *\n * Examples:\n *\n * math.tan(0.5) // returns number 0.5463024898437905\n * math.sin(0.5) / math.cos(0.5) // returns number 0.5463024898437905\n * math.tan(math.pi / 4) // returns number 1\n * math.tan(math.unit(45, 'deg')) // returns number 1\n *\n * See also:\n *\n * atan, sin, cos\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Tangent of x\n */\n return typed(name, {\n number: Math.tan,\n\n Complex: function (x) {\n return x.tan()\n },\n\n BigNumber: function (x) {\n return x.tan()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function tan is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since tan(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { tanh as _tanh } from '../../utils/number.js'\n\nconst name = 'tanh'\nconst dependencies = ['typed']\n\nexport const createTanh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic tangent of a value,\n * defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.tanh(x)\n *\n * Examples:\n *\n * // tanh(x) = sinh(x) / cosh(x) = 1 / coth(x)\n * math.tanh(0.5) // returns 0.46211715726000974\n * math.sinh(0.5) / math.cosh(0.5) // returns 0.46211715726000974\n * 1 / math.coth(0.5) // returns 0.46211715726000974\n *\n * See also:\n *\n * sinh, cosh, coth\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic tangent of x\n */\n return typed('tanh', {\n number: _tanh,\n\n Complex: function (x) {\n return x.tanh()\n },\n\n BigNumber: function (x) {\n return x.tanh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function tanh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since tanh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setCartesian'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetCartesian = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the cartesian product of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setCartesian(set1, set2)\n *\n * Examples:\n *\n * math.setCartesian([1, 2], [3, 4]) // returns [[1, 3], [1, 4], [2, 3], [2, 4]]\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference, setPowerset\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The cartesian product of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result = []\n\n if (subset(size(a1), new Index(0)) !== 0 && subset(size(a2), new Index(0)) !== 0) { // if any of them is empty, return empty\n const b1 = flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural)\n const b2 = flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural)\n result = []\n for (let i = 0; i < b1.length; i++) {\n for (let j = 0; j < b2.length; j++) {\n result.push([b1[i], b2[j]])\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return result\n }\n // return a matrix otherwise\n return new DenseMatrix(result)\n }\n })\n})\n","import { flatten, generalize, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setDifference'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetDifference = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the difference of two (multi)sets: every element of set1, that is not the element of set2.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setDifference(set1, set2)\n *\n * Examples:\n *\n * math.setDifference([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2]\n * math.setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2]\n *\n * See also:\n *\n * setUnion, setIntersect, setSymDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The difference of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result\n if (subset(size(a1), new Index(0)) === 0) { // empty-anything=empty\n result = []\n } else if (subset(size(a2), new Index(0)) === 0) { // anything-empty=anything\n return flatten(a1.toArray())\n } else {\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n result = []\n let inb2\n for (let i = 0; i < b1.length; i++) {\n inb2 = false\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n inb2 = true\n break\n }\n }\n if (!inb2) {\n result.push(b1[i])\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return generalize(result)\n }\n // return a matrix otherwise\n return new DenseMatrix(generalize(result))\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setDistinct'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetDistinct = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Collect the distinct elements of a multiset.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setDistinct(set)\n *\n * Examples:\n *\n * math.setDistinct([1, 1, 1, 2, 2, 3]) // returns [1, 2, 3]\n *\n * See also:\n *\n * setMultiplicity\n *\n * @param {Array | Matrix} a A multiset\n * @return {Array | Matrix} A set containing the distinc elements of the multiset\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n let result\n if (subset(size(a), new Index(0)) === 0) { // if empty, return empty\n result = []\n } else {\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n result = []\n result.push(b[0])\n for (let i = 1; i < b.length; i++) {\n if (compareNatural(b[i], b[i - 1]) !== 0) {\n result.push(b[i])\n }\n }\n }\n // return an array, if the input was an array\n if (Array.isArray(a)) {\n return result\n }\n // return a matrix otherwise\n return new DenseMatrix(result)\n }\n })\n})\n","import { flatten, generalize, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setIntersect'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetIntersect = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the intersection of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setIntersect(set1, set2)\n *\n * Examples:\n *\n * math.setIntersect([1, 2, 3, 4], [3, 4, 5, 6]) // returns [3, 4]\n * math.setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [3, 4]\n *\n * See also:\n *\n * setUnion, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The intersection of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result\n if (subset(size(a1), new Index(0)) === 0 || subset(size(a2), new Index(0)) === 0) { // of any of them is empty, return empty\n result = []\n } else {\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n result = []\n for (let i = 0; i < b1.length; i++) {\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n result.push(b1[i])\n break\n }\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return generalize(result)\n }\n // return a matrix otherwise\n return new DenseMatrix(generalize(result))\n }\n })\n})\n","import { flatten, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setIsSubset'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetIsSubset = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Check whether a (multi)set is a subset of another (multi)set. (Every element of set1 is the element of set2.)\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setIsSubset(set1, set2)\n *\n * Examples:\n *\n * math.setIsSubset([1, 2], [3, 4, 5, 6]) // returns false\n * math.setIsSubset([3, 4], [3, 4, 5, 6]) // returns true\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {boolean} true | false\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // empty is a subset of anything\n return true\n } else if (subset(size(a2), new Index(0)) === 0) { // anything is not a subset of empty\n return false\n }\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n let inb2\n for (let i = 0; i < b1.length; i++) {\n inb2 = false\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n inb2 = true\n break\n }\n }\n if (inb2 === false) {\n return false\n }\n }\n return true\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setMultiplicity'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetMultiplicity = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Count the multiplicity of an element in a multiset.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setMultiplicity(element, set)\n *\n * Examples:\n *\n * math.setMultiplicity(1, [1, 2, 2, 4]) // returns 1\n * math.setMultiplicity(2, [1, 2, 2, 4]) // returns 2\n *\n * See also:\n *\n * setDistinct, setSize\n *\n * @param {number | BigNumber | Fraction | Complex} e An element in the multiset\n * @param {Array | Matrix} a A multiset\n * @return {number} The number of how many times the multiset contains the element\n */\n return typed(name, {\n 'number | BigNumber | Fraction | Complex, Array | Matrix': function (e, a) {\n if (subset(size(a), new Index(0)) === 0) { // if empty, return 0\n return 0\n }\n const b = flatten(Array.isArray(a) ? a : a.toArray())\n let count = 0\n for (let i = 0; i < b.length; i++) {\n if (compareNatural(b[i], e) === 0) {\n count++\n }\n }\n return count\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setPowerset'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetPowerset = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Create the powerset of a (multi)set. (The powerset contains very possible subsets of a (multi)set.)\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setPowerset(set)\n *\n * Examples:\n *\n * math.setPowerset([1, 2, 3]) // returns [[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]\n *\n * See also:\n *\n * setCartesian\n *\n * @param {Array | Matrix} a A (multi)set\n * @return {Array} The powerset of the (multi)set\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n if (subset(size(a), new Index(0)) === 0) { // if empty, return empty\n return []\n }\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n const result = []\n let number = 0\n while (number.toString(2).length <= b.length) {\n result.push(_subset(b, number.toString(2).split('').reverse()))\n number++\n }\n // can not return a matrix, because of the different size of the subarrays\n return _sort(result)\n }\n })\n\n // create subset\n function _subset (array, bitarray) {\n const result = []\n for (let i = 0; i < bitarray.length; i++) {\n if (bitarray[i] === '1') {\n result.push(array[i])\n }\n }\n return result\n }\n\n // sort subsests by length\n function _sort (array) {\n let temp = []\n for (let i = array.length - 1; i > 0; i--) {\n for (let j = 0; j < i; j++) {\n if (array[j].length > array[j + 1].length) {\n temp = array[j]\n array[j] = array[j + 1]\n array[j + 1] = temp\n }\n }\n }\n return array\n }\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setSize'\nconst dependencies = ['typed', 'compareNatural']\n\nexport const createSetSize = /* #__PURE__ */ factory(name, dependencies, ({ typed, compareNatural }) => {\n /**\n * Count the number of elements of a (multi)set. When a second parameter is 'true', count only the unique values.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setSize(set)\n * math.setSize(set, unique)\n *\n * Examples:\n *\n * math.setSize([1, 2, 2, 4]) // returns 4\n * math.setSize([1, 2, 2, 4], true) // returns 3\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a A multiset\n * @return {number} The number of elements of the (multi)set\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n return Array.isArray(a) ? flatten(a).length : flatten(a.toArray()).length\n },\n 'Array | Matrix, boolean': function (a, unique) {\n if (unique === false || a.length === 0) {\n return Array.isArray(a) ? flatten(a).length : flatten(a.toArray()).length\n } else {\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n let count = 1\n for (let i = 1; i < b.length; i++) {\n if (compareNatural(b[i], b[i - 1]) !== 0) {\n count++\n }\n }\n return count\n }\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setSymDifference'\nconst dependencies = ['typed', 'size', 'concat', 'subset', 'setDifference', 'Index']\n\nexport const createSetSymDifference = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, concat, subset, setDifference, Index }) => {\n /**\n * Create the symmetric difference of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setSymDifference(set1, set2)\n *\n * Examples:\n *\n * math.setSymDifference([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2, 5, 6]\n * math.setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2, 5, 6]\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The symmetric difference of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // if any of them is empty, return the other one\n return flatten(a2)\n } else if (subset(size(a2), new Index(0)) === 0) {\n return flatten(a1)\n }\n const b1 = flatten(a1)\n const b2 = flatten(a2)\n return concat(setDifference(b1, b2), setDifference(b2, b1))\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setUnion'\nconst dependencies = ['typed', 'size', 'concat', 'subset', 'setIntersect', 'setSymDifference', 'Index']\n\nexport const createSetUnion = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, concat, subset, setIntersect, setSymDifference, Index }) => {\n /**\n * Create the union of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setUnion(set1, set2)\n *\n * Examples:\n *\n * math.setUnion([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2, 3, 4, 5, 6]\n * math.setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2, 3, 4, 5, 6]\n *\n * See also:\n *\n * setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The union of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // if any of them is empty, return the other one\n return flatten(a2)\n } else if (subset(size(a2), new Index(0)) === 0) {\n return flatten(a1)\n }\n const b1 = flatten(a1)\n const b2 = flatten(a2)\n return concat(setSymDifference(b1, b2), setIntersect(b1, b2))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { extend } from '../../utils/object.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'add'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'addScalar',\n 'equalScalar',\n 'DenseMatrix',\n 'SparseMatrix'\n]\n\nexport const createAdd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, addScalar, equalScalar, DenseMatrix, SparseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Add two or more values, `x + y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.add(x, y)\n * math.add(x, y, z, ...)\n *\n * Examples:\n *\n * math.add(2, 3) // returns number 5\n * math.add(2, 3, 4) // returns number 9\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(-4, 1)\n * math.add(a, b) // returns Complex -2 + 4i\n *\n * math.add([1, 2, 3], 4) // returns Array [5, 6, 7]\n *\n * const c = math.unit('5 cm')\n * const d = math.unit('2.1 mm')\n * math.add(c, d) // returns Unit 52.1 mm\n *\n * math.add(\"2.3\", \"4\") // returns number 6.3\n *\n * See also:\n *\n * subtract, sum\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to add\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to add\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Sum of `x` and `y`\n */\n return typed(name, extend({\n // we extend the signatures of addScalar with signatures dealing with matrices\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, addScalar)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, addScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, addScalar, true)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, addScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, addScalar, false)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, y, addScalar, false)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, addScalar, true)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, addScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, addScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, addScalar, true).valueOf()\n },\n\n 'any, any': addScalar,\n\n 'any, any, ...any': function (x, y, rest) {\n let result = this(x, y)\n\n for (let i = 0; i < rest.length; i++) {\n result = this(result, rest[i])\n }\n\n return result\n }\n }, addScalar.signatures))\n})\n","import { factory } from '../../utils/factory.js'\nimport { flatten } from '../../utils/array.js'\n\nconst name = 'hypot'\nconst dependencies = [\n 'typed',\n 'abs',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'sqrt',\n 'smaller',\n 'isPositive'\n]\n\nexport const createHypot = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, addScalar, divideScalar, multiplyScalar, sqrt, smaller, isPositive }) => {\n /**\n * Calculate the hypotenusa of a list with values. The hypotenusa is defined as:\n *\n * hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...)\n *\n * For matrix input, the hypotenusa is calculated for all values in the matrix.\n *\n * Syntax:\n *\n * math.hypot(a, b, ...)\n * math.hypot([a, b, c, ...])\n *\n * Examples:\n *\n * math.hypot(3, 4) // 5\n * math.hypot(3, 4, 5) // 7.0710678118654755\n * math.hypot([3, 4, 5]) // 7.0710678118654755\n * math.hypot(-2) // 2\n *\n * See also:\n *\n * abs, norm\n *\n * @param {... number | BigNumber | Array | Matrix} args A list with numeric values or an Array or Matrix.\n * Matrix and Array input is flattened and returns a\n * single number for the whole matrix.\n * @return {number | BigNumber} Returns the hypothenusa of the input values.\n */\n return typed(name, {\n '... number | BigNumber': _hypot,\n\n Array: function (x) {\n return this.apply(this, flatten(x))\n },\n\n Matrix: function (x) {\n return this.apply(this, flatten(x.toArray()))\n }\n })\n\n /**\n * Calculate the hypotenusa for an Array with values\n * @param {Array.} args\n * @return {number | BigNumber} Returns the result\n * @private\n */\n function _hypot (args) {\n // code based on `hypot` from es6-shim:\n // https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1619-L1633\n let result = 0\n let largest = 0\n\n for (let i = 0; i < args.length; i++) {\n const value = abs(args[i])\n if (smaller(largest, value)) {\n result = multiplyScalar(result,\n multiplyScalar(divideScalar(largest, value), divideScalar(largest, value)))\n result = addScalar(result, 1)\n largest = value\n } else {\n result = addScalar(result, isPositive(value)\n ? multiplyScalar(divideScalar(value, largest), divideScalar(value, largest))\n : value)\n }\n }\n\n return multiplyScalar(largest, sqrt(result))\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'norm'\nconst dependencies = [\n 'typed',\n 'abs',\n 'add',\n 'pow',\n 'conj',\n 'sqrt',\n 'multiply',\n 'equalScalar',\n 'larger',\n 'smaller',\n 'matrix',\n 'ctranspose',\n 'eigs'\n]\n\nexport const createNorm = /* #__PURE__ */ factory(\n name,\n dependencies,\n ({\n typed,\n abs,\n add,\n pow,\n conj,\n sqrt,\n multiply,\n equalScalar,\n larger,\n smaller,\n matrix,\n ctranspose,\n eigs\n }) => {\n /**\n * Calculate the norm of a number, vector or matrix.\n *\n * The second parameter p is optional. If not provided, it defaults to 2.\n *\n * Syntax:\n *\n * math.norm(x)\n * math.norm(x, p)\n *\n * Examples:\n *\n * math.abs(-3.5) // returns 3.5\n * math.norm(-3.5) // returns 3.5\n *\n * math.norm(math.complex(3, -4)) // returns 5\n *\n * math.norm([1, 2, -3], Infinity) // returns 3\n * math.norm([1, 2, -3], -Infinity) // returns 1\n *\n * math.norm([3, 4], 2) // returns 5\n *\n * math.norm([[1, 2], [3, 4]], 1) // returns 6\n * math.norm([[1, 2], [3, 4]], 'inf') // returns 7\n * math.norm([[1, 2], [3, 4]], 'fro') // returns 5.477225575051661\n *\n * See also:\n *\n * abs, hypot\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the norm\n * @param {number | BigNumber | string} [p=2]\n * Vector space.\n * Supported numbers include Infinity and -Infinity.\n * Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm)\n * @return {number | BigNumber} the p-norm\n */\n return typed(name, {\n number: Math.abs,\n\n Complex: function (x) {\n return x.abs()\n },\n\n BigNumber: function (x) {\n // norm(x) = abs(x)\n return x.abs()\n },\n\n boolean: function (x) {\n // norm(x) = abs(x)\n return Math.abs(x)\n },\n\n Array: function (x) {\n return _norm(matrix(x), 2)\n },\n\n Matrix: function (x) {\n return _norm(x, 2)\n },\n\n 'number | Complex | BigNumber | boolean, number | BigNumber | string': function (\n x\n ) {\n // ignore second parameter, TODO: remove the option of second parameter for these types\n return this(x)\n },\n\n 'Array, number | BigNumber | string': function (x, p) {\n return _norm(matrix(x), p)\n },\n\n 'Matrix, number | BigNumber | string': function (x, p) {\n return _norm(x, p)\n }\n })\n\n /**\n * Calculate the plus infinity norm for a vector\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNormPlusInfinity (x) {\n // norm(x, Infinity) = max(abs(x))\n let pinf = 0\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n const v = abs(value)\n if (larger(v, pinf)) {\n pinf = v\n }\n }, true)\n return pinf\n }\n\n /**\n * Calculate the minus infinity norm for a vector\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNormMinusInfinity (x) {\n // norm(x, -Infinity) = min(abs(x))\n let ninf\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n const v = abs(value)\n if (!ninf || smaller(v, ninf)) {\n ninf = v\n }\n }, true)\n return ninf || 0\n }\n\n /**\n * Calculate the norm for a vector\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNorm (x, p) {\n // check p\n if (p === Number.POSITIVE_INFINITY || p === 'inf') {\n return _vectorNormPlusInfinity(x)\n }\n if (p === Number.NEGATIVE_INFINITY || p === '-inf') {\n return _vectorNormMinusInfinity(x)\n }\n if (p === 'fro') {\n return _norm(x, 2)\n }\n if (typeof p === 'number' && !isNaN(p)) {\n // check p != 0\n if (!equalScalar(p, 0)) {\n // norm(x, p) = sum(abs(xi) ^ p) ^ 1/p\n let n = 0\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n n = add(pow(abs(value), p), n)\n }, true)\n return pow(n, 1 / p)\n }\n return Number.POSITIVE_INFINITY\n }\n // invalid parameter value\n throw new Error('Unsupported parameter value')\n }\n\n /**\n * Calculate the Frobenius norm for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormFrobenius (x) {\n // norm(x) = sqrt(sum(diag(x'x)))\n let fro = 0\n x.forEach(function (value, index) {\n fro = add(fro, multiply(value, conj(value)))\n })\n return abs(sqrt(fro))\n }\n\n /**\n * Calculate the norm L1 for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormOne (x) {\n // norm(x) = the largest column sum\n const c = []\n // result\n let maxc = 0\n // skip zeros since abs(0) == 0\n x.forEach(function (value, index) {\n const j = index[1]\n const cj = add(c[j] || 0, abs(value))\n if (larger(cj, maxc)) {\n maxc = cj\n }\n c[j] = cj\n }, true)\n return maxc\n }\n\n /**\n * Calculate the norm L2 for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormTwo (x) {\n // norm(x) = sqrt( max eigenvalue of A*.A)\n const sizeX = x.size()\n if (sizeX[0] !== sizeX[1]) {\n throw new RangeError('Invalid matrix dimensions')\n }\n const tx = ctranspose(x)\n const squaredX = multiply(tx, x)\n const eigenVals = eigs(squaredX).values\n const rho = eigenVals.get([eigenVals.size()[0] - 1])\n return abs(sqrt(rho))\n }\n\n /**\n * Calculate the infinity norm for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormInfinity (x) {\n // norm(x) = the largest row sum\n const r = []\n // result\n let maxr = 0\n // skip zeros since abs(0) == 0\n x.forEach(function (value, index) {\n const i = index[0]\n const ri = add(r[i] || 0, abs(value))\n if (larger(ri, maxr)) {\n maxr = ri\n }\n r[i] = ri\n }, true)\n return maxr\n }\n\n /**\n * Calculate the norm for a 2D Matrix (M*N)\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNorm (x, p) {\n // check p\n if (p === 1) {\n return _matrixNormOne(x)\n }\n if (p === Number.POSITIVE_INFINITY || p === 'inf') {\n return _matrixNormInfinity(x)\n }\n if (p === 'fro') {\n return _matrixNormFrobenius(x)\n }\n if (p === 2) {\n return _matrixNormTwo(x)\n } // invalid parameter value\n\n throw new Error('Unsupported parameter value ' + p)\n }\n\n /**\n * Calculate the norm for an array\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _norm (x, p) {\n // size\n const sizeX = x.size()\n\n // check if it is a vector\n if (sizeX.length === 1) {\n return _vectorNorm(x, p)\n }\n // MxN matrix\n if (sizeX.length === 2) {\n if (sizeX[0] && sizeX[1]) {\n return _matrixNorm(x, p)\n } else {\n throw new RangeError('Invalid matrix dimensions')\n }\n }\n }\n }\n)\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'dot'\nconst dependencies = ['typed', 'addScalar', 'multiplyScalar', 'conj', 'size']\n\nexport const createDot = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, multiplyScalar, conj, size }) => {\n /**\n * Calculate the dot product of two vectors. The dot product of\n * `A = [a1, a2, ..., an]` and `B = [b1, b2, ..., bn]` is defined as:\n *\n * dot(A, B) = conj(a1) * b1 + conj(a2) * b2 + ... + conj(an) * bn\n *\n * Syntax:\n *\n * math.dot(x, y)\n *\n * Examples:\n *\n * math.dot([2, 4, 1], [2, 2, 3]) // returns number 15\n * math.multiply([2, 4, 1], [2, 2, 3]) // returns number 15\n *\n * See also:\n *\n * multiply, cross\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {number} Returns the dot product of `x` and `y`\n */\n return typed(name, {\n 'Array | DenseMatrix, Array | DenseMatrix': _denseDot,\n 'SparseMatrix, SparseMatrix': _sparseDot\n })\n\n function _validateDim (x, y) {\n const xSize = _size(x)\n const ySize = _size(y)\n let xLen, yLen\n\n if (xSize.length === 1) {\n xLen = xSize[0]\n } else if (xSize.length === 2 && xSize[1] === 1) {\n xLen = xSize[0]\n } else {\n throw new RangeError('Expected a column vector, instead got a matrix of size (' + xSize.join(', ') + ')')\n }\n\n if (ySize.length === 1) {\n yLen = ySize[0]\n } else if (ySize.length === 2 && ySize[1] === 1) {\n yLen = ySize[0]\n } else {\n throw new RangeError('Expected a column vector, instead got a matrix of size (' + ySize.join(', ') + ')')\n }\n\n if (xLen !== yLen) throw new RangeError('Vectors must have equal length (' + xLen + ' != ' + yLen + ')')\n if (xLen === 0) throw new RangeError('Cannot calculate the dot product of empty vectors')\n\n return xLen\n }\n\n function _denseDot (a, b) {\n const N = _validateDim(a, b)\n\n const adata = isMatrix(a) ? a._data : a\n const adt = isMatrix(a) ? a._datatype : undefined\n\n const bdata = isMatrix(b) ? b._data : b\n const bdt = isMatrix(b) ? b._datatype : undefined\n\n // are these 2-dimensional column vectors? (as opposed to 1-dimensional vectors)\n const aIsColumn = _size(a).length === 2\n const bIsColumn = _size(b).length === 2\n\n let add = addScalar\n let mul = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n const dt = adt\n // find signatures that matches (dt, dt)\n add = typed.find(addScalar, [dt, dt])\n mul = typed.find(multiplyScalar, [dt, dt])\n }\n\n // both vectors 1-dimensional\n if (!aIsColumn && !bIsColumn) {\n let c = mul(conj(adata[0]), bdata[0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i]), bdata[i]))\n }\n return c\n }\n\n // a is 1-dim, b is column\n if (!aIsColumn && bIsColumn) {\n let c = mul(conj(adata[0]), bdata[0][0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i]), bdata[i][0]))\n }\n return c\n }\n\n // a is column, b is 1-dim\n if (aIsColumn && !bIsColumn) {\n let c = mul(conj(adata[0][0]), bdata[0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i][0]), bdata[i]))\n }\n return c\n }\n\n // both vectors are column\n if (aIsColumn && bIsColumn) {\n let c = mul(conj(adata[0][0]), bdata[0][0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i][0]), bdata[i][0]))\n }\n return c\n }\n }\n\n function _sparseDot (x, y) {\n _validateDim(x, y)\n\n const xindex = x._index\n const xvalues = x._values\n\n const yindex = y._index\n const yvalues = y._values\n\n // TODO optimize add & mul using datatype\n let c = 0\n const add = addScalar\n const mul = multiplyScalar\n\n let i = 0\n let j = 0\n while (i < xindex.length && j < yindex.length) {\n const I = xindex[i]\n const J = yindex[j]\n\n if (I < J) {\n i++\n continue\n }\n if (I > J) {\n j++\n continue\n }\n if (I === J) {\n c = add(c, mul(xvalues[i], yvalues[j]))\n i++\n j++\n }\n }\n\n return c\n }\n\n // TODO remove this once #1771 is fixed\n function _size (x) {\n return isMatrix(x) ? x.size() : size(x)\n }\n})\n","import { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'trace'\nconst dependencies = ['typed', 'matrix', 'add']\n\nexport const createTrace = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, add }) => {\n /**\n * Calculate the trace of a matrix: the sum of the elements on the main\n * diagonal of a square matrix.\n *\n * Syntax:\n *\n * math.trace(x)\n *\n * Examples:\n *\n * math.trace([[1, 2], [3, 4]]) // returns 5\n *\n * const A = [\n * [1, 2, 3],\n * [-1, 2, 3],\n * [2, 0, 3]\n * ]\n * math.trace(A) // returns 6\n *\n * See also:\n *\n * diag\n *\n * @param {Array | Matrix} x A matrix\n *\n * @return {number} The trace of `x`\n */\n return typed('trace', {\n Array: function _arrayTrace (x) {\n // use dense matrix implementation\n return _denseTrace(matrix(x))\n },\n\n SparseMatrix: _sparseTrace,\n\n DenseMatrix: _denseTrace,\n\n any: clone\n })\n\n function _denseTrace (m) {\n // matrix size & data\n const size = m._size\n const data = m._data\n\n // process dimensions\n switch (size.length) {\n case 1:\n // vector\n if (size[0] === 1) {\n // return data[0]\n return clone(data[0])\n }\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n case 2:\n {\n // two dimensional\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n // calulate sum\n let sum = 0\n // loop diagonal\n for (let i = 0; i < rows; i++) { sum = add(sum, data[i][i]) }\n // return trace\n return sum\n } else {\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n }\n }\n default:\n // multi dimensional\n throw new RangeError('Matrix must be two dimensional (size: ' + format(size) + ')')\n }\n }\n\n function _sparseTrace (m) {\n // matrix arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n const size = m._size\n // check dimensions\n const rows = size[0]\n const columns = size[1]\n // matrix must be square\n if (rows === columns) {\n // calulate sum\n let sum = 0\n // check we have data (avoid looping columns)\n if (values.length > 0) {\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = index[k]\n // check row\n if (i === j) {\n // accumulate value\n sum = add(sum, values[k])\n // exit loop\n break\n }\n if (i > j) {\n // exit loop, no value on the diagonal for column j\n break\n }\n }\n }\n }\n // return trace\n return sum\n }\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { isBigNumber, isMatrix } from '../../../utils/is.js'\n\nconst name = 'index'\nconst dependencies = ['typed', 'Index']\n\nexport const createIndex = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index }) => {\n /**\n * Create an index. An Index can store ranges having start, step, and end\n * for multiple dimensions.\n * Matrix.get, Matrix.set, and math.subset accept an Index as input.\n *\n * Syntax:\n *\n * math.index(range1, range2, ...)\n *\n * Where each range can be any of:\n *\n * - A number\n * - A string for getting/setting an object property\n * - An instance of `Range`\n * - A one-dimensional Array or a Matrix with numbers\n *\n * Indexes must be zero-based, integer numbers.\n *\n * Examples:\n *\n * const b = [1, 2, 3, 4, 5]\n * math.subset(b, math.index([1, 2, 3])) // returns [2, 3, 4]\n *\n * const a = math.matrix([[1, 2], [3, 4]])\n * a.subset(math.index(0, 1)) // returns 2\n *\n * See also:\n *\n * bignumber, boolean, complex, matrix, number, string, unit\n *\n * @param {...*} ranges Zero or more ranges or numbers.\n * @return {Index} Returns the created index\n */\n return typed(name, {\n '...number | string | BigNumber | Range | Array | Matrix': function (args) {\n const ranges = args.map(function (arg) {\n if (isBigNumber(arg)) {\n return arg.toNumber() // convert BigNumber to Number\n } else if (Array.isArray(arg) || isMatrix(arg)) {\n return arg.map(function (elem) {\n // convert BigNumber to Number\n return isBigNumber(elem) ? elem.toNumber() : elem\n })\n } else {\n return arg\n }\n })\n\n const res = new Index()\n Index.apply(res, ranges)\n return res\n }\n })\n})\n","// Reserved keywords not allowed to use in the parser\nexport const keywords = {\n end: true\n}\n","import { isNode } from '../../utils/is.js'\n\nimport { keywords } from '../keywords.js'\nimport { deepStrictEqual, hasOwnProperty } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Node'\nconst dependencies = ['mathWithTransform']\n\nexport const createNode = /* #__PURE__ */ factory(name, dependencies, ({ mathWithTransform }) => {\n /**\n * Node\n */\n function Node () {\n if (!(this instanceof Node)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n }\n\n /**\n * Evaluate the node\n * @param {Object} [scope] Scope to read/write variables\n * @return {*} Returns the result\n */\n Node.prototype.evaluate = function (scope) {\n return this.compile().evaluate(scope)\n }\n\n Node.prototype.type = 'Node'\n\n Node.prototype.isNode = true\n\n Node.prototype.comment = ''\n\n /**\n * Compile the node into an optimized, evauatable JavaScript function\n * @return {{evaluate: function([Object])}} object\n * Returns an object with a function 'evaluate',\n * which can be invoked as expr.evaluate([scope: Object]),\n * where scope is an optional object with\n * variables.\n */\n Node.prototype.compile = function () {\n const expr = this._compile(mathWithTransform, {})\n const args = {}\n const context = null\n\n function evaluate (scope) {\n const s = scope || {}\n _validateScope(s)\n return expr(s, args, context)\n }\n\n return {\n evaluate\n }\n }\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n Node.prototype._compile = function (math, argNames) {\n throw new Error('Method _compile should be implemented by type ' + this.type)\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n Node.prototype.forEach = function (callback) {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot run forEach on a Node interface')\n }\n\n /**\n * Create a new Node having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {OperatorNode} Returns a transformed copy of the node\n */\n Node.prototype.map = function (callback) {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot run map on a Node interface')\n }\n\n /**\n * Validate whether an object is a Node, for use with map\n * @param {Node} node\n * @returns {Node} Returns the input if it's a node, else throws an Error\n * @protected\n */\n Node.prototype._ifNode = function (node) {\n if (!isNode(node)) {\n throw new TypeError('Callback function must return a Node')\n }\n\n return node\n }\n\n /**\n * Recursively traverse all nodes in a node tree. Executes given callback for\n * this node and each of its child nodes.\n * @param {function(node: Node, path: string, parent: Node)} callback\n * A callback called for every node in the node tree.\n */\n Node.prototype.traverse = function (callback) {\n // execute callback for itself\n // eslint-disable-next-line\n callback(this, null, null)\n\n // recursively traverse over all childs of a node\n function _traverse (node, callback) {\n node.forEach(function (child, path, parent) {\n callback(child, path, parent)\n _traverse(child, callback)\n })\n }\n\n _traverse(this, callback)\n }\n\n /**\n * Recursively transform a node tree via a transform function.\n *\n * For example, to replace all nodes of type SymbolNode having name 'x' with a\n * ConstantNode with value 2:\n *\n * const res = Node.transform(function (node, path, parent) {\n * if (node && node.isSymbolNode) && (node.name === 'x')) {\n * return new ConstantNode(2)\n * }\n * else {\n * return node\n * }\n * })\n *\n * @param {function(node: Node, path: string, parent: Node) : Node} callback\n * A mapping function accepting a node, and returning\n * a replacement for the node or the original node.\n * Signature: callback(node: Node, index: string, parent: Node) : Node\n * @return {Node} Returns the original node or its replacement\n */\n Node.prototype.transform = function (callback) {\n function _transform (child, path, parent) {\n const replacement = callback(child, path, parent)\n\n if (replacement !== child) {\n // stop iterating when the node is replaced\n return replacement\n }\n\n return child.map(_transform)\n }\n\n return _transform(this, null, null)\n }\n\n /**\n * Find any node in the node tree matching given filter function. For example, to\n * find all nodes of type SymbolNode having name 'x':\n *\n * const results = Node.filter(function (node) {\n * return (node && node.isSymbolNode) && (node.name === 'x')\n * })\n *\n * @param {function(node: Node, path: string, parent: Node) : Node} callback\n * A test function returning true when a node matches, and false\n * otherwise. Function signature:\n * callback(node: Node, index: string, parent: Node) : boolean\n * @return {Node[]} nodes An array with nodes matching given filter criteria\n */\n Node.prototype.filter = function (callback) {\n const nodes = []\n\n this.traverse(function (node, path, parent) {\n if (callback(node, path, parent)) {\n nodes.push(node)\n }\n })\n\n return nodes\n }\n\n /**\n * Create a shallow clone of this node\n * @return {Node}\n */\n Node.prototype.clone = function () {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot clone a Node interface')\n }\n\n /**\n * Create a deep clone of this node\n * @return {Node}\n */\n Node.prototype.cloneDeep = function () {\n return this.map(function (node) {\n return node.cloneDeep()\n })\n }\n\n /**\n * Deep compare this node with another node.\n * @param {Node} other\n * @return {boolean} Returns true when both nodes are of the same type and\n * contain the same values (as do their childs)\n */\n Node.prototype.equals = function (other) {\n return other\n ? deepStrictEqual(this, other)\n : false\n }\n\n /**\n * Get string representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\"or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toString = function (options) {\n let customString\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customString = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n return this._toString(options)\n }\n\n /**\n * Get a JSON representation of the node\n * Both .toJSON() and the static .fromJSON(json) should be implemented by all\n * implementations of Node\n * @returns {Object}\n */\n Node.prototype.toJSON = function () {\n throw new Error('Cannot serialize object: toJSON not implemented by ' + this.type)\n }\n\n /**\n * Get HTML representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\" or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toHTML = function (options) {\n let customString\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customString = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n return this.toHTML(options)\n }\n\n /**\n * Internal function to generate the string output.\n * This has to be implemented by every Node\n *\n * @throws {Error}\n */\n Node.prototype._toString = function () {\n // must be implemented by each of the Node implementations\n throw new Error('_toString not implemented for ' + this.type)\n }\n\n /**\n * Get LaTeX representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\"or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toTex = function (options) {\n let customTex\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customTex = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customTex !== 'undefined') {\n return customTex\n }\n\n return this._toTex(options)\n }\n\n /**\n * Internal function to generate the LaTeX output.\n * This has to be implemented by every Node\n *\n * @param {Object} [options]\n * @throws {Error}\n */\n Node.prototype._toTex = function (options) {\n // must be implemented by each of the Node implementations\n throw new Error('_toTex not implemented for ' + this.type)\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n Node.prototype.getIdentifier = function () {\n return this.type\n }\n\n /**\n * Get the content of the current Node.\n * @return {Node} node\n **/\n Node.prototype.getContent = function () {\n return this\n }\n\n /**\n * Validate the symbol names of a scope.\n * Throws an error when the scope contains an illegal symbol.\n * @param {Object} scope\n */\n function _validateScope (scope) {\n for (const symbol in scope) {\n if (hasOwnProperty(scope, symbol)) {\n if (symbol in keywords) {\n throw new Error('Scope contains an illegal symbol, \"' + symbol + '\" is a reserved keyword')\n }\n }\n }\n }\n\n return Node\n}, { isClass: true, isNode: true })\n","import { IndexError } from '../../../error/IndexError.js'\n\n/**\n * Transform zero-based indices to one-based indices in errors\n * @param {Error} err\n * @returns {Error | IndexError} Returns the transformed error\n */\nexport function errorTransform (err) {\n if (err && err.isIndexError) {\n return new IndexError(\n err.index + 1,\n err.min + 1,\n err.max !== undefined ? err.max + 1 : undefined)\n }\n\n return err\n}\n","import { errorTransform } from '../../transform/utils/errorTransform.js'\nimport { getSafeProperty } from '../../../utils/customs.js'\n\nexport function accessFactory ({ subset }) {\n /**\n * Retrieve part of an object:\n *\n * - Retrieve a property from an object\n * - Retrieve a part of a string\n * - Retrieve a matrix subset\n *\n * @param {Object | Array | Matrix | string} object\n * @param {Index} index\n * @return {Object | Array | Matrix | string} Returns the subset\n */\n return function access (object, index) {\n try {\n if (Array.isArray(object)) {\n return subset(object, index)\n } else if (object && typeof object.subset === 'function') { // Matrix\n return object.subset(index)\n } else if (typeof object === 'string') {\n // TODO: move getStringSubset into a separate util file, use that\n return subset(object, index)\n } else if (typeof object === 'object') {\n if (!index.isObjectProperty()) {\n throw new TypeError('Cannot apply a numeric index as object property')\n }\n\n return getSafeProperty(object, index.getObjectProperty())\n } else {\n throw new TypeError('Cannot apply index: unsupported type of object')\n }\n } catch (err) {\n throw errorTransform(err)\n }\n }\n}\n","import {\n isAccessorNode,\n isArrayNode,\n isConstantNode,\n isFunctionNode,\n isIndexNode,\n isNode,\n isObjectNode,\n isParenthesisNode,\n isSymbolNode\n} from '../../utils/is.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { accessFactory } from './utils/access.js'\n\nconst name = 'AccessorNode'\nconst dependencies = [\n 'subset',\n 'Node'\n]\n\nexport const createAccessorNode = /* #__PURE__ */ factory(name, dependencies, ({ subset, Node }) => {\n const access = accessFactory({ subset })\n\n /**\n * @constructor AccessorNode\n * @extends {Node}\n * Access an object property or get a matrix subset\n *\n * @param {Node} object The object from which to retrieve\n * a property or subset.\n * @param {IndexNode} index IndexNode containing ranges\n */\n function AccessorNode (object, index) {\n if (!(this instanceof AccessorNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (!isNode(object)) {\n throw new TypeError('Node expected for parameter \"object\"')\n }\n if (!isIndexNode(index)) {\n throw new TypeError('IndexNode expected for parameter \"index\"')\n }\n\n this.object = object || null\n this.index = index\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n if (this.index) {\n return (this.index.isObjectProperty())\n ? this.index.getObjectProperty()\n : ''\n } else {\n return this.object.name || ''\n }\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n AccessorNode.prototype = new Node()\n\n AccessorNode.prototype.type = 'AccessorNode'\n\n AccessorNode.prototype.isAccessorNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n AccessorNode.prototype._compile = function (math, argNames) {\n const evalObject = this.object._compile(math, argNames)\n const evalIndex = this.index._compile(math, argNames)\n\n if (this.index.isObjectProperty()) {\n const prop = this.index.getObjectProperty()\n return function evalAccessorNode (scope, args, context) {\n return getSafeProperty(evalObject(scope, args, context), prop)\n }\n } else {\n return function evalAccessorNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n const index = evalIndex(scope, args, object) // we pass object here instead of context\n return access(object, index)\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n AccessorNode.prototype.forEach = function (callback) {\n callback(this.object, 'object', this)\n callback(this.index, 'index', this)\n }\n\n /**\n * Create a new AccessorNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {AccessorNode} Returns a transformed copy of the node\n */\n AccessorNode.prototype.map = function (callback) {\n return new AccessorNode(\n this._ifNode(callback(this.object, 'object', this)),\n this._ifNode(callback(this.index, 'index', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {AccessorNode}\n */\n AccessorNode.prototype.clone = function () {\n return new AccessorNode(this.object, this.index)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype._toString = function (options) {\n let object = this.object.toString(options)\n if (needParenthesis(this.object)) {\n object = '(' + object + ')'\n }\n\n return object + this.index.toString(options)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype.toHTML = function (options) {\n let object = this.object.toHTML(options)\n if (needParenthesis(this.object)) {\n object = '(' + object + ')'\n }\n\n return object + this.index.toHTML(options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype._toTex = function (options) {\n let object = this.object.toTex(options)\n if (needParenthesis(this.object)) {\n object = '\\\\left(\\' + object + \\'\\\\right)'\n }\n\n return object + this.index.toTex(options)\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n AccessorNode.prototype.toJSON = function () {\n return {\n mathjs: 'AccessorNode',\n object: this.object,\n index: this.index\n }\n }\n\n /**\n * Instantiate an AccessorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"AccessorNode\", object: ..., index: ...}`,\n * where mathjs is optional\n * @returns {AccessorNode}\n */\n AccessorNode.fromJSON = function (json) {\n return new AccessorNode(json.object, json.index)\n }\n\n /**\n * Are parenthesis needed?\n * @private\n */\n function needParenthesis (node) {\n // TODO: maybe make a method on the nodes which tells whether they need parenthesis?\n return !(\n isAccessorNode(node) ||\n isArrayNode(node) ||\n isConstantNode(node) ||\n isFunctionNode(node) ||\n isObjectNode(node) ||\n isParenthesisNode(node) ||\n isSymbolNode(node))\n }\n\n return AccessorNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ArrayNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createArrayNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ArrayNode\n * @extends {Node}\n * Holds an 1-dimensional array with items\n * @param {Node[]} [items] 1 dimensional array with items\n */\n function ArrayNode (items) {\n if (!(this instanceof ArrayNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.items = items || []\n\n // validate input\n if (!Array.isArray(this.items) || !this.items.every(isNode)) {\n throw new TypeError('Array containing Nodes expected')\n }\n }\n\n ArrayNode.prototype = new Node()\n\n ArrayNode.prototype.type = 'ArrayNode'\n\n ArrayNode.prototype.isArrayNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ArrayNode.prototype._compile = function (math, argNames) {\n const evalItems = map(this.items, function (item) {\n return item._compile(math, argNames)\n })\n\n const asMatrix = (math.config.matrix !== 'Array')\n if (asMatrix) {\n const matrix = math.matrix\n return function evalArrayNode (scope, args, context) {\n return matrix(map(evalItems, function (evalItem) {\n return evalItem(scope, args, context)\n }))\n }\n } else {\n return function evalArrayNode (scope, args, context) {\n return map(evalItems, function (evalItem) {\n return evalItem(scope, args, context)\n })\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ArrayNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.items.length; i++) {\n const node = this.items[i]\n callback(node, 'items[' + i + ']', this)\n }\n }\n\n /**\n * Create a new ArrayNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ArrayNode} Returns a transformed copy of the node\n */\n ArrayNode.prototype.map = function (callback) {\n const items = []\n for (let i = 0; i < this.items.length; i++) {\n items[i] = this._ifNode(callback(this.items[i], 'items[' + i + ']', this))\n }\n return new ArrayNode(items)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ArrayNode}\n */\n ArrayNode.prototype.clone = function () {\n return new ArrayNode(this.items.slice(0))\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ArrayNode.prototype._toString = function (options) {\n const items = this.items.map(function (node) {\n return node.toString(options)\n })\n return '[' + items.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ArrayNode.prototype.toJSON = function () {\n return {\n mathjs: 'ArrayNode',\n items: this.items\n }\n }\n\n /**\n * Instantiate an ArrayNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ArrayNode\", items: [...]}`,\n * where mathjs is optional\n * @returns {ArrayNode}\n */\n ArrayNode.fromJSON = function (json) {\n return new ArrayNode(json.items)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ArrayNode.prototype.toHTML = function (options) {\n const items = this.items.map(function (node) {\n return node.toHTML(options)\n })\n return '[' + items.join(',') + ']'\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ArrayNode.prototype._toTex = function (options) {\n let s = '\\\\begin{bmatrix}'\n\n this.items.forEach(function (node) {\n if (node.items) {\n s += node.items.map(function (childNode) {\n return childNode.toTex(options)\n }).join('&')\n } else {\n s += node.toTex(options)\n }\n\n // new line\n s += '\\\\\\\\'\n })\n s += '\\\\end{bmatrix}'\n return s\n }\n\n return ArrayNode\n}, { isClass: true, isNode: true })\n","// list of identifiers of nodes in order of their precedence\n// also contains information about left/right associativity\n// and which other operator the operator is associative with\n// Example:\n// addition is associative with addition and subtraction, because:\n// (a+b)+c=a+(b+c)\n// (a+b)-c=a+(b-c)\n//\n// postfix operators are left associative, prefix operators\n// are right associative\n//\n// It's also possible to set the following properties:\n// latexParens: if set to false, this node doesn't need to be enclosed\n// in parentheses when using LaTeX\n// latexLeftParens: if set to false, this !OperatorNode's!\n// left argument doesn't need to be enclosed\n// in parentheses\n// latexRightParens: the same for the right argument\nimport { hasOwnProperty } from '../utils/object.js'\n\nexport const properties = [\n { // assignment\n AssignmentNode: {},\n FunctionAssignmentNode: {}\n },\n { // conditional expression\n ConditionalNode: {\n latexLeftParens: false,\n latexRightParens: false,\n latexParens: false\n // conditionals don't need parentheses in LaTeX because\n // they are 2 dimensional\n }\n },\n { // logical or\n 'OperatorNode:or': {\n associativity: 'left',\n associativeWith: []\n }\n\n },\n { // logical xor\n 'OperatorNode:xor': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // logical and\n 'OperatorNode:and': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise or\n 'OperatorNode:bitOr': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise xor\n 'OperatorNode:bitXor': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise and\n 'OperatorNode:bitAnd': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // relational operators\n 'OperatorNode:equal': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:unequal': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:smaller': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:larger': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:smallerEq': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:largerEq': {\n associativity: 'left',\n associativeWith: []\n },\n RelationalNode: {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitshift operators\n 'OperatorNode:leftShift': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:rightArithShift': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:rightLogShift': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // unit conversion\n 'OperatorNode:to': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // range\n RangeNode: {}\n },\n { // addition, subtraction\n 'OperatorNode:add': {\n associativity: 'left',\n associativeWith: ['OperatorNode:add', 'OperatorNode:subtract']\n },\n 'OperatorNode:subtract': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // multiply, divide, modulus\n 'OperatorNode:multiply': {\n associativity: 'left',\n associativeWith: [\n 'OperatorNode:multiply',\n 'OperatorNode:divide',\n 'Operator:dotMultiply',\n 'Operator:dotDivide'\n ]\n },\n 'OperatorNode:divide': {\n associativity: 'left',\n associativeWith: [],\n latexLeftParens: false,\n latexRightParens: false,\n latexParens: false\n // fractions don't require parentheses because\n // they're 2 dimensional, so parens aren't needed\n // in LaTeX\n },\n 'OperatorNode:dotMultiply': {\n associativity: 'left',\n associativeWith: [\n 'OperatorNode:multiply',\n 'OperatorNode:divide',\n 'OperatorNode:dotMultiply',\n 'OperatorNode:doDivide'\n ]\n },\n 'OperatorNode:dotDivide': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:mod': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // unary prefix operators\n 'OperatorNode:unaryPlus': {\n associativity: 'right'\n },\n 'OperatorNode:unaryMinus': {\n associativity: 'right'\n },\n 'OperatorNode:bitNot': {\n associativity: 'right'\n },\n 'OperatorNode:not': {\n associativity: 'right'\n }\n },\n { // exponentiation\n 'OperatorNode:pow': {\n associativity: 'right',\n associativeWith: [],\n latexRightParens: false\n // the exponent doesn't need parentheses in\n // LaTeX because it's 2 dimensional\n // (it's on top)\n },\n 'OperatorNode:dotPow': {\n associativity: 'right',\n associativeWith: []\n }\n },\n { // factorial\n 'OperatorNode:factorial': {\n associativity: 'left'\n }\n },\n { // matrix transpose\n 'OperatorNode:transpose': {\n associativity: 'left'\n }\n }\n]\n\n/**\n * Get the precedence of a Node.\n * Higher number for higher precedence, starting with 0.\n * Returns null if the precedence is undefined.\n *\n * @param {Node} _node\n * @param {string} parenthesis\n * @return {number | null}\n */\nexport function getPrecedence (_node, parenthesis) {\n let node = _node\n if (parenthesis !== 'keep') {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n node = _node.getContent()\n }\n const identifier = node.getIdentifier()\n for (let i = 0; i < properties.length; i++) {\n if (identifier in properties[i]) {\n return i\n }\n }\n return null\n}\n\n/**\n * Get the associativity of an operator (left or right).\n * Returns a string containing 'left' or 'right' or null if\n * the associativity is not defined.\n *\n * @param {Node} _node\n * @param {string} parenthesis\n * @return {string|null}\n * @throws {Error}\n */\nexport function getAssociativity (_node, parenthesis) {\n let node = _node\n if (parenthesis !== 'keep') {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n node = _node.getContent()\n }\n const identifier = node.getIdentifier()\n const index = getPrecedence(node, parenthesis)\n if (index === null) {\n // node isn't in the list\n return null\n }\n const property = properties[index][identifier]\n\n if (hasOwnProperty(property, 'associativity')) {\n if (property.associativity === 'left') {\n return 'left'\n }\n if (property.associativity === 'right') {\n return 'right'\n }\n // associativity is invalid\n throw Error('\\'' + identifier + '\\' has the invalid associativity \\'' +\n property.associativity + '\\'.')\n }\n\n // associativity is undefined\n return null\n}\n\n/**\n * Check if an operator is associative with another operator.\n * Returns either true or false or null if not defined.\n *\n * @param {Node} nodeA\n * @param {Node} nodeB\n * @param {string} parenthesis\n * @return {boolean | null}\n */\nexport function isAssociativeWith (nodeA, nodeB, parenthesis) {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n const a = (parenthesis !== 'keep') ? nodeA.getContent() : nodeA\n const b = (parenthesis !== 'keep') ? nodeA.getContent() : nodeB\n const identifierA = a.getIdentifier()\n const identifierB = b.getIdentifier()\n const index = getPrecedence(a, parenthesis)\n if (index === null) {\n // node isn't in the list\n return null\n }\n const property = properties[index][identifierA]\n\n if (hasOwnProperty(property, 'associativeWith') &&\n (property.associativeWith instanceof Array)) {\n for (let i = 0; i < property.associativeWith.length; i++) {\n if (property.associativeWith[i] === identifierB) {\n return true\n }\n }\n return false\n }\n\n // associativeWith is not defined\n return null\n}\n","import { isAccessorNode, isIndexNode, isNode, isSymbolNode } from '../../utils/is.js'\nimport { getSafeProperty, setSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { accessFactory } from './utils/access.js'\nimport { assignFactory } from './utils/assign.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'AssignmentNode'\nconst dependencies = [\n 'subset',\n '?matrix', // FIXME: should not be needed at all, should be handled by subset\n 'Node'\n]\n\nexport const createAssignmentNode = /* #__PURE__ */ factory(name, dependencies, ({ subset, matrix, Node }) => {\n const access = accessFactory({ subset })\n const assign = assignFactory({ subset, matrix })\n\n /**\n * @constructor AssignmentNode\n * @extends {Node}\n *\n * Define a symbol, like `a=3.2`, update a property like `a.b=3.2`, or\n * replace a subset of a matrix like `A[2,2]=42`.\n *\n * Syntax:\n *\n * new AssignmentNode(symbol, value)\n * new AssignmentNode(object, index, value)\n *\n * Usage:\n *\n * new AssignmentNode(new SymbolNode('a'), new ConstantNode(2)) // a=2\n * new AssignmentNode(new SymbolNode('a'), new IndexNode('b'), new ConstantNode(2)) // a.b=2\n * new AssignmentNode(new SymbolNode('a'), new IndexNode(1, 2), new ConstantNode(3)) // a[1,2]=3\n *\n * @param {SymbolNode | AccessorNode} object Object on which to assign a value\n * @param {IndexNode} [index=null] Index, property name or matrix\n * index. Optional. If not provided\n * and `object` is a SymbolNode,\n * the property is assigned to the\n * global scope.\n * @param {Node} value The value to be assigned\n */\n function AssignmentNode (object, index, value) {\n if (!(this instanceof AssignmentNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.object = object\n this.index = value ? index : null\n this.value = value || index\n\n // validate input\n if (!isSymbolNode(object) && !isAccessorNode(object)) {\n throw new TypeError('SymbolNode or AccessorNode expected as \"object\"')\n }\n if (isSymbolNode(object) && object.name === 'end') {\n throw new Error('Cannot assign to symbol \"end\"')\n }\n if (this.index && !isIndexNode(this.index)) { // index is optional\n throw new TypeError('IndexNode expected as \"index\"')\n }\n if (!isNode(this.value)) {\n throw new TypeError('Node expected as \"value\"')\n }\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n if (this.index) {\n return (this.index.isObjectProperty())\n ? this.index.getObjectProperty()\n : ''\n } else {\n return this.object.name || ''\n }\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n AssignmentNode.prototype = new Node()\n\n AssignmentNode.prototype.type = 'AssignmentNode'\n\n AssignmentNode.prototype.isAssignmentNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n AssignmentNode.prototype._compile = function (math, argNames) {\n const evalObject = this.object._compile(math, argNames)\n const evalIndex = this.index ? this.index._compile(math, argNames) : null\n const evalValue = this.value._compile(math, argNames)\n const name = this.object.name\n\n if (!this.index) {\n // apply a variable to the scope, for example `a=2`\n if (!isSymbolNode(this.object)) {\n throw new TypeError('SymbolNode expected as object')\n }\n\n return function evalAssignmentNode (scope, args, context) {\n return setSafeProperty(scope, name, evalValue(scope, args, context))\n }\n } else if (this.index.isObjectProperty()) {\n // apply an object property for example `a.b=2`\n const prop = this.index.getObjectProperty()\n\n return function evalAssignmentNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n const value = evalValue(scope, args, context)\n return setSafeProperty(object, prop, value)\n }\n } else if (isSymbolNode(this.object)) {\n // update a matrix subset, for example `a[2]=3`\n return function evalAssignmentNode (scope, args, context) {\n const childObject = evalObject(scope, args, context)\n const value = evalValue(scope, args, context)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n setSafeProperty(scope, name, assign(childObject, index, value))\n return value\n }\n } else { // isAccessorNode(node.object) === true\n // update a matrix subset, for example `a.b[2]=3`\n\n // we will not use the compile function of the AccessorNode, but compile it\n // ourselves here as we need the parent object of the AccessorNode:\n // wee need to apply the updated object to parent object\n const evalParentObject = this.object.object._compile(math, argNames)\n\n if (this.object.index.isObjectProperty()) {\n const parentProp = this.object.index.getObjectProperty()\n\n return function evalAssignmentNode (scope, args, context) {\n const parent = evalParentObject(scope, args, context)\n const childObject = getSafeProperty(parent, parentProp)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n const value = evalValue(scope, args, context)\n setSafeProperty(parent, parentProp, assign(childObject, index, value))\n return value\n }\n } else {\n // if some parameters use the 'end' parameter, we need to calculate the size\n const evalParentIndex = this.object.index._compile(math, argNames)\n\n return function evalAssignmentNode (scope, args, context) {\n const parent = evalParentObject(scope, args, context)\n const parentIndex = evalParentIndex(scope, args, parent) // Important: we pass parent instead of context\n const childObject = access(parent, parentIndex)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n const value = evalValue(scope, args, context)\n\n assign(parent, parentIndex, assign(childObject, index, value))\n\n return value\n }\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n AssignmentNode.prototype.forEach = function (callback) {\n callback(this.object, 'object', this)\n if (this.index) {\n callback(this.index, 'index', this)\n }\n callback(this.value, 'value', this)\n }\n\n /**\n * Create a new AssignmentNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {AssignmentNode} Returns a transformed copy of the node\n */\n AssignmentNode.prototype.map = function (callback) {\n const object = this._ifNode(callback(this.object, 'object', this))\n const index = this.index\n ? this._ifNode(callback(this.index, 'index', this))\n : null\n const value = this._ifNode(callback(this.value, 'value', this))\n\n return new AssignmentNode(object, index, value)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {AssignmentNode}\n */\n AssignmentNode.prototype.clone = function () {\n return new AssignmentNode(this.object, this.index, this.value)\n }\n\n /*\n * Is parenthesis needed?\n * @param {node} node\n * @param {string} [parenthesis='keep']\n * @private\n */\n function needParenthesis (node, parenthesis) {\n if (!parenthesis) {\n parenthesis = 'keep'\n }\n\n const precedence = getPrecedence(node, parenthesis)\n const exprPrecedence = getPrecedence(node.value, parenthesis)\n return (parenthesis === 'all') ||\n ((exprPrecedence !== null) && (exprPrecedence <= precedence))\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype._toString = function (options) {\n const object = this.object.toString(options)\n const index = this.index ? this.index.toString(options) : ''\n let value = this.value.toString(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = '(' + value + ')'\n }\n\n return object + index + ' = ' + value\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n AssignmentNode.prototype.toJSON = function () {\n return {\n mathjs: 'AssignmentNode',\n object: this.object,\n index: this.index,\n value: this.value\n }\n }\n\n /**\n * Instantiate an AssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"AssignmentNode\", object: ..., index: ..., value: ...}`,\n * where mathjs is optional\n * @returns {AssignmentNode}\n */\n AssignmentNode.fromJSON = function (json) {\n return new AssignmentNode(json.object, json.index, json.value)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype.toHTML = function (options) {\n const object = this.object.toHTML(options)\n const index = this.index ? this.index.toHTML(options) : ''\n let value = this.value.toHTML(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = '(' + value + ')'\n }\n\n return object + index + '=' + value\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype._toTex = function (options) {\n const object = this.object.toTex(options)\n const index = this.index ? this.index.toTex(options) : ''\n let value = this.value.toTex(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = `\\\\left(${value}\\\\right)`\n }\n\n return object + index + ':=' + value\n }\n\n return AssignmentNode\n}, { isClass: true, isNode: true })\n","import { errorTransform } from '../../transform/utils/errorTransform.js'\nimport { setSafeProperty } from '../../../utils/customs.js'\n\nexport function assignFactory ({ subset, matrix }) {\n /**\n * Replace part of an object:\n *\n * - Assign a property to an object\n * - Replace a part of a string\n * - Replace a matrix subset\n *\n * @param {Object | Array | Matrix | string} object\n * @param {Index} index\n * @param {*} value\n * @return {Object | Array | Matrix | string} Returns the original object\n * except in case of a string\n */\n // TODO: change assign to return the value instead of the object\n return function assign (object, index, value) {\n try {\n if (Array.isArray(object)) {\n // we use matrix.subset here instead of the function subset because we must not clone the contents\n return matrix(object).subset(index, value).valueOf()\n } else if (object && typeof object.subset === 'function') { // Matrix\n return object.subset(index, value)\n } else if (typeof object === 'string') {\n // TODO: move setStringSubset into a separate util file, use that\n return subset(object, index, value)\n } else if (typeof object === 'object') {\n if (!index.isObjectProperty()) {\n throw TypeError('Cannot apply a numeric index as object property')\n }\n setSafeProperty(object, index.getObjectProperty(), value)\n return object\n } else {\n throw new TypeError('Cannot apply index: unsupported type of object')\n }\n } catch (err) {\n throw errorTransform(err)\n }\n }\n}\n","import { isNode } from '../../utils/is.js'\nimport { forEach, map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'BlockNode'\nconst dependencies = [\n 'ResultSet',\n 'Node'\n]\n\nexport const createBlockNode = /* #__PURE__ */ factory(name, dependencies, ({ ResultSet, Node }) => {\n /**\n * @constructor BlockNode\n * @extends {Node}\n * Holds a set with blocks\n * @param {Array.<{node: Node} | {node: Node, visible: boolean}>} blocks\n * An array with blocks, where a block is constructed as an Object\n * with properties block, which is a Node, and visible, which is\n * a boolean. The property visible is optional and is true by default\n */\n function BlockNode (blocks) {\n if (!(this instanceof BlockNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input, copy blocks\n if (!Array.isArray(blocks)) throw new Error('Array expected')\n this.blocks = blocks.map(function (block) {\n const node = block && block.node\n const visible = block && block.visible !== undefined ? block.visible : true\n\n if (!isNode(node)) throw new TypeError('Property \"node\" must be a Node')\n if (typeof visible !== 'boolean') throw new TypeError('Property \"visible\" must be a boolean')\n\n return {\n node: node,\n visible: visible\n }\n })\n }\n\n BlockNode.prototype = new Node()\n\n BlockNode.prototype.type = 'BlockNode'\n\n BlockNode.prototype.isBlockNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n BlockNode.prototype._compile = function (math, argNames) {\n const evalBlocks = map(this.blocks, function (block) {\n return {\n evaluate: block.node._compile(math, argNames),\n visible: block.visible\n }\n })\n\n return function evalBlockNodes (scope, args, context) {\n const results = []\n\n forEach(evalBlocks, function evalBlockNode (block) {\n const result = block.evaluate(scope, args, context)\n if (block.visible) {\n results.push(result)\n }\n })\n\n return new ResultSet(results)\n }\n }\n\n /**\n * Execute a callback for each of the child blocks of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n BlockNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.blocks.length; i++) {\n callback(this.blocks[i].node, 'blocks[' + i + '].node', this)\n }\n }\n\n /**\n * Create a new BlockNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {BlockNode} Returns a transformed copy of the node\n */\n BlockNode.prototype.map = function (callback) {\n const blocks = []\n for (let i = 0; i < this.blocks.length; i++) {\n const block = this.blocks[i]\n const node = this._ifNode(callback(block.node, 'blocks[' + i + '].node', this))\n blocks[i] = {\n node: node,\n visible: block.visible\n }\n }\n return new BlockNode(blocks)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {BlockNode}\n */\n BlockNode.prototype.clone = function () {\n const blocks = this.blocks.map(function (block) {\n return {\n node: block.node,\n visible: block.visible\n }\n })\n\n return new BlockNode(blocks)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n BlockNode.prototype._toString = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toString(options) + (param.visible ? '' : ';')\n }).join('\\n')\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n BlockNode.prototype.toJSON = function () {\n return {\n mathjs: 'BlockNode',\n blocks: this.blocks\n }\n }\n\n /**\n * Instantiate an BlockNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"BlockNode\", blocks: [{node: ..., visible: false}, ...]}`,\n * where mathjs is optional\n * @returns {BlockNode}\n */\n BlockNode.fromJSON = function (json) {\n return new BlockNode(json.blocks)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n BlockNode.prototype.toHTML = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toHTML(options) + (param.visible ? '' : ';')\n }).join('
')\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n BlockNode.prototype._toTex = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toTex(options) + (param.visible ? '' : ';')\n }).join('\\\\;\\\\;\\n')\n }\n\n return BlockNode\n}, { isClass: true, isNode: true })\n","import { isBigNumber, isComplex, isNode, isUnit, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'ConditionalNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createConditionalNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A lazy evaluating conditional operator: 'condition ? trueExpr : falseExpr'\n *\n * @param {Node} condition Condition, must result in a boolean\n * @param {Node} trueExpr Expression evaluated when condition is true\n * @param {Node} falseExpr Expression evaluated when condition is true\n *\n * @constructor ConditionalNode\n * @extends {Node}\n */\n function ConditionalNode (condition, trueExpr, falseExpr) {\n if (!(this instanceof ConditionalNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n if (!isNode(condition)) throw new TypeError('Parameter condition must be a Node')\n if (!isNode(trueExpr)) throw new TypeError('Parameter trueExpr must be a Node')\n if (!isNode(falseExpr)) throw new TypeError('Parameter falseExpr must be a Node')\n\n this.condition = condition\n this.trueExpr = trueExpr\n this.falseExpr = falseExpr\n }\n\n ConditionalNode.prototype = new Node()\n\n ConditionalNode.prototype.type = 'ConditionalNode'\n\n ConditionalNode.prototype.isConditionalNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ConditionalNode.prototype._compile = function (math, argNames) {\n const evalCondition = this.condition._compile(math, argNames)\n const evalTrueExpr = this.trueExpr._compile(math, argNames)\n const evalFalseExpr = this.falseExpr._compile(math, argNames)\n\n return function evalConditionalNode (scope, args, context) {\n return testCondition(evalCondition(scope, args, context))\n ? evalTrueExpr(scope, args, context)\n : evalFalseExpr(scope, args, context)\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ConditionalNode.prototype.forEach = function (callback) {\n callback(this.condition, 'condition', this)\n callback(this.trueExpr, 'trueExpr', this)\n callback(this.falseExpr, 'falseExpr', this)\n }\n\n /**\n * Create a new ConditionalNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ConditionalNode} Returns a transformed copy of the node\n */\n ConditionalNode.prototype.map = function (callback) {\n return new ConditionalNode(\n this._ifNode(callback(this.condition, 'condition', this)),\n this._ifNode(callback(this.trueExpr, 'trueExpr', this)),\n this._ifNode(callback(this.falseExpr, 'falseExpr', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ConditionalNode}\n */\n ConditionalNode.prototype.clone = function () {\n return new ConditionalNode(this.condition, this.trueExpr, this.falseExpr)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n // Enclose Arguments in parentheses if they are an OperatorNode\n // or have lower or equal precedence\n // NOTE: enclosing all OperatorNodes in parentheses is a decision\n // purely based on aesthetics and readability\n let condition = this.condition.toString(options)\n const conditionPrecedence = getPrecedence(this.condition, parenthesis)\n if ((parenthesis === 'all') ||\n (this.condition.type === 'OperatorNode') ||\n ((conditionPrecedence !== null) && (conditionPrecedence <= precedence))) {\n condition = '(' + condition + ')'\n }\n\n let trueExpr = this.trueExpr.toString(options)\n const truePrecedence = getPrecedence(this.trueExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.trueExpr.type === 'OperatorNode') ||\n ((truePrecedence !== null) && (truePrecedence <= precedence))) {\n trueExpr = '(' + trueExpr + ')'\n }\n\n let falseExpr = this.falseExpr.toString(options)\n const falsePrecedence = getPrecedence(this.falseExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.falseExpr.type === 'OperatorNode') ||\n ((falsePrecedence !== null) && (falsePrecedence <= precedence))) {\n falseExpr = '(' + falseExpr + ')'\n }\n return condition + ' ? ' + trueExpr + ' : ' + falseExpr\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ConditionalNode.prototype.toJSON = function () {\n return {\n mathjs: 'ConditionalNode',\n condition: this.condition,\n trueExpr: this.trueExpr,\n falseExpr: this.falseExpr\n }\n }\n\n /**\n * Instantiate an ConditionalNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ConditionalNode\", \"condition\": ..., \"trueExpr\": ..., \"falseExpr\": ...}`,\n * where mathjs is optional\n * @returns {ConditionalNode}\n */\n ConditionalNode.fromJSON = function (json) {\n return new ConditionalNode(json.condition, json.trueExpr, json.falseExpr)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n // Enclose Arguments in parentheses if they are an OperatorNode\n // or have lower or equal precedence\n // NOTE: enclosing all OperatorNodes in parentheses is a decision\n // purely based on aesthetics and readability\n let condition = this.condition.toHTML(options)\n const conditionPrecedence = getPrecedence(this.condition, parenthesis)\n if ((parenthesis === 'all') ||\n (this.condition.type === 'OperatorNode') ||\n ((conditionPrecedence !== null) && (conditionPrecedence <= precedence))) {\n condition = '(' + condition + ')'\n }\n\n let trueExpr = this.trueExpr.toHTML(options)\n const truePrecedence = getPrecedence(this.trueExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.trueExpr.type === 'OperatorNode') ||\n ((truePrecedence !== null) && (truePrecedence <= precedence))) {\n trueExpr = '(' + trueExpr + ')'\n }\n\n let falseExpr = this.falseExpr.toHTML(options)\n const falsePrecedence = getPrecedence(this.falseExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.falseExpr.type === 'OperatorNode') ||\n ((falsePrecedence !== null) && (falsePrecedence <= precedence))) {\n falseExpr = '(' + falseExpr + ')'\n }\n return condition + '?' + trueExpr + ':' + falseExpr\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype._toTex = function (options) {\n return '\\\\begin{cases} {' +\n this.trueExpr.toTex(options) + '}, &\\\\quad{\\\\text{if }\\\\;' +\n this.condition.toTex(options) +\n '}\\\\\\\\{' + this.falseExpr.toTex(options) +\n '}, &\\\\quad{\\\\text{otherwise}}\\\\end{cases}'\n }\n\n /**\n * Test whether a condition is met\n * @param {*} condition\n * @returns {boolean} true if condition is true or non-zero, else false\n */\n function testCondition (condition) {\n if (typeof condition === 'number' ||\n typeof condition === 'boolean' ||\n typeof condition === 'string') {\n return !!condition\n }\n\n if (condition) {\n if (isBigNumber(condition)) {\n return !condition.isZero()\n }\n\n if (isComplex(condition)) {\n return !!((condition.re || condition.im))\n }\n\n if (isUnit(condition)) {\n return !!condition.value\n }\n }\n\n if (condition === null || condition === undefined) {\n return false\n }\n\n throw new TypeError('Unsupported type of condition \"' + typeOf(condition) + '\"')\n }\n\n return ConditionalNode\n}, { isClass: true, isNode: true })\n","/* eslint no-template-curly-in-string: \"off\" */\n\nimport escapeLatexLib from 'escape-latex'\nimport { hasOwnProperty } from './object.js'\n\nexport const latexSymbols = {\n // GREEK LETTERS\n Alpha: 'A',\n alpha: '\\\\alpha',\n Beta: 'B',\n beta: '\\\\beta',\n Gamma: '\\\\Gamma',\n gamma: '\\\\gamma',\n Delta: '\\\\Delta',\n delta: '\\\\delta',\n Epsilon: 'E',\n epsilon: '\\\\epsilon',\n varepsilon: '\\\\varepsilon',\n Zeta: 'Z',\n zeta: '\\\\zeta',\n Eta: 'H',\n eta: '\\\\eta',\n Theta: '\\\\Theta',\n theta: '\\\\theta',\n vartheta: '\\\\vartheta',\n Iota: 'I',\n iota: '\\\\iota',\n Kappa: 'K',\n kappa: '\\\\kappa',\n varkappa: '\\\\varkappa',\n Lambda: '\\\\Lambda',\n lambda: '\\\\lambda',\n Mu: 'M',\n mu: '\\\\mu',\n Nu: 'N',\n nu: '\\\\nu',\n Xi: '\\\\Xi',\n xi: '\\\\xi',\n Omicron: 'O',\n omicron: 'o',\n Pi: '\\\\Pi',\n pi: '\\\\pi',\n varpi: '\\\\varpi',\n Rho: 'P',\n rho: '\\\\rho',\n varrho: '\\\\varrho',\n Sigma: '\\\\Sigma',\n sigma: '\\\\sigma',\n varsigma: '\\\\varsigma',\n Tau: 'T',\n tau: '\\\\tau',\n Upsilon: '\\\\Upsilon',\n upsilon: '\\\\upsilon',\n Phi: '\\\\Phi',\n phi: '\\\\phi',\n varphi: '\\\\varphi',\n Chi: 'X',\n chi: '\\\\chi',\n Psi: '\\\\Psi',\n psi: '\\\\psi',\n Omega: '\\\\Omega',\n omega: '\\\\omega',\n // logic\n true: '\\\\mathrm{True}',\n false: '\\\\mathrm{False}',\n // other\n i: 'i', // TODO use \\i ??\n inf: '\\\\infty',\n Inf: '\\\\infty',\n infinity: '\\\\infty',\n Infinity: '\\\\infty',\n oo: '\\\\infty',\n lim: '\\\\lim',\n undefined: '\\\\mathbf{?}'\n}\n\nexport const latexOperators = {\n transpose: '^\\\\top',\n ctranspose: '^H',\n factorial: '!',\n pow: '^',\n dotPow: '.^\\\\wedge', // TODO find ideal solution\n unaryPlus: '+',\n unaryMinus: '-',\n bitNot: '\\\\~', // TODO find ideal solution\n not: '\\\\neg',\n multiply: '\\\\cdot',\n divide: '\\\\frac', // TODO how to handle that properly?\n dotMultiply: '.\\\\cdot', // TODO find ideal solution\n dotDivide: '.:', // TODO find ideal solution\n mod: '\\\\mod',\n add: '+',\n subtract: '-',\n to: '\\\\rightarrow',\n leftShift: '<<',\n rightArithShift: '>>',\n rightLogShift: '>>>',\n equal: '=',\n unequal: '\\\\neq',\n smaller: '<',\n larger: '>',\n smallerEq: '\\\\leq',\n largerEq: '\\\\geq',\n bitAnd: '\\\\&',\n bitXor: '\\\\underline{|}',\n bitOr: '|',\n and: '\\\\wedge',\n xor: '\\\\veebar',\n or: '\\\\vee'\n}\n\nexport const latexFunctions = {\n // arithmetic\n abs: { 1: '\\\\left|${args[0]}\\\\right|' },\n add: { 2: `\\\\left(\\${args[0]}${latexOperators.add}\\${args[1]}\\\\right)` },\n cbrt: { 1: '\\\\sqrt[3]{${args[0]}}' },\n ceil: { 1: '\\\\left\\\\lceil${args[0]}\\\\right\\\\rceil' },\n cube: { 1: '\\\\left(${args[0]}\\\\right)^3' },\n divide: { 2: '\\\\frac{${args[0]}}{${args[1]}}' },\n dotDivide: { 2: `\\\\left(\\${args[0]}${latexOperators.dotDivide}\\${args[1]}\\\\right)` },\n dotMultiply: { 2: `\\\\left(\\${args[0]}${latexOperators.dotMultiply}\\${args[1]}\\\\right)` },\n dotPow: { 2: `\\\\left(\\${args[0]}${latexOperators.dotPow}\\${args[1]}\\\\right)` },\n exp: { 1: '\\\\exp\\\\left(${args[0]}\\\\right)' },\n expm1: `\\\\left(e${latexOperators.pow}{\\${args[0]}}-1\\\\right)`,\n fix: { 1: '\\\\mathrm{${name}}\\\\left(${args[0]}\\\\right)' },\n floor: { 1: '\\\\left\\\\lfloor${args[0]}\\\\right\\\\rfloor' },\n gcd: '\\\\gcd\\\\left(${args}\\\\right)',\n hypot: '\\\\hypot\\\\left(${args}\\\\right)',\n log: {\n 1: '\\\\ln\\\\left(${args[0]}\\\\right)',\n 2: '\\\\log_{${args[1]}}\\\\left(${args[0]}\\\\right)'\n },\n log10: { 1: '\\\\log_{10}\\\\left(${args[0]}\\\\right)' },\n log1p: {\n 1: '\\\\ln\\\\left(${args[0]}+1\\\\right)',\n 2: '\\\\log_{${args[1]}}\\\\left(${args[0]}+1\\\\right)'\n },\n log2: '\\\\log_{2}\\\\left(${args[0]}\\\\right)',\n mod: { 2: `\\\\left(\\${args[0]}${latexOperators.mod}\\${args[1]}\\\\right)` },\n multiply: { 2: `\\\\left(\\${args[0]}${latexOperators.multiply}\\${args[1]}\\\\right)` },\n norm: {\n 1: '\\\\left\\\\|${args[0]}\\\\right\\\\|',\n 2: undefined // use default template\n },\n nthRoot: { 2: '\\\\sqrt[${args[1]}]{${args[0]}}' },\n nthRoots: { 2: '\\\\{y : $y^{args[1]} = {${args[0]}}\\\\}' },\n pow: { 2: `\\\\left(\\${args[0]}\\\\right)${latexOperators.pow}{\\${args[1]}}` },\n round: {\n 1: '\\\\left\\\\lfloor${args[0]}\\\\right\\\\rceil',\n 2: undefined // use default template\n },\n sign: { 1: '\\\\mathrm{${name}}\\\\left(${args[0]}\\\\right)' },\n sqrt: { 1: '\\\\sqrt{${args[0]}}' },\n square: { 1: '\\\\left(${args[0]}\\\\right)^2' },\n subtract: { 2: `\\\\left(\\${args[0]}${latexOperators.subtract}\\${args[1]}\\\\right)` },\n unaryMinus: { 1: `${latexOperators.unaryMinus}\\\\left(\\${args[0]}\\\\right)` },\n unaryPlus: { 1: `${latexOperators.unaryPlus}\\\\left(\\${args[0]}\\\\right)` },\n\n // bitwise\n bitAnd: { 2: `\\\\left(\\${args[0]}${latexOperators.bitAnd}\\${args[1]}\\\\right)` },\n bitNot: { 1: latexOperators.bitNot + '\\\\left(${args[0]}\\\\right)' },\n bitOr: { 2: `\\\\left(\\${args[0]}${latexOperators.bitOr}\\${args[1]}\\\\right)` },\n bitXor: { 2: `\\\\left(\\${args[0]}${latexOperators.bitXor}\\${args[1]}\\\\right)` },\n leftShift: { 2: `\\\\left(\\${args[0]}${latexOperators.leftShift}\\${args[1]}\\\\right)` },\n rightArithShift: { 2: `\\\\left(\\${args[0]}${latexOperators.rightArithShift}\\${args[1]}\\\\right)` },\n rightLogShift: { 2: `\\\\left(\\${args[0]}${latexOperators.rightLogShift}\\${args[1]}\\\\right)` },\n\n // combinatorics\n bellNumbers: { 1: '\\\\mathrm{B}_{${args[0]}}' },\n catalan: { 1: '\\\\mathrm{C}_{${args[0]}}' },\n stirlingS2: { 2: '\\\\mathrm{S}\\\\left(${args}\\\\right)' },\n\n // complex\n arg: { 1: '\\\\arg\\\\left(${args[0]}\\\\right)' },\n conj: { 1: '\\\\left(${args[0]}\\\\right)^*' },\n im: { 1: '\\\\Im\\\\left\\\\lbrace${args[0]}\\\\right\\\\rbrace' },\n re: { 1: '\\\\Re\\\\left\\\\lbrace${args[0]}\\\\right\\\\rbrace' },\n\n // logical\n and: { 2: `\\\\left(\\${args[0]}${latexOperators.and}\\${args[1]}\\\\right)` },\n not: { 1: latexOperators.not + '\\\\left(${args[0]}\\\\right)' },\n or: { 2: `\\\\left(\\${args[0]}${latexOperators.or}\\${args[1]}\\\\right)` },\n xor: { 2: `\\\\left(\\${args[0]}${latexOperators.xor}\\${args[1]}\\\\right)` },\n\n // matrix\n cross: { 2: '\\\\left(${args[0]}\\\\right)\\\\times\\\\left(${args[1]}\\\\right)' },\n ctranspose: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.ctranspose}` },\n det: { 1: '\\\\det\\\\left(${args[0]}\\\\right)' },\n dot: { 2: '\\\\left(${args[0]}\\\\cdot${args[1]}\\\\right)' },\n expm: { 1: '\\\\exp\\\\left(${args[0]}\\\\right)' },\n inv: { 1: '\\\\left(${args[0]}\\\\right)^{-1}' },\n sqrtm: { 1: `{\\${args[0]}}${latexOperators.pow}{\\\\frac{1}{2}}` },\n trace: { 1: '\\\\mathrm{tr}\\\\left(${args[0]}\\\\right)' },\n transpose: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.transpose}` },\n\n // probability\n combinations: { 2: '\\\\binom{${args[0]}}{${args[1]}}' },\n combinationsWithRep: { 2: '\\\\left(\\\\!\\\\!{\\\\binom{${args[0]}}{${args[1]}}}\\\\!\\\\!\\\\right)' },\n factorial: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.factorial}` },\n gamma: { 1: '\\\\Gamma\\\\left(${args[0]}\\\\right)' },\n\n // relational\n equal: { 2: `\\\\left(\\${args[0]}${latexOperators.equal}\\${args[1]}\\\\right)` },\n larger: { 2: `\\\\left(\\${args[0]}${latexOperators.larger}\\${args[1]}\\\\right)` },\n largerEq: { 2: `\\\\left(\\${args[0]}${latexOperators.largerEq}\\${args[1]}\\\\right)` },\n smaller: { 2: `\\\\left(\\${args[0]}${latexOperators.smaller}\\${args[1]}\\\\right)` },\n smallerEq: { 2: `\\\\left(\\${args[0]}${latexOperators.smallerEq}\\${args[1]}\\\\right)` },\n unequal: { 2: `\\\\left(\\${args[0]}${latexOperators.unequal}\\${args[1]}\\\\right)` },\n\n // special\n erf: { 1: 'erf\\\\left(${args[0]}\\\\right)' },\n\n // statistics\n max: '\\\\max\\\\left(${args}\\\\right)',\n min: '\\\\min\\\\left(${args}\\\\right)',\n variance: '\\\\mathrm{Var}\\\\left(${args}\\\\right)',\n\n // trigonometry\n acos: { 1: '\\\\cos^{-1}\\\\left(${args[0]}\\\\right)' },\n acosh: { 1: '\\\\cosh^{-1}\\\\left(${args[0]}\\\\right)' },\n acot: { 1: '\\\\cot^{-1}\\\\left(${args[0]}\\\\right)' },\n acoth: { 1: '\\\\coth^{-1}\\\\left(${args[0]}\\\\right)' },\n acsc: { 1: '\\\\csc^{-1}\\\\left(${args[0]}\\\\right)' },\n acsch: { 1: '\\\\mathrm{csch}^{-1}\\\\left(${args[0]}\\\\right)' },\n asec: { 1: '\\\\sec^{-1}\\\\left(${args[0]}\\\\right)' },\n asech: { 1: '\\\\mathrm{sech}^{-1}\\\\left(${args[0]}\\\\right)' },\n asin: { 1: '\\\\sin^{-1}\\\\left(${args[0]}\\\\right)' },\n asinh: { 1: '\\\\sinh^{-1}\\\\left(${args[0]}\\\\right)' },\n atan: { 1: '\\\\tan^{-1}\\\\left(${args[0]}\\\\right)' },\n atan2: { 2: '\\\\mathrm{atan2}\\\\left(${args}\\\\right)' },\n atanh: { 1: '\\\\tanh^{-1}\\\\left(${args[0]}\\\\right)' },\n cos: { 1: '\\\\cos\\\\left(${args[0]}\\\\right)' },\n cosh: { 1: '\\\\cosh\\\\left(${args[0]}\\\\right)' },\n cot: { 1: '\\\\cot\\\\left(${args[0]}\\\\right)' },\n coth: { 1: '\\\\coth\\\\left(${args[0]}\\\\right)' },\n csc: { 1: '\\\\csc\\\\left(${args[0]}\\\\right)' },\n csch: { 1: '\\\\mathrm{csch}\\\\left(${args[0]}\\\\right)' },\n sec: { 1: '\\\\sec\\\\left(${args[0]}\\\\right)' },\n sech: { 1: '\\\\mathrm{sech}\\\\left(${args[0]}\\\\right)' },\n sin: { 1: '\\\\sin\\\\left(${args[0]}\\\\right)' },\n sinh: { 1: '\\\\sinh\\\\left(${args[0]}\\\\right)' },\n tan: { 1: '\\\\tan\\\\left(${args[0]}\\\\right)' },\n tanh: { 1: '\\\\tanh\\\\left(${args[0]}\\\\right)' },\n\n // unit\n to: { 2: `\\\\left(\\${args[0]}${latexOperators.to}\\${args[1]}\\\\right)` },\n\n // utils\n numeric: function (node, options) {\n // Not sure if this is strictly right but should work correctly for the vast majority of use cases.\n return node.args[0].toTex()\n },\n\n // type\n number: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(\\\\left(${args[0]}\\\\right)${args[1]}\\\\right)'\n },\n string: {\n 0: '\\\\mathtt{\"\"}',\n 1: '\\\\mathrm{string}\\\\left(${args[0]}\\\\right)'\n },\n bignumber: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)'\n },\n complex: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: `\\\\left(\\\\left(\\${args[0]}\\\\right)+${latexSymbols.i}\\\\cdot\\\\left(\\${args[1]}\\\\right)\\\\right)`\n },\n matrix: {\n 0: '\\\\begin{bmatrix}\\\\end{bmatrix}',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(${args[0]}\\\\right)'\n },\n sparse: {\n 0: '\\\\begin{bsparse}\\\\end{bsparse}',\n 1: '\\\\left(${args[0]}\\\\right)'\n },\n unit: {\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(\\\\left(${args[0]}\\\\right)${args[1]}\\\\right)'\n }\n\n}\n\nexport const defaultTemplate = '\\\\mathrm{${name}}\\\\left(${args}\\\\right)'\n\nconst latexUnits = {\n deg: '^\\\\circ'\n}\n\nexport function escapeLatex (string) {\n return escapeLatexLib(string, { preserveFormatting: true })\n}\n\n// @param {string} name\n// @param {boolean} isUnit\nexport function toSymbol (name, isUnit) {\n isUnit = typeof isUnit === 'undefined' ? false : isUnit\n if (isUnit) {\n if (hasOwnProperty(latexUnits, name)) {\n return latexUnits[name]\n }\n\n return '\\\\mathrm{' + escapeLatex(name) + '}'\n }\n\n if (hasOwnProperty(latexSymbols, name)) {\n return latexSymbols[name]\n }\n\n return escapeLatex(name)\n}\n","import { format } from '../../utils/string.js'\nimport { typeOf } from '../../utils/is.js'\nimport { escapeLatex } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ConstantNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createConstantNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A ConstantNode holds a constant value like a number or string.\n *\n * Usage:\n *\n * new ConstantNode(2.3)\n * new ConstantNode('hello')\n *\n * @param {*} value Value can be any type (number, BigNumber, string, ...)\n * @constructor ConstantNode\n * @extends {Node}\n */\n function ConstantNode (value) {\n if (!(this instanceof ConstantNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.value = value\n }\n\n ConstantNode.prototype = new Node()\n\n ConstantNode.prototype.type = 'ConstantNode'\n\n ConstantNode.prototype.isConstantNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ConstantNode.prototype._compile = function (math, argNames) {\n const value = this.value\n\n return function evalConstantNode () {\n return value\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ConstantNode.prototype.forEach = function (callback) {\n // nothing to do, we don't have childs\n }\n\n /**\n * Create a new ConstantNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {ConstantNode} Returns a clone of the node\n */\n ConstantNode.prototype.map = function (callback) {\n return this.clone()\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ConstantNode}\n */\n ConstantNode.prototype.clone = function () {\n return new ConstantNode(this.value)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype._toString = function (options) {\n return format(this.value, options)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype.toHTML = function (options) {\n const value = this._toString(options)\n\n switch (typeOf(this.value)) {\n case 'number':\n case 'BigNumber':\n case 'Fraction':\n return '' + value + ''\n case 'string':\n return '' + value + ''\n case 'boolean':\n return '' + value + ''\n case 'null':\n return '' + value + ''\n case 'undefined':\n return '' + value + ''\n\n default:\n return '' + value + ''\n }\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ConstantNode.prototype.toJSON = function () {\n return {\n mathjs: 'ConstantNode',\n value: this.value\n }\n }\n\n /**\n * Instantiate a ConstantNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SymbolNode\", value: 2.3}`,\n * where mathjs is optional\n * @returns {ConstantNode}\n */\n ConstantNode.fromJSON = function (json) {\n return new ConstantNode(json.value)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype._toTex = function (options) {\n const value = this._toString(options)\n\n switch (typeOf(this.value)) {\n case 'string':\n return '\\\\mathtt{' + escapeLatex(value) + '}'\n\n case 'number':\n case 'BigNumber':\n {\n if (!isFinite(this.value)) {\n return (this.value.valueOf() < 0)\n ? '-\\\\infty'\n : '\\\\infty'\n }\n\n const index = value.toLowerCase().indexOf('e')\n if (index !== -1) {\n return value.substring(0, index) + '\\\\cdot10^{' +\n value.substring(index + 1) + '}'\n }\n }\n return value\n case 'Fraction':\n return this.value.toLatex()\n\n default:\n return value\n }\n }\n\n return ConstantNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\n\nimport { keywords } from '../keywords.js'\nimport { escape } from '../../utils/string.js'\nimport { forEach, join } from '../../utils/array.js'\nimport { toSymbol } from '../../utils/latex.js'\nimport { getPrecedence } from '../operators.js'\nimport { setSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'FunctionAssignmentNode'\nconst dependencies = [\n 'typed',\n 'Node'\n]\n\nexport const createFunctionAssignmentNode = /* #__PURE__ */ factory(name, dependencies, ({ typed, Node }) => {\n /**\n * @constructor FunctionAssignmentNode\n * @extends {Node}\n * Function assignment\n *\n * @param {string} name Function name\n * @param {string[] | Array.<{name: string, type: string}>} params\n * Array with function parameter names, or an\n * array with objects containing the name\n * and type of the parameter\n * @param {Node} expr The function expression\n */\n function FunctionAssignmentNode (name, params, expr) {\n if (!(this instanceof FunctionAssignmentNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof name !== 'string') throw new TypeError('String expected for parameter \"name\"')\n if (!Array.isArray(params)) throw new TypeError('Array containing strings or objects expected for parameter \"params\"')\n if (!isNode(expr)) throw new TypeError('Node expected for parameter \"expr\"')\n if (name in keywords) throw new Error('Illegal function name, \"' + name + '\" is a reserved keyword')\n\n this.name = name\n this.params = params.map(function (param) {\n return (param && param.name) || param\n })\n this.types = params.map(function (param) {\n return (param && param.type) || 'any'\n })\n this.expr = expr\n }\n\n FunctionAssignmentNode.prototype = new Node()\n\n FunctionAssignmentNode.prototype.type = 'FunctionAssignmentNode'\n\n FunctionAssignmentNode.prototype.isFunctionAssignmentNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n FunctionAssignmentNode.prototype._compile = function (math, argNames) {\n const childArgNames = Object.create(argNames)\n forEach(this.params, function (param) {\n childArgNames[param] = true\n })\n\n // compile the function expression with the child args\n const evalExpr = this.expr._compile(math, childArgNames)\n const name = this.name\n const params = this.params\n const signature = join(this.types, ',')\n const syntax = name + '(' + join(this.params, ', ') + ')'\n\n return function evalFunctionAssignmentNode (scope, args, context) {\n const signatures = {}\n signatures[signature] = function () {\n const childArgs = Object.create(args)\n\n for (let i = 0; i < params.length; i++) {\n childArgs[params[i]] = arguments[i]\n }\n\n return evalExpr(scope, childArgs, context)\n }\n const fn = typed(name, signatures)\n fn.syntax = syntax\n\n setSafeProperty(scope, name, fn)\n\n return fn\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n FunctionAssignmentNode.prototype.forEach = function (callback) {\n callback(this.expr, 'expr', this)\n }\n\n /**\n * Create a new FunctionAssignmentNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {FunctionAssignmentNode} Returns a transformed copy of the node\n */\n FunctionAssignmentNode.prototype.map = function (callback) {\n const expr = this._ifNode(callback(this.expr, 'expr', this))\n\n return new FunctionAssignmentNode(this.name, this.params.slice(0), expr)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {FunctionAssignmentNode}\n */\n FunctionAssignmentNode.prototype.clone = function () {\n return new FunctionAssignmentNode(this.name, this.params.slice(0), this.expr)\n }\n\n /**\n * Is parenthesis needed?\n * @param {Node} node\n * @param {Object} parenthesis\n * @private\n */\n function needParenthesis (node, parenthesis) {\n const precedence = getPrecedence(node, parenthesis)\n const exprPrecedence = getPrecedence(node.expr, parenthesis)\n\n return (parenthesis === 'all') ||\n ((exprPrecedence !== null) && (exprPrecedence <= precedence))\n }\n\n /**\n * get string representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n let expr = this.expr.toString(options)\n if (needParenthesis(this, parenthesis)) {\n expr = '(' + expr + ')'\n }\n return this.name + '(' + this.params.join(', ') + ') = ' + expr\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n FunctionAssignmentNode.prototype.toJSON = function () {\n const types = this.types\n\n return {\n mathjs: 'FunctionAssignmentNode',\n name: this.name,\n params: this.params.map(function (param, index) {\n return {\n name: param,\n type: types[index]\n }\n }),\n expr: this.expr\n }\n }\n\n /**\n * Instantiate an FunctionAssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"FunctionAssignmentNode\", name: ..., params: ..., expr: ...}`,\n * where mathjs is optional\n * @returns {FunctionAssignmentNode}\n */\n FunctionAssignmentNode.fromJSON = function (json) {\n return new FunctionAssignmentNode(json.name, json.params, json.expr)\n }\n\n /**\n * get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const params = []\n for (let i = 0; i < this.params.length; i++) {\n params.push('' + escape(this.params[i]) + '')\n }\n let expr = this.expr.toHTML(options)\n if (needParenthesis(this, parenthesis)) {\n expr = '(' + expr + ')'\n }\n return '' + escape(this.name) + '' + '(' + params.join(',') + ')=' + expr\n }\n\n /**\n * get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n let expr = this.expr.toTex(options)\n if (needParenthesis(this, parenthesis)) {\n expr = `\\\\left(${expr}\\\\right)`\n }\n\n return '\\\\mathrm{' + this.name +\n '}\\\\left(' + this.params.map(toSymbol).join(',') + '\\\\right):=' + expr\n }\n\n return FunctionAssignmentNode\n}, { isClass: true, isNode: true })\n","import { isBigNumber, isConstantNode, isNode, isRangeNode, isSymbolNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { escape } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\nimport { getSafeProperty } from '../../utils/customs.js'\n\nconst name = 'IndexNode'\nconst dependencies = [\n 'Range',\n 'Node',\n 'size'\n]\n\nexport const createIndexNode = /* #__PURE__ */ factory(name, dependencies, ({ Range, Node, size }) => {\n /**\n * @constructor IndexNode\n * @extends Node\n *\n * Describes a subset of a matrix or an object property.\n * Cannot be used on its own, needs to be used within an AccessorNode or\n * AssignmentNode.\n *\n * @param {Node[]} dimensions\n * @param {boolean} [dotNotation=false] Optional property describing whether\n * this index was written using dot\n * notation like `a.b`, or using bracket\n * notation like `a[\"b\"]` (default).\n * Used to stringify an IndexNode.\n */\n function IndexNode (dimensions, dotNotation) {\n if (!(this instanceof IndexNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.dimensions = dimensions\n this.dotNotation = dotNotation || false\n\n // validate input\n if (!Array.isArray(dimensions) || !dimensions.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"dimensions\"')\n }\n if (this.dotNotation && !this.isObjectProperty()) {\n throw new Error('dotNotation only applicable for object properties')\n }\n }\n\n IndexNode.prototype = new Node()\n\n IndexNode.prototype.type = 'IndexNode'\n\n IndexNode.prototype.isIndexNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n IndexNode.prototype._compile = function (math, argNames) {\n // TODO: implement support for bignumber (currently bignumbers are silently\n // reduced to numbers when changing the value to zero-based)\n\n // TODO: Optimization: when the range values are ConstantNodes,\n // we can beforehand resolve the zero-based value\n\n // optimization for a simple object property\n const evalDimensions = map(this.dimensions, function (range, i) {\n if (isRangeNode(range)) {\n if (range.needsEnd()) {\n // create a range containing end (like '4:end')\n const childArgNames = Object.create(argNames)\n childArgNames.end = true\n\n const evalStart = range.start._compile(math, childArgNames)\n const evalEnd = range.end._compile(math, childArgNames)\n const evalStep = range.step\n ? range.step._compile(math, childArgNames)\n : function () { return 1 }\n\n return function evalDimension (scope, args, context) {\n const s = size(context).valueOf()\n const childArgs = Object.create(args)\n childArgs.end = s[i]\n\n return createRange(\n evalStart(scope, childArgs, context),\n evalEnd(scope, childArgs, context),\n evalStep(scope, childArgs, context)\n )\n }\n } else {\n // create range\n const evalStart = range.start._compile(math, argNames)\n const evalEnd = range.end._compile(math, argNames)\n const evalStep = range.step\n ? range.step._compile(math, argNames)\n : function () { return 1 }\n\n return function evalDimension (scope, args, context) {\n return createRange(\n evalStart(scope, args, context),\n evalEnd(scope, args, context),\n evalStep(scope, args, context)\n )\n }\n }\n } else if (isSymbolNode(range) && range.name === 'end') {\n // SymbolNode 'end'\n const childArgNames = Object.create(argNames)\n childArgNames.end = true\n\n const evalRange = range._compile(math, childArgNames)\n\n return function evalDimension (scope, args, context) {\n const s = size(context).valueOf()\n const childArgs = Object.create(args)\n childArgs.end = s[i]\n\n return evalRange(scope, childArgs, context)\n }\n } else {\n // ConstantNode\n const evalRange = range._compile(math, argNames)\n return function evalDimension (scope, args, context) {\n return evalRange(scope, args, context)\n }\n }\n })\n\n const index = getSafeProperty(math, 'index')\n\n return function evalIndexNode (scope, args, context) {\n const dimensions = map(evalDimensions, function (evalDimension) {\n return evalDimension(scope, args, context)\n })\n\n return index(...dimensions)\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n IndexNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.dimensions.length; i++) {\n callback(this.dimensions[i], 'dimensions[' + i + ']', this)\n }\n }\n\n /**\n * Create a new IndexNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {IndexNode} Returns a transformed copy of the node\n */\n IndexNode.prototype.map = function (callback) {\n const dimensions = []\n for (let i = 0; i < this.dimensions.length; i++) {\n dimensions[i] = this._ifNode(callback(this.dimensions[i], 'dimensions[' + i + ']', this))\n }\n\n return new IndexNode(dimensions, this.dotNotation)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {IndexNode}\n */\n IndexNode.prototype.clone = function () {\n return new IndexNode(this.dimensions.slice(0), this.dotNotation)\n }\n\n /**\n * Test whether this IndexNode contains a single property name\n * @return {boolean}\n */\n IndexNode.prototype.isObjectProperty = function () {\n return this.dimensions.length === 1 &&\n isConstantNode(this.dimensions[0]) &&\n typeof this.dimensions[0].value === 'string'\n }\n\n /**\n * Returns the property name if IndexNode contains a property.\n * If not, returns null.\n * @return {string | null}\n */\n IndexNode.prototype.getObjectProperty = function () {\n return this.isObjectProperty() ? this.dimensions[0].value : null\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype._toString = function (options) {\n // format the parameters like \"[1, 0:5]\"\n return this.dotNotation\n ? ('.' + this.getObjectProperty())\n : ('[' + this.dimensions.join(', ') + ']')\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n IndexNode.prototype.toJSON = function () {\n return {\n mathjs: 'IndexNode',\n dimensions: this.dimensions,\n dotNotation: this.dotNotation\n }\n }\n\n /**\n * Instantiate an IndexNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"IndexNode\", dimensions: [...], dotNotation: false}`,\n * where mathjs is optional\n * @returns {IndexNode}\n */\n IndexNode.fromJSON = function (json) {\n return new IndexNode(json.dimensions, json.dotNotation)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype.toHTML = function (options) {\n // format the parameters like \"[1, 0:5]\"\n const dimensions = []\n for (let i = 0; i < this.dimensions.length; i++) {\n dimensions[i] = this.dimensions[i].toHTML()\n }\n if (this.dotNotation) {\n return '.' + '' + escape(this.getObjectProperty()) + ''\n } else {\n return '[' + dimensions.join(',') + ']'\n }\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype._toTex = function (options) {\n const dimensions = this.dimensions.map(function (range) {\n return range.toTex(options)\n })\n\n return this.dotNotation\n ? ('.' + this.getObjectProperty() + '')\n : ('_{' + dimensions.join(',') + '}')\n }\n\n // helper function to create a Range from start, step and end\n function createRange (start, end, step) {\n return new Range(\n isBigNumber(start) ? start.toNumber() : start,\n isBigNumber(end) ? end.toNumber() : end,\n isBigNumber(step) ? step.toNumber() : step\n )\n }\n\n return IndexNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { escape, stringify } from '../../utils/string.js'\nimport { isSafeProperty } from '../../utils/customs.js'\nimport { hasOwnProperty } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ObjectNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createObjectNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ObjectNode\n * @extends {Node}\n * Holds an object with keys/values\n * @param {Object.} [properties] object with key/value pairs\n */\n function ObjectNode (properties) {\n if (!(this instanceof ObjectNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.properties = properties || {}\n\n // validate input\n if (properties) {\n if (!(typeof properties === 'object') || !Object.keys(properties).every(function (key) {\n return isNode(properties[key])\n })) {\n throw new TypeError('Object containing Nodes expected')\n }\n }\n }\n\n ObjectNode.prototype = new Node()\n\n ObjectNode.prototype.type = 'ObjectNode'\n\n ObjectNode.prototype.isObjectNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ObjectNode.prototype._compile = function (math, argNames) {\n const evalEntries = {}\n\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n // we stringify/parse the key here to resolve unicode characters,\n // so you cannot create a key like {\"co\\\\u006Estructor\": null}\n const stringifiedKey = stringify(key)\n const parsedKey = JSON.parse(stringifiedKey)\n if (!isSafeProperty(this.properties, parsedKey)) {\n throw new Error('No access to property \"' + parsedKey + '\"')\n }\n\n evalEntries[parsedKey] = this.properties[key]._compile(math, argNames)\n }\n }\n\n return function evalObjectNode (scope, args, context) {\n const obj = {}\n\n for (const key in evalEntries) {\n if (hasOwnProperty(evalEntries, key)) {\n obj[key] = evalEntries[key](scope, args, context)\n }\n }\n\n return obj\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ObjectNode.prototype.forEach = function (callback) {\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n callback(this.properties[key], 'properties[' + stringify(key) + ']', this)\n }\n }\n }\n\n /**\n * Create a new ObjectNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ObjectNode} Returns a transformed copy of the node\n */\n ObjectNode.prototype.map = function (callback) {\n const properties = {}\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n properties[key] = this._ifNode(callback(this.properties[key],\n 'properties[' + stringify(key) + ']', this))\n }\n }\n return new ObjectNode(properties)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ObjectNode}\n */\n ObjectNode.prototype.clone = function () {\n const properties = {}\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n properties[key] = this.properties[key]\n }\n }\n return new ObjectNode(properties)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ObjectNode.prototype._toString = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push(stringify(key) + ': ' + this.properties[key].toString(options))\n }\n }\n return '{' + entries.join(', ') + '}'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ObjectNode.prototype.toJSON = function () {\n return {\n mathjs: 'ObjectNode',\n properties: this.properties\n }\n }\n\n /**\n * Instantiate an OperatorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ObjectNode\", \"properties\": {...}}`,\n * where mathjs is optional\n * @returns {ObjectNode}\n */\n ObjectNode.fromJSON = function (json) {\n return new ObjectNode(json.properties)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ObjectNode.prototype.toHTML = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push('' + escape(key) + '' + ':' + this.properties[key].toHTML(options))\n }\n }\n return '{' + entries.join(',') + '}'\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ObjectNode.prototype._toTex = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push('\\\\mathbf{' + key + ':} & ' + this.properties[key].toTex(options) + '\\\\\\\\')\n }\n }\n return `\\\\left\\\\{\\\\begin{array}{ll}${entries.join('\\n')}\\\\end{array}\\\\right\\\\}`\n }\n\n return ObjectNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { escape } from '../../utils/string.js'\nimport { getSafeProperty, isSafeMethod } from '../../utils/customs.js'\nimport { getAssociativity, getPrecedence, isAssociativeWith, properties } from '../operators.js'\nimport { latexOperators } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'OperatorNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createOperatorNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor OperatorNode\n * @extends {Node}\n * An operator with two arguments, like 2+3\n *\n * @param {string} op Operator name, for example '+'\n * @param {string} fn Function name, for example 'add'\n * @param {Node[]} args Operator arguments\n * @param {boolean} [implicit] Is this an implicit multiplication?\n */\n function OperatorNode (op, fn, args, implicit) {\n if (!(this instanceof OperatorNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof op !== 'string') {\n throw new TypeError('string expected for parameter \"op\"')\n }\n if (typeof fn !== 'string') {\n throw new TypeError('string expected for parameter \"fn\"')\n }\n if (!Array.isArray(args) || !args.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"args\"')\n }\n\n this.implicit = (implicit === true)\n this.op = op\n this.fn = fn\n this.args = args || []\n }\n\n OperatorNode.prototype = new Node()\n\n OperatorNode.prototype.type = 'OperatorNode'\n\n OperatorNode.prototype.isOperatorNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n OperatorNode.prototype._compile = function (math, argNames) {\n // validate fn\n if (typeof this.fn !== 'string' || !isSafeMethod(math, this.fn)) {\n if (!math[this.fn]) {\n throw new Error('Function ' + this.fn + ' missing in provided namespace \"math\"')\n } else {\n throw new Error('No access to function \"' + this.fn + '\"')\n }\n }\n\n const fn = getSafeProperty(math, this.fn)\n const evalArgs = map(this.args, function (arg) {\n return arg._compile(math, argNames)\n })\n\n if (evalArgs.length === 1) {\n const evalArg0 = evalArgs[0]\n return function evalOperatorNode (scope, args, context) {\n return fn(evalArg0(scope, args, context))\n }\n } else if (evalArgs.length === 2) {\n const evalArg0 = evalArgs[0]\n const evalArg1 = evalArgs[1]\n return function evalOperatorNode (scope, args, context) {\n return fn(evalArg0(scope, args, context), evalArg1(scope, args, context))\n }\n } else {\n return function evalOperatorNode (scope, args, context) {\n return fn.apply(null, map(evalArgs, function (evalArg) {\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n OperatorNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.args.length; i++) {\n callback(this.args[i], 'args[' + i + ']', this)\n }\n }\n\n /**\n * Create a new OperatorNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {OperatorNode} Returns a transformed copy of the node\n */\n OperatorNode.prototype.map = function (callback) {\n const args = []\n for (let i = 0; i < this.args.length; i++) {\n args[i] = this._ifNode(callback(this.args[i], 'args[' + i + ']', this))\n }\n return new OperatorNode(this.op, this.fn, args, this.implicit)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {OperatorNode}\n */\n OperatorNode.prototype.clone = function () {\n return new OperatorNode(this.op, this.fn, this.args.slice(0), this.implicit)\n }\n\n /**\n * Check whether this is an unary OperatorNode:\n * has exactly one argument, like `-a`.\n * @return {boolean} Returns true when an unary operator node, false otherwise.\n */\n OperatorNode.prototype.isUnary = function () {\n return this.args.length === 1\n }\n\n /**\n * Check whether this is a binary OperatorNode:\n * has exactly two arguments, like `a + b`.\n * @return {boolean} Returns true when a binary operator node, false otherwise.\n */\n OperatorNode.prototype.isBinary = function () {\n return this.args.length === 2\n }\n\n /**\n * Calculate which parentheses are necessary. Gets an OperatorNode\n * (which is the root of the tree) and an Array of Nodes\n * (this.args) and returns an array where 'true' means that an argument\n * has to be enclosed in parentheses whereas 'false' means the opposite.\n *\n * @param {OperatorNode} root\n * @param {string} parenthesis\n * @param {Node[]} args\n * @param {boolean} latex\n * @return {boolean[]}\n * @private\n */\n function calculateNecessaryParentheses (root, parenthesis, implicit, args, latex) {\n // precedence of the root OperatorNode\n const precedence = getPrecedence(root, parenthesis)\n const associativity = getAssociativity(root, parenthesis)\n\n if ((parenthesis === 'all') || ((args.length > 2) && (root.getIdentifier() !== 'OperatorNode:add') && (root.getIdentifier() !== 'OperatorNode:multiply'))) {\n return args.map(function (arg) {\n switch (arg.getContent().type) { // Nodes that don't need extra parentheses\n case 'ArrayNode':\n case 'ConstantNode':\n case 'SymbolNode':\n case 'ParenthesisNode':\n return false\n default:\n return true\n }\n })\n }\n\n let result\n switch (args.length) {\n case 0:\n result = []\n break\n\n case 1: // unary operators\n {\n // precedence of the operand\n const operandPrecedence = getPrecedence(args[0], parenthesis)\n\n // handle special cases for LaTeX, where some of the parentheses aren't needed\n if (latex && (operandPrecedence !== null)) {\n let operandIdentifier\n let rootIdentifier\n if (parenthesis === 'keep') {\n operandIdentifier = args[0].getIdentifier()\n rootIdentifier = root.getIdentifier()\n } else {\n // Ignore Parenthesis Nodes when not in 'keep' mode\n operandIdentifier = args[0].getContent().getIdentifier()\n rootIdentifier = root.getContent().getIdentifier()\n }\n if (properties[precedence][rootIdentifier].latexLeftParens === false) {\n result = [false]\n break\n }\n\n if (properties[operandPrecedence][operandIdentifier].latexParens === false) {\n result = [false]\n break\n }\n }\n\n if (operandPrecedence === null) {\n // if the operand has no defined precedence, no parens are needed\n result = [false]\n break\n }\n\n if (operandPrecedence <= precedence) {\n // if the operands precedence is lower, parens are needed\n result = [true]\n break\n }\n\n // otherwise, no parens needed\n result = [false]\n }\n break\n case 2: // binary operators\n {\n let lhsParens // left hand side needs parenthesis?\n // precedence of the left hand side\n const lhsPrecedence = getPrecedence(args[0], parenthesis)\n // is the root node associative with the left hand side\n const assocWithLhs = isAssociativeWith(root, args[0], parenthesis)\n\n if (lhsPrecedence === null) {\n // if the left hand side has no defined precedence, no parens are needed\n // FunctionNode for example\n lhsParens = false\n } else if ((lhsPrecedence === precedence) && (associativity === 'right') && !assocWithLhs) {\n // In case of equal precedence, if the root node is left associative\n // parens are **never** necessary for the left hand side.\n // If it is right associative however, parens are necessary\n // if the root node isn't associative with the left hand side\n lhsParens = true\n } else if (lhsPrecedence < precedence) {\n lhsParens = true\n } else {\n lhsParens = false\n }\n\n let rhsParens // right hand side needs parenthesis?\n // precedence of the right hand side\n const rhsPrecedence = getPrecedence(args[1], parenthesis)\n // is the root node associative with the right hand side?\n const assocWithRhs = isAssociativeWith(root, args[1], parenthesis)\n\n if (rhsPrecedence === null) {\n // if the right hand side has no defined precedence, no parens are needed\n // FunctionNode for example\n rhsParens = false\n } else if ((rhsPrecedence === precedence) && (associativity === 'left') && !assocWithRhs) {\n // In case of equal precedence, if the root node is right associative\n // parens are **never** necessary for the right hand side.\n // If it is left associative however, parens are necessary\n // if the root node isn't associative with the right hand side\n rhsParens = true\n } else if (rhsPrecedence < precedence) {\n rhsParens = true\n } else {\n rhsParens = false\n }\n\n // handle special cases for LaTeX, where some of the parentheses aren't needed\n if (latex) {\n let rootIdentifier\n let lhsIdentifier\n let rhsIdentifier\n if (parenthesis === 'keep') {\n rootIdentifier = root.getIdentifier()\n lhsIdentifier = root.args[0].getIdentifier()\n rhsIdentifier = root.args[1].getIdentifier()\n } else {\n // Ignore ParenthesisNodes when not in 'keep' mode\n rootIdentifier = root.getContent().getIdentifier()\n lhsIdentifier = root.args[0].getContent().getIdentifier()\n rhsIdentifier = root.args[1].getContent().getIdentifier()\n }\n\n if (lhsPrecedence !== null) {\n if (properties[precedence][rootIdentifier].latexLeftParens === false) {\n lhsParens = false\n }\n\n if (properties[lhsPrecedence][lhsIdentifier].latexParens === false) {\n lhsParens = false\n }\n }\n\n if (rhsPrecedence !== null) {\n if (properties[precedence][rootIdentifier].latexRightParens === false) {\n rhsParens = false\n }\n\n if (properties[rhsPrecedence][rhsIdentifier].latexParens === false) {\n rhsParens = false\n }\n }\n }\n\n result = [lhsParens, rhsParens]\n }\n break\n\n default:\n if ((root.getIdentifier() === 'OperatorNode:add') || (root.getIdentifier() === 'OperatorNode:multiply')) {\n result = args.map(function (arg) {\n const argPrecedence = getPrecedence(arg, parenthesis)\n const assocWithArg = isAssociativeWith(root, arg, parenthesis)\n const argAssociativity = getAssociativity(arg, parenthesis)\n if (argPrecedence === null) {\n // if the argument has no defined precedence, no parens are needed\n return false\n } else if ((precedence === argPrecedence) && (associativity === argAssociativity) && !assocWithArg) {\n return true\n } else if (argPrecedence < precedence) {\n return true\n }\n\n return false\n })\n }\n break\n }\n\n // handles an edge case of 'auto' parentheses with implicit multiplication of ConstantNode\n // In that case print parentheses for ParenthesisNodes even though they normally wouldn't be\n // printed.\n if ((args.length >= 2) && (root.getIdentifier() === 'OperatorNode:multiply') && root.implicit && (parenthesis === 'auto') && (implicit === 'hide')) {\n result = args.map(function (arg, index) {\n const isParenthesisNode = (arg.getIdentifier() === 'ParenthesisNode')\n if (result[index] || isParenthesisNode) { // put in parenthesis?\n return true\n }\n\n return false\n })\n }\n\n return result\n }\n\n /**\n * Get string representation.\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, false)\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toString(options)\n if (parens[0]) {\n operand = '(' + operand + ')'\n }\n\n // for example for \"not\", we want a space between operand and argument\n const opIsNamed = /[a-zA-Z]+/.test(this.op)\n\n if (assoc === 'right') { // prefix operator\n return this.op + (opIsNamed ? ' ' : '') + operand\n } else if (assoc === 'left') { // postfix\n return operand + (opIsNamed ? ' ' : '') + this.op\n }\n\n // fall back to postfix\n return operand + this.op\n } else if (args.length === 2) {\n let lhs = args[0].toString(options) // left hand side\n let rhs = args[1].toString(options) // right hand side\n if (parens[0]) { // left hand side in parenthesis?\n lhs = '(' + lhs + ')'\n }\n if (parens[1]) { // right hand side in parenthesis?\n rhs = '(' + rhs + ')'\n }\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return lhs + ' ' + rhs\n }\n\n return lhs + ' ' + this.op + ' ' + rhs\n } else if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n const stringifiedArgs = args.map(function (arg, index) {\n arg = arg.toString(options)\n if (parens[index]) { // put in parenthesis?\n arg = '(' + arg + ')'\n }\n\n return arg\n })\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return stringifiedArgs.join(' ')\n }\n\n return stringifiedArgs.join(' ' + this.op + ' ')\n } else {\n // fallback to formatting as a function call\n return this.fn + '(' + this.args.join(', ') + ')'\n }\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n OperatorNode.prototype.toJSON = function () {\n return {\n mathjs: 'OperatorNode',\n op: this.op,\n fn: this.fn,\n args: this.args,\n implicit: this.implicit\n }\n }\n\n /**\n * Instantiate an OperatorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"OperatorNode\", \"op\": \"+\", \"fn\": \"add\", \"args\": [...], \"implicit\": false}`,\n * where mathjs is optional\n * @returns {OperatorNode}\n */\n OperatorNode.fromJSON = function (json) {\n return new OperatorNode(json.op, json.fn, json.args, json.implicit)\n }\n\n /**\n * Get HTML representation.\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, false)\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toHTML(options)\n if (parens[0]) {\n operand = '(' + operand + ')'\n }\n\n if (assoc === 'right') { // prefix operator\n return '' + escape(this.op) + '' + operand\n } else { // postfix when assoc === 'left' or undefined\n return operand + '' + escape(this.op) + ''\n }\n } else if (args.length === 2) { // binary operatoes\n let lhs = args[0].toHTML(options) // left hand side\n let rhs = args[1].toHTML(options) // right hand side\n if (parens[0]) { // left hand side in parenthesis?\n lhs = '(' + lhs + ')'\n }\n if (parens[1]) { // right hand side in parenthesis?\n rhs = '(' + rhs + ')'\n }\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return lhs + '' + rhs\n }\n\n return lhs + '' + escape(this.op) + '' + rhs\n } else {\n const stringifiedArgs = args.map(function (arg, index) {\n arg = arg.toHTML(options)\n if (parens[index]) { // put in parenthesis?\n arg = '(' + arg + ')'\n }\n\n return arg\n })\n\n if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return stringifiedArgs.join('')\n }\n\n return stringifiedArgs.join('' + escape(this.op) + '')\n } else {\n // fallback to formatting as a function call\n return '' + escape(this.fn) + '(' + stringifiedArgs.join(',') + ')'\n }\n }\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, true)\n let op = latexOperators[this.fn]\n op = typeof op === 'undefined' ? this.op : op // fall back to using this.op\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toTex(options)\n if (parens[0]) {\n operand = `\\\\left(${operand}\\\\right)`\n }\n\n if (assoc === 'right') { // prefix operator\n return op + operand\n } else if (assoc === 'left') { // postfix operator\n return operand + op\n }\n\n // fall back to postfix\n return operand + op\n } else if (args.length === 2) { // binary operators\n const lhs = args[0] // left hand side\n let lhsTex = lhs.toTex(options)\n if (parens[0]) {\n lhsTex = `\\\\left(${lhsTex}\\\\right)`\n }\n\n const rhs = args[1] // right hand side\n let rhsTex = rhs.toTex(options)\n if (parens[1]) {\n rhsTex = `\\\\left(${rhsTex}\\\\right)`\n }\n\n // handle some exceptions (due to the way LaTeX works)\n let lhsIdentifier\n if (parenthesis === 'keep') {\n lhsIdentifier = lhs.getIdentifier()\n } else {\n // Ignore ParenthesisNodes if in 'keep' mode\n lhsIdentifier = lhs.getContent().getIdentifier()\n }\n switch (this.getIdentifier()) {\n case 'OperatorNode:divide':\n // op contains '\\\\frac' at this point\n return op + '{' + lhsTex + '}' + '{' + rhsTex + '}'\n case 'OperatorNode:pow':\n lhsTex = '{' + lhsTex + '}'\n rhsTex = '{' + rhsTex + '}'\n switch (lhsIdentifier) {\n case 'ConditionalNode': //\n case 'OperatorNode:divide':\n lhsTex = `\\\\left(${lhsTex}\\\\right)`\n }\n break\n case 'OperatorNode:multiply':\n if (this.implicit && (implicit === 'hide')) {\n return lhsTex + '~' + rhsTex\n }\n }\n return lhsTex + op + rhsTex\n } else if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n const texifiedArgs = args.map(function (arg, index) {\n arg = arg.toTex(options)\n if (parens[index]) {\n arg = `\\\\left(${arg}\\\\right)`\n }\n return arg\n })\n\n if ((this.getIdentifier() === 'OperatorNode:multiply') && this.implicit) {\n return texifiedArgs.join('~')\n }\n\n return texifiedArgs.join(op)\n } else {\n // fall back to formatting as a function call\n // as this is a fallback, it doesn't use\n // fancy function names\n return '\\\\mathrm{' + this.fn + '}\\\\left(' +\n args.map(function (arg) {\n return arg.toTex(options)\n }).join(',') + '\\\\right)'\n }\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n OperatorNode.prototype.getIdentifier = function () {\n return this.type + ':' + this.fn\n }\n\n return OperatorNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ParenthesisNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createParenthesisNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ParenthesisNode\n * @extends {Node}\n * A parenthesis node describes manual parenthesis from the user input\n * @param {Node} content\n * @extends {Node}\n */\n function ParenthesisNode (content) {\n if (!(this instanceof ParenthesisNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (!isNode(content)) {\n throw new TypeError('Node expected for parameter \"content\"')\n }\n\n this.content = content\n }\n\n ParenthesisNode.prototype = new Node()\n\n ParenthesisNode.prototype.type = 'ParenthesisNode'\n\n ParenthesisNode.prototype.isParenthesisNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ParenthesisNode.prototype._compile = function (math, argNames) {\n return this.content._compile(math, argNames)\n }\n\n /**\n * Get the content of the current Node.\n * @return {Node} content\n * @override\n **/\n ParenthesisNode.prototype.getContent = function () {\n return this.content.getContent()\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ParenthesisNode.prototype.forEach = function (callback) {\n callback(this.content, 'content', this)\n }\n\n /**\n * Create a new ParenthesisNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {ParenthesisNode} Returns a clone of the node\n */\n ParenthesisNode.prototype.map = function (callback) {\n const content = callback(this.content, 'content', this)\n return new ParenthesisNode(content)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ParenthesisNode}\n */\n ParenthesisNode.prototype.clone = function () {\n return new ParenthesisNode(this.content)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype._toString = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return '(' + this.content.toString(options) + ')'\n }\n return this.content.toString(options)\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ParenthesisNode.prototype.toJSON = function () {\n return {\n mathjs: 'ParenthesisNode',\n content: this.content\n }\n }\n\n /**\n * Instantiate an ParenthesisNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ParenthesisNode\", \"content\": ...}`,\n * where mathjs is optional\n * @returns {ParenthesisNode}\n */\n ParenthesisNode.fromJSON = function (json) {\n return new ParenthesisNode(json.content)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype.toHTML = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return '(' + this.content.toHTML(options) + ')'\n }\n return this.content.toHTML(options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype._toTex = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return `\\\\left(${this.content.toTex(options)}\\\\right)`\n }\n return this.content.toTex(options)\n }\n\n return ParenthesisNode\n}, { isClass: true, isNode: true })\n","import { isNode, isSymbolNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'RangeNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createRangeNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor RangeNode\n * @extends {Node}\n * create a range\n * @param {Node} start included lower-bound\n * @param {Node} end included upper-bound\n * @param {Node} [step] optional step\n */\n function RangeNode (start, end, step) {\n if (!(this instanceof RangeNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate inputs\n if (!isNode(start)) throw new TypeError('Node expected')\n if (!isNode(end)) throw new TypeError('Node expected')\n if (step && !isNode(step)) throw new TypeError('Node expected')\n if (arguments.length > 3) throw new Error('Too many arguments')\n\n this.start = start // included lower-bound\n this.end = end // included upper-bound\n this.step = step || null // optional step\n }\n\n RangeNode.prototype = new Node()\n\n RangeNode.prototype.type = 'RangeNode'\n\n RangeNode.prototype.isRangeNode = true\n\n /**\n * Check whether the RangeNode needs the `end` symbol to be defined.\n * This end is the size of the Matrix in current dimension.\n * @return {boolean}\n */\n RangeNode.prototype.needsEnd = function () {\n // find all `end` symbols in this RangeNode\n const endSymbols = this.filter(function (node) {\n return isSymbolNode(node) && (node.name === 'end')\n })\n\n return endSymbols.length > 0\n }\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n RangeNode.prototype._compile = function (math, argNames) {\n const range = math.range\n const evalStart = this.start._compile(math, argNames)\n const evalEnd = this.end._compile(math, argNames)\n\n if (this.step) {\n const evalStep = this.step._compile(math, argNames)\n\n return function evalRangeNode (scope, args, context) {\n return range(\n evalStart(scope, args, context),\n evalEnd(scope, args, context),\n evalStep(scope, args, context)\n )\n }\n } else {\n return function evalRangeNode (scope, args, context) {\n return range(\n evalStart(scope, args, context),\n evalEnd(scope, args, context)\n )\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n RangeNode.prototype.forEach = function (callback) {\n callback(this.start, 'start', this)\n callback(this.end, 'end', this)\n if (this.step) {\n callback(this.step, 'step', this)\n }\n }\n\n /**\n * Create a new RangeNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {RangeNode} Returns a transformed copy of the node\n */\n RangeNode.prototype.map = function (callback) {\n return new RangeNode(\n this._ifNode(callback(this.start, 'start', this)),\n this._ifNode(callback(this.end, 'end', this)),\n this.step && this._ifNode(callback(this.step, 'step', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {RangeNode}\n */\n RangeNode.prototype.clone = function () {\n return new RangeNode(this.start, this.end, this.step && this.step)\n }\n\n /**\n * Calculate the necessary parentheses\n * @param {Node} node\n * @param {string} parenthesis\n * @return {Object} parentheses\n * @private\n */\n function calculateNecessaryParentheses (node, parenthesis) {\n const precedence = getPrecedence(node, parenthesis)\n const parens = {}\n\n const startPrecedence = getPrecedence(node.start, parenthesis)\n parens.start = ((startPrecedence !== null) && (startPrecedence <= precedence)) ||\n (parenthesis === 'all')\n\n if (node.step) {\n const stepPrecedence = getPrecedence(node.step, parenthesis)\n parens.step = ((stepPrecedence !== null) && (stepPrecedence <= precedence)) ||\n (parenthesis === 'all')\n }\n\n const endPrecedence = getPrecedence(node.end, parenthesis)\n parens.end = ((endPrecedence !== null) && (endPrecedence <= precedence)) ||\n (parenthesis === 'all')\n\n return parens\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n RangeNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n // format string as start:step:stop\n let str\n\n let start = this.start.toString(options)\n if (parens.start) {\n start = '(' + start + ')'\n }\n str = start\n\n if (this.step) {\n let step = this.step.toString(options)\n if (parens.step) {\n step = '(' + step + ')'\n }\n str += ':' + step\n }\n\n let end = this.end.toString(options)\n if (parens.end) {\n end = '(' + end + ')'\n }\n str += ':' + end\n\n return str\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n RangeNode.prototype.toJSON = function () {\n return {\n mathjs: 'RangeNode',\n start: this.start,\n end: this.end,\n step: this.step\n }\n }\n\n /**\n * Instantiate an RangeNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"RangeNode\", \"start\": ..., \"end\": ..., \"step\": ...}`,\n * where mathjs is optional\n * @returns {RangeNode}\n */\n RangeNode.fromJSON = function (json) {\n return new RangeNode(json.start, json.end, json.step)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n RangeNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n // format string as start:step:stop\n let str\n\n let start = this.start.toHTML(options)\n if (parens.start) {\n start = '(' + start + ')'\n }\n str = start\n\n if (this.step) {\n let step = this.step.toHTML(options)\n if (parens.step) {\n step = '(' + step + ')'\n }\n str += ':' + step\n }\n\n let end = this.end.toHTML(options)\n if (parens.end) {\n end = '(' + end + ')'\n }\n str += ':' + end\n\n return str\n }\n\n /**\n * Get LaTeX representation\n * @params {Object} options\n * @return {string} str\n */\n RangeNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n let str = this.start.toTex(options)\n if (parens.start) {\n str = `\\\\left(${str}\\\\right)`\n }\n\n if (this.step) {\n let step = this.step.toTex(options)\n if (parens.step) {\n step = `\\\\left(${step}\\\\right)`\n }\n str += ':' + step\n }\n\n let end = this.end.toTex(options)\n if (parens.end) {\n end = `\\\\left(${end}\\\\right)`\n }\n str += ':' + end\n\n return str\n }\n\n return RangeNode\n}, { isClass: true, isNode: true })\n","import { getPrecedence } from '../operators.js'\nimport { escape } from '../../utils/string.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { latexOperators } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'RelationalNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createRelationalNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A node representing a chained conditional expression, such as 'x > y > z'\n *\n * @param {String[]} conditionals An array of conditional operators used to compare the parameters\n * @param {Node[]} params The parameters that will be compared\n *\n * @constructor RelationalNode\n * @extends {Node}\n */\n function RelationalNode (conditionals, params) {\n if (!(this instanceof RelationalNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n if (!Array.isArray(conditionals)) throw new TypeError('Parameter conditionals must be an array')\n if (!Array.isArray(params)) throw new TypeError('Parameter params must be an array')\n if (conditionals.length !== params.length - 1) throw new TypeError('Parameter params must contain exactly one more element than parameter conditionals')\n\n this.conditionals = conditionals\n this.params = params\n }\n\n RelationalNode.prototype = new Node()\n\n RelationalNode.prototype.type = 'RelationalNode'\n\n RelationalNode.prototype.isRelationalNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n RelationalNode.prototype._compile = function (math, argNames) {\n const self = this\n\n const compiled = this.params.map(p => p._compile(math, argNames))\n\n return function evalRelationalNode (scope, args, context) {\n let evalLhs\n let evalRhs = compiled[0](scope, args, context)\n\n for (let i = 0; i < self.conditionals.length; i++) {\n evalLhs = evalRhs\n evalRhs = compiled[i + 1](scope, args, context)\n const condFn = getSafeProperty(math, self.conditionals[i])\n if (!condFn(evalLhs, evalRhs)) {\n return false\n }\n }\n return true\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n RelationalNode.prototype.forEach = function (callback) {\n this.params.forEach((n, i) => callback(n, 'params[' + i + ']', this), this)\n }\n\n /**\n * Create a new RelationalNode having its childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {RelationalNode} Returns a transformed copy of the node\n */\n RelationalNode.prototype.map = function (callback) {\n return new RelationalNode(this.conditionals.slice(), this.params.map((n, i) => this._ifNode(callback(n, 'params[' + i + ']', this)), this))\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {RelationalNode}\n */\n RelationalNode.prototype.clone = function () {\n return new RelationalNode(this.conditionals, this.params)\n }\n\n /**\n * Get string representation.\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '(' + p.toString(options) + ')'\n : p.toString(options)\n })\n\n const operatorMap = {\n equal: '==',\n unequal: '!=',\n smaller: '<',\n larger: '>',\n smallerEq: '<=',\n largerEq: '>='\n }\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += ' ' + operatorMap[this.conditionals[i]] + ' ' + paramStrings[i + 1]\n }\n\n return ret\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n RelationalNode.prototype.toJSON = function () {\n return {\n mathjs: 'RelationalNode',\n conditionals: this.conditionals,\n params: this.params\n }\n }\n\n /**\n * Instantiate a RelationalNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"RelationalNode\", \"condition\": ..., \"trueExpr\": ..., \"falseExpr\": ...}`,\n * where mathjs is optional\n * @returns {RelationalNode}\n */\n RelationalNode.fromJSON = function (json) {\n return new RelationalNode(json.conditionals, json.params)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '(' + p.toHTML(options) + ')'\n : p.toHTML(options)\n })\n\n const operatorMap = {\n equal: '==',\n unequal: '!=',\n smaller: '<',\n larger: '>',\n smallerEq: '<=',\n largerEq: '>='\n }\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += '' + escape(operatorMap[this.conditionals[i]]) + '' + paramStrings[i + 1]\n }\n\n return ret\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '\\\\left(' + p.toTex(options) + '\\right)'\n : p.toTex(options)\n })\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += latexOperators[this.conditionals[i]] + paramStrings[i + 1]\n }\n\n return ret\n }\n\n return RelationalNode\n}, { isClass: true, isNode: true })\n","import { escape } from '../../utils/string.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { toSymbol } from '../../utils/latex.js'\n\nconst name = 'SymbolNode'\nconst dependencies = [\n 'math',\n '?Unit',\n 'Node'\n]\n\nexport const createSymbolNode = /* #__PURE__ */ factory(name, dependencies, ({ math, Unit, Node }) => {\n /**\n * Check whether some name is a valueless unit like \"inch\".\n * @param {string} name\n * @return {boolean}\n */\n function isValuelessUnit (name) {\n return Unit ? Unit.isValuelessUnit(name) : false\n }\n\n /**\n * @constructor SymbolNode\n * @extends {Node}\n * A symbol node can hold and resolve a symbol\n * @param {string} name\n * @extends {Node}\n */\n function SymbolNode (name) {\n if (!(this instanceof SymbolNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof name !== 'string') throw new TypeError('String expected for parameter \"name\"')\n\n this.name = name\n }\n\n SymbolNode.prototype = new Node()\n\n SymbolNode.prototype.type = 'SymbolNode'\n\n SymbolNode.prototype.isSymbolNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n SymbolNode.prototype._compile = function (math, argNames) {\n const name = this.name\n\n if (argNames[name] === true) {\n // this is a FunctionAssignment argument\n // (like an x when inside the expression of a function assignment `f(x) = ...`)\n return function (scope, args, context) {\n return args[name]\n }\n } else if (name in math) {\n return function (scope, args, context) {\n return name in scope\n ? getSafeProperty(scope, name)\n : getSafeProperty(math, name)\n }\n } else {\n const isUnit = isValuelessUnit(name)\n\n return function (scope, args, context) {\n return name in scope\n ? getSafeProperty(scope, name)\n : isUnit\n ? new Unit(null, name)\n : undef(name)\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n SymbolNode.prototype.forEach = function (callback) {\n // nothing to do, we don't have childs\n }\n\n /**\n * Create a new SymbolNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {SymbolNode} Returns a clone of the node\n */\n SymbolNode.prototype.map = function (callback) {\n return this.clone()\n }\n\n /**\n * Throws an error 'Undefined symbol {name}'\n * @param {string} name\n */\n function undef (name) {\n throw new Error('Undefined symbol ' + name)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {SymbolNode}\n */\n SymbolNode.prototype.clone = function () {\n return new SymbolNode(this.name)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype._toString = function (options) {\n return this.name\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype.toHTML = function (options) {\n const name = escape(this.name)\n\n if (name === 'true' || name === 'false') {\n return '' + name + ''\n } else if (name === 'i') {\n return '' + name + ''\n } else if (name === 'Infinity') {\n return '' + name + ''\n } else if (name === 'NaN') {\n return '' + name + ''\n } else if (name === 'null') {\n return '' + name + ''\n } else if (name === 'undefined') {\n return '' + name + ''\n }\n\n return '' + name + ''\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n SymbolNode.prototype.toJSON = function () {\n return {\n mathjs: 'SymbolNode',\n name: this.name\n }\n }\n\n /**\n * Instantiate a SymbolNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SymbolNode\", name: \"x\"}`,\n * where mathjs is optional\n * @returns {SymbolNode}\n */\n SymbolNode.fromJSON = function (json) {\n return new SymbolNode(json.name)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype._toTex = function (options) {\n let isUnit = false\n if ((typeof math[this.name] === 'undefined') && isValuelessUnit(this.name)) {\n isUnit = true\n }\n const symbol = toSymbol(this.name, isUnit)\n if (symbol[0] === '\\\\') {\n // no space needed if the symbol starts with '\\'\n return symbol\n }\n // the space prevents symbols from breaking stuff like '\\cdot' if it's written right before the symbol\n return ' ' + symbol\n }\n\n return SymbolNode\n}, { isClass: true, isNode: true })\n","import { isAccessorNode, isFunctionAssignmentNode, isIndexNode, isNode, isSymbolNode } from '../../utils/is.js'\n\nimport { escape } from '../../utils/string.js'\nimport { hasOwnProperty } from '../../utils/object.js'\nimport { map } from '../../utils/array.js'\nimport { getSafeProperty, validateSafeMethod } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { defaultTemplate, latexFunctions } from '../../utils/latex.js'\n\nconst name = 'FunctionNode'\nconst dependencies = [\n 'math',\n 'Node',\n 'SymbolNode'\n]\n\nexport const createFunctionNode = /* #__PURE__ */ factory(name, dependencies, ({ math, Node, SymbolNode }) => {\n /**\n * @constructor FunctionNode\n * @extends {./Node}\n * invoke a list with arguments on a node\n * @param {./Node | string} fn Node resolving with a function on which to invoke\n * the arguments, typically a SymboNode or AccessorNode\n * @param {./Node[]} args\n */\n function FunctionNode (fn, args) {\n if (!(this instanceof FunctionNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (typeof fn === 'string') {\n fn = new SymbolNode(fn)\n }\n\n // validate input\n if (!isNode(fn)) throw new TypeError('Node expected as parameter \"fn\"')\n if (!Array.isArray(args) || !args.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"args\"')\n }\n\n this.fn = fn\n this.args = args || []\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n return this.fn.name || ''\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n FunctionNode.prototype = new Node()\n\n FunctionNode.prototype.type = 'FunctionNode'\n\n FunctionNode.prototype.isFunctionNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n FunctionNode.prototype._compile = function (math, argNames) {\n if (!(this instanceof FunctionNode)) {\n throw new TypeError('No valid FunctionNode')\n }\n\n // compile arguments\n const evalArgs = map(this.args, function (arg) {\n return arg._compile(math, argNames)\n })\n\n if (isSymbolNode(this.fn)) {\n // we can statically determine whether the function has an rawArgs property\n const name = this.fn.name\n const fn = name in math ? getSafeProperty(math, name) : undefined\n const isRaw = (typeof fn === 'function') && (fn.rawArgs === true)\n\n if (isRaw) {\n // pass unevaluated parameters (nodes) to the function\n // \"raw\" evaluation\n const rawArgs = this.args\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(rawArgs, math, Object.assign({}, scope, args))\n }\n } else {\n // \"regular\" evaluation\n if (evalArgs.length === 1) {\n const evalArg0 = evalArgs[0]\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(evalArg0(scope, args, context))\n }\n } else if (evalArgs.length === 2) {\n const evalArg0 = evalArgs[0]\n const evalArg1 = evalArgs[1]\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(evalArg0(scope, args, context), evalArg1(scope, args, context))\n }\n } else {\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn).apply(null, map(evalArgs, function (evalArg) {\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n } else if (isAccessorNode(this.fn) &&\n isIndexNode(this.fn.index) && this.fn.index.isObjectProperty()) {\n // execute the function with the right context: the object of the AccessorNode\n\n const evalObject = this.fn.object._compile(math, argNames)\n const prop = this.fn.index.getObjectProperty()\n const rawArgs = this.args\n\n return function evalFunctionNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n validateSafeMethod(object, prop)\n const isRaw = object[prop] && object[prop].rawArgs\n\n return isRaw\n ? object[prop](rawArgs, math, Object.assign({}, scope, args)) // \"raw\" evaluation\n : object[prop].apply(object, map(evalArgs, function (evalArg) { // \"regular\" evaluation\n return evalArg(scope, args, context)\n }))\n }\n } else { // node.fn.isAccessorNode && !node.fn.index.isObjectProperty()\n // we have to dynamically determine whether the function has a rawArgs property\n const evalFn = this.fn._compile(math, argNames)\n const rawArgs = this.args\n\n return function evalFunctionNode (scope, args, context) {\n const fn = evalFn(scope, args, context)\n const isRaw = fn && fn.rawArgs\n\n return isRaw\n ? fn(rawArgs, math, Object.assign({}, scope, args)) // \"raw\" evaluation\n : fn.apply(fn, map(evalArgs, function (evalArg) { // \"regular\" evaluation\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n FunctionNode.prototype.forEach = function (callback) {\n callback(this.fn, 'fn', this)\n\n for (let i = 0; i < this.args.length; i++) {\n callback(this.args[i], 'args[' + i + ']', this)\n }\n }\n\n /**\n * Create a new FunctionNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {FunctionNode} Returns a transformed copy of the node\n */\n FunctionNode.prototype.map = function (callback) {\n const fn = this._ifNode(callback(this.fn, 'fn', this))\n const args = []\n for (let i = 0; i < this.args.length; i++) {\n args[i] = this._ifNode(callback(this.args[i], 'args[' + i + ']', this))\n }\n return new FunctionNode(fn, args)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {FunctionNode}\n */\n FunctionNode.prototype.clone = function () {\n return new FunctionNode(this.fn, this.args.slice(0))\n }\n\n // backup Node's toString function\n // @private\n const nodeToString = FunctionNode.prototype.toString\n\n /**\n * Get string representation. (wrapper function)\n * This overrides parts of Node's toString function.\n * If callback is an object containing callbacks, it\n * calls the correct callback for the current node,\n * otherwise it falls back to calling Node's toString\n * function.\n *\n * @param {Object} options\n * @return {string} str\n * @override\n */\n FunctionNode.prototype.toString = function (options) {\n let customString\n const name = this.fn.toString(options)\n if (options && (typeof options.handler === 'object') && hasOwnProperty(options.handler, name)) {\n // callback is a map of callback functions\n customString = options.handler[name](this, options)\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n // fall back to Node's toString\n return nodeToString.call(this, options)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype._toString = function (options) {\n const args = this.args.map(function (arg) {\n return arg.toString(options)\n })\n\n const fn = isFunctionAssignmentNode(this.fn)\n ? ('(' + this.fn.toString(options) + ')')\n : this.fn.toString(options)\n\n // format the arguments like \"add(2, 4.2)\"\n return fn + '(' + args.join(', ') + ')'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n FunctionNode.prototype.toJSON = function () {\n return {\n mathjs: 'FunctionNode',\n fn: this.fn,\n args: this.args\n }\n }\n\n /**\n * Instantiate an AssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"FunctionNode\", fn: ..., args: ...}`,\n * where mathjs is optional\n * @returns {FunctionNode}\n */\n FunctionNode.fromJSON = function (json) {\n return new FunctionNode(json.fn, json.args)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype.toHTML = function (options) {\n const args = this.args.map(function (arg) {\n return arg.toHTML(options)\n })\n\n // format the arguments like \"add(2, 4.2)\"\n return '' + escape(this.fn) + '(' + args.join(',') + ')'\n }\n\n /*\n * Expand a LaTeX template\n *\n * @param {string} template\n * @param {Node} node\n * @param {Object} options\n * @private\n **/\n function expandTemplate (template, node, options) {\n let latex = ''\n\n // Match everything of the form ${identifier} or ${identifier[2]} or $$\n // while submatching identifier and 2 (in the second case)\n const regex = /\\$(?:\\{([a-z_][a-z_0-9]*)(?:\\[([0-9]+)\\])?\\}|\\$)/gi\n\n let inputPos = 0 // position in the input string\n let match\n while ((match = regex.exec(template)) !== null) { // go through all matches\n // add everything in front of the match to the LaTeX string\n latex += template.substring(inputPos, match.index)\n inputPos = match.index\n\n if (match[0] === '$$') { // escaped dollar sign\n latex += '$'\n inputPos++\n } else { // template parameter\n inputPos += match[0].length\n const property = node[match[1]]\n if (!property) {\n throw new ReferenceError('Template: Property ' + match[1] + ' does not exist.')\n }\n if (match[2] === undefined) { // no square brackets\n switch (typeof property) {\n case 'string':\n latex += property\n break\n case 'object':\n if (isNode(property)) {\n latex += property.toTex(options)\n } else if (Array.isArray(property)) {\n // make array of Nodes into comma separated list\n latex += property.map(function (arg, index) {\n if (isNode(arg)) {\n return arg.toTex(options)\n }\n throw new TypeError('Template: ' + match[1] + '[' + index + '] is not a Node.')\n }).join(',')\n } else {\n throw new TypeError('Template: ' + match[1] + ' has to be a Node, String or array of Nodes')\n }\n break\n default:\n throw new TypeError('Template: ' + match[1] + ' has to be a Node, String or array of Nodes')\n }\n } else { // with square brackets\n if (isNode(property[match[2]] && property[match[2]])) {\n latex += property[match[2]].toTex(options)\n } else {\n throw new TypeError('Template: ' + match[1] + '[' + match[2] + '] is not a Node.')\n }\n }\n }\n }\n latex += template.slice(inputPos) // append rest of the template\n\n return latex\n }\n\n // backup Node's toTex function\n // @private\n const nodeToTex = FunctionNode.prototype.toTex\n\n /**\n * Get LaTeX representation. (wrapper function)\n * This overrides parts of Node's toTex function.\n * If callback is an object containing callbacks, it\n * calls the correct callback for the current node,\n * otherwise it falls back to calling Node's toTex\n * function.\n *\n * @param {Object} options\n * @return {string}\n */\n FunctionNode.prototype.toTex = function (options) {\n let customTex\n if (options && (typeof options.handler === 'object') && hasOwnProperty(options.handler, this.name)) {\n // callback is a map of callback functions\n customTex = options.handler[this.name](this, options)\n }\n\n if (typeof customTex !== 'undefined') {\n return customTex\n }\n\n // fall back to Node's toTex\n return nodeToTex.call(this, options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype._toTex = function (options) {\n const args = this.args.map(function (arg) { // get LaTeX of the arguments\n return arg.toTex(options)\n })\n\n let latexConverter\n\n if (latexFunctions[this.name]) {\n latexConverter = latexFunctions[this.name]\n }\n\n // toTex property on the function itself\n if (math[this.name] &&\n ((typeof math[this.name].toTex === 'function') ||\n (typeof math[this.name].toTex === 'object') ||\n (typeof math[this.name].toTex === 'string'))\n ) {\n // .toTex is a callback function\n latexConverter = math[this.name].toTex\n }\n\n let customToTex\n switch (typeof latexConverter) {\n case 'function': // a callback function\n customToTex = latexConverter(this, options)\n break\n case 'string': // a template string\n customToTex = expandTemplate(latexConverter, this, options)\n break\n case 'object': // an object with different \"converters\" for different numbers of arguments\n switch (typeof latexConverter[args.length]) {\n case 'function':\n customToTex = latexConverter[args.length](this, options)\n break\n case 'string':\n customToTex = expandTemplate(latexConverter[args.length], this, options)\n break\n }\n }\n\n if (typeof customToTex !== 'undefined') {\n return customToTex\n }\n\n return expandTemplate(defaultTemplate, this, options)\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n FunctionNode.prototype.getIdentifier = function () {\n return this.type + ':' + this.name\n }\n\n return FunctionNode\n}, { isClass: true, isNode: true })\n","import { factory } from '../utils/factory.js'\nimport { isAccessorNode, isConstantNode, isFunctionNode, isOperatorNode, isSymbolNode } from '../utils/is.js'\nimport { deepMap } from '../utils/collection.js'\nimport { hasOwnProperty } from '../utils/object.js'\n\nconst name = 'parse'\nconst dependencies = [\n 'typed',\n 'numeric',\n 'config',\n 'AccessorNode',\n 'ArrayNode',\n 'AssignmentNode',\n 'BlockNode',\n 'ConditionalNode',\n 'ConstantNode',\n 'FunctionAssignmentNode',\n 'FunctionNode',\n 'IndexNode',\n 'ObjectNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'RangeNode',\n 'RelationalNode',\n 'SymbolNode'\n]\n\nexport const createParse = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n numeric,\n config,\n AccessorNode,\n ArrayNode,\n AssignmentNode,\n BlockNode,\n ConditionalNode,\n ConstantNode,\n FunctionAssignmentNode,\n FunctionNode,\n IndexNode,\n ObjectNode,\n OperatorNode,\n ParenthesisNode,\n RangeNode,\n RelationalNode,\n SymbolNode\n}) => {\n /**\n * Parse an expression. Returns a node tree, which can be evaluated by\n * invoking node.evaluate().\n *\n * Note the evaluating arbitrary expressions may involve security risks,\n * see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.\n *\n * Syntax:\n *\n * math.parse(expr)\n * math.parse(expr, options)\n * math.parse([expr1, expr2, expr3, ...])\n * math.parse([expr1, expr2, expr3, ...], options)\n *\n * Example:\n *\n * const node1 = math.parse('sqrt(3^2 + 4^2)')\n * node1.compile().evaluate() // 5\n *\n * let scope = {a:3, b:4}\n * const node2 = math.parse('a * b') // 12\n * const code2 = node2.compile()\n * code2.evaluate(scope) // 12\n * scope.a = 5\n * code2.evaluate(scope) // 20\n *\n * const nodes = math.parse(['a = 3', 'b = 4', 'a * b'])\n * nodes[2].compile().evaluate() // 12\n *\n * See also:\n *\n * evaluate, compile\n *\n * @param {string | string[] | Matrix} expr Expression to be parsed\n * @param {{nodes: Object}} [options] Available options:\n * - `nodes` a set of custom nodes\n * @return {Node | Node[]} node\n * @throws {Error}\n */\n const parse = typed(name, {\n string: function (expression) {\n return parseStart(expression, {})\n },\n 'Array | Matrix': function (expressions) {\n return parseMultiple(expressions, {})\n },\n 'string, Object': function (expression, options) {\n const extraNodes = options.nodes !== undefined ? options.nodes : {}\n\n return parseStart(expression, extraNodes)\n },\n 'Array | Matrix, Object': parseMultiple\n })\n\n function parseMultiple (expressions, options = {}) {\n const extraNodes = options.nodes !== undefined ? options.nodes : {}\n\n // parse an array or matrix with expressions\n return deepMap(expressions, function (elem) {\n if (typeof elem !== 'string') throw new TypeError('String expected')\n\n return parseStart(elem, extraNodes)\n })\n }\n\n // token types enumeration\n const TOKENTYPE = {\n NULL: 0,\n DELIMITER: 1,\n NUMBER: 2,\n SYMBOL: 3,\n UNKNOWN: 4\n }\n\n // map with all delimiters\n const DELIMITERS = {\n ',': true,\n '(': true,\n ')': true,\n '[': true,\n ']': true,\n '{': true,\n '}': true,\n '\"': true,\n '\\'': true,\n ';': true,\n\n '+': true,\n '-': true,\n '*': true,\n '.*': true,\n '/': true,\n './': true,\n '%': true,\n '^': true,\n '.^': true,\n '~': true,\n '!': true,\n '&': true,\n '|': true,\n '^|': true,\n '=': true,\n ':': true,\n '?': true,\n\n '==': true,\n '!=': true,\n '<': true,\n '>': true,\n '<=': true,\n '>=': true,\n\n '<<': true,\n '>>': true,\n '>>>': true\n }\n\n // map with all named delimiters\n const NAMED_DELIMITERS = {\n mod: true,\n to: true,\n in: true,\n and: true,\n xor: true,\n or: true,\n not: true\n }\n\n const CONSTANTS = {\n true: true,\n false: false,\n null: null,\n undefined: undefined\n }\n\n const NUMERIC_CONSTANTS = [\n 'NaN',\n 'Infinity'\n ]\n\n function initialState () {\n return {\n extraNodes: {}, // current extra nodes, must be careful not to mutate\n expression: '', // current expression\n comment: '', // last parsed comment\n index: 0, // current index in expr\n token: '', // current token\n tokenType: TOKENTYPE.NULL, // type of the token\n nestingLevel: 0, // level of nesting inside parameters, used to ignore newline characters\n conditionalLevel: null // when a conditional is being parsed, the level of the conditional is stored here\n }\n }\n\n /**\n * View upto `length` characters of the expression starting at the current character.\n *\n * @param {Object} state\n * @param {number} [length=1] Number of characters to view\n * @returns {string}\n * @private\n */\n function currentString (state, length) {\n return state.expression.substr(state.index, length)\n }\n\n /**\n * View the current character. Returns '' if end of expression is reached.\n *\n * @param {Object} state\n * @returns {string}\n * @private\n */\n function currentCharacter (state) {\n return currentString(state, 1)\n }\n\n /**\n * Get the next character from the expression.\n * The character is stored into the char c. If the end of the expression is\n * reached, the function puts an empty string in c.\n * @private\n */\n function next (state) {\n state.index++\n }\n\n /**\n * Preview the previous character from the expression.\n * @return {string} cNext\n * @private\n */\n function prevCharacter (state) {\n return state.expression.charAt(state.index - 1)\n }\n\n /**\n * Preview the next character from the expression.\n * @return {string} cNext\n * @private\n */\n function nextCharacter (state) {\n return state.expression.charAt(state.index + 1)\n }\n\n /**\n * Get next token in the current string expr.\n * The token and token type are available as token and tokenType\n * @private\n */\n function getToken (state) {\n state.tokenType = TOKENTYPE.NULL\n state.token = ''\n state.comment = ''\n\n // skip over whitespaces\n // space, tab, and newline when inside parameters\n while (parse.isWhitespace(currentCharacter(state), state.nestingLevel)) {\n next(state)\n }\n\n // skip comment\n if (currentCharacter(state) === '#') {\n while (currentCharacter(state) !== '\\n' && currentCharacter(state) !== '') {\n state.comment += currentCharacter(state)\n next(state)\n }\n }\n\n // check for end of expression\n if (currentCharacter(state) === '') {\n // token is still empty\n state.tokenType = TOKENTYPE.DELIMITER\n return\n }\n\n // check for new line character\n if (currentCharacter(state) === '\\n' && !state.nestingLevel) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = currentCharacter(state)\n next(state)\n return\n }\n\n const c1 = currentCharacter(state)\n const c2 = currentString(state, 2)\n const c3 = currentString(state, 3)\n if (c3.length === 3 && DELIMITERS[c3]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c3\n next(state)\n next(state)\n next(state)\n return\n }\n\n // check for delimiters consisting of 2 characters\n if (c2.length === 2 && DELIMITERS[c2]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c2\n next(state)\n next(state)\n return\n }\n\n // check for delimiters consisting of 1 character\n if (DELIMITERS[c1]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c1\n next(state)\n return\n }\n\n // check for a number\n if (parse.isDigitDot(c1)) {\n state.tokenType = TOKENTYPE.NUMBER\n\n // check for binary, octal, or hex\n const c2 = currentString(state, 2)\n if (c2 === '0b' || c2 === '0o' || c2 === '0x') {\n state.token += currentCharacter(state)\n next(state)\n state.token += currentCharacter(state)\n next(state)\n while (parse.isHexDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n return\n }\n\n // get number, can have a single dot\n if (currentCharacter(state) === '.') {\n state.token += currentCharacter(state)\n next(state)\n\n if (!parse.isDigit(currentCharacter(state))) {\n // this is no number, it is just a dot (can be dot notation)\n state.tokenType = TOKENTYPE.DELIMITER\n }\n } else {\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n }\n\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n // check for exponential notation like \"2.3e-4\", \"1.23e50\" or \"2e+4\"\n if (currentCharacter(state) === 'E' || currentCharacter(state) === 'e') {\n if (parse.isDigit(nextCharacter(state)) || nextCharacter(state) === '-' || nextCharacter(state) === '+') {\n state.token += currentCharacter(state)\n next(state)\n\n if (currentCharacter(state) === '+' || currentCharacter(state) === '-') {\n state.token += currentCharacter(state)\n next(state)\n }\n // Scientific notation MUST be followed by an exponent\n if (!parse.isDigit(currentCharacter(state))) {\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n\n if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n } else if (nextCharacter(state) === '.') {\n next(state)\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n }\n\n return\n }\n\n // check for variables, functions, named operators\n if (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state))) {\n while (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state)) || parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n\n if (hasOwnProperty(NAMED_DELIMITERS, state.token)) {\n state.tokenType = TOKENTYPE.DELIMITER\n } else {\n state.tokenType = TOKENTYPE.SYMBOL\n }\n\n return\n }\n\n // something unknown is found, wrong characters -> a syntax error\n state.tokenType = TOKENTYPE.UNKNOWN\n while (currentCharacter(state) !== '') {\n state.token += currentCharacter(state)\n next(state)\n }\n throw createSyntaxError(state, 'Syntax error in part \"' + state.token + '\"')\n }\n\n /**\n * Get next token and skip newline tokens\n */\n function getTokenSkipNewline (state) {\n do {\n getToken(state)\n }\n while (state.token === '\\n') // eslint-disable-line no-unmodified-loop-condition\n }\n\n /**\n * Open parameters.\n * New line characters will be ignored until closeParams(state) is called\n */\n function openParams (state) {\n state.nestingLevel++\n }\n\n /**\n * Close parameters.\n * New line characters will no longer be ignored\n */\n function closeParams (state) {\n state.nestingLevel--\n }\n\n /**\n * Checks whether the current character `c` is a valid alpha character:\n *\n * - A latin letter (upper or lower case) Ascii: a-z, A-Z\n * - An underscore Ascii: _\n * - A dollar sign Ascii: $\n * - A latin letter with accents Unicode: \\u00C0 - \\u02AF\n * - A greek letter Unicode: \\u0370 - \\u03FF\n * - A mathematical alphanumeric symbol Unicode: \\u{1D400} - \\u{1D7FF} excluding invalid code points\n *\n * The previous and next characters are needed to determine whether\n * this character is part of a unicode surrogate pair.\n *\n * @param {string} c Current character in the expression\n * @param {string} cPrev Previous character\n * @param {string} cNext Next character\n * @return {boolean}\n */\n parse.isAlpha = function isAlpha (c, cPrev, cNext) {\n return parse.isValidLatinOrGreek(c) ||\n parse.isValidMathSymbol(c, cNext) ||\n parse.isValidMathSymbol(cPrev, c)\n }\n\n /**\n * Test whether a character is a valid latin, greek, or letter-like character\n * @param {string} c\n * @return {boolean}\n */\n parse.isValidLatinOrGreek = function isValidLatinOrGreek (c) {\n return /^[a-zA-Z_$\\u00C0-\\u02AF\\u0370-\\u03FF\\u2100-\\u214F]$/.test(c)\n }\n\n /**\n * Test whether two given 16 bit characters form a surrogate pair of a\n * unicode math symbol.\n *\n * https://unicode-table.com/en/\n * https://www.wikiwand.com/en/Mathematical_operators_and_symbols_in_Unicode\n *\n * Note: In ES6 will be unicode aware:\n * https://stackoverflow.com/questions/280712/javascript-unicode-regexes\n * https://mathiasbynens.be/notes/es6-unicode-regex\n *\n * @param {string} high\n * @param {string} low\n * @return {boolean}\n */\n parse.isValidMathSymbol = function isValidMathSymbol (high, low) {\n return /^[\\uD835]$/.test(high) &&\n /^[\\uDC00-\\uDFFF]$/.test(low) &&\n /^[^\\uDC55\\uDC9D\\uDCA0\\uDCA1\\uDCA3\\uDCA4\\uDCA7\\uDCA8\\uDCAD\\uDCBA\\uDCBC\\uDCC4\\uDD06\\uDD0B\\uDD0C\\uDD15\\uDD1D\\uDD3A\\uDD3F\\uDD45\\uDD47-\\uDD49\\uDD51\\uDEA6\\uDEA7\\uDFCC\\uDFCD]$/.test(low)\n }\n\n /**\n * Check whether given character c is a white space character: space, tab, or enter\n * @param {string} c\n * @param {number} nestingLevel\n * @return {boolean}\n */\n parse.isWhitespace = function isWhitespace (c, nestingLevel) {\n // TODO: also take '\\r' carriage return as newline? Or does that give problems on mac?\n return c === ' ' || c === '\\t' || (c === '\\n' && nestingLevel > 0)\n }\n\n /**\n * Test whether the character c is a decimal mark (dot).\n * This is the case when it's not the start of a delimiter '.*', './', or '.^'\n * @param {string} c\n * @param {string} cNext\n * @return {boolean}\n */\n parse.isDecimalMark = function isDecimalMark (c, cNext) {\n return c === '.' && cNext !== '/' && cNext !== '*' && cNext !== '^'\n }\n\n /**\n * checks if the given char c is a digit or dot\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isDigitDot = function isDigitDot (c) {\n return ((c >= '0' && c <= '9') || c === '.')\n }\n\n /**\n * checks if the given char c is a digit\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isDigit = function isDigit (c) {\n return (c >= '0' && c <= '9')\n }\n\n /**\n * checks if the given char c is a hex digit\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isHexDigit = function isHexDigit (c) {\n return ((c >= '0' && c <= '9') ||\n (c >= 'a' && c <= 'f') ||\n (c >= 'A' && c <= 'F'))\n }\n\n /**\n * Start of the parse levels below, in order of precedence\n * @return {Node} node\n * @private\n */\n function parseStart (expression, extraNodes) {\n const state = initialState()\n Object.assign(state, { expression, extraNodes })\n getToken(state)\n\n const node = parseBlock(state)\n\n // check for garbage at the end of the expression\n // an expression ends with a empty character '' and tokenType DELIMITER\n if (state.token !== '') {\n if (state.tokenType === TOKENTYPE.DELIMITER) {\n // user entered a not existing operator like \"//\"\n\n // TODO: give hints for aliases, for example with \"<>\" give as hint \" did you mean !== ?\"\n throw createError(state, 'Unexpected operator ' + state.token)\n } else {\n throw createSyntaxError(state, 'Unexpected part \"' + state.token + '\"')\n }\n }\n\n return node\n }\n\n /**\n * Parse a block with expressions. Expressions can be separated by a newline\n * character '\\n', or by a semicolon ';'. In case of a semicolon, no output\n * of the preceding line is returned.\n * @return {Node} node\n * @private\n */\n function parseBlock (state) {\n let node\n const blocks = []\n let visible\n\n if (state.token !== '' && state.token !== '\\n' && state.token !== ';') {\n node = parseAssignment(state)\n node.comment = state.comment\n }\n\n // TODO: simplify this loop\n while (state.token === '\\n' || state.token === ';') { // eslint-disable-line no-unmodified-loop-condition\n if (blocks.length === 0 && node) {\n visible = (state.token !== ';')\n blocks.push({\n node: node,\n visible: visible\n })\n }\n\n getToken(state)\n if (state.token !== '\\n' && state.token !== ';' && state.token !== '') {\n node = parseAssignment(state)\n node.comment = state.comment\n\n visible = (state.token !== ';')\n blocks.push({\n node: node,\n visible: visible\n })\n }\n }\n\n if (blocks.length > 0) {\n return new BlockNode(blocks)\n } else {\n if (!node) {\n node = new ConstantNode(undefined)\n node.comment = state.comment\n }\n\n return node\n }\n }\n\n /**\n * Assignment of a function or variable,\n * - can be a variable like 'a=2.3'\n * - or a updating an existing variable like 'matrix(2,3:5)=[6,7,8]'\n * - defining a function like 'f(x) = x^2'\n * @return {Node} node\n * @private\n */\n function parseAssignment (state) {\n let name, args, value, valid\n\n const node = parseConditional(state)\n\n if (state.token === '=') {\n if (isSymbolNode(node)) {\n // parse a variable assignment like 'a = 2/3'\n name = node.name\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new AssignmentNode(new SymbolNode(name), value)\n } else if (isAccessorNode(node)) {\n // parse a matrix subset assignment like 'A[1,2] = 4'\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new AssignmentNode(node.object, node.index, value)\n } else if (isFunctionNode(node) && isSymbolNode(node.fn)) {\n // parse function assignment like 'f(x) = x^2'\n valid = true\n args = []\n\n name = node.name\n node.args.forEach(function (arg, index) {\n if (isSymbolNode(arg)) {\n args[index] = arg.name\n } else {\n valid = false\n }\n })\n\n if (valid) {\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new FunctionAssignmentNode(name, args, value)\n }\n }\n\n throw createSyntaxError(state, 'Invalid left hand side of assignment operator =')\n }\n\n return node\n }\n\n /**\n * conditional operation\n *\n * condition ? truePart : falsePart\n *\n * Note: conditional operator is right-associative\n *\n * @return {Node} node\n * @private\n */\n function parseConditional (state) {\n let node = parseLogicalOr(state)\n\n while (state.token === '?') { // eslint-disable-line no-unmodified-loop-condition\n // set a conditional level, the range operator will be ignored as long\n // as conditionalLevel === state.nestingLevel.\n const prev = state.conditionalLevel\n state.conditionalLevel = state.nestingLevel\n getTokenSkipNewline(state)\n\n const condition = node\n const trueExpr = parseAssignment(state)\n\n if (state.token !== ':') throw createSyntaxError(state, 'False part of conditional expression expected')\n\n state.conditionalLevel = null\n getTokenSkipNewline(state)\n\n const falseExpr = parseAssignment(state) // Note: check for conditional operator again, right associativity\n\n node = new ConditionalNode(condition, trueExpr, falseExpr)\n\n // restore the previous conditional level\n state.conditionalLevel = prev\n }\n\n return node\n }\n\n /**\n * logical or, 'x or y'\n * @return {Node} node\n * @private\n */\n function parseLogicalOr (state) {\n let node = parseLogicalXor(state)\n\n while (state.token === 'or') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('or', 'or', [node, parseLogicalXor(state)])\n }\n\n return node\n }\n\n /**\n * logical exclusive or, 'x xor y'\n * @return {Node} node\n * @private\n */\n function parseLogicalXor (state) {\n let node = parseLogicalAnd(state)\n\n while (state.token === 'xor') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('xor', 'xor', [node, parseLogicalAnd(state)])\n }\n\n return node\n }\n\n /**\n * logical and, 'x and y'\n * @return {Node} node\n * @private\n */\n function parseLogicalAnd (state) {\n let node = parseBitwiseOr(state)\n\n while (state.token === 'and') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('and', 'and', [node, parseBitwiseOr(state)])\n }\n\n return node\n }\n\n /**\n * bitwise or, 'x | y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseOr (state) {\n let node = parseBitwiseXor(state)\n\n while (state.token === '|') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('|', 'bitOr', [node, parseBitwiseXor(state)])\n }\n\n return node\n }\n\n /**\n * bitwise exclusive or (xor), 'x ^| y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseXor (state) {\n let node = parseBitwiseAnd(state)\n\n while (state.token === '^|') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('^|', 'bitXor', [node, parseBitwiseAnd(state)])\n }\n\n return node\n }\n\n /**\n * bitwise and, 'x & y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseAnd (state) {\n let node = parseRelational(state)\n\n while (state.token === '&') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('&', 'bitAnd', [node, parseRelational(state)])\n }\n\n return node\n }\n\n /**\n * Parse a chained conditional, like 'a > b >= c'\n * @return {Node} node\n */\n function parseRelational (state) {\n const params = [parseShift(state)]\n const conditionals = []\n\n const operators = {\n '==': 'equal',\n '!=': 'unequal',\n '<': 'smaller',\n '>': 'larger',\n '<=': 'smallerEq',\n '>=': 'largerEq'\n }\n\n while (hasOwnProperty(operators, state.token)) { // eslint-disable-line no-unmodified-loop-condition\n const cond = { name: state.token, fn: operators[state.token] }\n conditionals.push(cond)\n getTokenSkipNewline(state)\n params.push(parseShift(state))\n }\n\n if (params.length === 1) {\n return params[0]\n } else if (params.length === 2) {\n return new OperatorNode(conditionals[0].name, conditionals[0].fn, params)\n } else {\n return new RelationalNode(conditionals.map(c => c.fn), params)\n }\n }\n\n /**\n * Bitwise left shift, bitwise right arithmetic shift, bitwise right logical shift\n * @return {Node} node\n * @private\n */\n function parseShift (state) {\n let node, name, fn, params\n\n node = parseConversion(state)\n\n const operators = {\n '<<': 'leftShift',\n '>>': 'rightArithShift',\n '>>>': 'rightLogShift'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n params = [node, parseConversion(state)]\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * conversion operators 'to' and 'in'\n * @return {Node} node\n * @private\n */\n function parseConversion (state) {\n let node, name, fn, params\n\n node = parseRange(state)\n\n const operators = {\n to: 'to',\n in: 'to' // alias of 'to'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n\n if (name === 'in' && state.token === '') {\n // end of expression -> this is the unit 'in' ('inch')\n node = new OperatorNode('*', 'multiply', [node, new SymbolNode('in')], true)\n } else {\n // operator 'a to b' or 'a in b'\n params = [node, parseRange(state)]\n node = new OperatorNode(name, fn, params)\n }\n }\n\n return node\n }\n\n /**\n * parse range, \"start:end\", \"start:step:end\", \":\", \"start:\", \":end\", etc\n * @return {Node} node\n * @private\n */\n function parseRange (state) {\n let node\n const params = []\n\n if (state.token === ':') {\n // implicit start=1 (one-based)\n node = new ConstantNode(1)\n } else {\n // explicit start\n node = parseAddSubtract(state)\n }\n\n if (state.token === ':' && (state.conditionalLevel !== state.nestingLevel)) {\n // we ignore the range operator when a conditional operator is being processed on the same level\n params.push(node)\n\n // parse step and end\n while (state.token === ':' && params.length < 3) { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n\n if (state.token === ')' || state.token === ']' || state.token === ',' || state.token === '') {\n // implicit end\n params.push(new SymbolNode('end'))\n } else {\n // explicit end\n params.push(parseAddSubtract(state))\n }\n }\n\n if (params.length === 3) {\n // params = [start, step, end]\n node = new RangeNode(params[0], params[2], params[1]) // start, end, step\n } else { // length === 2\n // params = [start, end]\n node = new RangeNode(params[0], params[1]) // start, end\n }\n }\n\n return node\n }\n\n /**\n * add or subtract\n * @return {Node} node\n * @private\n */\n function parseAddSubtract (state) {\n let node, name, fn, params\n\n node = parseMultiplyDivide(state)\n\n const operators = {\n '+': 'add',\n '-': 'subtract'\n }\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n params = [node, parseMultiplyDivide(state)]\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * multiply, divide, modulus\n * @return {Node} node\n * @private\n */\n function parseMultiplyDivide (state) {\n let node, last, name, fn\n\n node = parseImplicitMultiplication(state)\n last = node\n\n const operators = {\n '*': 'multiply',\n '.*': 'dotMultiply',\n '/': 'divide',\n './': 'dotDivide',\n '%': 'mod',\n mod: 'mod'\n }\n\n while (true) {\n if (hasOwnProperty(operators, state.token)) {\n // explicit operators\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n\n last = parseImplicitMultiplication(state)\n node = new OperatorNode(name, fn, [node, last])\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * implicit multiplication\n * @return {Node} node\n * @private\n */\n function parseImplicitMultiplication (state) {\n let node, last\n\n node = parseRule2(state)\n last = node\n\n while (true) {\n if ((state.tokenType === TOKENTYPE.SYMBOL) ||\n (state.token === 'in' && isConstantNode(node)) ||\n (state.tokenType === TOKENTYPE.NUMBER &&\n !isConstantNode(last) &&\n (!isOperatorNode(last) || last.op === '!')) ||\n (state.token === '(')) {\n // parse implicit multiplication\n //\n // symbol: implicit multiplication like '2a', '(2+3)a', 'a b'\n // number: implicit multiplication like '(2+3)2'\n // parenthesis: implicit multiplication like '2(3+4)', '(3+4)(1+2)'\n last = parseRule2(state)\n node = new OperatorNode('*', 'multiply', [node, last], true /* implicit */)\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * Infamous \"rule 2\" as described in https://github.com/josdejong/mathjs/issues/792#issuecomment-361065370\n * Explicit division gets higher precedence than implicit multiplication\n * when the division matches this pattern: [number] / [number] [symbol]\n * @return {Node} node\n * @private\n */\n function parseRule2 (state) {\n let node = parseUnary(state)\n let last = node\n const tokenStates = []\n\n while (true) {\n // Match the \"number /\" part of the pattern \"number / number symbol\"\n if (state.token === '/' && isConstantNode(last)) {\n // Look ahead to see if the next token is a number\n tokenStates.push(Object.assign({}, state))\n getTokenSkipNewline(state)\n\n // Match the \"number / number\" part of the pattern\n if (state.tokenType === TOKENTYPE.NUMBER) {\n // Look ahead again\n tokenStates.push(Object.assign({}, state))\n getTokenSkipNewline(state)\n\n // Match the \"symbol\" part of the pattern, or a left parenthesis\n if (state.tokenType === TOKENTYPE.SYMBOL || state.token === '(') {\n // We've matched the pattern \"number / number symbol\".\n // Rewind once and build the \"number / number\" node; the symbol will be consumed later\n Object.assign(state, tokenStates.pop())\n tokenStates.pop()\n last = parseUnary(state)\n node = new OperatorNode('/', 'divide', [node, last])\n } else {\n // Not a match, so rewind\n tokenStates.pop()\n Object.assign(state, tokenStates.pop())\n break\n }\n } else {\n // Not a match, so rewind\n Object.assign(state, tokenStates.pop())\n break\n }\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * Unary plus and minus, and logical and bitwise not\n * @return {Node} node\n * @private\n */\n function parseUnary (state) {\n let name, params, fn\n const operators = {\n '-': 'unaryMinus',\n '+': 'unaryPlus',\n '~': 'bitNot',\n not: 'not'\n }\n\n if (hasOwnProperty(operators, state.token)) {\n fn = operators[state.token]\n name = state.token\n\n getTokenSkipNewline(state)\n params = [parseUnary(state)]\n\n return new OperatorNode(name, fn, params)\n }\n\n return parsePow(state)\n }\n\n /**\n * power\n * Note: power operator is right associative\n * @return {Node} node\n * @private\n */\n function parsePow (state) {\n let node, name, fn, params\n\n node = parseLeftHandOperators(state)\n\n if (state.token === '^' || state.token === '.^') {\n name = state.token\n fn = (name === '^') ? 'pow' : 'dotPow'\n\n getTokenSkipNewline(state)\n params = [node, parseUnary(state)] // Go back to unary, we can have '2^-3'\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * Left hand operators: factorial x!, ctranspose x'\n * @return {Node} node\n * @private\n */\n function parseLeftHandOperators (state) {\n let node, name, fn, params\n\n node = parseCustomNodes(state)\n\n const operators = {\n '!': 'factorial',\n '\\'': 'ctranspose'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getToken(state)\n params = [node]\n\n node = new OperatorNode(name, fn, params)\n node = parseAccessors(state, node)\n }\n\n return node\n }\n\n /**\n * Parse a custom node handler. A node handler can be used to process\n * nodes in a custom way, for example for handling a plot.\n *\n * A handler must be passed as second argument of the parse function.\n * - must extend math.Node\n * - must contain a function _compile(defs: Object) : string\n * - must contain a function find(filter: Object) : Node[]\n * - must contain a function toString() : string\n * - the constructor is called with a single argument containing all parameters\n *\n * For example:\n *\n * nodes = {\n * 'plot': PlotHandler\n * }\n *\n * The constructor of the handler is called as:\n *\n * node = new PlotHandler(params)\n *\n * The handler will be invoked when evaluating an expression like:\n *\n * node = math.parse('plot(sin(x), x)', nodes)\n *\n * @return {Node} node\n * @private\n */\n function parseCustomNodes (state) {\n let params = []\n\n if (state.tokenType === TOKENTYPE.SYMBOL && hasOwnProperty(state.extraNodes, state.token)) {\n const CustomNode = state.extraNodes[state.token]\n\n getToken(state)\n\n // parse parameters\n if (state.token === '(') {\n params = []\n\n openParams(state)\n getToken(state)\n\n if (state.token !== ')') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n }\n\n // create a new custom node\n // noinspection JSValidateTypes\n return new CustomNode(params)\n }\n\n return parseSymbol(state)\n }\n\n /**\n * parse symbols: functions, variables, constants, units\n * @return {Node} node\n * @private\n */\n function parseSymbol (state) {\n let node, name\n\n if (state.tokenType === TOKENTYPE.SYMBOL ||\n (state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS)) {\n name = state.token\n\n getToken(state)\n\n if (hasOwnProperty(CONSTANTS, name)) { // true, false, null, ...\n node = new ConstantNode(CONSTANTS[name])\n } else if (NUMERIC_CONSTANTS.indexOf(name) !== -1) { // NaN, Infinity\n node = new ConstantNode(numeric(name, 'number'))\n } else {\n node = new SymbolNode(name)\n }\n\n // parse function parameters and matrix index\n node = parseAccessors(state, node)\n return node\n }\n\n return parseDoubleQuotesString(state)\n }\n\n /**\n * parse accessors:\n * - function invocation in round brackets (...), for example sqrt(2)\n * - index enclosed in square brackets [...], for example A[2,3]\n * - dot notation for properties, like foo.bar\n * @param {Object} state\n * @param {Node} node Node on which to apply the parameters. If there\n * are no parameters in the expression, the node\n * itself is returned\n * @param {string[]} [types] Filter the types of notations\n * can be ['(', '[', '.']\n * @return {Node} node\n * @private\n */\n function parseAccessors (state, node, types) {\n let params\n\n while ((state.token === '(' || state.token === '[' || state.token === '.') &&\n (!types || types.indexOf(state.token) !== -1)) { // eslint-disable-line no-unmodified-loop-condition\n params = []\n\n if (state.token === '(') {\n if (isSymbolNode(node) || isAccessorNode(node)) {\n // function invocation like fn(2, 3) or obj.fn(2, 3)\n openParams(state)\n getToken(state)\n\n if (state.token !== ')') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new FunctionNode(node, params)\n } else {\n // implicit multiplication like (2+3)(4+5) or sqrt(2)(1+2)\n // don't parse it here but let it be handled by parseImplicitMultiplication\n // with correct precedence\n return node\n }\n } else if (state.token === '[') {\n // index notation like variable[2, 3]\n openParams(state)\n getToken(state)\n\n if (state.token !== ']') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ']') {\n throw createSyntaxError(state, 'Parenthesis ] expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new AccessorNode(node, new IndexNode(params))\n } else {\n // dot notation like variable.prop\n getToken(state)\n\n if (state.tokenType !== TOKENTYPE.SYMBOL) {\n throw createSyntaxError(state, 'Property name expected after dot')\n }\n params.push(new ConstantNode(state.token))\n getToken(state)\n\n const dotNotation = true\n node = new AccessorNode(node, new IndexNode(params, dotNotation))\n }\n }\n\n return node\n }\n\n /**\n * Parse a double quotes string.\n * @return {Node} node\n * @private\n */\n function parseDoubleQuotesString (state) {\n let node, str\n\n if (state.token === '\"') {\n str = parseDoubleQuotesStringToken(state)\n\n // create constant\n node = new ConstantNode(str)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseSingleQuotesString(state)\n }\n\n /**\n * Parse a string surrounded by double quotes \"...\"\n * @return {string}\n */\n function parseDoubleQuotesStringToken (state) {\n let str = ''\n\n while (currentCharacter(state) !== '' && currentCharacter(state) !== '\"') {\n if (currentCharacter(state) === '\\\\') {\n // escape character, immediately process the next\n // character to prevent stopping at a next '\\\"'\n str += currentCharacter(state)\n next(state)\n }\n\n str += currentCharacter(state)\n next(state)\n }\n\n getToken(state)\n if (state.token !== '\"') {\n throw createSyntaxError(state, 'End of string \" expected')\n }\n getToken(state)\n\n return JSON.parse('\"' + str + '\"') // unescape escaped characters\n }\n\n /**\n * Parse a single quotes string.\n * @return {Node} node\n * @private\n */\n function parseSingleQuotesString (state) {\n let node, str\n\n if (state.token === '\\'') {\n str = parseSingleQuotesStringToken(state)\n\n // create constant\n node = new ConstantNode(str)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseMatrix(state)\n }\n\n /**\n * Parse a string surrounded by single quotes '...'\n * @return {string}\n */\n function parseSingleQuotesStringToken (state) {\n let str = ''\n\n while (currentCharacter(state) !== '' && currentCharacter(state) !== '\\'') {\n if (currentCharacter(state) === '\\\\') {\n // escape character, immediately process the next\n // character to prevent stopping at a next '\\''\n str += currentCharacter(state)\n next(state)\n }\n\n str += currentCharacter(state)\n next(state)\n }\n\n getToken(state)\n if (state.token !== '\\'') {\n throw createSyntaxError(state, 'End of string \\' expected')\n }\n getToken(state)\n\n return JSON.parse('\"' + str + '\"') // unescape escaped characters\n }\n\n /**\n * parse the matrix\n * @return {Node} node\n * @private\n */\n function parseMatrix (state) {\n let array, params, rows, cols\n\n if (state.token === '[') {\n // matrix [...]\n openParams(state)\n getToken(state)\n\n if (state.token !== ']') {\n // this is a non-empty matrix\n const row = parseRow(state)\n\n if (state.token === ';') {\n // 2 dimensional array\n rows = 1\n params = [row]\n\n // the rows of the matrix are separated by dot-comma's\n while (state.token === ';') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n\n params[rows] = parseRow(state)\n rows++\n }\n\n if (state.token !== ']') {\n throw createSyntaxError(state, 'End of matrix ] expected')\n }\n closeParams(state)\n getToken(state)\n\n // check if the number of columns matches in all rows\n cols = params[0].items.length\n for (let r = 1; r < rows; r++) {\n if (params[r].items.length !== cols) {\n throw createError(state, 'Column dimensions mismatch ' +\n '(' + params[r].items.length + ' !== ' + cols + ')')\n }\n }\n\n array = new ArrayNode(params)\n } else {\n // 1 dimensional vector\n if (state.token !== ']') {\n throw createSyntaxError(state, 'End of matrix ] expected')\n }\n closeParams(state)\n getToken(state)\n\n array = row\n }\n } else {\n // this is an empty matrix \"[ ]\"\n closeParams(state)\n getToken(state)\n array = new ArrayNode([])\n }\n\n return parseAccessors(state, array)\n }\n\n return parseObject(state)\n }\n\n /**\n * Parse a single comma-separated row from a matrix, like 'a, b, c'\n * @return {ArrayNode} node\n */\n function parseRow (state) {\n const params = [parseAssignment(state)]\n let len = 1\n\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n\n // parse expression\n params[len] = parseAssignment(state)\n len++\n }\n\n return new ArrayNode(params)\n }\n\n /**\n * parse an object, enclosed in angle brackets{...}, for example {value: 2}\n * @return {Node} node\n * @private\n */\n function parseObject (state) {\n if (state.token === '{') {\n openParams(state)\n let key\n\n const properties = {}\n do {\n getToken(state)\n\n if (state.token !== '}') {\n // parse key\n if (state.token === '\"') {\n key = parseDoubleQuotesStringToken(state)\n } else if (state.token === '\\'') {\n key = parseSingleQuotesStringToken(state)\n } else if (state.tokenType === TOKENTYPE.SYMBOL || (state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS)) {\n key = state.token\n getToken(state)\n } else {\n throw createSyntaxError(state, 'Symbol or string expected as object key')\n }\n\n // parse key/value separator\n if (state.token !== ':') {\n throw createSyntaxError(state, 'Colon : expected after object key')\n }\n getToken(state)\n\n // parse key\n properties[key] = parseAssignment(state)\n }\n }\n while (state.token === ',') // eslint-disable-line no-unmodified-loop-condition\n\n if (state.token !== '}') {\n throw createSyntaxError(state, 'Comma , or bracket } expected after object value')\n }\n closeParams(state)\n getToken(state)\n\n let node = new ObjectNode(properties)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseNumber(state)\n }\n\n /**\n * parse a number\n * @return {Node} node\n * @private\n */\n function parseNumber (state) {\n let numberStr\n\n if (state.tokenType === TOKENTYPE.NUMBER) {\n // this is a number\n numberStr = state.token\n getToken(state)\n\n return new ConstantNode(numeric(numberStr, config.number))\n }\n\n return parseParentheses(state)\n }\n\n /**\n * parentheses\n * @return {Node} node\n * @private\n */\n function parseParentheses (state) {\n let node\n\n // check if it is a parenthesized expression\n if (state.token === '(') {\n // parentheses (...)\n openParams(state)\n getToken(state)\n\n node = parseAssignment(state) // start again\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new ParenthesisNode(node)\n node = parseAccessors(state, node)\n return node\n }\n\n return parseEnd(state)\n }\n\n /**\n * Evaluated when the expression is not yet ended but expected to end\n * @return {Node} res\n * @private\n */\n function parseEnd (state) {\n if (state.token === '') {\n // syntax error or unexpected end of expression\n throw createSyntaxError(state, 'Unexpected end of expression')\n } else {\n throw createSyntaxError(state, 'Value expected')\n }\n }\n\n /**\n * Shortcut for getting the current row value (one based)\n * Returns the line of the currently handled expression\n * @private\n */\n /* TODO: implement keeping track on the row number\n function row () {\n return null\n }\n */\n\n /**\n * Shortcut for getting the current col value (one based)\n * Returns the column (position) where the last state.token starts\n * @private\n */\n function col (state) {\n return state.index - state.token.length + 1\n }\n\n /**\n * Create an error\n * @param {Object} state\n * @param {string} message\n * @return {SyntaxError} instantiated error\n * @private\n */\n function createSyntaxError (state, message) {\n const c = col(state)\n const error = new SyntaxError(message + ' (char ' + c + ')')\n error.char = c\n\n return error\n }\n\n /**\n * Create an error\n * @param {Object} state\n * @param {string} message\n * @return {Error} instantiated error\n * @private\n */\n function createError (state, message) {\n const c = col(state)\n const error = new SyntaxError(message + ' (char ' + c + ')')\n error.char = c\n\n return error\n }\n\n return parse\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'compile'\nconst dependencies = ['typed', 'parse']\n\nexport const createCompile = /* #__PURE__ */ factory(name, dependencies, ({ typed, parse }) => {\n /**\n * Parse and compile an expression.\n * Returns a an object with a function `evaluate([scope])` to evaluate the\n * compiled expression.\n *\n * Syntax:\n *\n * math.compile(expr) // returns one node\n * math.compile([expr1, expr2, expr3, ...]) // returns an array with nodes\n *\n * Examples:\n *\n * const code1 = math.compile('sqrt(3^2 + 4^2)')\n * code1.evaluate() // 5\n *\n * let scope = {a: 3, b: 4}\n * const code2 = math.compile('a * b') // 12\n * code2.evaluate(scope) // 12\n * scope.a = 5\n * code2.evaluate(scope) // 20\n *\n * const nodes = math.compile(['a = 3', 'b = 4', 'a * b'])\n * nodes[2].evaluate() // 12\n *\n * See also:\n *\n * parse, evaluate\n *\n * @param {string | string[] | Array | Matrix} expr\n * The expression to be compiled\n * @return {{evaluate: Function} | Array.<{evaluate: Function}>} code\n * An object with the compiled expression\n * @throws {Error}\n */\n return typed(name, {\n string: function (expr) {\n return parse(expr).compile()\n },\n\n 'Array | Matrix': function (expr) {\n return deepMap(expr, function (entry) {\n return parse(entry).compile()\n })\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'evaluate'\nconst dependencies = ['typed', 'parse']\n\nexport const createEvaluate = /* #__PURE__ */ factory(name, dependencies, ({ typed, parse }) => {\n /**\n * Evaluate an expression.\n *\n * Note the evaluating arbitrary expressions may involve security risks,\n * see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.\n *\n * Syntax:\n *\n * math.evaluate(expr)\n * math.evaluate(expr, scope)\n * math.evaluate([expr1, expr2, expr3, ...])\n * math.evaluate([expr1, expr2, expr3, ...], scope)\n *\n * Example:\n *\n * math.evaluate('(2+3)/4') // 1.25\n * math.evaluate('sqrt(3^2 + 4^2)') // 5\n * math.evaluate('sqrt(-4)') // 2i\n * math.evaluate(['a=3', 'b=4', 'a*b']) // [3, 4, 12]\n *\n * let scope = {a:3, b:4}\n * math.evaluate('a * b', scope) // 12\n *\n * See also:\n *\n * parse, compile\n *\n * @param {string | string[] | Matrix} expr The expression to be evaluated\n * @param {Object} [scope] Scope to read/write variables\n * @return {*} The result of the expression\n * @throws {Error}\n */\n return typed(name, {\n string: function (expr) {\n const scope = {}\n return parse(expr).compile().evaluate(scope)\n },\n\n 'string, Object': function (expr, scope) {\n return parse(expr).compile().evaluate(scope)\n },\n\n 'Array | Matrix': function (expr) {\n const scope = {}\n return deepMap(expr, function (entry) {\n return parse(entry).compile().evaluate(scope)\n })\n },\n\n 'Array | Matrix, Object': function (expr, scope) {\n return deepMap(expr, function (entry) {\n return parse(entry).compile().evaluate(scope)\n })\n }\n })\n})\n","import { factory } from '../utils/factory.js'\nimport { extend, hasOwnProperty } from '../utils/object.js'\nimport { getSafeProperty, setSafeProperty } from '../utils/customs.js'\n\nconst name = 'Parser'\nconst dependencies = ['parse']\n\nexport const createParserClass = /* #__PURE__ */ factory(name, dependencies, ({ parse }) => {\n /**\n * @constructor Parser\n * Parser contains methods to evaluate or parse expressions, and has a number\n * of convenience methods to get, set, and remove variables from memory. Parser\n * keeps a scope containing variables in memory, which is used for all\n * evaluations.\n *\n * Methods:\n * const result = parser.evaluate(expr) // evaluate an expression\n * const value = parser.get(name) // retrieve a variable from the parser\n * const values = parser.getAll() // retrieve all defined variables\n * parser.set(name, value) // set a variable in the parser\n * parser.remove(name) // clear a variable from the\n * // parsers scope\n * parser.clear() // clear the parsers scope\n *\n * Example usage:\n * const parser = new Parser()\n * // Note: there is a convenience method which can be used instead:\n * // const parser = new math.parser()\n *\n * // evaluate expressions\n * parser.evaluate('sqrt(3^2 + 4^2)') // 5\n * parser.evaluate('sqrt(-4)') // 2i\n * parser.evaluate('2 inch in cm') // 5.08 cm\n * parser.evaluate('cos(45 deg)') // 0.7071067811865476\n *\n * // define variables and functions\n * parser.evaluate('x = 7 / 2') // 3.5\n * parser.evaluate('x + 3') // 6.5\n * parser.evaluate('function f(x, y) = x^y') // f(x, y)\n * parser.evaluate('f(2, 3)') // 8\n *\n * // get and set variables and functions\n * const x = parser.get('x') // 7\n * const f = parser.get('f') // function\n * const g = f(3, 2) // 9\n * parser.set('h', 500)\n * const i = parser.evaluate('h / 2') // 250\n * parser.set('hello', function (name) {\n * return 'hello, ' + name + '!'\n * })\n * parser.evaluate('hello(\"user\")') // \"hello, user!\"\n *\n * // clear defined functions and variables\n * parser.clear()\n *\n */\n function Parser () {\n if (!(this instanceof Parser)) {\n throw new SyntaxError(\n 'Constructor must be called with the new operator')\n }\n this.scope = {}\n }\n\n /**\n * Attach type information\n */\n Parser.prototype.type = 'Parser'\n Parser.prototype.isParser = true\n\n /**\n * Parse and evaluate the given expression\n * @param {string} expr A string containing an expression, for example \"2+3\"\n * @return {*} result The result, or undefined when the expression was empty\n * @throws {Error}\n */\n Parser.prototype.evaluate = function (expr) {\n // TODO: validate arguments\n return parse(expr)\n .compile()\n .evaluate(this.scope)\n }\n\n /**\n * Get a variable (a function or variable) by name from the parsers scope.\n * Returns undefined when not found\n * @param {string} name\n * @return {* | undefined} value\n */\n Parser.prototype.get = function (name) {\n // TODO: validate arguments\n return name in this.scope\n ? getSafeProperty(this.scope, name)\n : undefined\n }\n\n /**\n * Get a map with all defined variables\n * @return {Object} values\n */\n Parser.prototype.getAll = function () {\n return extend({}, this.scope)\n }\n\n /**\n * Set a symbol (a function or variable) by name from the parsers scope.\n * @param {string} name\n * @param {* | undefined} value\n */\n Parser.prototype.set = function (name, value) {\n // TODO: validate arguments\n return setSafeProperty(this.scope, name, value)\n }\n\n /**\n * Remove a variable from the parsers scope\n * @param {string} name\n */\n Parser.prototype.remove = function (name) {\n // TODO: validate arguments\n delete this.scope[name]\n }\n\n /**\n * Clear the scope with variables and functions\n */\n Parser.prototype.clear = function () {\n for (const name in this.scope) {\n if (hasOwnProperty(this.scope, name)) {\n delete this.scope[name]\n }\n }\n }\n\n return Parser\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'parser'\nconst dependencies = ['typed', 'Parser']\n\nexport const createParser = /* #__PURE__ */ factory(name, dependencies, ({ typed, Parser }) => {\n /**\n * Create a parser. The function creates a new `math.Parser` object.\n *\n * Syntax:\n *\n * math.parser()\n *\n * Examples:\n *\n * const parser = new math.parser()\n *\n * // evaluate expressions\n * const a = parser.evaluate('sqrt(3^2 + 4^2)') // 5\n * const b = parser.evaluate('sqrt(-4)') // 2i\n * const c = parser.evaluate('2 inch in cm') // 5.08 cm\n * const d = parser.evaluate('cos(45 deg)') // 0.7071067811865476\n *\n * // define variables and functions\n * parser.evaluate('x = 7 / 2') // 3.5\n * parser.evaluate('x + 3') // 6.5\n * parser.evaluate('function f(x, y) = x^y') // f(x, y)\n * parser.evaluate('f(2, 3)') // 8\n *\n * // get and set variables and functions\n * const x = parser.get('x') // 7\n * const f = parser.get('f') // function\n * const g = f(3, 2) // 9\n * parser.set('h', 500)\n * const i = parser.evaluate('h / 2') // 250\n * parser.set('hello', function (name) {\n * return 'hello, ' + name + '!'\n * })\n * parser.evaluate('hello(\"user\")') // \"hello, user!\"\n *\n * // clear defined functions and variables\n * parser.clear()\n *\n * See also:\n *\n * evaluate, compile, parse\n *\n * @return {Parser} Parser\n */\n return typed(name, {\n '': function () {\n return new Parser()\n }\n })\n})\n","import { clone } from '../../../utils/object.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'lup'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'abs',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'larger',\n 'equalScalar',\n 'unaryMinus',\n 'DenseMatrix',\n 'SparseMatrix',\n 'Spa'\n]\n\nexport const createLup = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n matrix,\n abs,\n addScalar,\n divideScalar,\n multiplyScalar,\n subtract,\n larger,\n equalScalar,\n unaryMinus,\n DenseMatrix,\n SparseMatrix,\n Spa\n }\n) => {\n /**\n * Calculate the Matrix LU decomposition with partial pivoting. Matrix `A` is decomposed in two matrices (`L`, `U`) and a\n * row permutation vector `p` where `A[p,:] = L * U`\n *\n * Syntax:\n *\n * math.lup(A)\n *\n * Example:\n *\n * const m = [[2, 1], [1, 4]]\n * const r = math.lup(m)\n * // r = {\n * // L: [[1, 0], [0.5, 1]],\n * // U: [[2, 1], [0, 3.5]],\n * // P: [0, 1]\n * // }\n *\n * See also:\n *\n * slu, lsolve, lusolve, usolve\n *\n * @param {Matrix | Array} A A two dimensional matrix or array for which to get the LUP decomposition.\n *\n * @return {{L: Array | Matrix, U: Array | Matrix, P: Array.}} The lower triangular matrix, the upper triangular matrix and the permutation matrix.\n */\n return typed(name, {\n\n DenseMatrix: function (m) {\n return _denseLUP(m)\n },\n\n SparseMatrix: function (m) {\n return _sparseLUP(m)\n },\n\n Array: function (a) {\n // create dense matrix from array\n const m = matrix(a)\n // lup, use matrix implementation\n const r = _denseLUP(m)\n // result\n return {\n L: r.L.valueOf(),\n U: r.U.valueOf(),\n p: r.p\n }\n }\n })\n\n function _denseLUP (m) {\n // rows & columns\n const rows = m._size[0]\n const columns = m._size[1]\n // minimum rows and columns\n let n = Math.min(rows, columns)\n // matrix array, clone original data\n const data = clone(m._data)\n // l matrix arrays\n const ldata = []\n const lsize = [rows, n]\n // u matrix arrays\n const udata = []\n const usize = [n, columns]\n // vars\n let i, j, k\n // permutation vector\n const p = []\n for (i = 0; i < rows; i++) { p[i] = i }\n // loop columns\n for (j = 0; j < columns; j++) {\n // skip first column in upper triangular matrix\n if (j > 0) {\n // loop rows\n for (i = 0; i < rows; i++) {\n // min i,j\n const min = Math.min(i, j)\n // v[i, j]\n let s = 0\n // loop up to min\n for (k = 0; k < min; k++) {\n // s = l[i, k] - data[k, j]\n s = addScalar(s, multiplyScalar(data[i][k], data[k][j]))\n }\n data[i][j] = subtract(data[i][j], s)\n }\n }\n // row with larger value in cvector, row >= j\n let pi = j\n let pabsv = 0\n let vjj = 0\n // loop rows\n for (i = j; i < rows; i++) {\n // data @ i, j\n const v = data[i][j]\n // absolute value\n const absv = abs(v)\n // value is greater than pivote value\n if (larger(absv, pabsv)) {\n // store row\n pi = i\n // update max value\n pabsv = absv\n // value @ [j, j]\n vjj = v\n }\n }\n // swap rows (j <-> pi)\n if (j !== pi) {\n // swap values j <-> pi in p\n p[j] = [p[pi], p[pi] = p[j]][0]\n // swap j <-> pi in data\n DenseMatrix._swapRows(j, pi, data)\n }\n // check column is in lower triangular matrix\n if (j < rows) {\n // loop rows (lower triangular matrix)\n for (i = j + 1; i < rows; i++) {\n // value @ i, j\n const vij = data[i][j]\n if (!equalScalar(vij, 0)) {\n // update data\n data[i][j] = divideScalar(data[i][j], vjj)\n }\n }\n }\n }\n // loop columns\n for (j = 0; j < columns; j++) {\n // loop rows\n for (i = 0; i < rows; i++) {\n // initialize row in arrays\n if (j === 0) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i] = []\n }\n // L\n ldata[i] = []\n }\n // check we are in the upper triangular matrix\n if (i < j) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = data[i][j]\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = 0\n }\n continue\n }\n // diagonal value\n if (i === j) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = data[i][j]\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = 1\n }\n continue\n }\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = 0\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = data[i][j]\n }\n }\n }\n // l matrix\n const l = new DenseMatrix({\n data: ldata,\n size: lsize\n })\n // u matrix\n const u = new DenseMatrix({\n data: udata,\n size: usize\n })\n // p vector\n const pv = []\n for (i = 0, n = p.length; i < n; i++) { pv[p[i]] = i }\n // return matrices\n return {\n L: l,\n U: u,\n p: pv,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\nP: ' + this.p\n }\n }\n }\n\n function _sparseLUP (m) {\n // rows & columns\n const rows = m._size[0]\n const columns = m._size[1]\n // minimum rows and columns\n const n = Math.min(rows, columns)\n // matrix arrays (will not be modified, thanks to permutation vector)\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // l matrix arrays\n const lvalues = []\n const lindex = []\n const lptr = []\n const lsize = [rows, n]\n // u matrix arrays\n const uvalues = []\n const uindex = []\n const uptr = []\n const usize = [n, columns]\n // vars\n let i, j, k\n // permutation vectors, (current index -> original index) and (original index -> current index)\n const pvCo = []\n const pvOc = []\n for (i = 0; i < rows; i++) {\n pvCo[i] = i\n pvOc[i] = i\n }\n // swap indices in permutation vectors (condition x < y)!\n const swapIndeces = function (x, y) {\n // find pv indeces getting data from x and y\n const kx = pvOc[x]\n const ky = pvOc[y]\n // update permutation vector current -> original\n pvCo[kx] = y\n pvCo[ky] = x\n // update permutation vector original -> current\n pvOc[x] = ky\n pvOc[y] = kx\n }\n // loop columns\n for (j = 0; j < columns; j++) {\n // sparse accumulator\n const spa = new Spa()\n // check lower triangular matrix has a value @ column j\n if (j < rows) {\n // update ptr\n lptr.push(lvalues.length)\n // first value in j column for lower triangular matrix\n lvalues.push(1)\n lindex.push(j)\n }\n // update ptr\n uptr.push(uvalues.length)\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // copy column j into sparse accumulator\n for (k = k0; k < k1; k++) {\n // row\n i = index[k]\n // copy column values into sparse accumulator (use permutation vector)\n spa.set(pvCo[i], values[k])\n }\n // skip first column in upper triangular matrix\n if (j > 0) {\n // loop rows in column j (above diagonal)\n spa.forEach(0, j - 1, function (k, vkj) {\n // loop rows in column k (L)\n SparseMatrix._forEachRow(k, lvalues, lindex, lptr, function (i, vik) {\n // check row is below k\n if (i > k) {\n // update spa value\n spa.accumulate(i, unaryMinus(multiplyScalar(vik, vkj)))\n }\n })\n })\n }\n // row with larger value in spa, row >= j\n let pi = j\n let vjj = spa.get(j)\n let pabsv = abs(vjj)\n // loop values in spa (order by row, below diagonal)\n spa.forEach(j + 1, rows - 1, function (x, v) {\n // absolute value\n const absv = abs(v)\n // value is greater than pivote value\n if (larger(absv, pabsv)) {\n // store row\n pi = x\n // update max value\n pabsv = absv\n // value @ [j, j]\n vjj = v\n }\n })\n // swap rows (j <-> pi)\n if (j !== pi) {\n // swap values j <-> pi in L\n SparseMatrix._swapRows(j, pi, lsize[1], lvalues, lindex, lptr)\n // swap values j <-> pi in U\n SparseMatrix._swapRows(j, pi, usize[1], uvalues, uindex, uptr)\n // swap values in spa\n spa.swap(j, pi)\n // update permutation vector (swap values @ j, pi)\n swapIndeces(j, pi)\n }\n // loop values in spa (order by row)\n spa.forEach(0, rows - 1, function (x, v) {\n // check we are above diagonal\n if (x <= j) {\n // update upper triangular matrix\n uvalues.push(v)\n uindex.push(x)\n } else {\n // update value\n v = divideScalar(v, vjj)\n // check value is non zero\n if (!equalScalar(v, 0)) {\n // update lower triangular matrix\n lvalues.push(v)\n lindex.push(x)\n }\n }\n })\n }\n // update ptrs\n uptr.push(uvalues.length)\n lptr.push(lvalues.length)\n\n // return matrices\n return {\n L: new SparseMatrix({\n values: lvalues,\n index: lindex,\n ptr: lptr,\n size: lsize\n }),\n U: new SparseMatrix({\n values: uvalues,\n index: uindex,\n ptr: uptr,\n size: usize\n }),\n p: pvCo,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\nP: ' + this.p\n }\n }\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'qr'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'zeros',\n 'identity',\n 'isZero',\n 'equal',\n 'sign',\n 'sqrt',\n 'conj',\n 'unaryMinus',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'complex'\n]\n\nexport const createQr = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n matrix,\n zeros,\n identity,\n isZero,\n equal,\n sign,\n sqrt,\n conj,\n unaryMinus,\n addScalar,\n divideScalar,\n multiplyScalar,\n subtract,\n complex\n }\n) => {\n /**\n * Calculate the Matrix QR decomposition. Matrix `A` is decomposed in\n * two matrices (`Q`, `R`) where `Q` is an\n * orthogonal matrix and `R` is an upper triangular matrix.\n *\n * Syntax:\n *\n * math.qr(A)\n *\n * Example:\n *\n * const m = [\n * [1, -1, 4],\n * [1, 4, -2],\n * [1, 4, 2],\n * [1, -1, 0]\n * ]\n * const result = math.qr(m)\n * // r = {\n * // Q: [\n * // [0.5, -0.5, 0.5],\n * // [0.5, 0.5, -0.5],\n * // [0.5, 0.5, 0.5],\n * // [0.5, -0.5, -0.5],\n * // ],\n * // R: [\n * // [2, 3, 2],\n * // [0, 5, -2],\n * // [0, 0, 4],\n * // [0, 0, 0]\n * // ]\n * // }\n *\n * See also:\n *\n * lup, lusolve\n *\n * @param {Matrix | Array} A A two dimensional matrix or array\n * for which to get the QR decomposition.\n *\n * @return {{Q: Array | Matrix, R: Array | Matrix}} Q: the orthogonal\n * matrix and R: the upper triangular matrix\n */\n return Object.assign(typed(name, {\n\n DenseMatrix: function (m) {\n return _denseQR(m)\n },\n\n SparseMatrix: function (m) {\n return _sparseQR(m)\n },\n\n Array: function (a) {\n // create dense matrix from array\n const m = matrix(a)\n // lup, use matrix implementation\n const r = _denseQR(m)\n // result\n return {\n Q: r.Q.valueOf(),\n R: r.R.valueOf()\n }\n }\n }), { _denseQRimpl })\n\n function _denseQRimpl (m) {\n // rows & columns (m x n)\n const rows = m._size[0] // m\n const cols = m._size[1] // n\n\n const Q = identity([rows], 'dense')\n const Qdata = Q._data\n\n const R = m.clone()\n const Rdata = R._data\n\n // vars\n let i, j, k\n\n const w = zeros([rows], '')\n\n for (k = 0; k < Math.min(cols, rows); ++k) {\n /*\n * **k-th Household matrix**\n *\n * The matrix I - 2*v*transpose(v)\n * x = first column of A\n * x1 = first element of x\n * alpha = x1 / |x1| * |x|\n * e1 = tranpose([1, 0, 0, ...])\n * u = x - alpha * e1\n * v = u / |u|\n *\n * Household matrix = I - 2 * v * tranpose(v)\n *\n * * Initially Q = I and R = A.\n * * Household matrix is a reflection in a plane normal to v which\n * will zero out all but the top right element in R.\n * * Appplying reflection to both Q and R will not change product.\n * * Repeat this process on the (1,1) minor to get R as an upper\n * triangular matrix.\n * * Reflections leave the magnitude of the columns of Q unchanged\n * so Q remains othoganal.\n *\n */\n\n const pivot = Rdata[k][k]\n const sgn = unaryMinus(equal(pivot, 0) ? 1 : sign(pivot))\n const conjSgn = conj(sgn)\n\n let alphaSquared = 0\n\n for (i = k; i < rows; i++) {\n alphaSquared = addScalar(alphaSquared, multiplyScalar(Rdata[i][k], conj(Rdata[i][k])))\n }\n\n const alpha = multiplyScalar(sgn, sqrt(alphaSquared))\n\n if (!isZero(alpha)) {\n // first element in vector u\n const u1 = subtract(pivot, alpha)\n\n // w = v * u1 / |u| (only elements k to (rows-1) are used)\n w[k] = 1\n\n for (i = k + 1; i < rows; i++) {\n w[i] = divideScalar(Rdata[i][k], u1)\n }\n\n // tau = - conj(u1 / alpha)\n const tau = unaryMinus(conj(divideScalar(u1, alpha)))\n\n let s\n\n /*\n * tau and w have been choosen so that\n *\n * 2 * v * tranpose(v) = tau * w * tranpose(w)\n */\n\n /*\n * -- calculate R = R - tau * w * tranpose(w) * R --\n * Only do calculation with rows k to (rows-1)\n * Additionally columns 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n for (j = k; j < cols; j++) {\n s = 0.0\n\n // calculate jth element of [tranpose(w) * R]\n for (i = k; i < rows; i++) {\n s = addScalar(s, multiplyScalar(conj(w[i]), Rdata[i][j]))\n }\n\n // calculate the jth element of [tau * transpose(w) * R]\n s = multiplyScalar(s, tau)\n\n for (i = k; i < rows; i++) {\n Rdata[i][j] = multiplyScalar(\n subtract(Rdata[i][j], multiplyScalar(w[i], s)),\n conjSgn\n )\n }\n }\n /*\n * -- calculate Q = Q - tau * Q * w * transpose(w) --\n * Q is a square matrix (rows x rows)\n * Only do calculation with columns k to (rows-1)\n * Additionally rows 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n for (i = 0; i < rows; i++) {\n s = 0.0\n\n // calculate ith element of [Q * w]\n for (j = k; j < rows; j++) {\n s = addScalar(s, multiplyScalar(Qdata[i][j], w[j]))\n }\n\n // calculate the ith element of [tau * Q * w]\n s = multiplyScalar(s, tau)\n\n for (j = k; j < rows; ++j) {\n Qdata[i][j] = divideScalar(\n subtract(Qdata[i][j], multiplyScalar(s, conj(w[j]))),\n conjSgn\n )\n }\n }\n }\n }\n\n // return matrices\n return {\n Q: Q,\n R: R,\n toString: function () {\n return 'Q: ' + this.Q.toString() + '\\nR: ' + this.R.toString()\n }\n }\n }\n\n function _denseQR (m) {\n const ret = _denseQRimpl(m)\n const Rdata = ret.R._data\n if (m._data.length > 0) {\n const zero = Rdata[0][0].type === 'Complex' ? complex(0) : 0\n\n for (let i = 0; i < Rdata.length; ++i) {\n for (let j = 0; j < i && j < (Rdata[0] || []).length; ++j) {\n Rdata[i][j] = zero\n }\n }\n }\n\n return ret\n }\n\n function _sparseQR (m) {\n throw new Error('qr not implemented for sparse matrices yet')\n }\n})\n","/**\n * Depth-first search and postorder of a tree rooted at node j\n *\n * @param {Number} j The tree node\n * @param {Number} k\n * @param {Array} w The workspace array\n * @param {Number} head The index offset within the workspace for the head array\n * @param {Number} next The index offset within the workspace for the next array\n * @param {Array} post The post ordering array\n * @param {Number} stack The index offset within the workspace for the stack array\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csTdfs (j, k, w, head, next, post, stack) {\n // variables\n let top = 0\n // place j on the stack\n w[stack] = j\n // while (stack is not empty)\n while (top >= 0) {\n // p = top of stack\n const p = w[stack + top]\n // i = youngest child of p\n const i = w[head + p]\n if (i === -1) {\n // p has no unordered children left\n top--\n // node p is the kth postordered node\n post[k++] = p\n } else {\n // remove i from children of p\n w[head + p] = w[next + i]\n // increment top\n ++top\n // start dfs on child node i\n w[stack + top] = i\n }\n }\n return k\n}\n","/**\n * This function \"flips\" its input about the integer -1.\n *\n * @param {Number} i The value to flip\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csFlip (i) {\n // flip the value\n return -i - 2\n}\n","import { factory } from '../../../utils/factory.js'\nimport { csFkeep } from './csFkeep.js'\nimport { csFlip } from './csFlip.js'\nimport { csTdfs } from './csTdfs.js'\n\nconst name = 'csAmd'\nconst dependencies = [\n 'add',\n 'multiply',\n 'transpose'\n]\n\nexport const createCsAmd = /* #__PURE__ */ factory(name, dependencies, ({ add, multiply, transpose }) => {\n /**\n * Approximate minimum degree ordering. The minimum degree algorithm is a widely used\n * heuristic for finding a permutation P so that P*A*P' has fewer nonzeros in its factorization\n * than A. It is a gready method that selects the sparsest pivot row and column during the course\n * of a right looking sparse Cholesky factorization.\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n *\n * @param {Number} order 0: Natural, 1: Cholesky, 2: LU, 3: QR\n * @param {Matrix} m Sparse Matrix\n */\n return function csAmd (order, a) {\n // check input parameters\n if (!a || order <= 0 || order > 3) { return null }\n // a matrix arrays\n const asize = a._size\n // rows and columns\n const m = asize[0]\n const n = asize[1]\n // initialize vars\n let lemax = 0\n // dense threshold\n let dense = Math.max(16, 10 * Math.sqrt(n))\n dense = Math.min(n - 2, dense)\n // create target matrix C\n const cm = _createTargetMatrix(order, a, m, n, dense)\n // drop diagonal entries\n csFkeep(cm, _diag, null)\n // C matrix arrays\n const cindex = cm._index\n const cptr = cm._ptr\n\n // number of nonzero elements in C\n let cnz = cptr[n]\n\n // allocate result (n+1)\n const P = []\n\n // create workspace (8 * (n + 1))\n const W = []\n const len = 0 // first n + 1 entries\n const nv = n + 1 // next n + 1 entries\n const next = 2 * (n + 1) // next n + 1 entries\n const head = 3 * (n + 1) // next n + 1 entries\n const elen = 4 * (n + 1) // next n + 1 entries\n const degree = 5 * (n + 1) // next n + 1 entries\n const w = 6 * (n + 1) // next n + 1 entries\n const hhead = 7 * (n + 1) // last n + 1 entries\n\n // use P as workspace for last\n const last = P\n\n // initialize quotient graph\n let mark = _initializeQuotientGraph(n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree)\n\n // initialize degree lists\n let nel = _initializeDegreeLists(n, cptr, W, degree, elen, w, dense, nv, head, last, next)\n\n // minimum degree node\n let mindeg = 0\n\n // vars\n let i, j, k, k1, k2, e, pj, ln, nvi, pk, eln, p1, p2, pn, h, d\n\n // while (selecting pivots) do\n while (nel < n) {\n // select node of minimum approximate degree. amd() is now ready to start eliminating the graph. It first\n // finds a node k of minimum degree and removes it from its degree list. The variable nel keeps track of thow\n // many nodes have been eliminated.\n for (k = -1; mindeg < n && (k = W[head + mindeg]) === -1; mindeg++);\n if (W[next + k] !== -1) { last[W[next + k]] = -1 }\n // remove k from degree list\n W[head + mindeg] = W[next + k]\n // elenk = |Ek|\n const elenk = W[elen + k]\n // # of nodes k represents\n let nvk = W[nv + k]\n // W[nv + k] nodes of A eliminated\n nel += nvk\n\n // Construct a new element. The new element Lk is constructed in place if |Ek| = 0. nv[i] is\n // negated for all nodes i in Lk to flag them as members of this set. Each node i is removed from the\n // degree lists. All elements e in Ek are absorved into element k.\n let dk = 0\n // flag k as in Lk\n W[nv + k] = -nvk\n let p = cptr[k]\n // do in place if W[elen + k] === 0\n const pk1 = (elenk === 0) ? p : cnz\n let pk2 = pk1\n for (k1 = 1; k1 <= elenk + 1; k1++) {\n if (k1 > elenk) {\n // search the nodes in k\n e = k\n // list of nodes starts at cindex[pj]\n pj = p\n // length of list of nodes in k\n ln = W[len + k] - elenk\n } else {\n // search the nodes in e\n e = cindex[p++]\n pj = cptr[e]\n // length of list of nodes in e\n ln = W[len + e]\n }\n for (k2 = 1; k2 <= ln; k2++) {\n i = cindex[pj++]\n // check node i dead, or seen\n if ((nvi = W[nv + i]) <= 0) { continue }\n // W[degree + Lk] += size of node i\n dk += nvi\n // negate W[nv + i] to denote i in Lk\n W[nv + i] = -nvi\n // place i in Lk\n cindex[pk2++] = i\n if (W[next + i] !== -1) { last[W[next + i]] = last[i] }\n // check we need to remove i from degree list\n if (last[i] !== -1) { W[next + last[i]] = W[next + i] } else { W[head + W[degree + i]] = W[next + i] }\n }\n if (e !== k) {\n // absorb e into k\n cptr[e] = csFlip(k)\n // e is now a dead element\n W[w + e] = 0\n }\n }\n // cindex[cnz...nzmax] is free\n if (elenk !== 0) { cnz = pk2 }\n // external degree of k - |Lk\\i|\n W[degree + k] = dk\n // element k is in cindex[pk1..pk2-1]\n cptr[k] = pk1\n W[len + k] = pk2 - pk1\n // k is now an element\n W[elen + k] = -2\n\n // Find set differences. The scan1 function now computes the set differences |Le \\ Lk| for all elements e. At the start of the\n // scan, no entry in the w array is greater than or equal to mark.\n\n // clear w if necessary\n mark = _wclear(mark, lemax, W, w, n)\n // scan 1: find |Le\\Lk|\n for (pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check if W[elen + i] empty, skip it\n if ((eln = W[elen + i]) <= 0) { continue }\n // W[nv + i] was negated\n nvi = -W[nv + i]\n const wnvi = mark - nvi\n // scan Ei\n for (p = cptr[i], p1 = cptr[i] + eln - 1; p <= p1; p++) {\n e = cindex[p]\n if (W[w + e] >= mark) {\n // decrement |Le\\Lk|\n W[w + e] -= nvi\n } else if (W[w + e] !== 0) {\n // ensure e is a live element, 1st time e seen in scan 1\n W[w + e] = W[degree + e] + wnvi\n }\n }\n }\n\n // degree update\n // The second pass computes the approximate degree di, prunes the sets Ei and Ai, and computes a hash\n // function h(i) for all nodes in Lk.\n\n // scan2: degree update\n for (pk = pk1; pk < pk2; pk++) {\n // consider node i in Lk\n i = cindex[pk]\n p1 = cptr[i]\n p2 = p1 + W[elen + i] - 1\n pn = p1\n // scan Ei\n for (h = 0, d = 0, p = p1; p <= p2; p++) {\n e = cindex[p]\n // check e is an unabsorbed element\n if (W[w + e] !== 0) {\n // dext = |Le\\Lk|\n const dext = W[w + e] - mark\n if (dext > 0) {\n // sum up the set differences\n d += dext\n // keep e in Ei\n cindex[pn++] = e\n // compute the hash of node i\n h += e\n } else {\n // aggressive absorb. e->k\n cptr[e] = csFlip(k)\n // e is a dead element\n W[w + e] = 0\n }\n }\n }\n // W[elen + i] = |Ei|\n W[elen + i] = pn - p1 + 1\n const p3 = pn\n const p4 = p1 + W[len + i]\n // prune edges in Ai\n for (p = p2 + 1; p < p4; p++) {\n j = cindex[p]\n // check node j dead or in Lk\n const nvj = W[nv + j]\n if (nvj <= 0) { continue }\n // degree(i) += |j|\n d += nvj\n // place j in node list of i\n cindex[pn++] = j\n // compute hash for node i\n h += j\n }\n // check for mass elimination\n if (d === 0) {\n // absorb i into k\n cptr[i] = csFlip(k)\n nvi = -W[nv + i]\n // |Lk| -= |i|\n dk -= nvi\n // |k| += W[nv + i]\n nvk += nvi\n nel += nvi\n W[nv + i] = 0\n // node i is dead\n W[elen + i] = -1\n } else {\n // update degree(i)\n W[degree + i] = Math.min(W[degree + i], d)\n // move first node to end\n cindex[pn] = cindex[p3]\n // move 1st el. to end of Ei\n cindex[p3] = cindex[p1]\n // add k as 1st element in of Ei\n cindex[p1] = k\n // new len of adj. list of node i\n W[len + i] = pn - p1 + 1\n // finalize hash of i\n h = (h < 0 ? -h : h) % n\n // place i in hash bucket\n W[next + i] = W[hhead + h]\n W[hhead + h] = i\n // save hash of i in last[i]\n last[i] = h\n }\n }\n // finalize |Lk|\n W[degree + k] = dk\n lemax = Math.max(lemax, dk)\n // clear w\n mark = _wclear(mark + lemax, lemax, W, w, n)\n\n // Supernode detection. Supernode detection relies on the hash function h(i) computed for each node i.\n // If two nodes have identical adjacency lists, their hash functions wil be identical.\n for (pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check i is dead, skip it\n if (W[nv + i] >= 0) { continue }\n // scan hash bucket of node i\n h = last[i]\n i = W[hhead + h]\n // hash bucket will be empty\n W[hhead + h] = -1\n for (; i !== -1 && W[next + i] !== -1; i = W[next + i], mark++) {\n ln = W[len + i]\n eln = W[elen + i]\n for (p = cptr[i] + 1; p <= cptr[i] + ln - 1; p++) { W[w + cindex[p]] = mark }\n let jlast = i\n // compare i with all j\n for (j = W[next + i]; j !== -1;) {\n let ok = W[len + j] === ln && W[elen + j] === eln\n for (p = cptr[j] + 1; ok && p <= cptr[j] + ln - 1; p++) {\n // compare i and j\n if (W[w + cindex[p]] !== mark) { ok = 0 }\n }\n // check i and j are identical\n if (ok) {\n // absorb j into i\n cptr[j] = csFlip(i)\n W[nv + i] += W[nv + j]\n W[nv + j] = 0\n // node j is dead\n W[elen + j] = -1\n // delete j from hash bucket\n j = W[next + j]\n W[next + jlast] = j\n } else {\n // j and i are different\n jlast = j\n j = W[next + j]\n }\n }\n }\n }\n\n // Finalize new element. The elimination of node k is nearly complete. All nodes i in Lk are scanned one last time.\n // Node i is removed from Lk if it is dead. The flagged status of nv[i] is cleared.\n for (p = pk1, pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check i is dead, skip it\n if ((nvi = -W[nv + i]) <= 0) { continue }\n // restore W[nv + i]\n W[nv + i] = nvi\n // compute external degree(i)\n d = W[degree + i] + dk - nvi\n d = Math.min(d, n - nel - nvi)\n if (W[head + d] !== -1) { last[W[head + d]] = i }\n // put i back in degree list\n W[next + i] = W[head + d]\n last[i] = -1\n W[head + d] = i\n // find new minimum degree\n mindeg = Math.min(mindeg, d)\n W[degree + i] = d\n // place i in Lk\n cindex[p++] = i\n }\n // # nodes absorbed into k\n W[nv + k] = nvk\n // length of adj list of element k\n if ((W[len + k] = p - pk1) === 0) {\n // k is a root of the tree\n cptr[k] = -1\n // k is now a dead element\n W[w + k] = 0\n }\n if (elenk !== 0) {\n // free unused space in Lk\n cnz = p\n }\n }\n\n // Postordering. The elimination is complete, but no permutation has been computed. All that is left\n // of the graph is the assembly tree (ptr) and a set of dead nodes and elements (i is a dead node if\n // nv[i] is zero and a dead element if nv[i] > 0). It is from this information only that the final permutation\n // is computed. The tree is restored by unflipping all of ptr.\n\n // fix assembly tree\n for (i = 0; i < n; i++) { cptr[i] = csFlip(cptr[i]) }\n for (j = 0; j <= n; j++) { W[head + j] = -1 }\n // place unordered nodes in lists\n for (j = n; j >= 0; j--) {\n // skip if j is an element\n if (W[nv + j] > 0) { continue }\n // place j in list of its parent\n W[next + j] = W[head + cptr[j]]\n W[head + cptr[j]] = j\n }\n // place elements in lists\n for (e = n; e >= 0; e--) {\n // skip unless e is an element\n if (W[nv + e] <= 0) { continue }\n if (cptr[e] !== -1) {\n // place e in list of its parent\n W[next + e] = W[head + cptr[e]]\n W[head + cptr[e]] = e\n }\n }\n // postorder the assembly tree\n for (k = 0, i = 0; i <= n; i++) {\n if (cptr[i] === -1) { k = csTdfs(i, k, W, head, next, P, w) }\n }\n // remove last item in array\n P.splice(P.length - 1, 1)\n // return P\n return P\n }\n\n /**\n * Creates the matrix that will be used by the approximate minimum degree ordering algorithm. The function accepts the matrix M as input and returns a permutation\n * vector P. The amd algorithm operates on a symmetrix matrix, so one of three symmetric matrices is formed.\n *\n * Order: 0\n * A natural ordering P=null matrix is returned.\n *\n * Order: 1\n * Matrix must be square. This is appropriate for a Cholesky or LU factorization.\n * P = M + M'\n *\n * Order: 2\n * Dense columns from M' are dropped, M recreated from M'. This is appropriatefor LU factorization of unsymmetric matrices.\n * P = M' * M\n *\n * Order: 3\n * This is best used for QR factorization or LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.\n * P = M' * M\n */\n function _createTargetMatrix (order, a, m, n, dense) {\n // compute A'\n const at = transpose(a)\n\n // check order = 1, matrix must be square\n if (order === 1 && n === m) {\n // C = A + A'\n return add(a, at)\n }\n\n // check order = 2, drop dense columns from M'\n if (order === 2) {\n // transpose arrays\n const tindex = at._index\n const tptr = at._ptr\n // new column index\n let p2 = 0\n // loop A' columns (rows)\n for (let j = 0; j < m; j++) {\n // column j of AT starts here\n let p = tptr[j]\n // new column j starts here\n tptr[j] = p2\n // skip dense col j\n if (tptr[j + 1] - p > dense) { continue }\n // map rows in column j of A\n for (const p1 = tptr[j + 1]; p < p1; p++) { tindex[p2++] = tindex[p] }\n }\n // finalize AT\n tptr[m] = p2\n // recreate A from new transpose matrix\n a = transpose(at)\n // use A' * A\n return multiply(at, a)\n }\n\n // use A' * A, square or rectangular matrix\n return multiply(at, a)\n }\n\n /**\n * Initialize quotient graph. There are four kind of nodes and elements that must be represented:\n *\n * - A live node is a node i (or a supernode) that has not been selected as a pivot nad has not been merged into another supernode.\n * - A dead node i is one that has been removed from the graph, having been absorved into r = flip(ptr[i]).\n * - A live element e is one that is in the graph, having been formed when node e was selected as the pivot.\n * - A dead element e is one that has benn absorved into a subsequent element s = flip(ptr[e]).\n */\n function _initializeQuotientGraph (n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree) {\n // Initialize quotient graph\n for (let k = 0; k < n; k++) { W[len + k] = cptr[k + 1] - cptr[k] }\n W[len + n] = 0\n // initialize workspace\n for (let i = 0; i <= n; i++) {\n // degree list i is empty\n W[head + i] = -1\n last[i] = -1\n W[next + i] = -1\n // hash list i is empty\n W[hhead + i] = -1\n // node i is just one node\n W[nv + i] = 1\n // node i is alive\n W[w + i] = 1\n // Ek of node i is empty\n W[elen + i] = 0\n // degree of node i\n W[degree + i] = W[len + i]\n }\n // clear w\n const mark = _wclear(0, 0, W, w, n)\n // n is a dead element\n W[elen + n] = -2\n // n is a root of assembly tree\n cptr[n] = -1\n // n is a dead element\n W[w + n] = 0\n // return mark\n return mark\n }\n\n /**\n * Initialize degree lists. Each node is placed in its degree lists. Nodes of zero degree are eliminated immediately. Nodes with\n * degree >= dense are alsol eliminated and merged into a placeholder node n, a dead element. Thes nodes will appera last in the\n * output permutation p.\n */\n function _initializeDegreeLists (n, cptr, W, degree, elen, w, dense, nv, head, last, next) {\n // result\n let nel = 0\n // loop columns\n for (let i = 0; i < n; i++) {\n // degree @ i\n const d = W[degree + i]\n // check node i is empty\n if (d === 0) {\n // element i is dead\n W[elen + i] = -2\n nel++\n // i is a root of assembly tree\n cptr[i] = -1\n W[w + i] = 0\n } else if (d > dense) {\n // absorb i into element n\n W[nv + i] = 0\n // node i is dead\n W[elen + i] = -1\n nel++\n cptr[i] = csFlip(n)\n W[nv + n]++\n } else {\n const h = W[head + d]\n if (h !== -1) { last[h] = i }\n // put node i in degree list d\n W[next + i] = W[head + d]\n W[head + d] = i\n }\n }\n return nel\n }\n\n function _wclear (mark, lemax, W, w, n) {\n if (mark < 2 || (mark + lemax < 0)) {\n for (let k = 0; k < n; k++) {\n if (W[w + k] !== 0) { W[w + k] = 1 }\n }\n mark = 2\n }\n // at this point, W [0..n-1] < mark holds\n return mark\n }\n\n function _diag (i, j) {\n return i !== j\n }\n})\n","/**\n * Keeps entries in the matrix when the callback function returns true, removes the entry otherwise\n *\n * @param {Matrix} a The sparse matrix\n * @param {function} callback The callback function, function will be invoked with the following args:\n * - The entry row\n * - The entry column\n * - The entry value\n * - The state parameter\n * @param {any} other The state\n *\n * @return The number of nonzero elements in the matrix\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csFkeep (a, callback, other) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n // columns\n const n = asize[1]\n // nonzero items\n let nz = 0\n // loop columns\n for (let j = 0; j < n; j++) {\n // get current location of col j\n let p = aptr[j]\n // record new location of col j\n aptr[j] = nz\n for (; p < aptr[j + 1]; p++) {\n // check we need to keep this item\n if (callback(aindex[p], j, avalues ? avalues[p] : 1, other)) {\n // keep A(i,j)\n aindex[nz] = aindex[p]\n // check we need to process values (pattern only)\n if (avalues) { avalues[nz] = avalues[p] }\n // increment nonzero items\n nz++\n }\n }\n }\n // finalize A\n aptr[n] = nz\n // trim arrays\n aindex.splice(nz, aindex.length - nz)\n // check we need to process values (pattern only)\n if (avalues) { avalues.splice(nz, avalues.length - nz) }\n // return number of nonzero items\n return nz\n}\n","/**\n * This function determines if j is a leaf of the ith row subtree.\n * Consider A(i,j), node j in ith row subtree and return lca(jprev,j)\n *\n * @param {Number} i The ith row subtree\n * @param {Number} j The node to test\n * @param {Array} w The workspace array\n * @param {Number} first The index offset within the workspace for the first array\n * @param {Number} maxfirst The index offset within the workspace for the maxfirst array\n * @param {Number} prevleaf The index offset within the workspace for the prevleaf array\n * @param {Number} ancestor The index offset within the workspace for the ancestor array\n *\n * @return {Object}\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csLeaf (i, j, w, first, maxfirst, prevleaf, ancestor) {\n let s, sparent\n\n // our result\n let jleaf = 0\n let q\n\n // check j is a leaf\n if (i <= j || w[first + j] <= w[maxfirst + i]) { return (-1) }\n // update max first[j] seen so far\n w[maxfirst + i] = w[first + j]\n // jprev = previous leaf of ith subtree\n const jprev = w[prevleaf + i]\n w[prevleaf + i] = j\n\n // check j is first or subsequent leaf\n if (jprev === -1) {\n // 1st leaf, q = root of ith subtree\n jleaf = 1\n q = i\n } else {\n // update jleaf\n jleaf = 2\n // q = least common ancester (jprev,j)\n for (q = jprev; q !== w[ancestor + q]; q = w[ancestor + q]);\n for (s = jprev; s !== q; s = sparent) {\n // path compression\n sparent = w[ancestor + s]\n w[ancestor + s] = q\n }\n }\n return {\n jleaf: jleaf,\n q: q\n }\n}\n","import { factory } from '../../../utils/factory.js'\nimport { csLeaf } from './csLeaf.js'\n\nconst name = 'csCounts'\nconst dependencies = [\n 'transpose'\n]\n\nexport const createCsCounts = /* #__PURE__ */ factory(name, dependencies, ({ transpose }) => {\n /**\n * Computes the column counts using the upper triangular part of A.\n * It transposes A internally, none of the input parameters are modified.\n *\n * @param {Matrix} a The sparse matrix A\n *\n * @param {Matrix} ata Count the columns of A'A instead\n *\n * @return An array of size n of the column counts or null on error\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function (a, parent, post, ata) {\n // check inputs\n if (!a || !parent || !post) { return null }\n // a matrix arrays\n const asize = a._size\n // rows and columns\n const m = asize[0]\n const n = asize[1]\n // variables\n let i, j, k, J, p, p0, p1\n\n // workspace size\n const s = 4 * n + (ata ? (n + m + 1) : 0)\n // allocate workspace\n const w = [] // (s)\n const ancestor = 0 // first n entries\n const maxfirst = n // next n entries\n const prevleaf = 2 * n // next n entries\n const first = 3 * n // next n entries\n const head = 4 * n // next n + 1 entries (used when ata is true)\n const next = 5 * n + 1 // last entries in workspace\n // clear workspace w[0..s-1]\n for (k = 0; k < s; k++) { w[k] = -1 }\n\n // allocate result\n const colcount = [] // (n)\n\n // AT = A'\n const at = transpose(a)\n // at arrays\n const tindex = at._index\n const tptr = at._ptr\n\n // find w[first + j]\n for (k = 0; k < n; k++) {\n j = post[k]\n // colcount[j]=1 if j is a leaf\n colcount[j] = (w[first + j] === -1) ? 1 : 0\n for (; j !== -1 && w[first + j] === -1; j = parent[j]) { w[first + j] = k }\n }\n\n // initialize ata if needed\n if (ata) {\n // invert post\n for (k = 0; k < n; k++) { w[post[k]] = k }\n // loop rows (columns in AT)\n for (i = 0; i < m; i++) {\n // values in column i of AT\n for (k = n, p0 = tptr[i], p1 = tptr[i + 1], p = p0; p < p1; p++) { k = Math.min(k, w[tindex[p]]) }\n // place row i in linked list k\n w[next + i] = w[head + k]\n w[head + k] = i\n }\n }\n\n // each node in its own set\n for (i = 0; i < n; i++) { w[ancestor + i] = i }\n\n for (k = 0; k < n; k++) {\n // j is the kth node in postordered etree\n j = post[k]\n // check j is not a root\n if (parent[j] !== -1) { colcount[parent[j]]-- }\n\n // J=j for LL'=A case\n for (J = (ata ? w[head + k] : j); J !== -1; J = (ata ? w[next + J] : -1)) {\n for (p = tptr[J]; p < tptr[J + 1]; p++) {\n i = tindex[p]\n const r = csLeaf(i, j, w, first, maxfirst, prevleaf, ancestor)\n // check A(i,j) is in skeleton\n if (r.jleaf >= 1) { colcount[j]++ }\n // check account for overlap in q\n if (r.jleaf === 2) { colcount[r.q]-- }\n }\n }\n if (parent[j] !== -1) { w[ancestor + j] = parent[j] }\n }\n // sum up colcount's of each child\n for (j = 0; j < n; j++) {\n if (parent[j] !== -1) { colcount[parent[j]] += colcount[j] }\n }\n return colcount\n }\n})\n","import { csPermute } from './csPermute.js'\nimport { csPost } from './csPost.js'\nimport { csEtree } from './csEtree.js'\nimport { createCsAmd } from './csAmd.js'\nimport { createCsCounts } from './csCounts.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'csSqr'\nconst dependencies = [\n 'add',\n 'multiply',\n 'transpose'\n]\n\nexport const createCsSqr = /* #__PURE__ */ factory(name, dependencies, ({ add, multiply, transpose }) => {\n const csAmd = createCsAmd({ add, multiply, transpose })\n const csCounts = createCsCounts({ transpose })\n\n /**\n * Symbolic ordering and analysis for QR and LU decompositions.\n *\n * @param {Number} order The ordering strategy (see csAmd for more details)\n * @param {Matrix} a The A matrix\n * @param {boolean} qr Symbolic ordering and analysis for QR decomposition (true) or\n * symbolic ordering and analysis for LU decomposition (false)\n *\n * @return {Object} The Symbolic ordering and analysis for matrix A\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csSqr (order, a, qr) {\n // a arrays\n const aptr = a._ptr\n const asize = a._size\n // columns\n const n = asize[1]\n // vars\n let k\n // symbolic analysis result\n const s = {}\n // fill-reducing ordering\n s.q = csAmd(order, a)\n // validate results\n if (order && !s.q) { return null }\n // QR symbolic analysis\n if (qr) {\n // apply permutations if needed\n const c = order ? csPermute(a, null, s.q, 0) : a\n // etree of C'*C, where C=A(:,q)\n s.parent = csEtree(c, 1)\n // post order elimination tree\n const post = csPost(s.parent, n)\n // col counts chol(C'*C)\n s.cp = csCounts(c, s.parent, post, 1)\n // check we have everything needed to calculate number of nonzero elements\n if (c && s.parent && s.cp && _vcount(c, s)) {\n // calculate number of nonzero elements\n for (s.unz = 0, k = 0; k < n; k++) { s.unz += s.cp[k] }\n }\n } else {\n // for LU factorization only, guess nnz(L) and nnz(U)\n s.unz = 4 * (aptr[n]) + n\n s.lnz = s.unz\n }\n // return result S\n return s\n }\n\n /**\n * Compute nnz(V) = s.lnz, s.pinv, s.leftmost, s.m2 from A and s.parent\n */\n function _vcount (a, s) {\n // a arrays\n const aptr = a._ptr\n const aindex = a._index\n const asize = a._size\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n // initialize s arrays\n s.pinv = [] // (m + n)\n s.leftmost = [] // (m)\n // vars\n const parent = s.parent\n const pinv = s.pinv\n const leftmost = s.leftmost\n // workspace, next: first m entries, head: next n entries, tail: next n entries, nque: next n entries\n const w = [] // (m + 3 * n)\n const next = 0\n const head = m\n const tail = m + n\n const nque = m + 2 * n\n // vars\n let i, k, p, p0, p1\n // initialize w\n for (k = 0; k < n; k++) {\n // queue k is empty\n w[head + k] = -1\n w[tail + k] = -1\n w[nque + k] = 0\n }\n // initialize row arrays\n for (i = 0; i < m; i++) { leftmost[i] = -1 }\n // loop columns backwards\n for (k = n - 1; k >= 0; k--) {\n // values & index for column k\n for (p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {\n // leftmost[i] = min(find(A(i,:)))\n leftmost[aindex[p]] = k\n }\n }\n // scan rows in reverse order\n for (i = m - 1; i >= 0; i--) {\n // row i is not yet ordered\n pinv[i] = -1\n k = leftmost[i]\n // check row i is empty\n if (k === -1) { continue }\n // first row in queue k\n if (w[nque + k]++ === 0) { w[tail + k] = i }\n // put i at head of queue k\n w[next + i] = w[head + k]\n w[head + k] = i\n }\n s.lnz = 0\n s.m2 = m\n // find row permutation and nnz(V)\n for (k = 0; k < n; k++) {\n // remove row i from queue k\n i = w[head + k]\n // count V(k,k) as nonzero\n s.lnz++\n // add a fictitious row\n if (i < 0) { i = s.m2++ }\n // associate row i with V(:,k)\n pinv[i] = k\n // skip if V(k+1:m,k) is empty\n if (--nque[k] <= 0) { continue }\n // nque[k] is nnz (V(k+1:m,k))\n s.lnz += w[nque + k]\n // move all rows to parent of k\n const pa = parent[k]\n if (pa !== -1) {\n if (w[nque + pa] === 0) { w[tail + pa] = w[tail + k] }\n w[next + w[tail + k]] = w[head + pa]\n w[head + pa] = w[next + i]\n w[nque + pa] += w[nque + k]\n }\n }\n for (i = 0; i < m; i++) {\n if (pinv[i] < 0) { pinv[i] = k++ }\n }\n return true\n }\n})\n","/**\n * Permutes a sparse matrix C = P * A * Q\n *\n * @param {SparseMatrix} a The Matrix A\n * @param {Array} pinv The row permutation vector\n * @param {Array} q The column permutation vector\n * @param {boolean} values Create a pattern matrix (false), values and pattern otherwise\n *\n * @return {Matrix} C = P * A * Q, null on error\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csPermute (a, pinv, q, values) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n // c arrays\n const cvalues = values && a._values ? [] : null\n const cindex = [] // (aptr[n])\n const cptr = [] // (n + 1)\n // initialize vars\n let nz = 0\n // loop columns\n for (let k = 0; k < n; k++) {\n // column k of C is column q[k] of A\n cptr[k] = nz\n // apply column permutation\n const j = q ? (q[k]) : k\n // loop values in column j of A\n for (let t0 = aptr[j], t1 = aptr[j + 1], t = t0; t < t1; t++) {\n // row i of A is row pinv[i] of C\n const r = pinv ? pinv[aindex[t]] : aindex[t]\n // index\n cindex[nz] = r\n // check we need to populate values\n if (cvalues) { cvalues[nz] = avalues[t] }\n // increment number of nonzero elements\n nz++\n }\n }\n // finalize the last column of C\n cptr[n] = nz\n // return C matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [m, n],\n datatype: adt\n })\n}\n","/**\n * Computes the elimination tree of Matrix A (using triu(A)) or the\n * elimination tree of A'A without forming A'A.\n *\n * @param {Matrix} a The A Matrix\n * @param {boolean} ata A value of true the function computes the etree of A'A\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csEtree (a, ata) {\n // check inputs\n if (!a) { return null }\n // a arrays\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n\n // allocate result\n const parent = [] // (n)\n\n // allocate workspace\n const w = [] // (n + (ata ? m : 0))\n const ancestor = 0 // first n entries in w\n const prev = n // last m entries (ata = true)\n\n let i, inext\n\n // check we are calculating A'A\n if (ata) {\n // initialize workspace\n for (i = 0; i < m; i++) { w[prev + i] = -1 }\n }\n // loop columns\n for (let k = 0; k < n; k++) {\n // node k has no parent yet\n parent[k] = -1\n // nor does k have an ancestor\n w[ancestor + k] = -1\n // values in column k\n for (let p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {\n // row\n const r = aindex[p]\n // node\n i = ata ? (w[prev + r]) : r\n // traverse from i to k\n for (; i !== -1 && i < k; i = inext) {\n // inext = ancestor of i\n inext = w[ancestor + i]\n // path compression\n w[ancestor + i] = k\n // check no anc., parent is k\n if (inext === -1) { parent[i] = k }\n }\n if (ata) { w[prev + r] = k }\n }\n }\n return parent\n}\n","import { csTdfs } from './csTdfs.js'\n\n/**\n * Post order a tree of forest\n *\n * @param {Array} parent The tree or forest\n * @param {Number} n Number of columns\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csPost (parent, n) {\n // check inputs\n if (!parent) { return null }\n // vars\n let k = 0\n let j\n // allocate result\n const post = [] // (n)\n // workspace, head: first n entries, next: next n entries, stack: last n entries\n const w = [] // (3 * n)\n const head = 0\n const next = n\n const stack = 2 * n\n // initialize workspace\n for (j = 0; j < n; j++) {\n // empty linked lists\n w[head + j] = -1\n }\n // traverse nodes in reverse order\n for (j = n - 1; j >= 0; j--) {\n // check j is a root\n if (parent[j] === -1) { continue }\n // add j to list of its parent\n w[next + j] = w[head + parent[j]]\n w[head + parent[j]] = j\n }\n // loop nodes\n for (j = 0; j < n; j++) {\n // skip j if it is not a root\n if (parent[j] !== -1) { continue }\n // depth-first search\n k = csTdfs(j, k, w, head, next, post, stack)\n }\n return post\n}\n","/**\n * Checks if the node at w[j] is marked\n *\n * @param {Array} w The array\n * @param {Number} j The array index\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csMarked (w, j) {\n // check node is marked\n return w[j] < 0\n}\n","import { csFlip } from './csFlip.js'\n\n/**\n * Marks the node at w[j]\n *\n * @param {Array} w The array\n * @param {Number} j The array index\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csMark (w, j) {\n // mark w[j]\n w[j] = csFlip(w[j])\n}\n","import { csFlip } from './csFlip.js'\n\n/**\n * Flips the value if it is negative of returns the same value otherwise.\n *\n * @param {Number} i The value to flip\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csUnflip (i) {\n // flip the value if it is negative\n return i < 0 ? csFlip(i) : i\n}\n","import { csMarked } from './csMarked.js'\nimport { csMark } from './csMark.js'\nimport { csUnflip } from './csUnflip.js'\n\n/**\n * Depth-first search computes the nonzero pattern xi of the directed graph G (Matrix) starting\n * at nodes in B (see csReach()).\n *\n * @param {Number} j The starting node for the DFS algorithm\n * @param {Matrix} g The G matrix to search, ptr array modified, then restored\n * @param {Number} top Start index in stack xi[top..n-1]\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} pinv The inverse row permutation vector, must be null for L * x = b\n *\n * @return {Number} New value of top\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csDfs (j, g, top, xi, pinv) {\n // g arrays\n const index = g._index\n const ptr = g._ptr\n const size = g._size\n // columns\n const n = size[1]\n // vars\n let i, p, p2\n // initialize head\n let head = 0\n // initialize the recursion stack\n xi[0] = j\n // loop\n while (head >= 0) {\n // get j from the top of the recursion stack\n j = xi[head]\n // apply permutation vector\n const jnew = pinv ? pinv[j] : j\n // check node j is marked\n if (!csMarked(ptr, j)) {\n // mark node j as visited\n csMark(ptr, j)\n // update stack (last n entries in xi)\n xi[n + head] = jnew < 0 ? 0 : csUnflip(ptr[jnew])\n }\n // node j done if no unvisited neighbors\n let done = 1\n // examine all neighbors of j, stack (last n entries in xi)\n for (p = xi[n + head], p2 = jnew < 0 ? 0 : csUnflip(ptr[jnew + 1]); p < p2; p++) {\n // consider neighbor node i\n i = index[p]\n // check we have visited node i, skip it\n if (csMarked(ptr, i)) { continue }\n // pause depth-first search of node j, update stack (last n entries in xi)\n xi[n + head] = p\n // start dfs at node i\n xi[++head] = i\n // node j is not done\n done = 0\n // break, to start dfs(i)\n break\n }\n // check depth-first search at node j is done\n if (done) {\n // remove j from the recursion stack\n head--\n // and place in the output stack\n xi[--top] = j\n }\n }\n return top\n}\n","import { csReach } from './csReach.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'csSpsolve'\nconst dependencies = [\n 'divideScalar',\n 'multiply',\n 'subtract'\n]\n\nexport const createCsSpsolve = /* #__PURE__ */ factory(name, dependencies, ({ divideScalar, multiply, subtract }) => {\n /**\n * The function csSpsolve() computes the solution to G * x = bk, where bk is the\n * kth column of B. When lo is true, the function assumes G = L is lower triangular with the\n * diagonal entry as the first entry in each column. When lo is true, the function assumes G = U\n * is upper triangular with the diagonal entry as the last entry in each column.\n *\n * @param {Matrix} g The G matrix\n * @param {Matrix} b The B matrix\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} x The soluton to the linear system G * x = b\n * @param {Array} pinv The inverse row permutation vector, must be null for L * x = b\n * @param {boolean} lo The lower (true) upper triangular (false) flag\n *\n * @return {Number} The index for the nonzero pattern\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csSpsolve (g, b, k, xi, x, pinv, lo) {\n // g arrays\n const gvalues = g._values\n const gindex = g._index\n const gptr = g._ptr\n const gsize = g._size\n // columns\n const n = gsize[1]\n // b arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n // vars\n let p, p0, p1, q\n // xi[top..n-1] = csReach(B(:,k))\n const top = csReach(g, b, k, xi, pinv)\n // clear x\n for (p = top; p < n; p++) { x[xi[p]] = 0 }\n // scatter b\n for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) { x[bindex[p]] = bvalues[p] }\n // loop columns\n for (let px = top; px < n; px++) {\n // x array index for px\n const j = xi[px]\n // apply permutation vector (U x = b), j maps to column J of G\n const J = pinv ? pinv[j] : j\n // check column J is empty\n if (J < 0) { continue }\n // column value indeces in G, p0 <= p < p1\n p0 = gptr[J]\n p1 = gptr[J + 1]\n // x(j) /= G(j,j)\n x[j] = divideScalar(x[j], gvalues[lo ? p0 : (p1 - 1)])\n // first entry L(j,j)\n p = lo ? (p0 + 1) : p0\n q = lo ? (p1) : (p1 - 1)\n // loop\n for (; p < q; p++) {\n // row\n const i = gindex[p]\n // x(i) -= G(i,j) * x(j)\n x[i] = subtract(x[i], multiply(gvalues[p], x[j]))\n }\n }\n // return top of stack\n return top\n }\n})\n","import { csMarked } from './csMarked.js'\nimport { csMark } from './csMark.js'\nimport { csDfs } from './csDfs.js'\n\n/**\n * The csReach function computes X = Reach(B), where B is the nonzero pattern of the n-by-1\n * sparse column of vector b. The function returns the set of nodes reachable from any node in B. The\n * nonzero pattern xi of the solution x to the sparse linear system Lx=b is given by X=Reach(B).\n *\n * @param {Matrix} g The G matrix\n * @param {Matrix} b The B matrix\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} pinv The inverse row permutation vector\n *\n * @return {Number} The index for the nonzero pattern\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csReach (g, b, k, xi, pinv) {\n // g arrays\n const gptr = g._ptr\n const gsize = g._size\n // b arrays\n const bindex = b._index\n const bptr = b._ptr\n // columns\n const n = gsize[1]\n // vars\n let p, p0, p1\n // initialize top\n let top = n\n // loop column indeces in B\n for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) {\n // node i\n const i = bindex[p]\n // check node i is marked\n if (!csMarked(gptr, i)) {\n // start a dfs at unmarked node i\n top = csDfs(i, g, top, xi, pinv)\n }\n }\n // loop columns from top -> n - 1\n for (p = top; p < n; p++) {\n // restore G\n csMark(gptr, xi[p])\n }\n return top\n}\n","import { factory } from '../../../utils/factory.js'\nimport { createCsSpsolve } from './csSpsolve.js'\n\nconst name = 'csLu'\nconst dependencies = [\n 'abs',\n 'divideScalar',\n 'multiply',\n 'subtract',\n 'larger',\n 'largerEq',\n 'SparseMatrix'\n]\n\nexport const createCsLu = /* #__PURE__ */ factory(name, dependencies, ({ abs, divideScalar, multiply, subtract, larger, largerEq, SparseMatrix }) => {\n const csSpsolve = createCsSpsolve({ divideScalar, multiply, subtract })\n\n /**\n * Computes the numeric LU factorization of the sparse matrix A. Implements a Left-looking LU factorization\n * algorithm that computes L and U one column at a tume. At the kth step, it access columns 1 to k-1 of L\n * and column k of A. Given the fill-reducing column ordering q (see parameter s) computes L, U and pinv so\n * L * U = A(p, q), where p is the inverse of pinv.\n *\n * @param {Matrix} m The A Matrix to factorize\n * @param {Object} s The symbolic analysis from csSqr(). Provides the fill-reducing\n * column ordering q\n * @param {Number} tol Partial pivoting threshold (1 for partial pivoting)\n *\n * @return {Number} The numeric LU factorization of A or null\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csLu (m, s, tol) {\n // validate input\n if (!m) { return null }\n // m arrays\n const size = m._size\n // columns\n const n = size[1]\n // symbolic analysis result\n let q\n let lnz = 100\n let unz = 100\n // update symbolic analysis parameters\n if (s) {\n q = s.q\n lnz = s.lnz || lnz\n unz = s.unz || unz\n }\n // L arrays\n const lvalues = [] // (lnz)\n const lindex = [] // (lnz)\n const lptr = [] // (n + 1)\n // L\n const L = new SparseMatrix({\n values: lvalues,\n index: lindex,\n ptr: lptr,\n size: [n, n]\n })\n // U arrays\n const uvalues = [] // (unz)\n const uindex = [] // (unz)\n const uptr = [] // (n + 1)\n // U\n const U = new SparseMatrix({\n values: uvalues,\n index: uindex,\n ptr: uptr,\n size: [n, n]\n })\n // inverse of permutation vector\n const pinv = [] // (n)\n // vars\n let i, p\n // allocate arrays\n const x = [] // (n)\n const xi = [] // (2 * n)\n // initialize variables\n for (i = 0; i < n; i++) {\n // clear workspace\n x[i] = 0\n // no rows pivotal yet\n pinv[i] = -1\n // no cols of L yet\n lptr[i + 1] = 0\n }\n // reset number of nonzero elements in L and U\n lnz = 0\n unz = 0\n // compute L(:,k) and U(:,k)\n for (let k = 0; k < n; k++) {\n // update ptr\n lptr[k] = lnz\n uptr[k] = unz\n // apply column permutations if needed\n const col = q ? q[k] : k\n // solve triangular system, x = L\\A(:,col)\n const top = csSpsolve(L, m, col, xi, x, pinv, 1)\n // find pivot\n let ipiv = -1\n let a = -1\n // loop xi[] from top -> n\n for (p = top; p < n; p++) {\n // x[i] is nonzero\n i = xi[p]\n // check row i is not yet pivotal\n if (pinv[i] < 0) {\n // absolute value of x[i]\n const xabs = abs(x[i])\n // check absoulte value is greater than pivot value\n if (larger(xabs, a)) {\n // largest pivot candidate so far\n a = xabs\n ipiv = i\n }\n } else {\n // x(i) is the entry U(pinv[i],k)\n uindex[unz] = pinv[i]\n uvalues[unz++] = x[i]\n }\n }\n // validate we found a valid pivot\n if (ipiv === -1 || a <= 0) { return null }\n // update actual pivot column, give preference to diagonal value\n if (pinv[col] < 0 && largerEq(abs(x[col]), multiply(a, tol))) { ipiv = col }\n // the chosen pivot\n const pivot = x[ipiv]\n // last entry in U(:,k) is U(k,k)\n uindex[unz] = k\n uvalues[unz++] = pivot\n // ipiv is the kth pivot row\n pinv[ipiv] = k\n // first entry in L(:,k) is L(k,k) = 1\n lindex[lnz] = ipiv\n lvalues[lnz++] = 1\n // L(k+1:n,k) = x / pivot\n for (p = top; p < n; p++) {\n // row\n i = xi[p]\n // check x(i) is an entry in L(:,k)\n if (pinv[i] < 0) {\n // save unpermuted row in L\n lindex[lnz] = i\n // scale pivot column\n lvalues[lnz++] = divideScalar(x[i], pivot)\n }\n // x[0..n-1] = 0 for next k\n x[i] = 0\n }\n }\n // update ptr\n lptr[n] = lnz\n uptr[n] = unz\n // fix row indices of L for final pinv\n for (p = 0; p < lnz; p++) { lindex[p] = pinv[lindex[p]] }\n // trim arrays\n lvalues.splice(lnz, lvalues.length - lnz)\n lindex.splice(lnz, lindex.length - lnz)\n uvalues.splice(unz, uvalues.length - unz)\n uindex.splice(unz, uindex.length - unz)\n // return LU factor\n return {\n L: L,\n U: U,\n pinv: pinv\n }\n }\n})\n","import { isInteger } from '../../../utils/number.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createCsSqr } from '../sparse/csSqr.js'\nimport { createCsLu } from '../sparse/csLu.js'\n\nconst name = 'slu'\nconst dependencies = [\n 'typed',\n 'abs',\n 'add',\n 'multiply',\n 'transpose',\n 'divideScalar',\n 'subtract',\n 'larger',\n 'largerEq',\n 'SparseMatrix'\n]\n\nexport const createSlu = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, multiply, transpose, divideScalar, subtract, larger, largerEq, SparseMatrix }) => {\n const csSqr = createCsSqr({ add, multiply, transpose })\n const csLu = createCsLu({ abs, divideScalar, multiply, subtract, larger, largerEq, SparseMatrix })\n\n /**\n * Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix `A` is decomposed in two matrices (`L`, `U`) and two permutation vectors (`pinv`, `q`) where\n *\n * `P * A * Q = L * U`\n *\n * Syntax:\n *\n * math.slu(A, order, threshold)\n *\n * Examples:\n *\n * const A = math.sparse([[4,3], [6, 3]])\n * math.slu(A, 1, 0.001)\n * // returns:\n * // {\n * // L: [[1, 0], [1.5, 1]]\n * // U: [[4, 3], [0, -1.5]]\n * // p: [0, 1]\n * // q: [0, 1]\n * // }\n *\n * See also:\n *\n * lup, lsolve, usolve, lusolve\n *\n * @param {SparseMatrix} A A two dimensional sparse matrix for which to get the LU decomposition.\n * @param {Number} order The Symbolic Ordering and Analysis order:\n * 0 - Natural ordering, no permutation vector q is returned\n * 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A'\n * 2 - Symbolic ordering and analisis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'.\n * This is appropriatefor LU factorization of unsymmetric matrices.\n * 3 - Symbolic ordering and analisis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows.\n * A dense row is a row with more than 10*sqr(columns) entries.\n * @param {Number} threshold Partial pivoting threshold (1 for partial pivoting)\n *\n * @return {Object} The lower triangular matrix, the upper triangular matrix and the permutation vectors.\n */\n return typed(name, {\n\n 'SparseMatrix, number, number': function (a, order, threshold) {\n // verify order\n if (!isInteger(order) || order < 0 || order > 3) { throw new Error('Symbolic Ordering and Analysis order must be an integer number in the interval [0, 3]') }\n // verify threshold\n if (threshold < 0 || threshold > 1) { throw new Error('Partial pivoting threshold must be a number from 0 to 1') }\n\n // perform symbolic ordering and analysis\n const s = csSqr(order, a, false)\n\n // perform lu decomposition\n const f = csLu(a, s, threshold)\n\n // return decomposition\n return {\n L: f.L,\n U: f.U,\n p: f.pinv,\n q: s.q,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\np: ' + this.p.toString() + (this.q ? '\\nq: ' + this.q.toString() : '') + '\\n'\n }\n }\n }\n })\n})\n","/**\n * Permutes a vector; x = P'b. In MATLAB notation, x(p)=b.\n *\n * @param {Array} p The permutation vector of length n. null value denotes identity\n * @param {Array} b The input vector\n *\n * @return {Array} The output vector x = P'b\n */\nexport function csIpvec (p, b) {\n // vars\n let k\n const n = b.length\n const x = []\n // check permutation vector was provided, p = null denotes identity\n if (p) {\n // loop vector\n for (k = 0; k < n; k++) {\n // apply permutation\n x[p[k]] = b[k]\n }\n } else {\n // loop vector\n for (k = 0; k < n; k++) {\n // x[i] = b[i]\n x[k] = b[k]\n }\n }\n return x\n}\n","import { isArray, isMatrix } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\nimport { csIpvec } from '../sparse/csIpvec.js'\n\nconst name = 'lusolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'lup',\n 'slu',\n 'usolve',\n 'lsolve',\n 'DenseMatrix'\n]\n\nexport const createLusolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, lup, slu, usolve, lsolve, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.\n *\n * Syntax:\n *\n * math.lusolve(A, b) // returns column vector with the solution to the linear system A * x = b\n * math.lusolve(lup, b) // returns column vector with the solution to the linear system A * x = b, lup = math.lup(A)\n *\n * Examples:\n *\n * const m = [[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]\n *\n * const x = math.lusolve(m, [-1, -1, -1, -1]) // x = [[-1], [-0.5], [-1/3], [-0.25]]\n *\n * const f = math.lup(m)\n * const x1 = math.lusolve(f, [-1, -1, -1, -1]) // x1 = [[-1], [-0.5], [-1/3], [-0.25]]\n * const x2 = math.lusolve(f, [1, 2, 1, -1]) // x2 = [[1], [1], [1/3], [-0.25]]\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = math.lusolve(a, b) // [[2], [5]]\n *\n * See also:\n *\n * lup, slu, lsolve, usolve\n *\n * @param {Matrix | Array | Object} A Invertible Matrix or the Matrix LU decomposition\n * @param {Matrix | Array} b Column Vector\n * @param {number} [order] The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix\n * @param {Number} [threshold] Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.\n *\n * @return {DenseMatrix | Array} Column vector with the solution to the linear system A * x = b\n */\n return typed(name, {\n\n 'Array, Array | Matrix': function (a, b) {\n a = matrix(a)\n const d = lup(a)\n const x = _lusolve(d.L, d.U, d.p, null, b)\n return x.valueOf()\n },\n\n 'DenseMatrix, Array | Matrix': function (a, b) {\n const d = lup(a)\n return _lusolve(d.L, d.U, d.p, null, b)\n },\n\n 'SparseMatrix, Array | Matrix': function (a, b) {\n const d = lup(a)\n return _lusolve(d.L, d.U, d.p, null, b)\n },\n\n 'SparseMatrix, Array | Matrix, number, number': function (a, b, order, threshold) {\n const d = slu(a, order, threshold)\n return _lusolve(d.L, d.U, d.p, d.q, b)\n },\n\n 'Object, Array | Matrix': function (d, b) {\n return _lusolve(d.L, d.U, d.p, d.q, b)\n }\n })\n\n function _toMatrix (a) {\n if (isMatrix(a)) { return a }\n if (isArray(a)) { return matrix(a) }\n throw new TypeError('Invalid Matrix LU decomposition')\n }\n\n function _lusolve (l, u, p, q, b) {\n // verify decomposition\n l = _toMatrix(l)\n u = _toMatrix(u)\n\n // apply row permutations if needed (b is a DenseMatrix)\n if (p) {\n b = solveValidation(l, b, true)\n b._data = csIpvec(p, b._data)\n }\n\n // use forward substitution to resolve L * y = b\n const y = lsolve(l, b)\n // use backward substitution to resolve U * x = y\n const x = usolve(u, y)\n\n // apply column permutations if needed (x is a DenseMatrix)\n if (q) { x._data = csIpvec(q, x._data) }\n\n return x\n }\n})\n","import { isHelp } from '../utils/is.js'\nimport { clone } from '../utils/object.js'\nimport { format } from '../utils/string.js'\nimport { factory } from '../utils/factory.js'\n\nconst name = 'Help'\nconst dependencies = ['parse']\n\nexport const createHelpClass = /* #__PURE__ */ factory(name, dependencies, ({ parse }) => {\n /**\n * Documentation object\n * @param {Object} doc Object containing properties:\n * {string} name\n * {string} category\n * {string} description\n * {string[]} syntax\n * {string[]} examples\n * {string[]} seealso\n * @constructor\n */\n function Help (doc) {\n if (!(this instanceof Help)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (!doc) throw new Error('Argument \"doc\" missing')\n\n this.doc = doc\n }\n\n /**\n * Attach type information\n */\n Help.prototype.type = 'Help'\n Help.prototype.isHelp = true\n\n /**\n * Generate a string representation of the Help object\n * @return {string} Returns a string\n * @private\n */\n Help.prototype.toString = function () {\n const doc = this.doc || {}\n let desc = '\\n'\n\n if (doc.name) {\n desc += 'Name: ' + doc.name + '\\n\\n'\n }\n if (doc.category) {\n desc += 'Category: ' + doc.category + '\\n\\n'\n }\n if (doc.description) {\n desc += 'Description:\\n ' + doc.description + '\\n\\n'\n }\n if (doc.syntax) {\n desc += 'Syntax:\\n ' + doc.syntax.join('\\n ') + '\\n\\n'\n }\n if (doc.examples) {\n desc += 'Examples:\\n'\n\n const scope = {}\n for (let i = 0; i < doc.examples.length; i++) {\n const expr = doc.examples[i]\n desc += ' ' + expr + '\\n'\n\n let res\n try {\n // note: res can be undefined when `expr` is an empty string\n res = parse(expr).compile().evaluate(scope)\n } catch (e) {\n res = e\n }\n if (res !== undefined && !isHelp(res)) {\n desc += ' ' + format(res, { precision: 14 }) + '\\n'\n }\n }\n desc += '\\n'\n }\n if (doc.seealso && doc.seealso.length) {\n desc += 'See also: ' + doc.seealso.join(', ') + '\\n'\n }\n\n return desc\n }\n\n /**\n * Export the help object to JSON\n */\n Help.prototype.toJSON = function () {\n const obj = clone(this.doc)\n obj.mathjs = 'Help'\n return obj\n }\n\n /**\n * Instantiate a Help object from a JSON object\n * @param {Object} json\n * @returns {Help} Returns a new Help object\n */\n Help.fromJSON = function (json) {\n const doc = {}\n\n Object.keys(json)\n .filter(prop => prop !== 'mathjs')\n .forEach(prop => {\n doc[prop] = json[prop]\n })\n\n return new Help(doc)\n }\n\n /**\n * Returns a string representation of the Help object\n */\n Help.prototype.valueOf = Help.prototype.toString\n\n return Help\n}, { isClass: true })\n","import { isChain } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { hasOwnProperty, lazy } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Chain'\nconst dependencies = ['?on', 'math']\n\nexport const createChainClass = /* #__PURE__ */ factory(name, dependencies, ({ on, math }) => {\n /**\n * @constructor Chain\n * Wrap any value in a chain, allowing to perform chained operations on\n * the value.\n *\n * All methods available in the math.js library can be called upon the chain,\n * and then will be evaluated with the value itself as first argument.\n * The chain can be closed by executing chain.done(), which will return\n * the final value.\n *\n * The Chain has a number of special functions:\n * - done() Finalize the chained operation and return the\n * chain's value.\n * - valueOf() The same as done()\n * - toString() Returns a string representation of the chain's value.\n *\n * @param {*} [value]\n */\n function Chain (value) {\n if (!(this instanceof Chain)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (isChain(value)) {\n this.value = value.value\n } else {\n this.value = value\n }\n }\n\n /**\n * Attach type information\n */\n Chain.prototype.type = 'Chain'\n Chain.prototype.isChain = true\n\n /**\n * Close the chain. Returns the final value.\n * Does the same as method valueOf()\n * @returns {*} value\n */\n Chain.prototype.done = function () {\n return this.value\n }\n\n /**\n * Close the chain. Returns the final value.\n * Does the same as method done()\n * @returns {*} value\n */\n Chain.prototype.valueOf = function () {\n return this.value\n }\n\n /**\n * Get a string representation of the value in the chain\n * @returns {string}\n */\n Chain.prototype.toString = function () {\n return format(this.value)\n }\n\n /**\n * Get a JSON representation of the chain\n * @returns {Object}\n */\n Chain.prototype.toJSON = function () {\n return {\n mathjs: 'Chain',\n value: this.value\n }\n }\n\n /**\n * Instantiate a Chain from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"Chain\", value: ...}`,\n * where mathjs is optional\n * @returns {Chain}\n */\n Chain.fromJSON = function (json) {\n return new Chain(json.value)\n }\n\n /**\n * Create a proxy method for the chain\n * @param {string} name\n * @param {Function} fn The function to be proxied\n * If fn is no function, it is silently ignored.\n * @private\n */\n function createProxy (name, fn) {\n if (typeof fn === 'function') {\n Chain.prototype[name] = chainify(fn)\n }\n }\n\n /**\n * Create a proxy method for the chain\n * @param {string} name\n * @param {function} resolver The function resolving with the\n * function to be proxied\n * @private\n */\n function createLazyProxy (name, resolver) {\n lazy(Chain.prototype, name, function outerResolver () {\n const fn = resolver()\n if (typeof fn === 'function') {\n return chainify(fn)\n }\n\n return undefined // if not a function, ignore\n })\n }\n\n /**\n * Make a function chainable\n * @param {function} fn\n * @return {Function} chain function\n * @private\n */\n function chainify (fn) {\n return function () {\n const args = [this.value] // `this` will be the context of a Chain instance\n for (let i = 0; i < arguments.length; i++) {\n args[i + 1] = arguments[i]\n }\n\n return new Chain(fn.apply(fn, args))\n }\n }\n\n /**\n * Create a proxy for a single method, or an object with multiple methods.\n * Example usage:\n *\n * Chain.createProxy('add', function add (x, y) {...})\n * Chain.createProxy({\n * add: function add (x, y) {...},\n * subtract: function subtract (x, y) {...}\n * }\n *\n * @param {string | Object} arg0 A name (string), or an object with\n * functions\n * @param {*} [arg1] A function, when arg0 is a name\n */\n Chain.createProxy = function (arg0, arg1) {\n if (typeof arg0 === 'string') {\n // createProxy(name, value)\n createProxy(arg0, arg1)\n } else {\n // createProxy(values)\n for (const name in arg0) {\n if (hasOwnProperty(arg0, name) && excludedNames[name] === undefined) {\n createLazyProxy(name, () => arg0[name])\n }\n }\n }\n }\n\n const excludedNames = {\n expression: true,\n docs: true,\n type: true,\n classes: true,\n json: true,\n error: true,\n isChain: true // conflicts with the property isChain of a Chain instance\n }\n\n // create proxy for everything that is in math.js\n Chain.createProxy(math)\n\n // register on the import event, automatically add a proxy for every imported function.\n if (on) {\n on('import', function (name, resolver, path) {\n if (!path) {\n // an imported function (not a data type or something special)\n createLazyProxy(name, resolver)\n }\n })\n }\n\n return Chain\n}, { isClass: true })\n","export const piDocs = {\n name: 'pi',\n category: 'Constants',\n syntax: [\n 'pi'\n ],\n description: 'The number pi is a mathematical constant that is the ratio of a circle\\'s circumference to its diameter, and is approximately equal to 3.14159',\n examples: [\n 'pi',\n 'sin(pi/2)'\n ],\n seealso: ['tau']\n}\n","export const eDocs = {\n name: 'e',\n category: 'Constants',\n syntax: [\n 'e'\n ],\n description: 'Euler\\'s number, the base of the natural logarithm. Approximately equal to 2.71828',\n examples: [\n 'e',\n 'e ^ 2',\n 'exp(2)',\n 'log(e)'\n ],\n seealso: ['exp']\n}\n","import { bignumberDocs } from './construction/bignumber.js'\nimport { typeOfDocs } from './function/utils/typeOf.js'\nimport { isZeroDocs } from './function/utils/isZero.js'\nimport { isPrimeDocs } from './function/utils/isPrime.js'\nimport { isPositiveDocs } from './function/utils/isPositive.js'\nimport { isNumericDocs } from './function/utils/isNumeric.js'\nimport { hasNumericValueDocs } from './function/utils/hasNumericValue.js'\nimport { isNegativeDocs } from './function/utils/isNegative.js'\nimport { isIntegerDocs } from './function/utils/isInteger.js'\nimport { isNaNDocs } from './function/utils/isNaN.js'\nimport { formatDocs } from './function/utils/format.js'\nimport { binDocs } from './function/utils/bin.js'\nimport { octDocs } from './function/utils/oct.js'\nimport { hexDocs } from './function/utils/hex.js'\nimport { cloneDocs } from './function/utils/clone.js'\nimport { toDocs } from './function/units/to.js'\nimport { tanhDocs } from './function/trigonometry/tanh.js'\nimport { tanDocs } from './function/trigonometry/tan.js'\nimport { sinhDocs } from './function/trigonometry/sinh.js'\nimport { sechDocs } from './function/trigonometry/sech.js'\nimport { secDocs } from './function/trigonometry/sec.js'\nimport { cschDocs } from './function/trigonometry/csch.js'\nimport { cscDocs } from './function/trigonometry/csc.js'\nimport { cothDocs } from './function/trigonometry/coth.js'\nimport { cotDocs } from './function/trigonometry/cot.js'\nimport { coshDocs } from './function/trigonometry/cosh.js'\nimport { cosDocs } from './function/trigonometry/cos.js'\nimport { atan2Docs } from './function/trigonometry/atan2.js'\nimport { atanhDocs } from './function/trigonometry/atanh.js'\nimport { atanDocs } from './function/trigonometry/atan.js'\nimport { asinhDocs } from './function/trigonometry/asinh.js'\nimport { asinDocs } from './function/trigonometry/asin.js'\nimport { asechDocs } from './function/trigonometry/asech.js'\nimport { asecDocs } from './function/trigonometry/asec.js'\nimport { acschDocs } from './function/trigonometry/acsch.js'\nimport { acscDocs } from './function/trigonometry/acsc.js'\nimport { acothDocs } from './function/trigonometry/acoth.js'\nimport { acotDocs } from './function/trigonometry/acot.js'\nimport { acoshDocs } from './function/trigonometry/acosh.js'\nimport { acosDocs } from './function/trigonometry/acos.js'\nimport { sumDocs } from './function/statistics/sum.js'\nimport { stdDocs } from './function/statistics/std.js'\nimport { quantileSeqDocs } from './function/statistics/quantileSeq.js'\nimport { prodDocs } from './function/statistics/prod.js'\nimport { modeDocs } from './function/statistics/mode.js'\nimport { minDocs } from './function/statistics/min.js'\nimport { medianDocs } from './function/statistics/median.js'\nimport { meanDocs } from './function/statistics/mean.js'\nimport { maxDocs } from './function/statistics/max.js'\nimport { madDocs } from './function/statistics/mad.js'\nimport { erfDocs } from './function/special/erf.js'\nimport { setUnionDocs } from './function/set/setUnion.js'\nimport { setSymDifferenceDocs } from './function/set/setSymDifference.js'\nimport { setSizeDocs } from './function/set/setSize.js'\nimport { setPowersetDocs } from './function/set/setPowerset.js'\nimport { setMultiplicityDocs } from './function/set/setMultiplicity.js'\nimport { setIsSubsetDocs } from './function/set/setIsSubset.js'\nimport { setIntersectDocs } from './function/set/setIntersect.js'\nimport { setDistinctDocs } from './function/set/setDistinct.js'\nimport { setDifferenceDocs } from './function/set/setDifference.js'\nimport { setCartesianDocs } from './function/set/setCartesian.js'\nimport { unequalDocs } from './function/relational/unequal.js'\nimport { smallerEqDocs } from './function/relational/smallerEq.js'\nimport { smallerDocs } from './function/relational/smaller.js'\nimport { largerEqDocs } from './function/relational/largerEq.js'\nimport { largerDocs } from './function/relational/larger.js'\nimport { equalTextDocs } from './function/relational/equalText.js'\nimport { equalDocs } from './function/relational/equal.js'\nimport { deepEqualDocs } from './function/relational/deepEqual.js'\nimport { compareTextDocs } from './function/relational/compareText.js'\nimport { compareNaturalDocs } from './function/relational/compareNatural.js'\nimport { compareDocs } from './function/relational/compare.js'\nimport { randomIntDocs } from './function/probability/randomInt.js'\nimport { randomDocs } from './function/probability/random.js'\nimport { pickRandomDocs } from './function/probability/pickRandom.js'\nimport { permutationsDocs } from './function/probability/permutations.js'\nimport { multinomialDocs } from './function/probability/multinomial.js'\nimport { kldivergenceDocs } from './function/probability/kldivergence.js'\nimport { gammaDocs } from './function/probability/gamma.js'\nimport { factorialDocs } from './function/probability/factorial.js'\nimport { combinationsDocs } from './function/probability/combinations.js'\nimport { combinationsWithRepDocs } from './function/probability/combinationsWithRep.js'\nimport { zerosDocs } from './function/matrix/zeros.js'\nimport { transposeDocs } from './function/matrix/transpose.js'\nimport { traceDocs } from './function/matrix/trace.js'\nimport { subsetDocs } from './function/matrix/subset.js'\nimport { squeezeDocs } from './function/matrix/squeeze.js'\nimport { sortDocs } from './function/matrix/sort.js'\nimport { sizeDocs } from './function/matrix/size.js'\nimport { diffDocs } from './function/matrix/diff.js'\nimport { reshapeDocs } from './function/matrix/reshape.js'\nimport { resizeDocs } from './function/matrix/resize.js'\nimport { rangeDocs } from './function/matrix/range.js'\nimport { partitionSelectDocs } from './function/matrix/partitionSelect.js'\nimport { onesDocs } from './function/matrix/ones.js'\nimport { mapDocs } from './function/matrix/map.js'\nimport { kronDocs } from './function/matrix/kron.js'\nimport { invDocs } from './function/matrix/inv.js'\nimport { forEachDocs } from './function/matrix/forEach.js'\nimport { flattenDocs } from './function/matrix/flatten.js'\nimport { filterDocs } from './function/matrix/filter.js'\nimport { identityDocs } from './function/matrix/identity.js'\nimport { getMatrixDataTypeDocs } from './function/matrix/getMatrixDataType.js'\nimport { dotDocs } from './function/matrix/dot.js'\nimport { diagDocs } from './function/matrix/diag.js'\nimport { detDocs } from './function/matrix/det.js'\nimport { ctransposeDocs } from './function/matrix/ctranspose.js'\nimport { crossDocs } from './function/matrix/cross.js'\nimport { concatDocs } from './function/matrix/concat.js'\nimport { xorDocs } from './function/logical/xor.js'\nimport { orDocs } from './function/logical/or.js'\nimport { notDocs } from './function/logical/not.js'\nimport { andDocs } from './function/logical/and.js'\nimport { intersectDocs } from './function/geometry/intersect.js'\nimport { distanceDocs } from './function/geometry/distance.js'\nimport { helpDocs } from './function/expression/help.js'\nimport { evaluateDocs } from './function/expression/evaluate.js'\nimport { imDocs } from './function/complex/im.js'\nimport { reDocs } from './function/complex/re.js'\nimport { conjDocs } from './function/complex/conj.js'\nimport { argDocs } from './function/complex/arg.js'\nimport { typedDocs } from './core/typed.js'\nimport { importDocs } from './core/import.js'\nimport { configDocs } from './core/config.js'\nimport { stirlingS2Docs } from './function/combinatorics/stirlingS2.js'\nimport { compositionDocs } from './function/combinatorics/composition.js'\nimport { catalanDocs } from './function/combinatorics/catalan.js'\nimport { bellNumbersDocs } from './function/combinatorics/bellNumbers.js'\nimport { rightLogShiftDocs } from './function/bitwise/rightLogShift.js'\nimport { rightArithShiftDocs } from './function/bitwise/rightArithShift.js'\nimport { leftShiftDocs } from './function/bitwise/leftShift.js'\nimport { bitXorDocs } from './function/bitwise/bitXor.js'\nimport { bitOrDocs } from './function/bitwise/bitOr.js'\nimport { bitNotDocs } from './function/bitwise/bitNot.js'\nimport { bitAndDocs } from './function/bitwise/bitAnd.js'\nimport { xgcdDocs } from './function/arithmetic/xgcd.js'\nimport { unaryPlusDocs } from './function/arithmetic/unaryPlus.js'\nimport { unaryMinusDocs } from './function/arithmetic/unaryMinus.js'\nimport { squareDocs } from './function/arithmetic/square.js'\nimport { sqrtmDocs } from './function/arithmetic/sqrtm.js'\nimport { sqrtDocs } from './function/arithmetic/sqrt.js'\nimport { signDocs } from './function/arithmetic/sign.js'\nimport { roundDocs } from './function/arithmetic/round.js'\nimport { powDocs } from './function/arithmetic/pow.js'\nimport { nthRootsDocs } from './function/arithmetic/nthRoots.js'\nimport { nthRootDocs } from './function/arithmetic/nthRoot.js'\nimport { normDocs } from './function/arithmetic/norm.js'\nimport { multiplyDocs } from './function/arithmetic/multiply.js'\nimport { modDocs } from './function/arithmetic/mod.js'\nimport { log10Docs } from './function/arithmetic/log10.js'\nimport { log1pDocs } from './function/arithmetic/log1p.js'\nimport { log2Docs } from './function/arithmetic/log2.js'\nimport { logDocs } from './function/arithmetic/log.js'\nimport { lcmDocs } from './function/arithmetic/lcm.js'\nimport { hypotDocs } from './function/arithmetic/hypot.js'\nimport { gcdDocs } from './function/arithmetic/gcd.js'\nimport { floorDocs } from './function/arithmetic/floor.js'\nimport { fixDocs } from './function/arithmetic/fix.js'\nimport { expm1Docs } from './function/arithmetic/expm1.js'\nimport { expmDocs } from './function/arithmetic/expm.js'\nimport { eigsDocs } from './function/matrix/eigs.js'\nimport { expDocs } from './function/arithmetic/exp.js'\nimport { dotMultiplyDocs } from './function/arithmetic/dotMultiply.js'\nimport { dotDivideDocs } from './function/arithmetic/dotDivide.js'\nimport { divideDocs } from './function/arithmetic/divide.js'\nimport { cubeDocs } from './function/arithmetic/cube.js'\nimport { ceilDocs } from './function/arithmetic/ceil.js'\nimport { cbrtDocs } from './function/arithmetic/cbrt.js'\nimport { addDocs } from './function/arithmetic/add.js'\nimport { absDocs } from './function/arithmetic/abs.js'\nimport { qrDocs } from './function/algebra/qr.js'\nimport { usolveDocs } from './function/algebra/usolve.js'\nimport { usolveAllDocs } from './function/algebra/usolveAll.js'\nimport { sluDocs } from './function/algebra/slu.js'\nimport { rationalizeDocs } from './function/algebra/rationalize.js'\nimport { simplifyDocs } from './function/algebra/simplify.js'\nimport { lupDocs } from './function/algebra/lup.js'\nimport { lsolveDocs } from './function/algebra/lsolve.js'\nimport { lsolveAllDocs } from './function/algebra/lsolveAll.js'\nimport { derivativeDocs } from './function/algebra/derivative.js'\nimport { versionDocs } from './constants/version.js'\nimport { trueDocs } from './constants/true.js'\nimport { tauDocs } from './constants/tau.js'\nimport { SQRT2Docs } from './constants/SQRT2.js'\nimport { SQRT12Docs } from './constants/SQRT1_2.js'\nimport { phiDocs } from './constants/phi.js'\nimport { piDocs } from './constants/pi.js'\nimport { nullDocs } from './constants/null.js'\nimport { NaNDocs } from './constants/NaN.js'\nimport { LOG10EDocs } from './constants/LOG10E.js'\nimport { LOG2EDocs } from './constants/LOG2E.js'\nimport { LN10Docs } from './constants/LN10.js'\nimport { LN2Docs } from './constants/LN2.js'\nimport { InfinityDocs } from './constants/Infinity.js'\nimport { iDocs } from './constants/i.js'\nimport { falseDocs } from './constants/false.js'\nimport { eDocs } from './constants/e.js'\nimport { unitDocs } from './construction/unit.js'\nimport { stringDocs } from './construction/string.js'\nimport { splitUnitDocs } from './construction/splitUnit.js'\nimport { sparseDocs } from './construction/sparse.js'\nimport { numberDocs } from './construction/number.js'\nimport { matrixDocs } from './construction/matrix.js'\nimport { indexDocs } from './construction/index.js'\nimport { fractionDocs } from './construction/fraction.js'\nimport { createUnitDocs } from './construction/createUnit.js'\nimport { complexDocs } from './construction/complex.js'\nimport { booleanDocs } from './construction/boolean.js'\nimport { dotPowDocs } from './function/arithmetic/dotPow.js'\nimport { lusolveDocs } from './function/algebra/lusolve.js'\nimport { subtractDocs } from './function/arithmetic/subtract.js'\nimport { varianceDocs } from './function/statistics/variance.js'\nimport { sinDocs } from './function/trigonometry/sin.js'\nimport { numericDocs } from './function/utils/numeric.js'\nimport { columnDocs } from './function/matrix/column.js'\nimport { rowDocs } from './function/matrix/row.js'\nimport { rotationMatrixDocs } from './function/matrix/rotationMatrix.js'\nimport { rotateDocs } from './function/matrix/rotate.js'\n\nexport const embeddedDocs = {\n\n // construction functions\n bignumber: bignumberDocs,\n boolean: booleanDocs,\n complex: complexDocs,\n createUnit: createUnitDocs,\n fraction: fractionDocs,\n index: indexDocs,\n matrix: matrixDocs,\n number: numberDocs,\n sparse: sparseDocs,\n splitUnit: splitUnitDocs,\n string: stringDocs,\n unit: unitDocs,\n\n // constants\n e: eDocs,\n E: eDocs,\n false: falseDocs,\n i: iDocs,\n Infinity: InfinityDocs,\n LN2: LN2Docs,\n LN10: LN10Docs,\n LOG2E: LOG2EDocs,\n LOG10E: LOG10EDocs,\n NaN: NaNDocs,\n null: nullDocs,\n pi: piDocs,\n PI: piDocs,\n phi: phiDocs,\n SQRT1_2: SQRT12Docs,\n SQRT2: SQRT2Docs,\n tau: tauDocs,\n true: trueDocs,\n version: versionDocs,\n\n // physical constants\n // TODO: more detailed docs for physical constants\n speedOfLight: { description: 'Speed of light in vacuum', examples: ['speedOfLight'] },\n gravitationConstant: { description: 'Newtonian constant of gravitation', examples: ['gravitationConstant'] },\n planckConstant: { description: 'Planck constant', examples: ['planckConstant'] },\n reducedPlanckConstant: { description: 'Reduced Planck constant', examples: ['reducedPlanckConstant'] },\n\n magneticConstant: { description: 'Magnetic constant (vacuum permeability)', examples: ['magneticConstant'] },\n electricConstant: { description: 'Electric constant (vacuum permeability)', examples: ['electricConstant'] },\n vacuumImpedance: { description: 'Characteristic impedance of vacuum', examples: ['vacuumImpedance'] },\n coulomb: { description: 'Coulomb\\'s constant', examples: ['coulomb'] },\n elementaryCharge: { description: 'Elementary charge', examples: ['elementaryCharge'] },\n bohrMagneton: { description: 'Borh magneton', examples: ['bohrMagneton'] },\n conductanceQuantum: { description: 'Conductance quantum', examples: ['conductanceQuantum'] },\n inverseConductanceQuantum: { description: 'Inverse conductance quantum', examples: ['inverseConductanceQuantum'] },\n // josephson: {description: 'Josephson constant', examples: ['josephson']},\n magneticFluxQuantum: { description: 'Magnetic flux quantum', examples: ['magneticFluxQuantum'] },\n nuclearMagneton: { description: 'Nuclear magneton', examples: ['nuclearMagneton'] },\n klitzing: { description: 'Von Klitzing constant', examples: ['klitzing'] },\n\n bohrRadius: { description: 'Borh radius', examples: ['bohrRadius'] },\n classicalElectronRadius: { description: 'Classical electron radius', examples: ['classicalElectronRadius'] },\n electronMass: { description: 'Electron mass', examples: ['electronMass'] },\n fermiCoupling: { description: 'Fermi coupling constant', examples: ['fermiCoupling'] },\n fineStructure: { description: 'Fine-structure constant', examples: ['fineStructure'] },\n hartreeEnergy: { description: 'Hartree energy', examples: ['hartreeEnergy'] },\n protonMass: { description: 'Proton mass', examples: ['protonMass'] },\n deuteronMass: { description: 'Deuteron Mass', examples: ['deuteronMass'] },\n neutronMass: { description: 'Neutron mass', examples: ['neutronMass'] },\n quantumOfCirculation: { description: 'Quantum of circulation', examples: ['quantumOfCirculation'] },\n rydberg: { description: 'Rydberg constant', examples: ['rydberg'] },\n thomsonCrossSection: { description: 'Thomson cross section', examples: ['thomsonCrossSection'] },\n weakMixingAngle: { description: 'Weak mixing angle', examples: ['weakMixingAngle'] },\n efimovFactor: { description: 'Efimov factor', examples: ['efimovFactor'] },\n\n atomicMass: { description: 'Atomic mass constant', examples: ['atomicMass'] },\n avogadro: { description: 'Avogadro\\'s number', examples: ['avogadro'] },\n boltzmann: { description: 'Boltzmann constant', examples: ['boltzmann'] },\n faraday: { description: 'Faraday constant', examples: ['faraday'] },\n firstRadiation: { description: 'First radiation constant', examples: ['firstRadiation'] },\n loschmidt: { description: 'Loschmidt constant at T=273.15 K and p=101.325 kPa', examples: ['loschmidt'] },\n gasConstant: { description: 'Gas constant', examples: ['gasConstant'] },\n molarPlanckConstant: { description: 'Molar Planck constant', examples: ['molarPlanckConstant'] },\n molarVolume: { description: 'Molar volume of an ideal gas at T=273.15 K and p=101.325 kPa', examples: ['molarVolume'] },\n sackurTetrode: { description: 'Sackur-Tetrode constant at T=1 K and p=101.325 kPa', examples: ['sackurTetrode'] },\n secondRadiation: { description: 'Second radiation constant', examples: ['secondRadiation'] },\n stefanBoltzmann: { description: 'Stefan-Boltzmann constant', examples: ['stefanBoltzmann'] },\n wienDisplacement: { description: 'Wien displacement law constant', examples: ['wienDisplacement'] },\n // spectralRadiance: {description: 'First radiation constant for spectral radiance', examples: ['spectralRadiance']},\n\n molarMass: { description: 'Molar mass constant', examples: ['molarMass'] },\n molarMassC12: { description: 'Molar mass constant of carbon-12', examples: ['molarMassC12'] },\n gravity: { description: 'Standard acceleration of gravity (standard acceleration of free-fall on Earth)', examples: ['gravity'] },\n\n planckLength: { description: 'Planck length', examples: ['planckLength'] },\n planckMass: { description: 'Planck mass', examples: ['planckMass'] },\n planckTime: { description: 'Planck time', examples: ['planckTime'] },\n planckCharge: { description: 'Planck charge', examples: ['planckCharge'] },\n planckTemperature: { description: 'Planck temperature', examples: ['planckTemperature'] },\n\n // functions - algebra\n derivative: derivativeDocs,\n lsolve: lsolveDocs,\n lsolveAll: lsolveAllDocs,\n lup: lupDocs,\n lusolve: lusolveDocs,\n simplify: simplifyDocs,\n rationalize: rationalizeDocs,\n slu: sluDocs,\n usolve: usolveDocs,\n usolveAll: usolveAllDocs,\n qr: qrDocs,\n\n // functions - arithmetic\n abs: absDocs,\n add: addDocs,\n cbrt: cbrtDocs,\n ceil: ceilDocs,\n cube: cubeDocs,\n divide: divideDocs,\n dotDivide: dotDivideDocs,\n dotMultiply: dotMultiplyDocs,\n dotPow: dotPowDocs,\n exp: expDocs,\n expm: expmDocs,\n expm1: expm1Docs,\n fix: fixDocs,\n floor: floorDocs,\n gcd: gcdDocs,\n hypot: hypotDocs,\n lcm: lcmDocs,\n log: logDocs,\n log2: log2Docs,\n log1p: log1pDocs,\n log10: log10Docs,\n mod: modDocs,\n multiply: multiplyDocs,\n norm: normDocs,\n nthRoot: nthRootDocs,\n nthRoots: nthRootsDocs,\n pow: powDocs,\n round: roundDocs,\n sign: signDocs,\n sqrt: sqrtDocs,\n sqrtm: sqrtmDocs,\n square: squareDocs,\n subtract: subtractDocs,\n unaryMinus: unaryMinusDocs,\n unaryPlus: unaryPlusDocs,\n xgcd: xgcdDocs,\n\n // functions - bitwise\n bitAnd: bitAndDocs,\n bitNot: bitNotDocs,\n bitOr: bitOrDocs,\n bitXor: bitXorDocs,\n leftShift: leftShiftDocs,\n rightArithShift: rightArithShiftDocs,\n rightLogShift: rightLogShiftDocs,\n\n // functions - combinatorics\n bellNumbers: bellNumbersDocs,\n catalan: catalanDocs,\n composition: compositionDocs,\n stirlingS2: stirlingS2Docs,\n\n // functions - core\n config: configDocs,\n import: importDocs,\n typed: typedDocs,\n\n // functions - complex\n arg: argDocs,\n conj: conjDocs,\n re: reDocs,\n im: imDocs,\n\n // functions - expression\n evaluate: evaluateDocs,\n help: helpDocs,\n\n // functions - geometry\n distance: distanceDocs,\n intersect: intersectDocs,\n\n // functions - logical\n and: andDocs,\n not: notDocs,\n or: orDocs,\n xor: xorDocs,\n\n // functions - matrix\n concat: concatDocs,\n cross: crossDocs,\n column: columnDocs,\n ctranspose: ctransposeDocs,\n det: detDocs,\n diag: diagDocs,\n diff: diffDocs,\n dot: dotDocs,\n getMatrixDataType: getMatrixDataTypeDocs,\n identity: identityDocs,\n filter: filterDocs,\n flatten: flattenDocs,\n forEach: forEachDocs,\n inv: invDocs,\n eigs: eigsDocs,\n kron: kronDocs,\n map: mapDocs,\n ones: onesDocs,\n partitionSelect: partitionSelectDocs,\n range: rangeDocs,\n resize: resizeDocs,\n reshape: reshapeDocs,\n rotate: rotateDocs,\n rotationMatrix: rotationMatrixDocs,\n row: rowDocs,\n size: sizeDocs,\n sort: sortDocs,\n squeeze: squeezeDocs,\n subset: subsetDocs,\n trace: traceDocs,\n transpose: transposeDocs,\n zeros: zerosDocs,\n\n // functions - probability\n combinations: combinationsDocs,\n combinationsWithRep: combinationsWithRepDocs,\n // distribution: distributionDocs,\n factorial: factorialDocs,\n gamma: gammaDocs,\n kldivergence: kldivergenceDocs,\n multinomial: multinomialDocs,\n permutations: permutationsDocs,\n pickRandom: pickRandomDocs,\n random: randomDocs,\n randomInt: randomIntDocs,\n\n // functions - relational\n compare: compareDocs,\n compareNatural: compareNaturalDocs,\n compareText: compareTextDocs,\n deepEqual: deepEqualDocs,\n equal: equalDocs,\n equalText: equalTextDocs,\n larger: largerDocs,\n largerEq: largerEqDocs,\n smaller: smallerDocs,\n smallerEq: smallerEqDocs,\n unequal: unequalDocs,\n\n // functions - set\n setCartesian: setCartesianDocs,\n setDifference: setDifferenceDocs,\n setDistinct: setDistinctDocs,\n setIntersect: setIntersectDocs,\n setIsSubset: setIsSubsetDocs,\n setMultiplicity: setMultiplicityDocs,\n setPowerset: setPowersetDocs,\n setSize: setSizeDocs,\n setSymDifference: setSymDifferenceDocs,\n setUnion: setUnionDocs,\n\n // functions - special\n erf: erfDocs,\n\n // functions - statistics\n mad: madDocs,\n max: maxDocs,\n mean: meanDocs,\n median: medianDocs,\n min: minDocs,\n mode: modeDocs,\n prod: prodDocs,\n quantileSeq: quantileSeqDocs,\n std: stdDocs,\n sum: sumDocs,\n variance: varianceDocs,\n\n // functions - trigonometry\n acos: acosDocs,\n acosh: acoshDocs,\n acot: acotDocs,\n acoth: acothDocs,\n acsc: acscDocs,\n acsch: acschDocs,\n asec: asecDocs,\n asech: asechDocs,\n asin: asinDocs,\n asinh: asinhDocs,\n atan: atanDocs,\n atanh: atanhDocs,\n atan2: atan2Docs,\n cos: cosDocs,\n cosh: coshDocs,\n cot: cotDocs,\n coth: cothDocs,\n csc: cscDocs,\n csch: cschDocs,\n sec: secDocs,\n sech: sechDocs,\n sin: sinDocs,\n sinh: sinhDocs,\n tan: tanDocs,\n tanh: tanhDocs,\n\n // functions - units\n to: toDocs,\n\n // functions - utils\n clone: cloneDocs,\n format: formatDocs,\n bin: binDocs,\n oct: octDocs,\n hex: hexDocs,\n isNaN: isNaNDocs,\n isInteger: isIntegerDocs,\n isNegative: isNegativeDocs,\n isNumeric: isNumericDocs,\n hasNumericValue: hasNumericValueDocs,\n isPositive: isPositiveDocs,\n isPrime: isPrimeDocs,\n isZero: isZeroDocs,\n // print: printDocs // TODO: add documentation for print as soon as the parser supports objects.\n typeOf: typeOfDocs,\n numeric: numericDocs\n}\n","export const bignumberDocs = {\n name: 'bignumber',\n category: 'Construction',\n syntax: [\n 'bignumber(x)'\n ],\n description:\n 'Create a big number from a number or string.',\n examples: [\n '0.1 + 0.2',\n 'bignumber(0.1) + bignumber(0.2)',\n 'bignumber(\"7.2\")',\n 'bignumber(\"7.2e500\")',\n 'bignumber([0.1, 0.2, 0.3])'\n ],\n seealso: [\n 'boolean', 'complex', 'fraction', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const booleanDocs = {\n name: 'boolean',\n category: 'Construction',\n syntax: [\n 'x',\n 'boolean(x)'\n ],\n description:\n 'Convert a string or number into a boolean.',\n examples: [\n 'boolean(0)',\n 'boolean(1)',\n 'boolean(3)',\n 'boolean(\"true\")',\n 'boolean(\"false\")',\n 'boolean([1, 0, 1, 1])'\n ],\n seealso: [\n 'bignumber', 'complex', 'index', 'matrix', 'number', 'string', 'unit'\n ]\n}\n","export const complexDocs = {\n name: 'complex',\n category: 'Construction',\n syntax: [\n 'complex()',\n 'complex(re, im)',\n 'complex(string)'\n ],\n description:\n 'Create a complex number.',\n examples: [\n 'complex()',\n 'complex(2, 3)',\n 'complex(\"7 - 2i\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'index', 'matrix', 'number', 'string', 'unit'\n ]\n}\n","export const createUnitDocs = {\n name: 'createUnit',\n category: 'Construction',\n syntax: [\n 'createUnit(definitions)',\n 'createUnit(name, definition)'\n ],\n description:\n 'Create a user-defined unit and register it with the Unit type.',\n examples: [\n 'createUnit(\"foo\")',\n 'createUnit(\"knot\", {definition: \"0.514444444 m/s\", aliases: [\"knots\", \"kt\", \"kts\"]})',\n 'createUnit(\"mph\", \"1 mile/hour\")'\n ],\n seealso: [\n 'unit', 'splitUnit'\n ]\n}\n","export const fractionDocs = {\n name: 'fraction',\n category: 'Construction',\n syntax: [\n 'fraction(num)',\n 'fraction(num,den)'\n ],\n description:\n 'Create a fraction from a number or from a numerator and denominator.',\n examples: [\n 'fraction(0.125)',\n 'fraction(1, 3) + fraction(2, 5)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const indexDocs = {\n name: 'index',\n category: 'Construction',\n syntax: [\n '[start]',\n '[start:end]',\n '[start:step:end]',\n '[start1, start 2, ...]',\n '[start1:end1, start2:end2, ...]',\n '[start1:step1:end1, start2:step2:end2, ...]'\n ],\n description:\n 'Create an index to get or replace a subset of a matrix',\n examples: [\n '[]',\n '[1, 2, 3]',\n 'A = [1, 2, 3; 4, 5, 6]',\n 'A[1, :]',\n 'A[1, 2] = 50',\n 'A[0:2, 0:2] = ones(2, 2)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'matrix,', 'number', 'range', 'string', 'unit'\n ]\n}\n","export const matrixDocs = {\n name: 'matrix',\n category: 'Construction',\n syntax: [\n '[]',\n '[a1, b1, ...; a2, b2, ...]',\n 'matrix()',\n 'matrix(\"dense\")',\n 'matrix([...])'\n ],\n description:\n 'Create a matrix.',\n examples: [\n '[]',\n '[1, 2, 3]',\n '[1, 2, 3; 4, 5, 6]',\n 'matrix()',\n 'matrix([3, 4])',\n 'matrix([3, 4; 5, 6], \"sparse\")',\n 'matrix([3, 4; 5, 6], \"sparse\", \"number\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'number', 'string', 'unit', 'sparse'\n ]\n}\n","export const numberDocs = {\n name: 'number',\n category: 'Construction',\n syntax: [\n 'x',\n 'number(x)',\n 'number(unit, valuelessUnit)'\n ],\n description:\n 'Create a number or convert a string or boolean into a number.',\n examples: [\n '2',\n '2e3',\n '4.05',\n 'number(2)',\n 'number(\"7.2\")',\n 'number(true)',\n 'number([true, false, true, true])',\n 'number(unit(\"52cm\"), \"m\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'fraction', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const sparseDocs = {\n name: 'sparse',\n category: 'Construction',\n syntax: [\n 'sparse()',\n 'sparse([a1, b1, ...; a1, b2, ...])',\n 'sparse([a1, b1, ...; a1, b2, ...], \"number\")'\n ],\n description:\n 'Create a sparse matrix.',\n examples: [\n 'sparse()',\n 'sparse([3, 4; 5, 6])',\n 'sparse([3, 0; 5, 0], \"number\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'number', 'string', 'unit', 'matrix'\n ]\n}\n","export const splitUnitDocs = {\n name: 'splitUnit',\n category: 'Construction',\n syntax: [\n 'splitUnit(unit: Unit, parts: Unit[])'\n ],\n description:\n 'Split a unit in an array of units whose sum is equal to the original unit.',\n examples: [\n 'splitUnit(1 m, [\"feet\", \"inch\"])'\n ],\n seealso: [\n 'unit', 'createUnit'\n ]\n}\n","export const stringDocs = {\n name: 'string',\n category: 'Construction',\n syntax: [\n '\"text\"',\n 'string(x)'\n ],\n description:\n 'Create a string or convert a value to a string',\n examples: [\n '\"Hello World!\"',\n 'string(4.2)',\n 'string(3 + 2i)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'number', 'unit'\n ]\n}\n","export const unitDocs = {\n name: 'unit',\n category: 'Construction',\n syntax: [\n 'value unit',\n 'unit(value, unit)',\n 'unit(string)'\n ],\n description:\n 'Create a unit.',\n examples: [\n '5.5 mm',\n '3 inch',\n 'unit(7.1, \"kilogram\")',\n 'unit(\"23 deg\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'number', 'string'\n ]\n}\n","export const falseDocs = {\n name: 'false',\n category: 'Constants',\n syntax: [\n 'false'\n ],\n description: 'Boolean value false',\n examples: [\n 'false'\n ],\n seealso: ['true']\n}\n","export const iDocs = {\n name: 'i',\n category: 'Constants',\n syntax: [\n 'i'\n ],\n description: 'Imaginary unit, defined as i*i=-1. A complex number is described as a + b*i, where a is the real part, and b is the imaginary part.',\n examples: [\n 'i',\n 'i * i',\n 'sqrt(-1)'\n ],\n seealso: []\n}\n","export const InfinityDocs = {\n name: 'Infinity',\n category: 'Constants',\n syntax: [\n 'Infinity'\n ],\n description: 'Infinity, a number which is larger than the maximum number that can be handled by a floating point number.',\n examples: [\n 'Infinity',\n '1 / 0'\n ],\n seealso: []\n}\n","export const LN2Docs = {\n name: 'LN2',\n category: 'Constants',\n syntax: [\n 'LN2'\n ],\n description: 'Returns the natural logarithm of 2, approximately equal to 0.693',\n examples: [\n 'LN2',\n 'log(2)'\n ],\n seealso: []\n}\n","export const LN10Docs = {\n name: 'LN10',\n category: 'Constants',\n syntax: [\n 'LN10'\n ],\n description: 'Returns the natural logarithm of 10, approximately equal to 2.302',\n examples: [\n 'LN10',\n 'log(10)'\n ],\n seealso: []\n}\n","export const LOG2EDocs = {\n name: 'LOG2E',\n category: 'Constants',\n syntax: [\n 'LOG2E'\n ],\n description: 'Returns the base-2 logarithm of E, approximately equal to 1.442',\n examples: [\n 'LOG2E',\n 'log(e, 2)'\n ],\n seealso: []\n}\n","export const LOG10EDocs = {\n name: 'LOG10E',\n category: 'Constants',\n syntax: [\n 'LOG10E'\n ],\n description: 'Returns the base-10 logarithm of E, approximately equal to 0.434',\n examples: [\n 'LOG10E',\n 'log(e, 10)'\n ],\n seealso: []\n}\n","export const NaNDocs = {\n name: 'NaN',\n category: 'Constants',\n syntax: [\n 'NaN'\n ],\n description: 'Not a number',\n examples: [\n 'NaN',\n '0 / 0'\n ],\n seealso: []\n}\n","export const nullDocs = {\n name: 'null',\n category: 'Constants',\n syntax: [\n 'null'\n ],\n description: 'Value null',\n examples: [\n 'null'\n ],\n seealso: ['true', 'false']\n}\n","export const phiDocs = {\n name: 'phi',\n category: 'Constants',\n syntax: [\n 'phi'\n ],\n description: 'Phi is the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Phi is defined as `(1 + sqrt(5)) / 2` and is approximately 1.618034...',\n examples: [\n 'phi'\n ],\n seealso: []\n}\n","export const SQRT12Docs = {\n name: 'SQRT1_2',\n category: 'Constants',\n syntax: [\n 'SQRT1_2'\n ],\n description: 'Returns the square root of 1/2, approximately equal to 0.707',\n examples: [\n 'SQRT1_2',\n 'sqrt(1/2)'\n ],\n seealso: []\n}\n","export const SQRT2Docs = {\n name: 'SQRT2',\n category: 'Constants',\n syntax: [\n 'SQRT2'\n ],\n description: 'Returns the square root of 2, approximately equal to 1.414',\n examples: [\n 'SQRT2',\n 'sqrt(2)'\n ],\n seealso: []\n}\n","export const tauDocs = {\n name: 'tau',\n category: 'Constants',\n syntax: [\n 'tau'\n ],\n description: 'Tau is the ratio constant of a circle\\'s circumference to radius, equal to 2 * pi, approximately 6.2832.',\n examples: [\n 'tau',\n '2 * pi'\n ],\n seealso: ['pi']\n}\n","export const trueDocs = {\n name: 'true',\n category: 'Constants',\n syntax: [\n 'true'\n ],\n description: 'Boolean value true',\n examples: [\n 'true'\n ],\n seealso: ['false']\n}\n","export const versionDocs = {\n name: 'version',\n category: 'Constants',\n syntax: [\n 'version'\n ],\n description: 'A string with the version number of math.js',\n examples: [\n 'version'\n ],\n seealso: []\n}\n","export const derivativeDocs = {\n name: 'derivative',\n category: 'Algebra',\n syntax: [\n 'derivative(expr, variable)',\n 'derivative(expr, variable, {simplify: boolean})'\n ],\n description: 'Takes the derivative of an expression expressed in parser Nodes. The derivative will be taken over the supplied variable in the second parameter. If there are multiple variables in the expression, it will return a partial derivative.',\n examples: [\n 'derivative(\"2x^3\", \"x\")',\n 'derivative(\"2x^3\", \"x\", {simplify: false})',\n 'derivative(\"2x^2 + 3x + 4\", \"x\")',\n 'derivative(\"sin(2x)\", \"x\")',\n 'f = parse(\"x^2 + x\")',\n 'x = parse(\"x\")',\n 'df = derivative(f, x)',\n 'df.evaluate({x: 3})'\n ],\n seealso: [\n 'simplify', 'parse', 'evaluate'\n ]\n}\n","export const lsolveDocs = {\n name: 'lsolve',\n category: 'Algebra',\n syntax: [\n 'x=lsolve(L, b)'\n ],\n description:\n 'Finds one solution of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lsolve(a, b)'\n ],\n seealso: [\n 'lsolveAll', 'lup', 'lusolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const lsolveAllDocs = {\n name: 'lsolveAll',\n category: 'Algebra',\n syntax: [\n 'x=lsolveAll(L, b)'\n ],\n description:\n 'Finds all solutions of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lsolve(a, b)'\n ],\n seealso: [\n 'lsolve', 'lup', 'lusolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const lupDocs = {\n name: 'lup',\n category: 'Algebra',\n syntax: [\n 'lup(m)'\n ],\n description:\n 'Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U',\n examples: [\n 'lup([[2, 1], [1, 4]])',\n 'lup(matrix([[2, 1], [1, 4]]))',\n 'lup(sparse([[2, 1], [1, 4]]))'\n ],\n seealso: [\n 'lusolve', 'lsolve', 'usolve', 'matrix', 'sparse', 'slu', 'qr'\n ]\n}\n","export const lusolveDocs = {\n name: 'lusolve',\n category: 'Algebra',\n syntax: [\n 'x=lusolve(A, b)',\n 'x=lusolve(lu, b)'\n ],\n description: 'Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lusolve(a, b)'\n ],\n seealso: [\n 'lup', 'slu', 'lsolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const simplifyDocs = {\n name: 'simplify',\n category: 'Algebra',\n syntax: [\n 'simplify(expr)',\n 'simplify(expr, rules)'\n ],\n description: 'Simplify an expression tree.',\n examples: [\n 'simplify(\"3 + 2 / 4\")',\n 'simplify(\"2x + x\")',\n 'f = parse(\"x * (x + 2 + x)\")',\n 'simplified = simplify(f)',\n 'simplified.evaluate({x: 2})'\n ],\n seealso: [\n 'derivative', 'parse', 'evaluate'\n ]\n}\n","export const rationalizeDocs = {\n name: 'rationalize',\n category: 'Algebra',\n syntax: [\n 'rationalize(expr)',\n 'rationalize(expr, scope)',\n 'rationalize(expr, scope, detailed)'\n ],\n description: 'Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.',\n examples: [\n 'rationalize(\"2x/y - y/(x+1)\")',\n 'rationalize(\"2x/y - y/(x+1)\", true)'\n ],\n seealso: [\n 'simplify'\n ]\n}\n","export const sluDocs = {\n name: 'slu',\n category: 'Algebra',\n syntax: [\n 'slu(A, order, threshold)'\n ],\n description: 'Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U',\n examples: [\n 'slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)'\n ],\n seealso: [\n 'lusolve', 'lsolve', 'usolve', 'matrix', 'sparse', 'lup', 'qr'\n ]\n}\n","export const usolveDocs = {\n name: 'usolve',\n category: 'Algebra',\n syntax: [\n 'x=usolve(U, b)'\n ],\n description:\n 'Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.',\n examples: [\n 'x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])'\n ],\n seealso: [\n 'usolveAll', 'lup', 'lusolve', 'lsolve', 'matrix', 'sparse'\n ]\n}\n","export const usolveAllDocs = {\n name: 'usolveAll',\n category: 'Algebra',\n syntax: [\n 'x=usolve(U, b)'\n ],\n description:\n 'Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.',\n examples: [\n 'x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])'\n ],\n seealso: [\n 'usolve', 'lup', 'lusolve', 'lsolve', 'matrix', 'sparse'\n ]\n}\n","export const qrDocs = {\n name: 'qr',\n category: 'Algebra',\n syntax: [\n 'qr(A)'\n ],\n description:\n 'Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.',\n examples: [\n 'qr([[1, -1, 4], [1, 4, -2], [1, 4, 2], [1, -1, 0]])'\n ],\n seealso: [\n 'lup', 'slu', 'matrix'\n ]\n}\n","export const absDocs = {\n name: 'abs',\n category: 'Arithmetic',\n syntax: [\n 'abs(x)'\n ],\n description: 'Compute the absolute value.',\n examples: [\n 'abs(3.5)',\n 'abs(-4.2)'\n ],\n seealso: ['sign']\n}\n","export const addDocs = {\n name: 'add',\n category: 'Operators',\n syntax: [\n 'x + y',\n 'add(x, y)'\n ],\n description: 'Add two values.',\n examples: [\n 'a = 2.1 + 3.6',\n 'a - 3.6',\n '3 + 2i',\n '3 cm + 2 inch',\n '\"2.3\" + \"4\"'\n ],\n seealso: [\n 'subtract'\n ]\n}\n","export const cbrtDocs = {\n name: 'cbrt',\n category: 'Arithmetic',\n syntax: [\n 'cbrt(x)',\n 'cbrt(x, allRoots)'\n ],\n description:\n 'Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned',\n examples: [\n 'cbrt(64)',\n 'cube(4)',\n 'cbrt(-8)',\n 'cbrt(2 + 3i)',\n 'cbrt(8i)',\n 'cbrt(8i, true)',\n 'cbrt(27 m^3)'\n ],\n seealso: [\n 'square',\n 'sqrt',\n 'cube',\n 'multiply'\n ]\n}\n","export const ceilDocs = {\n name: 'ceil',\n category: 'Arithmetic',\n syntax: [\n 'ceil(x)'\n ],\n description:\n 'Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.',\n examples: [\n 'ceil(3.2)',\n 'ceil(3.8)',\n 'ceil(-4.2)'\n ],\n seealso: ['floor', 'fix', 'round']\n}\n","export const cubeDocs = {\n name: 'cube',\n category: 'Arithmetic',\n syntax: [\n 'cube(x)'\n ],\n description: 'Compute the cube of a value. The cube of x is x * x * x.',\n examples: [\n 'cube(2)',\n '2^3',\n '2 * 2 * 2'\n ],\n seealso: [\n 'multiply',\n 'square',\n 'pow'\n ]\n}\n","export const divideDocs = {\n name: 'divide',\n category: 'Operators',\n syntax: [\n 'x / y',\n 'divide(x, y)'\n ],\n description: 'Divide two values.',\n examples: [\n 'a = 2 / 3',\n 'a * 3',\n '4.5 / 2',\n '3 + 4 / 2',\n '(3 + 4) / 2',\n '18 km / 4.5'\n ],\n seealso: [\n 'multiply'\n ]\n}\n","export const dotDivideDocs = {\n name: 'dotDivide',\n category: 'Operators',\n syntax: [\n 'x ./ y',\n 'dotDivide(x, y)'\n ],\n description: 'Divide two values element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'b = [2, 1, 1; 3, 2, 5]',\n 'a ./ b'\n ],\n seealso: [\n 'multiply',\n 'dotMultiply',\n 'divide'\n ]\n}\n","export const dotMultiplyDocs = {\n name: 'dotMultiply',\n category: 'Operators',\n syntax: [\n 'x .* y',\n 'dotMultiply(x, y)'\n ],\n description: 'Multiply two values element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'b = [2, 1, 1; 3, 2, 5]',\n 'a .* b'\n ],\n seealso: [\n 'multiply',\n 'divide',\n 'dotDivide'\n ]\n}\n","export const dotPowDocs = {\n name: 'dotPow',\n category: 'Operators',\n syntax: [\n 'x .^ y',\n 'dotPow(x, y)'\n ],\n description:\n 'Calculates the power of x to y element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a .^ 2'\n ],\n seealso: [\n 'pow'\n ]\n}\n","export const expDocs = {\n name: 'exp',\n category: 'Arithmetic',\n syntax: [\n 'exp(x)'\n ],\n description: 'Calculate the exponent of a value.',\n examples: [\n 'exp(1.3)',\n 'e ^ 1.3',\n 'log(exp(1.3))',\n 'x = 2.4',\n '(exp(i*x) == cos(x) + i*sin(x)) # Euler\\'s formula'\n ],\n seealso: [\n 'expm',\n 'expm1',\n 'pow',\n 'log'\n ]\n}\n","export const expmDocs = {\n name: 'expm',\n category: 'Arithmetic',\n syntax: [\n 'exp(x)'\n ],\n description: 'Compute the matrix exponential, expm(A) = e^A. ' +\n 'The matrix must be square. ' +\n 'Not to be confused with exp(a), which performs element-wise exponentiation.',\n examples: [\n 'expm([[0,2],[0,0]])'\n ],\n seealso: [\n 'exp'\n ]\n}\n","export const expm1Docs = {\n name: 'expm1',\n category: 'Arithmetic',\n syntax: [\n 'expm1(x)'\n ],\n description: 'Calculate the value of subtracting 1 from the exponential value.',\n examples: [\n 'expm1(2)',\n 'pow(e, 2) - 1',\n 'log(expm1(2) + 1)'\n ],\n seealso: [\n 'exp',\n 'pow',\n 'log'\n ]\n}\n","export const fixDocs = {\n name: 'fix',\n category: 'Arithmetic',\n syntax: [\n 'fix(x)'\n ],\n description:\n 'Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.',\n examples: [\n 'fix(3.2)',\n 'fix(3.8)',\n 'fix(-4.2)',\n 'fix(-4.8)'\n ],\n seealso: ['ceil', 'floor', 'round']\n}\n","export const floorDocs = {\n name: 'floor',\n category: 'Arithmetic',\n syntax: [\n 'floor(x)'\n ],\n description:\n 'Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.',\n examples: [\n 'floor(3.2)',\n 'floor(3.8)',\n 'floor(-4.2)'\n ],\n seealso: ['ceil', 'fix', 'round']\n}\n","export const gcdDocs = {\n name: 'gcd',\n category: 'Arithmetic',\n syntax: [\n 'gcd(a, b)',\n 'gcd(a, b, c, ...)'\n ],\n description: 'Compute the greatest common divisor.',\n examples: [\n 'gcd(8, 12)',\n 'gcd(-4, 6)',\n 'gcd(25, 15, -10)'\n ],\n seealso: ['lcm', 'xgcd']\n}\n","export const hypotDocs = {\n name: 'hypot',\n category: 'Arithmetic',\n syntax: [\n 'hypot(a, b, c, ...)',\n 'hypot([a, b, c, ...])'\n ],\n description: 'Calculate the hypotenusa of a list with values. ',\n examples: [\n 'hypot(3, 4)',\n 'sqrt(3^2 + 4^2)',\n 'hypot(-2)',\n 'hypot([3, 4, 5])'\n ],\n seealso: ['abs', 'norm']\n}\n","export const lcmDocs = {\n name: 'lcm',\n category: 'Arithmetic',\n syntax: [\n 'lcm(x, y)'\n ],\n description: 'Compute the least common multiple.',\n examples: [\n 'lcm(4, 6)',\n 'lcm(6, 21)',\n 'lcm(6, 21, 5)'\n ],\n seealso: ['gcd']\n}\n","export const logDocs = {\n name: 'log',\n category: 'Arithmetic',\n syntax: [\n 'log(x)',\n 'log(x, base)'\n ],\n description: 'Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).',\n examples: [\n 'log(3.5)',\n 'a = log(2.4)',\n 'exp(a)',\n '10 ^ 4',\n 'log(10000, 10)',\n 'log(10000) / log(10)',\n 'b = log(1024, 2)',\n '2 ^ b'\n ],\n seealso: [\n 'exp',\n 'log1p',\n 'log2',\n 'log10'\n ]\n}\n","export const log2Docs = {\n name: 'log2',\n category: 'Arithmetic',\n syntax: [\n 'log2(x)'\n ],\n description: 'Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.',\n examples: [\n 'log2(0.03125)',\n 'log2(16)',\n 'log2(16) / log2(2)',\n 'pow(2, 4)'\n ],\n seealso: [\n 'exp',\n 'log1p',\n 'log',\n 'log10'\n ]\n}\n","export const log1pDocs = {\n name: 'log1p',\n category: 'Arithmetic',\n syntax: [\n 'log1p(x)',\n 'log1p(x, base)'\n ],\n description: 'Calculate the logarithm of a `value+1`',\n examples: [\n 'log1p(2.5)',\n 'exp(log1p(1.4))',\n 'pow(10, 4)',\n 'log1p(9999, 10)',\n 'log1p(9999) / log(10)'\n ],\n seealso: [\n 'exp',\n 'log',\n 'log2',\n 'log10'\n ]\n}\n","export const log10Docs = {\n name: 'log10',\n category: 'Arithmetic',\n syntax: [\n 'log10(x)'\n ],\n description: 'Compute the 10-base logarithm of a value.',\n examples: [\n 'log10(0.00001)',\n 'log10(10000)',\n '10 ^ 4',\n 'log(10000) / log(10)',\n 'log(10000, 10)'\n ],\n seealso: [\n 'exp',\n 'log'\n ]\n}\n","export const modDocs = {\n name: 'mod',\n category: 'Operators',\n syntax: [\n 'x % y',\n 'x mod y',\n 'mod(x, y)'\n ],\n description:\n 'Calculates the modulus, the remainder of an integer division.',\n examples: [\n '7 % 3',\n '11 % 2',\n '10 mod 4',\n 'isOdd(x) = x % 2',\n 'isOdd(2)',\n 'isOdd(3)'\n ],\n seealso: ['divide']\n}\n","export const multiplyDocs = {\n name: 'multiply',\n category: 'Operators',\n syntax: [\n 'x * y',\n 'multiply(x, y)'\n ],\n description: 'multiply two values.',\n examples: [\n 'a = 2.1 * 3.4',\n 'a / 3.4',\n '2 * 3 + 4',\n '2 * (3 + 4)',\n '3 * 2.1 km'\n ],\n seealso: [\n 'divide'\n ]\n}\n","export const normDocs = {\n name: 'norm',\n category: 'Arithmetic',\n syntax: [\n 'norm(x)',\n 'norm(x, p)'\n ],\n description: 'Calculate the norm of a number, vector or matrix.',\n examples: [\n 'abs(-3.5)',\n 'norm(-3.5)',\n 'norm(3 - 4i)',\n 'norm([1, 2, -3], Infinity)',\n 'norm([1, 2, -3], -Infinity)',\n 'norm([3, 4], 2)',\n 'norm([[1, 2], [3, 4]], 1)',\n 'norm([[1, 2], [3, 4]], \"inf\")',\n 'norm([[1, 2], [3, 4]], \"fro\")'\n ]\n}\n","export const nthRootDocs = {\n name: 'nthRoot',\n category: 'Arithmetic',\n syntax: [\n 'nthRoot(a)',\n 'nthRoot(a, root)'\n ],\n description: 'Calculate the nth root of a value. ' +\n 'The principal nth root of a positive real number A, ' +\n 'is the positive real solution of the equation \"x^root = A\".',\n examples: [\n '4 ^ 3',\n 'nthRoot(64, 3)',\n 'nthRoot(9, 2)',\n 'sqrt(9)'\n ],\n seealso: [\n 'nthRoots',\n 'pow',\n 'sqrt'\n ]\n}\n","export const nthRootsDocs = {\n name: 'nthRoots',\n category: 'Arithmetic',\n syntax: [\n 'nthRoots(A)',\n 'nthRoots(A, root)'\n ],\n description: ('' +\n 'Calculate the nth roots of a value. ' +\n 'An nth root of a positive real number A, ' +\n 'is a positive real solution of the equation \"x^root = A\". ' +\n 'This function returns an array of complex values.'\n ),\n examples: [\n 'nthRoots(1)',\n 'nthRoots(1, 3)'\n ],\n seealso: [\n 'sqrt',\n 'pow',\n 'nthRoot'\n ]\n}\n","export const powDocs = {\n name: 'pow',\n category: 'Operators',\n syntax: [\n 'x ^ y',\n 'pow(x, y)'\n ],\n description:\n 'Calculates the power of x to y, x^y.',\n examples: [\n '2^3',\n '2*2*2',\n '1 + e ^ (pi * i)'\n ],\n seealso: [\n 'multiply',\n 'nthRoot',\n 'nthRoots',\n 'sqrt'\n ]\n}\n","export const roundDocs = {\n name: 'round',\n category: 'Arithmetic',\n syntax: [\n 'round(x)',\n 'round(x, n)'\n ],\n description:\n 'round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.',\n examples: [\n 'round(3.2)',\n 'round(3.8)',\n 'round(-4.2)',\n 'round(-4.8)',\n 'round(pi, 3)',\n 'round(123.45678, 2)'\n ],\n seealso: ['ceil', 'floor', 'fix']\n}\n","export const signDocs = {\n name: 'sign',\n category: 'Arithmetic',\n syntax: [\n 'sign(x)'\n ],\n description:\n 'Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.',\n examples: [\n 'sign(3.5)',\n 'sign(-4.2)',\n 'sign(0)'\n ],\n seealso: [\n 'abs'\n ]\n}\n","export const sqrtDocs = {\n name: 'sqrt',\n category: 'Arithmetic',\n syntax: [\n 'sqrt(x)'\n ],\n description:\n 'Compute the square root value. If x = y * y, then y is the square root of x.',\n examples: [\n 'sqrt(25)',\n '5 * 5',\n 'sqrt(-1)'\n ],\n seealso: [\n 'square',\n 'sqrtm',\n 'multiply',\n 'nthRoot',\n 'nthRoots',\n 'pow'\n ]\n}\n","export const sqrtmDocs = {\n name: 'sqrtm',\n category: 'Arithmetic',\n syntax: [\n 'sqrtm(x)'\n ],\n description:\n 'Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.',\n examples: [\n 'sqrtm([[1, 2], [3, 4]])'\n ],\n seealso: [\n 'sqrt',\n 'abs',\n 'square',\n 'multiply'\n ]\n}\n","export const squareDocs = {\n name: 'square',\n category: 'Arithmetic',\n syntax: [\n 'square(x)'\n ],\n description:\n 'Compute the square of a value. The square of x is x * x.',\n examples: [\n 'square(3)',\n 'sqrt(9)',\n '3^2',\n '3 * 3'\n ],\n seealso: [\n 'multiply',\n 'pow',\n 'sqrt',\n 'cube'\n ]\n}\n","export const subtractDocs = {\n name: 'subtract',\n category: 'Operators',\n syntax: [\n 'x - y',\n 'subtract(x, y)'\n ],\n description: 'subtract two values.',\n examples: [\n 'a = 5.3 - 2',\n 'a + 2',\n '2/3 - 1/6',\n '2 * 3 - 3',\n '2.1 km - 500m'\n ],\n seealso: [\n 'add'\n ]\n}\n","export const unaryMinusDocs = {\n name: 'unaryMinus',\n category: 'Operators',\n syntax: [\n '-x',\n 'unaryMinus(x)'\n ],\n description:\n 'Inverse the sign of a value. Converts booleans and strings to numbers.',\n examples: [\n '-4.5',\n '-(-5.6)',\n '-\"22\"'\n ],\n seealso: [\n 'add', 'subtract', 'unaryPlus'\n ]\n}\n","export const unaryPlusDocs = {\n name: 'unaryPlus',\n category: 'Operators',\n syntax: [\n '+x',\n 'unaryPlus(x)'\n ],\n description:\n 'Converts booleans and strings to numbers.',\n examples: [\n '+true',\n '+\"2\"'\n ],\n seealso: [\n 'add', 'subtract', 'unaryMinus'\n ]\n}\n","export const xgcdDocs = {\n name: 'xgcd',\n category: 'Arithmetic',\n syntax: [\n 'xgcd(a, b)'\n ],\n description: 'Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.',\n examples: [\n 'xgcd(8, 12)',\n 'gcd(8, 12)',\n 'xgcd(36163, 21199)'\n ],\n seealso: ['gcd', 'lcm']\n}\n","export const bitAndDocs = {\n name: 'bitAnd',\n category: 'Bitwise',\n syntax: [\n 'x & y',\n 'bitAnd(x, y)'\n ],\n description: 'Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0',\n examples: [\n '5 & 3',\n 'bitAnd(53, 131)',\n '[1, 12, 31] & 42'\n ],\n seealso: [\n 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitNotDocs = {\n name: 'bitNot',\n category: 'Bitwise',\n syntax: [\n '~x',\n 'bitNot(x)'\n ],\n description: 'Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.',\n examples: [\n '~1',\n '~2',\n 'bitNot([2, -3, 4])'\n ],\n seealso: [\n 'bitAnd', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitOrDocs = {\n name: 'bitOr',\n category: 'Bitwise',\n syntax: [\n 'x | y',\n 'bitOr(x, y)'\n ],\n description: 'Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.',\n examples: [\n '5 | 3',\n 'bitOr([1, 2, 3], 4)'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitXorDocs = {\n name: 'bitXor',\n category: 'Bitwise',\n syntax: [\n 'bitXor(x, y)'\n ],\n description: 'Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.',\n examples: [\n 'bitOr(1, 2)',\n 'bitXor([2, 3, 4], 4)'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const leftShiftDocs = {\n name: 'leftShift',\n category: 'Bitwise',\n syntax: [\n 'x << y',\n 'leftShift(x, y)'\n ],\n description: 'Bitwise left logical shift of a value x by y number of bits.',\n examples: [\n '4 << 1',\n '8 >> 1'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const rightArithShiftDocs = {\n name: 'rightArithShift',\n category: 'Bitwise',\n syntax: [\n 'x >> y',\n 'rightArithShift(x, y)'\n ],\n description: 'Bitwise right arithmetic shift of a value x by y number of bits.',\n examples: [\n '8 >> 1',\n '4 << 1',\n '-12 >> 2'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightLogShift'\n ]\n}\n","export const rightLogShiftDocs = {\n name: 'rightLogShift',\n category: 'Bitwise',\n syntax: [\n 'x >>> y',\n 'rightLogShift(x, y)'\n ],\n description: 'Bitwise right logical shift of a value x by y number of bits.',\n examples: [\n '8 >>> 1',\n '4 << 1',\n '-12 >>> 2'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift'\n ]\n}\n","export const bellNumbersDocs = {\n name: 'bellNumbers',\n category: 'Combinatorics',\n syntax: [\n 'bellNumbers(n)'\n ],\n description: 'The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.',\n examples: [\n 'bellNumbers(3)',\n 'bellNumbers(8)'\n ],\n seealso: ['stirlingS2']\n}\n","export const catalanDocs = {\n name: 'catalan',\n category: 'Combinatorics',\n syntax: [\n 'catalan(n)'\n ],\n description: 'The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.',\n examples: [\n 'catalan(3)',\n 'catalan(8)'\n ],\n seealso: ['bellNumbers']\n}\n","export const compositionDocs = {\n name: 'composition',\n category: 'Combinatorics',\n syntax: [\n 'composition(n, k)'\n ],\n description: 'The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.',\n examples: [\n 'composition(5, 3)'\n ],\n seealso: ['combinations']\n}\n","export const stirlingS2Docs = {\n name: 'stirlingS2',\n category: 'Combinatorics',\n syntax: [\n 'stirlingS2(n, k)'\n ],\n description: 'he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.',\n examples: [\n 'stirlingS2(5, 3)'\n ],\n seealso: ['bellNumbers']\n}\n","export const configDocs = {\n name: 'config',\n category: 'Core',\n syntax: [\n 'config()',\n 'config(options)'\n ],\n description: 'Get configuration or change configuration.',\n examples: [\n 'config()',\n '1/3 + 1/4',\n 'config({number: \"Fraction\"})',\n '1/3 + 1/4'\n ],\n seealso: []\n}\n","export const importDocs = {\n name: 'import',\n category: 'Core',\n syntax: [\n 'import(functions)',\n 'import(functions, options)'\n ],\n description: 'Import functions or constants from an object.',\n examples: [\n 'import({myFn: f(x)=x^2, myConstant: 32 })',\n 'myFn(2)',\n 'myConstant'\n ],\n seealso: []\n}\n","export const typedDocs = {\n name: 'typed',\n category: 'Core',\n syntax: [\n 'typed(signatures)',\n 'typed(name, signatures)'\n ],\n description: 'Create a typed function.',\n examples: [\n 'double = typed({ \"number, number\": f(x)=x+x })',\n 'double(2)',\n 'double(\"hello\")'\n ],\n seealso: []\n}\n","export const argDocs = {\n name: 'arg',\n category: 'Complex',\n syntax: [\n 'arg(x)'\n ],\n description:\n 'Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).',\n examples: [\n 'arg(2 + 2i)',\n 'atan2(3, 2)',\n 'arg(2 + 3i)'\n ],\n seealso: [\n 're',\n 'im',\n 'conj',\n 'abs'\n ]\n}\n","export const conjDocs = {\n name: 'conj',\n category: 'Complex',\n syntax: [\n 'conj(x)'\n ],\n description:\n 'Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.',\n examples: [\n 'conj(2 + 3i)',\n 'conj(2 - 3i)',\n 'conj(-5.2i)'\n ],\n seealso: [\n 're',\n 'im',\n 'abs',\n 'arg'\n ]\n}\n","export const reDocs = {\n name: 're',\n category: 'Complex',\n syntax: [\n 're(x)'\n ],\n description: 'Get the real part of a complex number.',\n examples: [\n 're(2 + 3i)',\n 'im(2 + 3i)',\n 're(-5.2i)',\n 're(2.4)'\n ],\n seealso: [\n 'im',\n 'conj',\n 'abs',\n 'arg'\n ]\n}\n","export const imDocs = {\n name: 'im',\n category: 'Complex',\n syntax: [\n 'im(x)'\n ],\n description: 'Get the imaginary part of a complex number.',\n examples: [\n 'im(2 + 3i)',\n 're(2 + 3i)',\n 'im(-5.2i)',\n 'im(2.4)'\n ],\n seealso: [\n 're',\n 'conj',\n 'abs',\n 'arg'\n ]\n}\n","export const evaluateDocs = {\n name: 'evaluate',\n category: 'Expression',\n syntax: [\n 'evaluate(expression)',\n 'evaluate([expr1, expr2, expr3, ...])'\n ],\n description: 'Evaluate an expression or an array with expressions.',\n examples: [\n 'evaluate(\"2 + 3\")',\n 'evaluate(\"sqrt(\" + 4 + \")\")'\n ],\n seealso: []\n}\n","export const helpDocs = {\n name: 'help',\n category: 'Expression',\n syntax: [\n 'help(object)',\n 'help(string)'\n ],\n description: 'Display documentation on a function or data type.',\n examples: [\n 'help(sqrt)',\n 'help(\"complex\")'\n ],\n seealso: []\n}\n","export const distanceDocs = {\n name: 'distance',\n category: 'Geometry',\n syntax: [\n 'distance([x1, y1], [x2, y2])',\n 'distance([[x1, y1], [x2, y2]])'\n ],\n description: 'Calculates the Euclidean distance between two points.',\n examples: [\n 'distance([0,0], [4,4])',\n 'distance([[0,0], [4,4]])'\n ],\n seealso: []\n}\n","export const intersectDocs = {\n name: 'intersect',\n category: 'Geometry',\n syntax: [\n 'intersect(expr1, expr2, expr3, expr4)',\n 'intersect(expr1, expr2, expr3)'\n ],\n description: 'Computes the intersection point of lines and/or planes.',\n examples: [\n 'intersect([0, 0], [10, 10], [10, 0], [0, 10])',\n 'intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])'\n ],\n seealso: []\n}\n","export const andDocs = {\n name: 'and',\n category: 'Logical',\n syntax: [\n 'x and y',\n 'and(x, y)'\n ],\n description: 'Logical and. Test whether two values are both defined with a nonzero/nonempty value.',\n examples: [\n 'true and false',\n 'true and true',\n '2 and 4'\n ],\n seealso: [\n 'not', 'or', 'xor'\n ]\n}\n","export const notDocs = {\n name: 'not',\n category: 'Logical',\n syntax: [\n 'not x',\n 'not(x)'\n ],\n description: 'Logical not. Flips the boolean value of given argument.',\n examples: [\n 'not true',\n 'not false',\n 'not 2',\n 'not 0'\n ],\n seealso: [\n 'and', 'or', 'xor'\n ]\n}\n","export const orDocs = {\n name: 'or',\n category: 'Logical',\n syntax: [\n 'x or y',\n 'or(x, y)'\n ],\n description: 'Logical or. Test if at least one value is defined with a nonzero/nonempty value.',\n examples: [\n 'true or false',\n 'false or false',\n '0 or 4'\n ],\n seealso: [\n 'not', 'and', 'xor'\n ]\n}\n","export const xorDocs = {\n name: 'xor',\n category: 'Logical',\n syntax: [\n 'x xor y',\n 'xor(x, y)'\n ],\n description: 'Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.',\n examples: [\n 'true xor false',\n 'false xor false',\n 'true xor true',\n '0 xor 4'\n ],\n seealso: [\n 'not', 'and', 'or'\n ]\n}\n","export const concatDocs = {\n name: 'concat',\n category: 'Matrix',\n syntax: [\n 'concat(A, B, C, ...)',\n 'concat(A, B, C, ..., dim)'\n ],\n description: 'Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.',\n examples: [\n 'A = [1, 2; 5, 6]',\n 'B = [3, 4; 7, 8]',\n 'concat(A, B)',\n 'concat(A, B, 1)',\n 'concat(A, B, 2)'\n ],\n seealso: [\n 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const crossDocs = {\n name: 'cross',\n category: 'Matrix',\n syntax: [\n 'cross(A, B)'\n ],\n description: 'Calculate the cross product for two vectors in three dimensional space.',\n examples: [\n 'cross([1, 1, 0], [0, 1, 1])',\n 'cross([3, -3, 1], [4, 9, 2])',\n 'cross([2, 3, 4], [5, 6, 7])'\n ],\n seealso: [\n 'multiply',\n 'dot'\n ]\n}\n","export const columnDocs = {\n name: 'column',\n category: 'Matrix',\n syntax: [\n 'column(x, index)'\n ],\n description: 'Return a column from a matrix or array.',\n examples: [\n 'A = [[1, 2], [3, 4]]',\n 'column(A, 1)',\n 'column(A, 2)'\n ],\n seealso: ['row']\n}\n","export const ctransposeDocs = {\n name: 'ctranspose',\n category: 'Matrix',\n syntax: [\n 'x\\'',\n 'ctranspose(x)'\n ],\n description: 'Complex Conjugate and Transpose a matrix',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a\\'',\n 'ctranspose(a)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'zeros'\n ]\n}\n","export const detDocs = {\n name: 'det',\n category: 'Matrix',\n syntax: [\n 'det(x)'\n ],\n description: 'Calculate the determinant of a matrix',\n examples: [\n 'det([1, 2; 3, 4])',\n 'det([-2, 2, 3; -1, 1, 3; 2, 0, -1])'\n ],\n seealso: [\n 'concat', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const diagDocs = {\n name: 'diag',\n category: 'Matrix',\n syntax: [\n 'diag(x)',\n 'diag(x, k)'\n ],\n description: 'Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.',\n examples: [\n 'diag(1:3)',\n 'diag(1:3, 1)',\n 'a = [1, 2, 3; 4, 5, 6; 7, 8, 9]',\n 'diag(a)'\n ],\n seealso: [\n 'concat', 'det', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const diffDocs = {\n name: 'diff',\n category: 'Matrix',\n syntax: [\n 'diff(arr)',\n 'diff(arr, dim)'\n ],\n description: [\n 'Create a new matrix or array with the difference of the passed matrix or array.',\n 'Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference',\n 'If no dimension parameter is passed it is assumed as dimension 0',\n 'Dimension is zero-based in javascript and one-based in the parser',\n 'Arrays must be \\'rectangular\\' meaning arrays like [1, 2]',\n 'If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays'\n ],\n examples: [\n 'diff([1, 2, 4, 7, 0])',\n 'diff([1, 2, 4, 7, 0], 0)',\n 'diff(matrix([1, 2, 4, 7, 0]))',\n 'diff([[1, 2], [3, 4]])',\n 'diff([[1, 2], [3, 4]], 0)',\n 'diff([[1, 2], [3, 4]], 1)',\n 'diff([[1, 2], [3, 4]], bignumber(1))',\n 'diff(matrix([[1, 2], [3, 4]]), 1)',\n 'diff([[1, 2], matrix([3, 4])], 1)'\n\n ],\n seealso: ['subtract', 'partitionSelect']\n}\n","export const dotDocs = {\n name: 'dot',\n category: 'Matrix',\n syntax: [\n 'dot(A, B)',\n 'A * B'\n ],\n description: 'Calculate the dot product of two vectors. ' +\n 'The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] ' +\n 'is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn',\n examples: [\n 'dot([2, 4, 1], [2, 2, 3])',\n '[2, 4, 1] * [2, 2, 3]'\n ],\n seealso: [\n 'multiply',\n 'cross'\n ]\n}\n","export const getMatrixDataTypeDocs = {\n name: 'getMatrixDataType',\n category: 'Matrix',\n syntax: [\n 'getMatrixDataType(x)'\n ],\n description: 'Find the data type of all elements in a matrix or array, ' +\n 'for example \"number\" if all items are a number ' +\n 'and \"Complex\" if all values are complex numbers. ' +\n 'If a matrix contains more than one data type, it will return \"mixed\".',\n examples: [\n 'getMatrixDataType([1, 2, 3])',\n 'getMatrixDataType([[5 cm], [2 inch]])',\n 'getMatrixDataType([1, \"text\"])',\n 'getMatrixDataType([1, bignumber(4)])'\n ],\n seealso: ['matrix', 'sparse', 'typeOf']\n}\n","export const identityDocs = {\n name: 'identity',\n category: 'Matrix',\n syntax: [\n 'identity(n)',\n 'identity(m, n)',\n 'identity([m, n])'\n ],\n description: 'Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.',\n examples: [\n 'identity(3)',\n 'identity(3, 5)',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'identity(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const filterDocs = {\n name: 'filter',\n category: 'Matrix',\n syntax: [\n 'filter(x, test)'\n ],\n description: 'Filter items in a matrix.',\n examples: [\n 'isPositive(x) = x > 0',\n 'filter([6, -2, -1, 4, 3], isPositive)',\n 'filter([6, -2, 0, 1, 0], x != 0)'\n ],\n seealso: ['sort', 'map', 'forEach']\n}\n","export const flattenDocs = {\n name: 'flatten',\n category: 'Matrix',\n syntax: [\n 'flatten(x)'\n ],\n description: 'Flatten a multi dimensional matrix into a single dimensional matrix.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'size(a)',\n 'b = flatten(a)',\n 'size(b)'\n ],\n seealso: [\n 'concat', 'resize', 'size', 'squeeze'\n ]\n}\n","export const forEachDocs = {\n name: 'forEach',\n category: 'Matrix',\n syntax: [\n 'forEach(x, callback)'\n ],\n description: 'Iterates over all elements of a matrix/array, and executes the given callback function.',\n examples: [\n 'forEach([1, 2, 3], function(val) { console.log(val) })'\n ],\n seealso: ['map', 'sort', 'filter']\n}\n","export const invDocs = {\n name: 'inv',\n category: 'Matrix',\n syntax: [\n 'inv(x)'\n ],\n description: 'Calculate the inverse of a matrix',\n examples: [\n 'inv([1, 2; 3, 4])',\n 'inv(4)',\n '1 / 4'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const eigsDocs = {\n name: 'eigs',\n category: 'Matrix',\n syntax: [\n 'eigs(x)'\n ],\n description: 'Calculate the eigenvalues and eigenvectors of a real symmetric matrix',\n examples: [\n 'eigs([[5, 2.3], [2.3, 1]])'\n ],\n seealso: [\n 'inv'\n ]\n}\n","export const kronDocs = {\n name: 'kron',\n category: 'Matrix',\n syntax: [\n 'kron(x, y)'\n ],\n description: 'Calculates the kronecker product of 2 matrices or vectors.',\n examples: [\n 'kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])',\n 'kron([1,1], [2,3,4])'\n ],\n seealso: [\n 'multiply', 'dot', 'cross'\n ]\n}\n","export const mapDocs = {\n name: 'map',\n category: 'Matrix',\n syntax: [\n 'map(x, callback)'\n ],\n description: 'Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.',\n examples: [\n 'map([1, 2, 3], square)'\n ],\n seealso: ['filter', 'forEach']\n}\n","export const onesDocs = {\n name: 'ones',\n category: 'Matrix',\n syntax: [\n 'ones(m)',\n 'ones(m, n)',\n 'ones(m, n, p, ...)',\n 'ones([m])',\n 'ones([m, n])',\n 'ones([m, n, p, ...])'\n ],\n description: 'Create a matrix containing ones.',\n examples: [\n 'ones(3)',\n 'ones(3, 5)',\n 'ones([2,3]) * 4.5',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'ones(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const partitionSelectDocs = {\n name: 'partitionSelect',\n category: 'Matrix',\n syntax: [\n 'partitionSelect(x, k)',\n 'partitionSelect(x, k, compare)'\n ],\n description: 'Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.',\n examples: [\n 'partitionSelect([5, 10, 1], 2)',\n 'partitionSelect([\"C\", \"B\", \"A\", \"D\"], 1)'\n ],\n seealso: ['sort']\n}\n","export const rangeDocs = {\n name: 'range',\n category: 'Type',\n syntax: [\n 'start:end',\n 'start:step:end',\n 'range(start, end)',\n 'range(start, end, step)',\n 'range(string)'\n ],\n description:\n 'Create a range. Lower bound of the range is included, upper bound is excluded.',\n examples: [\n '1:5',\n '3:-1:-3',\n 'range(3, 7)',\n 'range(0, 12, 2)',\n 'range(\"4:10\")',\n 'a = [1, 2, 3, 4; 5, 6, 7, 8]',\n 'a[1:2, 1:2]'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const resizeDocs = {\n name: 'resize',\n category: 'Matrix',\n syntax: [\n 'resize(x, size)',\n 'resize(x, size, defaultValue)'\n ],\n description: 'Resize a matrix.',\n examples: [\n 'resize([1,2,3,4,5], [3])',\n 'resize([1,2,3], [5])',\n 'resize([1,2,3], [5], -1)',\n 'resize(2, [2, 3])',\n 'resize(\"hello\", [8], \"!\")'\n ],\n seealso: [\n 'size', 'subset', 'squeeze', 'reshape'\n ]\n}\n","export const reshapeDocs = {\n name: 'reshape',\n category: 'Matrix',\n syntax: [\n 'reshape(x, sizes)'\n ],\n description: 'Reshape a multi dimensional array to fit the specified dimensions.',\n examples: [\n 'reshape([1, 2, 3, 4, 5, 6], [2, 3])',\n 'reshape([[1, 2], [3, 4]], [1, 4])',\n 'reshape([[1, 2], [3, 4]], [4])'\n ],\n seealso: [\n 'size', 'squeeze', 'resize'\n ]\n}\n","export const rotateDocs = {\n name: 'rotate',\n category: 'Matrix',\n syntax: [\n 'rotate(w, theta)',\n 'rotate(w, theta, v)'\n ],\n description: 'Returns a 2-D rotation matrix (2x2) for a given angle (in radians). ' +\n 'Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.',\n examples: [\n 'rotate([1, 0], math.pi / 2)',\n 'rotate(matrix([1, 0]), unit(\"35deg\"))',\n 'rotate([1, 0, 0], unit(\"90deg\"), [0, 0, 1])',\n 'rotate(matrix([1, 0, 0]), unit(\"90deg\"), matrix([0, 0, 1]))'\n ],\n seealso: [\n 'matrix', 'rotationMatrix'\n ]\n}\n","export const rotationMatrixDocs = {\n name: 'rotationMatrix',\n category: 'Matrix',\n syntax: [\n 'rotationMatrix(theta)',\n 'rotationMatrix(theta, v)',\n 'rotationMatrix(theta, v, format)'\n ],\n description: 'Returns a 2-D rotation matrix (2x2) for a given angle (in radians). ' +\n 'Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.',\n examples: [\n 'rotationMatrix(pi / 2)',\n 'rotationMatrix(unit(\"45deg\"), [0, 0, 1])',\n 'rotationMatrix(1, matrix([0, 0, 1]), \"sparse\")'\n ],\n seealso: [\n 'cos', 'sin'\n ]\n}\n","export const rowDocs = {\n name: 'row',\n category: 'Matrix',\n syntax: [\n 'row(x, index)'\n ],\n description: 'Return a row from a matrix or array.',\n examples: [\n 'A = [[1, 2], [3, 4]]',\n 'row(A, 1)',\n 'row(A, 2)'\n ],\n seealso: ['column']\n}\n","export const sizeDocs = {\n name: 'size',\n category: 'Matrix',\n syntax: [\n 'size(x)'\n ],\n description: 'Calculate the size of a matrix.',\n examples: [\n 'size(2.3)',\n 'size(\"hello world\")',\n 'a = [1, 2; 3, 4; 5, 6]',\n 'size(a)',\n 'size(1:6)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const sortDocs = {\n name: 'sort',\n category: 'Matrix',\n syntax: [\n 'sort(x)',\n 'sort(x, compare)'\n ],\n description: 'Sort the items in a matrix. Compare can be a string \"asc\", \"desc\", \"natural\", or a custom sort function.',\n examples: [\n 'sort([5, 10, 1])',\n 'sort([\"C\", \"B\", \"A\", \"D\"])',\n 'sortByLength(a, b) = size(a)[1] - size(b)[1]',\n 'sort([\"Langdon\", \"Tom\", \"Sara\"], sortByLength)',\n 'sort([\"10\", \"1\", \"2\"], \"natural\")'\n ],\n seealso: ['map', 'filter', 'forEach']\n}\n","export const squeezeDocs = {\n name: 'squeeze',\n category: 'Matrix',\n syntax: [\n 'squeeze(x)'\n ],\n description: 'Remove inner and outer singleton dimensions from a matrix.',\n examples: [\n 'a = zeros(3,2,1)',\n 'size(squeeze(a))',\n 'b = zeros(1,1,3)',\n 'size(squeeze(b))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const subsetDocs = {\n name: 'subset',\n category: 'Matrix',\n syntax: [\n 'value(index)',\n 'value(index) = replacement',\n 'subset(value, [index])',\n 'subset(value, [index], replacement)'\n ],\n description: 'Get or set a subset of a matrix or string. ' +\n 'Indexes are one-based. ' +\n 'Both the ranges lower-bound and upper-bound are included.',\n examples: [\n 'd = [1, 2; 3, 4]',\n 'e = []',\n 'e[1, 1:2] = [5, 6]',\n 'e[2, :] = [7, 8]',\n 'f = d * e',\n 'f[2, 1]',\n 'f[:, 1]'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const traceDocs = {\n name: 'trace',\n category: 'Matrix',\n syntax: [\n 'trace(A)'\n ],\n description: 'Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.',\n examples: [\n 'A = [1, 2, 3; -1, 2, 3; 2, 0, 3]',\n 'trace(A)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'\n ]\n}\n","export const transposeDocs = {\n name: 'transpose',\n category: 'Matrix',\n syntax: [\n 'x\\'',\n 'transpose(x)'\n ],\n description: 'Transpose a matrix',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a\\'',\n 'transpose(a)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'zeros'\n ]\n}\n","export const zerosDocs = {\n name: 'zeros',\n category: 'Matrix',\n syntax: [\n 'zeros(m)',\n 'zeros(m, n)',\n 'zeros(m, n, p, ...)',\n 'zeros([m])',\n 'zeros([m, n])',\n 'zeros([m, n, p, ...])'\n ],\n description: 'Create a matrix containing zeros.',\n examples: [\n 'zeros(3)',\n 'zeros(3, 5)',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'zeros(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose'\n ]\n}\n","export const combinationsDocs = {\n name: 'combinations',\n category: 'Probability',\n syntax: [\n 'combinations(n, k)'\n ],\n description: 'Compute the number of combinations of n items taken k at a time',\n examples: [\n 'combinations(7, 5)'\n ],\n seealso: ['combinationsWithRep', 'permutations', 'factorial']\n}\n","export const combinationsWithRepDocs = {\n name: 'combinationsWithRep',\n category: 'Probability',\n syntax: [\n 'combinationsWithRep(n, k)'\n ],\n description: 'Compute the number of combinations of n items taken k at a time with replacements.',\n examples: [\n 'combinationsWithRep(7, 5)'\n ],\n seealso: ['combinations', 'permutations', 'factorial']\n}\n","export const factorialDocs = {\n name: 'factorial',\n category: 'Probability',\n syntax: [\n 'n!',\n 'factorial(n)'\n ],\n description: 'Compute the factorial of a value',\n examples: [\n '5!',\n '5 * 4 * 3 * 2 * 1',\n '3!'\n ],\n seealso: ['combinations', 'combinationsWithRep', 'permutations', 'gamma']\n}\n","export const gammaDocs = {\n name: 'gamma',\n category: 'Probability',\n syntax: [\n 'gamma(n)'\n ],\n description: 'Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.',\n examples: [\n 'gamma(4)',\n '3!',\n 'gamma(1/2)',\n 'sqrt(pi)'\n ],\n seealso: ['factorial']\n}\n","export const kldivergenceDocs = {\n name: 'kldivergence',\n category: 'Probability',\n syntax: [\n 'kldivergence(x, y)'\n ],\n description: 'Calculate the Kullback-Leibler (KL) divergence between two distributions.',\n examples: [\n 'kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])'\n ],\n seealso: []\n}\n","export const multinomialDocs = {\n name: 'multinomial',\n category: 'Probability',\n syntax: [\n 'multinomial(A)'\n ],\n description: 'Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.',\n examples: [\n 'multinomial([1, 2, 1])'\n ],\n seealso: ['combinations', 'factorial']\n}\n","export const permutationsDocs = {\n name: 'permutations',\n category: 'Probability',\n syntax: [\n 'permutations(n)',\n 'permutations(n, k)'\n ],\n description: 'Compute the number of permutations of n items taken k at a time',\n examples: [\n 'permutations(5)',\n 'permutations(5, 3)'\n ],\n seealso: ['combinations', 'combinationsWithRep', 'factorial']\n}\n","export const pickRandomDocs = {\n name: 'pickRandom',\n category: 'Probability',\n syntax: [\n 'pickRandom(array)',\n 'pickRandom(array, number)',\n 'pickRandom(array, weights)',\n 'pickRandom(array, number, weights)',\n 'pickRandom(array, weights, number)'\n ],\n description:\n 'Pick a random entry from a given array.',\n examples: [\n 'pickRandom(0:10)',\n 'pickRandom([1, 3, 1, 6])',\n 'pickRandom([1, 3, 1, 6], 2)',\n 'pickRandom([1, 3, 1, 6], [2, 3, 2, 1])',\n 'pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])',\n 'pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)'\n ],\n seealso: ['random', 'randomInt']\n}\n","export const randomDocs = {\n name: 'random',\n category: 'Probability',\n syntax: [\n 'random()',\n 'random(max)',\n 'random(min, max)',\n 'random(size)',\n 'random(size, max)',\n 'random(size, min, max)'\n ],\n description:\n 'Return a random number.',\n examples: [\n 'random()',\n 'random(10, 20)',\n 'random([2, 3])'\n ],\n seealso: ['pickRandom', 'randomInt']\n}\n","export const randomIntDocs = {\n name: 'randomInt',\n category: 'Probability',\n syntax: [\n 'randomInt(max)',\n 'randomInt(min, max)',\n 'randomInt(size)',\n 'randomInt(size, max)',\n 'randomInt(size, min, max)'\n ],\n description:\n 'Return a random integer number',\n examples: [\n 'randomInt(10, 20)',\n 'randomInt([2, 3], 10)'\n ],\n seealso: ['pickRandom', 'random']\n}\n","export const compareDocs = {\n name: 'compare',\n category: 'Relational',\n syntax: [\n 'compare(x, y)'\n ],\n description:\n 'Compare two values. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compare(2, 3)',\n 'compare(3, 2)',\n 'compare(2, 2)',\n 'compare(5cm, 40mm)',\n 'compare(2, [1, 2, 3])'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compareNatural', 'compareText'\n ]\n}\n","export const compareNaturalDocs = {\n name: 'compareNatural',\n category: 'Relational',\n syntax: [\n 'compareNatural(x, y)'\n ],\n description:\n 'Compare two values of any type in a deterministic, natural way. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compareNatural(2, 3)',\n 'compareNatural(3, 2)',\n 'compareNatural(2, 2)',\n 'compareNatural(5cm, 40mm)',\n 'compareNatural(\"2\", \"10\")',\n 'compareNatural(2 + 3i, 2 + 4i)',\n 'compareNatural([1, 2, 4], [1, 2, 3])',\n 'compareNatural([1, 5], [1, 2, 3])',\n 'compareNatural([1, 2], [1, 2])',\n 'compareNatural({a: 2}, {a: 4})'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compare', 'compareText'\n ]\n}\n","export const compareTextDocs = {\n name: 'compareText',\n category: 'Relational',\n syntax: [\n 'compareText(x, y)'\n ],\n description:\n 'Compare two strings lexically. Comparison is case sensitive. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compareText(\"B\", \"A\")',\n 'compareText(\"A\", \"B\")',\n 'compareText(\"A\", \"A\")',\n 'compareText(\"2\", \"10\")',\n 'compare(\"2\", \"10\")',\n 'compare(2, 10)',\n 'compareNatural(\"2\", \"10\")',\n 'compareText(\"B\", [\"A\", \"B\", \"C\"])'\n ],\n seealso: [\n 'compare', 'compareNatural'\n ]\n}\n","export const deepEqualDocs = {\n name: 'deepEqual',\n category: 'Relational',\n syntax: [\n 'deepEqual(x, y)'\n ],\n description:\n 'Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.',\n examples: [\n 'deepEqual([1,3,4], [1,3,4])',\n 'deepEqual([1,3,4], [1,3])'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const equalDocs = {\n name: 'equal',\n category: 'Relational',\n syntax: [\n 'x == y',\n 'equal(x, y)'\n ],\n description:\n 'Check equality of two values. Returns true if the values are equal, and false if not.',\n examples: [\n '2+2 == 3',\n '2+2 == 4',\n 'a = 3.2',\n 'b = 6-2.8',\n 'a == b',\n '50cm == 0.5m'\n ],\n seealso: [\n 'unequal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare', 'deepEqual', 'equalText'\n ]\n}\n","export const equalTextDocs = {\n name: 'equalText',\n category: 'Relational',\n syntax: [\n 'equalText(x, y)'\n ],\n description:\n 'Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.',\n examples: [\n 'equalText(\"Hello\", \"Hello\")',\n 'equalText(\"a\", \"A\")',\n 'equal(\"2e3\", \"2000\")',\n 'equalText(\"2e3\", \"2000\")',\n 'equalText(\"B\", [\"A\", \"B\", \"C\"])'\n ],\n seealso: [\n 'compare', 'compareNatural', 'compareText', 'equal'\n ]\n}\n","export const largerDocs = {\n name: 'larger',\n category: 'Relational',\n syntax: [\n 'x > y',\n 'larger(x, y)'\n ],\n description:\n 'Check if value x is larger than y. Returns true if x is larger than y, and false if not.',\n examples: [\n '2 > 3',\n '5 > 2*2',\n 'a = 3.3',\n 'b = 6-2.8',\n '(a > b)',\n '(b < a)',\n '5 cm > 2 inch'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const largerEqDocs = {\n name: 'largerEq',\n category: 'Relational',\n syntax: [\n 'x >= y',\n 'largerEq(x, y)'\n ],\n description:\n 'Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.',\n examples: [\n '2 >= 1+1',\n '2 > 1+1',\n 'a = 3.2',\n 'b = 6-2.8',\n '(a >= b)'\n ],\n seealso: [\n 'equal', 'unequal', 'smallerEq', 'smaller', 'compare'\n ]\n}\n","export const smallerDocs = {\n name: 'smaller',\n category: 'Relational',\n syntax: [\n 'x < y',\n 'smaller(x, y)'\n ],\n description:\n 'Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.',\n examples: [\n '2 < 3',\n '5 < 2*2',\n 'a = 3.3',\n 'b = 6-2.8',\n '(a < b)',\n '5 cm < 2 inch'\n ],\n seealso: [\n 'equal', 'unequal', 'larger', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const smallerEqDocs = {\n name: 'smallerEq',\n category: 'Relational',\n syntax: [\n 'x <= y',\n 'smallerEq(x, y)'\n ],\n description:\n 'Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.',\n examples: [\n '2 <= 1+1',\n '2 < 1+1',\n 'a = 3.2',\n 'b = 6-2.8',\n '(a <= b)'\n ],\n seealso: [\n 'equal', 'unequal', 'larger', 'smaller', 'largerEq', 'compare'\n ]\n}\n","export const unequalDocs = {\n name: 'unequal',\n category: 'Relational',\n syntax: [\n 'x != y',\n 'unequal(x, y)'\n ],\n description:\n 'Check unequality of two values. Returns true if the values are unequal, and false if they are equal.',\n examples: [\n '2+2 != 3',\n '2+2 != 4',\n 'a = 3.2',\n 'b = 6-2.8',\n 'a != b',\n '50cm != 0.5m',\n '5 cm != 2 inch'\n ],\n seealso: [\n 'equal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare', 'deepEqual'\n ]\n}\n","export const setCartesianDocs = {\n name: 'setCartesian',\n category: 'Set',\n syntax: [\n 'setCartesian(set1, set2)'\n ],\n description:\n 'Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setCartesian([1, 2], [3, 4])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference', 'setPowerset'\n ]\n}\n","export const setDifferenceDocs = {\n name: 'setDifference',\n category: 'Set',\n syntax: [\n 'setDifference(set1, set2)'\n ],\n description:\n 'Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setDifference([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setSymDifference'\n ]\n}\n","export const setDistinctDocs = {\n name: 'setDistinct',\n category: 'Set',\n syntax: [\n 'setDistinct(set)'\n ],\n description:\n 'Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setDistinct([1, 1, 1, 2, 2, 3])'\n ],\n seealso: [\n 'setMultiplicity'\n ]\n}\n","export const setIntersectDocs = {\n name: 'setIntersect',\n category: 'Set',\n syntax: [\n 'setIntersect(set1, set2)'\n ],\n description:\n 'Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setIntersect([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setDifference'\n ]\n}\n","export const setIsSubsetDocs = {\n name: 'setIsSubset',\n category: 'Set',\n syntax: [\n 'setIsSubset(set1, set2)'\n ],\n description:\n 'Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setIsSubset([1, 2], [3, 4, 5, 6])',\n 'setIsSubset([3, 4], [3, 4, 5, 6])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setMultiplicityDocs = {\n name: 'setMultiplicity',\n category: 'Set',\n syntax: [\n 'setMultiplicity(element, set)'\n ],\n description:\n 'Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setMultiplicity(1, [1, 2, 2, 4])',\n 'setMultiplicity(2, [1, 2, 2, 4])'\n ],\n seealso: [\n 'setDistinct', 'setSize'\n ]\n}\n","export const setPowersetDocs = {\n name: 'setPowerset',\n category: 'Set',\n syntax: [\n 'setPowerset(set)'\n ],\n description:\n 'Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setPowerset([1, 2, 3])'\n ],\n seealso: [\n 'setCartesian'\n ]\n}\n","export const setSizeDocs = {\n name: 'setSize',\n category: 'Set',\n syntax: [\n 'setSize(set)',\n 'setSize(set, unique)'\n ],\n description:\n 'Count the number of elements of a (multi)set. When the second parameter \"unique\" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setSize([1, 2, 2, 4])',\n 'setSize([1, 2, 2, 4], true)'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setSymDifferenceDocs = {\n name: 'setSymDifference',\n category: 'Set',\n syntax: [\n 'setSymDifference(set1, set2)'\n ],\n description:\n 'Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setUnionDocs = {\n name: 'setUnion',\n category: 'Set',\n syntax: [\n 'setUnion(set1, set2)'\n ],\n description:\n 'Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setUnion([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setIntersect', 'setDifference'\n ]\n}\n","export const erfDocs = {\n name: 'erf',\n category: 'Special',\n syntax: [\n 'erf(x)'\n ],\n description: 'Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x',\n examples: [\n 'erf(0.2)',\n 'erf(-0.5)',\n 'erf(4)'\n ],\n seealso: []\n}\n","export const madDocs = {\n name: 'mad',\n category: 'Statistics',\n syntax: [\n 'mad(a, b, c, ...)',\n 'mad(A)'\n ],\n description: 'Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.',\n examples: [\n 'mad(10, 20, 30)',\n 'mad([1, 2, 3])'\n ],\n seealso: [\n 'mean',\n 'median',\n 'std',\n 'abs'\n ]\n}\n","export const maxDocs = {\n name: 'max',\n category: 'Statistics',\n syntax: [\n 'max(a, b, c, ...)',\n 'max(A)',\n 'max(A, dim)'\n ],\n description: 'Compute the maximum value of a list of values.',\n examples: [\n 'max(2, 3, 4, 1)',\n 'max([2, 3, 4, 1])',\n 'max([2, 5; 4, 3])',\n 'max([2, 5; 4, 3], 1)',\n 'max([2, 5; 4, 3], 2)',\n 'max(2.7, 7.1, -4.5, 2.0, 4.1)',\n 'min(2.7, 7.1, -4.5, 2.0, 4.1)'\n ],\n seealso: [\n 'mean',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const meanDocs = {\n name: 'mean',\n category: 'Statistics',\n syntax: [\n 'mean(a, b, c, ...)',\n 'mean(A)',\n 'mean(A, dim)'\n ],\n description: 'Compute the arithmetic mean of a list of values.',\n examples: [\n 'mean(2, 3, 4, 1)',\n 'mean([2, 3, 4, 1])',\n 'mean([2, 5; 4, 3])',\n 'mean([2, 5; 4, 3], 1)',\n 'mean([2, 5; 4, 3], 2)',\n 'mean([1.0, 2.7, 3.2, 4.0])'\n ],\n seealso: [\n 'max',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const medianDocs = {\n name: 'median',\n category: 'Statistics',\n syntax: [\n 'median(a, b, c, ...)',\n 'median(A)'\n ],\n description: 'Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.',\n examples: [\n 'median(5, 2, 7)',\n 'median([3, -1, 5, 7])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance',\n 'quantileSeq'\n ]\n}\n","export const minDocs = {\n name: 'min',\n category: 'Statistics',\n syntax: [\n 'min(a, b, c, ...)',\n 'min(A)',\n 'min(A, dim)'\n ],\n description: 'Compute the minimum value of a list of values.',\n examples: [\n 'min(2, 3, 4, 1)',\n 'min([2, 3, 4, 1])',\n 'min([2, 5; 4, 3])',\n 'min([2, 5; 4, 3], 1)',\n 'min([2, 5; 4, 3], 2)',\n 'min(2.7, 7.1, -4.5, 2.0, 4.1)',\n 'max(2.7, 7.1, -4.5, 2.0, 4.1)'\n ],\n seealso: [\n 'max',\n 'mean',\n 'median',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const modeDocs = {\n name: 'mode',\n category: 'Statistics',\n syntax: [\n 'mode(a, b, c, ...)',\n 'mode(A)',\n 'mode(A, a, b, B, c, ...)'\n ],\n description: 'Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.',\n examples: [\n 'mode(2, 1, 4, 3, 1)',\n 'mode([1, 2.7, 3.2, 4, 2.7])',\n 'mode(1, 4, 6, 1, 6)'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const prodDocs = {\n name: 'prod',\n category: 'Statistics',\n syntax: [\n 'prod(a, b, c, ...)',\n 'prod(A)'\n ],\n description: 'Compute the product of all values.',\n examples: [\n 'prod(2, 3, 4)',\n 'prod([2, 3, 4])',\n 'prod([2, 5; 4, 3])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'min',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const quantileSeqDocs = {\n name: 'quantileSeq',\n category: 'Statistics',\n syntax: [\n 'quantileSeq(A, prob[, sorted])',\n 'quantileSeq(A, [prob1, prob2, ...][, sorted])',\n 'quantileSeq(A, N[, sorted])'\n ],\n description: 'Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \\n\\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.',\n examples: [\n 'quantileSeq([3, -1, 5, 7], 0.5)',\n 'quantileSeq([3, -1, 5, 7], [1/3, 2/3])',\n 'quantileSeq([3, -1, 5, 7], 2)',\n 'quantileSeq([-1, 3, 5, 7], 0.5, true)'\n ],\n seealso: [\n 'mean',\n 'median',\n 'min',\n 'max',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const stdDocs = {\n name: 'std',\n category: 'Statistics',\n syntax: [\n 'std(a, b, c, ...)',\n 'std(A)',\n 'std(A, normalization)'\n ],\n description: 'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be \"unbiased\" (default), \"uncorrected\", or \"biased\".',\n examples: [\n 'std(2, 4, 6)',\n 'std([2, 4, 6, 8])',\n 'std([2, 4, 6, 8], \"uncorrected\")',\n 'std([2, 4, 6, 8], \"biased\")',\n 'std([1, 2, 3; 4, 5, 6])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'prod',\n 'sum',\n 'variance'\n ]\n}\n","export const sumDocs = {\n name: 'sum',\n category: 'Statistics',\n syntax: [\n 'sum(a, b, c, ...)',\n 'sum(A)'\n ],\n description: 'Compute the sum of all values.',\n examples: [\n 'sum(2, 3, 4, 1)',\n 'sum([2, 3, 4, 1])',\n 'sum([2, 5; 4, 3])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const varianceDocs = {\n name: 'variance',\n category: 'Statistics',\n syntax: [\n 'variance(a, b, c, ...)',\n 'variance(A)',\n 'variance(A, normalization)'\n ],\n description: 'Compute the variance of all values. Optional parameter normalization can be \"unbiased\" (default), \"uncorrected\", or \"biased\".',\n examples: [\n 'variance(2, 4, 6)',\n 'variance([2, 4, 6, 8])',\n 'variance([2, 4, 6, 8], \"uncorrected\")',\n 'variance([2, 4, 6, 8], \"biased\")',\n 'variance([1, 2, 3; 4, 5, 6])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum'\n ]\n}\n","export const acosDocs = {\n name: 'acos',\n category: 'Trigonometry',\n syntax: [\n 'acos(x)'\n ],\n description: 'Compute the inverse cosine of a value in radians.',\n examples: [\n 'acos(0.5)',\n 'acos(cos(2.3))'\n ],\n seealso: [\n 'cos',\n 'atan',\n 'asin'\n ]\n}\n","export const acoshDocs = {\n name: 'acosh',\n category: 'Trigonometry',\n syntax: [\n 'acosh(x)'\n ],\n description: 'Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.',\n examples: [\n 'acosh(1.5)'\n ],\n seealso: [\n 'cosh',\n 'asinh',\n 'atanh'\n ]\n}\n","export const acotDocs = {\n name: 'acot',\n category: 'Trigonometry',\n syntax: [\n 'acot(x)'\n ],\n description: 'Calculate the inverse cotangent of a value.',\n examples: [\n 'acot(0.5)',\n 'acot(cot(0.5))',\n 'acot(2)'\n ],\n seealso: [\n 'cot',\n 'atan'\n ]\n}\n","export const acothDocs = {\n name: 'acoth',\n category: 'Trigonometry',\n syntax: [\n 'acoth(x)'\n ],\n description: 'Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.',\n examples: [\n 'acoth(2)',\n 'acoth(0.5)'\n ],\n seealso: [\n 'acsch',\n 'asech'\n ]\n}\n","export const acscDocs = {\n name: 'acsc',\n category: 'Trigonometry',\n syntax: [\n 'acsc(x)'\n ],\n description: 'Calculate the inverse cotangent of a value.',\n examples: [\n 'acsc(2)',\n 'acsc(csc(0.5))',\n 'acsc(0.5)'\n ],\n seealso: [\n 'csc',\n 'asin',\n 'asec'\n ]\n}\n","export const acschDocs = {\n name: 'acsch',\n category: 'Trigonometry',\n syntax: [\n 'acsch(x)'\n ],\n description: 'Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.',\n examples: [\n 'acsch(0.5)'\n ],\n seealso: [\n 'asech',\n 'acoth'\n ]\n}\n","export const asecDocs = {\n name: 'asec',\n category: 'Trigonometry',\n syntax: [\n 'asec(x)'\n ],\n description: 'Calculate the inverse secant of a value.',\n examples: [\n 'asec(0.5)',\n 'asec(sec(0.5))',\n 'asec(2)'\n ],\n seealso: [\n 'acos',\n 'acot',\n 'acsc'\n ]\n}\n","export const asechDocs = {\n name: 'asech',\n category: 'Trigonometry',\n syntax: [\n 'asech(x)'\n ],\n description: 'Calculate the inverse secant of a value.',\n examples: [\n 'asech(0.5)'\n ],\n seealso: [\n 'acsch',\n 'acoth'\n ]\n}\n","export const asinDocs = {\n name: 'asin',\n category: 'Trigonometry',\n syntax: [\n 'asin(x)'\n ],\n description: 'Compute the inverse sine of a value in radians.',\n examples: [\n 'asin(0.5)',\n 'asin(sin(0.5))'\n ],\n seealso: [\n 'sin',\n 'acos',\n 'atan'\n ]\n}\n","export const asinhDocs = {\n name: 'asinh',\n category: 'Trigonometry',\n syntax: [\n 'asinh(x)'\n ],\n description: 'Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.',\n examples: [\n 'asinh(0.5)'\n ],\n seealso: [\n 'acosh',\n 'atanh'\n ]\n}\n","export const atanDocs = {\n name: 'atan',\n category: 'Trigonometry',\n syntax: [\n 'atan(x)'\n ],\n description: 'Compute the inverse tangent of a value in radians.',\n examples: [\n 'atan(0.5)',\n 'atan(tan(0.5))'\n ],\n seealso: [\n 'tan',\n 'acos',\n 'asin'\n ]\n}\n","export const atanhDocs = {\n name: 'atanh',\n category: 'Trigonometry',\n syntax: [\n 'atanh(x)'\n ],\n description: 'Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.',\n examples: [\n 'atanh(0.5)'\n ],\n seealso: [\n 'acosh',\n 'asinh'\n ]\n}\n","export const atan2Docs = {\n name: 'atan2',\n category: 'Trigonometry',\n syntax: [\n 'atan2(y, x)'\n ],\n description:\n 'Computes the principal value of the arc tangent of y/x in radians.',\n examples: [\n 'atan2(2, 2) / pi',\n 'angle = 60 deg in rad',\n 'x = cos(angle)',\n 'y = sin(angle)',\n 'atan2(y, x)'\n ],\n seealso: [\n 'sin',\n 'cos',\n 'tan'\n ]\n}\n","export const cosDocs = {\n name: 'cos',\n category: 'Trigonometry',\n syntax: [\n 'cos(x)'\n ],\n description: 'Compute the cosine of x in radians.',\n examples: [\n 'cos(2)',\n 'cos(pi / 4) ^ 2',\n 'cos(180 deg)',\n 'cos(60 deg)',\n 'sin(0.2)^2 + cos(0.2)^2'\n ],\n seealso: [\n 'acos',\n 'sin',\n 'tan'\n ]\n}\n","export const coshDocs = {\n name: 'cosh',\n category: 'Trigonometry',\n syntax: [\n 'cosh(x)'\n ],\n description: 'Compute the hyperbolic cosine of x in radians.',\n examples: [\n 'cosh(0.5)'\n ],\n seealso: [\n 'sinh',\n 'tanh',\n 'coth'\n ]\n}\n","export const cotDocs = {\n name: 'cot',\n category: 'Trigonometry',\n syntax: [\n 'cot(x)'\n ],\n description: 'Compute the cotangent of x in radians. Defined as 1/tan(x)',\n examples: [\n 'cot(2)',\n '1 / tan(2)'\n ],\n seealso: [\n 'sec',\n 'csc',\n 'tan'\n ]\n}\n","export const cothDocs = {\n name: 'coth',\n category: 'Trigonometry',\n syntax: [\n 'coth(x)'\n ],\n description: 'Compute the hyperbolic cotangent of x in radians.',\n examples: [\n 'coth(2)',\n '1 / tanh(2)'\n ],\n seealso: [\n 'sech',\n 'csch',\n 'tanh'\n ]\n}\n","export const cscDocs = {\n name: 'csc',\n category: 'Trigonometry',\n syntax: [\n 'csc(x)'\n ],\n description: 'Compute the cosecant of x in radians. Defined as 1/sin(x)',\n examples: [\n 'csc(2)',\n '1 / sin(2)'\n ],\n seealso: [\n 'sec',\n 'cot',\n 'sin'\n ]\n}\n","export const cschDocs = {\n name: 'csch',\n category: 'Trigonometry',\n syntax: [\n 'csch(x)'\n ],\n description: 'Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)',\n examples: [\n 'csch(2)',\n '1 / sinh(2)'\n ],\n seealso: [\n 'sech',\n 'coth',\n 'sinh'\n ]\n}\n","export const secDocs = {\n name: 'sec',\n category: 'Trigonometry',\n syntax: [\n 'sec(x)'\n ],\n description: 'Compute the secant of x in radians. Defined as 1/cos(x)',\n examples: [\n 'sec(2)',\n '1 / cos(2)'\n ],\n seealso: [\n 'cot',\n 'csc',\n 'cos'\n ]\n}\n","export const sechDocs = {\n name: 'sech',\n category: 'Trigonometry',\n syntax: [\n 'sech(x)'\n ],\n description: 'Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)',\n examples: [\n 'sech(2)',\n '1 / cosh(2)'\n ],\n seealso: [\n 'coth',\n 'csch',\n 'cosh'\n ]\n}\n","export const sinDocs = {\n name: 'sin',\n category: 'Trigonometry',\n syntax: [\n 'sin(x)'\n ],\n description: 'Compute the sine of x in radians.',\n examples: [\n 'sin(2)',\n 'sin(pi / 4) ^ 2',\n 'sin(90 deg)',\n 'sin(30 deg)',\n 'sin(0.2)^2 + cos(0.2)^2'\n ],\n seealso: [\n 'asin',\n 'cos',\n 'tan'\n ]\n}\n","export const sinhDocs = {\n name: 'sinh',\n category: 'Trigonometry',\n syntax: [\n 'sinh(x)'\n ],\n description: 'Compute the hyperbolic sine of x in radians.',\n examples: [\n 'sinh(0.5)'\n ],\n seealso: [\n 'cosh',\n 'tanh'\n ]\n}\n","export const tanDocs = {\n name: 'tan',\n category: 'Trigonometry',\n syntax: [\n 'tan(x)'\n ],\n description: 'Compute the tangent of x in radians.',\n examples: [\n 'tan(0.5)',\n 'sin(0.5) / cos(0.5)',\n 'tan(pi / 4)',\n 'tan(45 deg)'\n ],\n seealso: [\n 'atan',\n 'sin',\n 'cos'\n ]\n}\n","export const tanhDocs = {\n name: 'tanh',\n category: 'Trigonometry',\n syntax: [\n 'tanh(x)'\n ],\n description: 'Compute the hyperbolic tangent of x in radians.',\n examples: [\n 'tanh(0.5)',\n 'sinh(0.5) / cosh(0.5)'\n ],\n seealso: [\n 'sinh',\n 'cosh'\n ]\n}\n","export const toDocs = {\n name: 'to',\n category: 'Units',\n syntax: [\n 'x to unit',\n 'to(x, unit)'\n ],\n description: 'Change the unit of a value.',\n examples: [\n '5 inch to cm',\n '3.2kg to g',\n '16 bytes in bits'\n ],\n seealso: []\n}\n","export const cloneDocs = {\n name: 'clone',\n category: 'Utils',\n syntax: [\n 'clone(x)'\n ],\n description: 'Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices',\n examples: [\n 'clone(3.5)',\n 'clone(2 - 4i)',\n 'clone(45 deg)',\n 'clone([1, 2; 3, 4])',\n 'clone(\"hello world\")'\n ],\n seealso: []\n}\n","export const formatDocs = {\n name: 'format',\n category: 'Utils',\n syntax: [\n 'format(value)',\n 'format(value, precision)'\n ],\n description: 'Format a value of any type as string.',\n examples: [\n 'format(2.3)',\n 'format(3 - 4i)',\n 'format([])',\n 'format(pi, 3)'\n ],\n seealso: ['print']\n}\n","export const binDocs = {\n name: 'bin',\n category: 'Utils',\n syntax: [\n 'bin(value)'\n ],\n description: 'Format a number as binary',\n examples: [\n 'bin(2)'\n ],\n seealso: ['oct', 'hex']\n}\n","export const octDocs = {\n name: 'oct',\n category: 'Utils',\n syntax: [\n 'oct(value)'\n ],\n description: 'Format a number as octal',\n examples: [\n 'oct(56)'\n ],\n seealso: ['bin', 'hex']\n}\n","export const hexDocs = {\n name: 'hex',\n category: 'Utils',\n syntax: [\n 'hex(value)'\n ],\n description: 'Format a number as hexadecimal',\n examples: [\n 'hex(240)'\n ],\n seealso: ['bin', 'oct']\n}\n","export const isNaNDocs = {\n name: 'isNaN',\n category: 'Utils',\n syntax: [\n 'isNaN(x)'\n ],\n description: 'Test whether a value is NaN (not a number)',\n examples: [\n 'isNaN(2)',\n 'isNaN(0 / 0)',\n 'isNaN(NaN)',\n 'isNaN(Infinity)'\n ],\n seealso: ['isNegative', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isIntegerDocs = {\n name: 'isInteger',\n category: 'Utils',\n syntax: [\n 'isInteger(x)'\n ],\n description: 'Test whether a value is an integer number.',\n examples: [\n 'isInteger(2)',\n 'isInteger(3.5)',\n 'isInteger([3, 0.5, -2])'\n ],\n seealso: ['isNegative', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isNegativeDocs = {\n name: 'isNegative',\n category: 'Utils',\n syntax: [\n 'isNegative(x)'\n ],\n description: 'Test whether a value is negative: smaller than zero.',\n examples: [\n 'isNegative(2)',\n 'isNegative(0)',\n 'isNegative(-4)',\n 'isNegative([3, 0.5, -2])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isNumericDocs = {\n name: 'isNumeric',\n category: 'Utils',\n syntax: [\n 'isNumeric(x)'\n ],\n description: 'Test whether a value is a numeric value. ' +\n 'Returns true when the input is a number, BigNumber, Fraction, or boolean.',\n examples: [\n 'isNumeric(2)',\n 'isNumeric(\"2\")',\n 'hasNumericValue(\"2\")',\n 'isNumeric(0)',\n 'isNumeric(bignumber(500))',\n 'isNumeric(fraction(0.125))',\n 'isNumeric(2 + 3i)',\n 'isNumeric([2.3, \"foo\", false])'\n ],\n seealso: ['isInteger', 'isZero', 'isNegative', 'isPositive', 'isNaN', 'hasNumericValue']\n}\n","export const hasNumericValueDocs = {\n name: 'hasNumericValue',\n category: 'Utils',\n syntax: [\n 'hasNumericValue(x)'\n ],\n description: 'Test whether a value is an numeric value. ' +\n 'In case of a string, true is returned if the string contains a numeric value.',\n examples: [\n 'hasNumericValue(2)',\n 'hasNumericValue(\"2\")',\n 'isNumeric(\"2\")',\n 'hasNumericValue(0)',\n 'hasNumericValue(bignumber(500))',\n 'hasNumericValue(fraction(0.125))',\n 'hasNumericValue(2 + 3i)',\n 'hasNumericValue([2.3, \"foo\", false])'\n ],\n seealso: ['isInteger', 'isZero', 'isNegative', 'isPositive', 'isNaN', 'isNumeric']\n}\n","export const isPositiveDocs = {\n name: 'isPositive',\n category: 'Utils',\n syntax: [\n 'isPositive(x)'\n ],\n description: 'Test whether a value is positive: larger than zero.',\n examples: [\n 'isPositive(2)',\n 'isPositive(0)',\n 'isPositive(-4)',\n 'isPositive([3, 0.5, -2])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isZero']\n}\n","export const isPrimeDocs = {\n name: 'isPrime',\n category: 'Utils',\n syntax: [\n 'isPrime(x)'\n ],\n description: 'Test whether a value is prime: has no divisors other than itself and one.',\n examples: [\n 'isPrime(3)',\n 'isPrime(-2)',\n 'isPrime([2, 17, 100])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isZero']\n}\n","export const isZeroDocs = {\n name: 'isZero',\n category: 'Utils',\n syntax: [\n 'isZero(x)'\n ],\n description: 'Test whether a value is zero.',\n examples: [\n 'isZero(2)',\n 'isZero(0)',\n 'isZero(-4)',\n 'isZero([3, 0, -2, 0])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isPositive']\n}\n","export const typeOfDocs = {\n name: 'typeOf',\n category: 'Utils',\n syntax: [\n 'typeOf(x)'\n ],\n description: 'Get the type of a variable.',\n examples: [\n 'typeOf(3.5)',\n 'typeOf(2 - 4i)',\n 'typeOf(45 deg)',\n 'typeOf(\"hello world\")'\n ],\n seealso: ['getMatrixDataType']\n}\n","export const numericDocs = {\n name: 'numeric',\n category: 'Utils',\n syntax: [\n 'numeric(x)'\n ],\n description: 'Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.',\n examples: [\n 'numeric(\"4\")',\n 'numeric(\"4\", \"number\")',\n 'numeric(\"4\", \"BigNumber\")',\n 'numeric(\"4\", \"Fraction)',\n 'numeric(4, \"Fraction\")',\n 'numeric(fraction(2, 5), \"number)'\n ],\n seealso: ['number', 'fraction', 'bignumber', 'string', 'format']\n}\n","import { factory } from '../../utils/factory.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { embeddedDocs } from '../embeddedDocs/embeddedDocs.js'\nimport { hasOwnProperty } from '../../utils/object.js'\n\nconst name = 'help'\nconst dependencies = ['typed', 'mathWithTransform', 'Help']\n\nexport const createHelp = /* #__PURE__ */ factory(name, dependencies, ({ typed, mathWithTransform, Help }) => {\n /**\n * Retrieve help on a function or data type.\n * Help files are retrieved from the embedded documentation in math.docs.\n *\n * Syntax:\n *\n * math.help(search)\n *\n * Examples:\n *\n * console.log(math.help('sin').toString())\n * console.log(math.help(math.add).toString())\n * console.log(math.help(math.add).toJSON())\n *\n * @param {Function | string | Object} search A function or function name\n * for which to get help\n * @return {Help} A help object\n */\n return typed(name, {\n any: function (search) {\n let prop\n let searchName = search\n\n if (typeof search !== 'string') {\n for (prop in mathWithTransform) {\n // search in functions and constants\n if (hasOwnProperty(mathWithTransform, prop) && (search === mathWithTransform[prop])) {\n searchName = prop\n break\n }\n }\n\n /* TODO: implement help for data types\n if (!text) {\n // search data type\n for (prop in math.type) {\n if (hasOwnProperty(math, prop)) {\n if (search === math.type[prop]) {\n text = prop\n break\n }\n }\n }\n }\n */\n }\n\n const doc = getSafeProperty(embeddedDocs, searchName)\n if (!doc) {\n const searchText = typeof searchName === 'function' ? searchName.name : searchName\n throw new Error('No documentation found on \"' + searchText + '\"')\n }\n return new Help(doc)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'chain'\nconst dependencies = ['typed', 'Chain']\n\nexport const createChain = /* #__PURE__ */ factory(name, dependencies, ({ typed, Chain }) => {\n /**\n * Wrap any value in a chain, allowing to perform chained operations on\n * the value.\n *\n * All methods available in the math.js library can be called upon the chain,\n * and then will be evaluated with the value itself as first argument.\n * The chain can be closed by executing `chain.done()`, which returns\n * the final value.\n *\n * The chain has a number of special functions:\n *\n * - `done()` Finalize the chain and return the chain's value.\n * - `valueOf()` The same as `done()`\n * - `toString()` Executes `math.format()` onto the chain's value, returning\n * a string representation of the value.\n *\n * Syntax:\n *\n * math.chain(value)\n *\n * Examples:\n *\n * math.chain(3)\n * .add(4)\n * .subtract(2)\n * .done() // 5\n *\n * math.chain( [[1, 2], [3, 4]] )\n * .subset(math.index(0, 0), 8)\n * .multiply(3)\n * .done() // [[24, 6], [9, 12]]\n *\n * @param {*} [value] A value of any type on which to start a chained operation.\n * @return {math.Chain} The created chain\n */\n return typed(name, {\n '': function () {\n return new Chain()\n },\n\n any: function (value) {\n return new Chain(value)\n }\n })\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'det'\nconst dependencies = ['typed', 'matrix', 'subtract', 'multiply', 'unaryMinus', 'lup']\n\nexport const createDet = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, multiply, unaryMinus, lup }) => {\n /**\n * Calculate the determinant of a matrix.\n *\n * Syntax:\n *\n * math.det(x)\n *\n * Examples:\n *\n * math.det([[1, 2], [3, 4]]) // returns -2\n *\n * const A = [\n * [-2, 2, 3],\n * [-1, 1, 3],\n * [2, 0, -1]\n * ]\n * math.det(A) // returns 6\n *\n * See also:\n *\n * inv\n *\n * @param {Array | Matrix} x A matrix\n * @return {number} The determinant of `x`\n */\n return typed(name, {\n any: function (x) {\n return clone(x)\n },\n\n 'Array | Matrix': function det (x) {\n let size\n if (isMatrix(x)) {\n size = x.size()\n } else if (Array.isArray(x)) {\n x = matrix(x)\n size = x.size()\n } else {\n // a scalar\n size = []\n }\n\n switch (size.length) {\n case 0:\n // scalar\n return clone(x)\n\n case 1:\n // vector\n if (size[0] === 1) {\n return clone(x.valueOf()[0])\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n {\n // two dimensional array\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n return _det(x.clone().valueOf(), rows, cols)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n\n default:\n // multi dimensional array\n throw new RangeError('Matrix must be two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n }\n })\n\n /**\n * Calculate the determinant of a matrix\n * @param {Array[]} matrix A square, two dimensional matrix\n * @param {number} rows Number of rows of the matrix (zero-based)\n * @param {number} cols Number of columns of the matrix (zero-based)\n * @returns {number} det\n * @private\n */\n function _det (matrix, rows, cols) {\n if (rows === 1) {\n // this is a 1 x 1 matrix\n return clone(matrix[0][0])\n } else if (rows === 2) {\n // this is a 2 x 2 matrix\n // the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12\n return subtract(\n multiply(matrix[0][0], matrix[1][1]),\n multiply(matrix[1][0], matrix[0][1])\n )\n } else {\n // Compute the LU decomposition\n const decomp = lup(matrix)\n\n // The determinant is the product of the diagonal entries of U (and those of L, but they are all 1)\n let det = decomp.U[0][0]\n for (let i = 1; i < rows; i++) {\n det = multiply(det, decomp.U[i][i])\n }\n\n // The determinant will be multiplied by 1 or -1 depending on the parity of the permutation matrix.\n // This can be determined by counting the cycles. This is roughly a linear time algorithm.\n let evenCycles = 0\n let i = 0\n const visited = []\n while (true) {\n while (visited[i]) {\n i++\n }\n if (i >= rows) break\n let j = i\n let cycleLen = 0\n while (!visited[decomp.p[j]]) {\n visited[decomp.p[j]] = true\n j = decomp.p[j]\n cycleLen++\n }\n if (cycleLen % 2 === 0) {\n evenCycles++\n }\n }\n\n return evenCycles % 2 === 0 ? det : unaryMinus(det)\n }\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { format } from '../../utils/string.js'\n\nconst name = 'inv'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'addScalar',\n 'multiply',\n 'unaryMinus',\n 'det',\n 'identity',\n 'abs'\n]\n\nexport const createInv = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, addScalar, multiply, unaryMinus, det, identity, abs }) => {\n /**\n * Calculate the inverse of a square matrix.\n *\n * Syntax:\n *\n * math.inv(x)\n *\n * Examples:\n *\n * math.inv([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]]\n * math.inv(4) // returns 0.25\n * 1 / 4 // returns 0.25\n *\n * See also:\n *\n * det, transpose\n *\n * @param {number | Complex | Array | Matrix} x Matrix to be inversed\n * @return {number | Complex | Array | Matrix} The inverse of `x`.\n */\n return typed(name, {\n 'Array | Matrix': function (x) {\n const size = isMatrix(x) ? x.size() : arraySize(x)\n switch (size.length) {\n case 1:\n // vector\n if (size[0] === 1) {\n if (isMatrix(x)) {\n return matrix([\n divideScalar(1, x.valueOf()[0])\n ])\n } else {\n return [\n divideScalar(1, x[0])\n ]\n }\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n // two dimensional array\n {\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n if (isMatrix(x)) {\n return matrix(\n _inv(x.valueOf(), rows, cols),\n x.storage()\n )\n } else {\n // return an Array\n return _inv(x, rows, cols)\n }\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n\n default:\n // multi dimensional array\n throw new RangeError('Matrix must be two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n },\n\n any: function (x) {\n // scalar\n return divideScalar(1, x) // FIXME: create a BigNumber one when configured for bignumbers\n }\n })\n\n /**\n * Calculate the inverse of a square matrix\n * @param {Array[]} mat A square matrix\n * @param {number} rows Number of rows\n * @param {number} cols Number of columns, must equal rows\n * @return {Array[]} inv Inverse matrix\n * @private\n */\n function _inv (mat, rows, cols) {\n let r, s, f, value, temp\n\n if (rows === 1) {\n // this is a 1 x 1 matrix\n value = mat[0][0]\n if (value === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n return [[\n divideScalar(1, value)\n ]]\n } else if (rows === 2) {\n // this is a 2 x 2 matrix\n const d = det(mat)\n if (d === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n return [\n [\n divideScalar(mat[1][1], d),\n divideScalar(unaryMinus(mat[0][1]), d)\n ],\n [\n divideScalar(unaryMinus(mat[1][0]), d),\n divideScalar(mat[0][0], d)\n ]\n ]\n } else {\n // this is a matrix of 3 x 3 or larger\n // calculate inverse using gauss-jordan elimination\n // https://en.wikipedia.org/wiki/Gaussian_elimination\n // http://mathworld.wolfram.com/MatrixInverse.html\n // http://math.uww.edu/~mcfarlat/inverse.htm\n\n // make a copy of the matrix (only the arrays, not of the elements)\n const A = mat.concat()\n for (r = 0; r < rows; r++) {\n A[r] = A[r].concat()\n }\n\n // create an identity matrix which in the end will contain the\n // matrix inverse\n const B = identity(rows).valueOf()\n\n // loop over all columns, and perform row reductions\n for (let c = 0; c < cols; c++) {\n // Pivoting: Swap row c with row r, where row r contains the largest element A[r][c]\n let ABig = abs(A[c][c])\n let rBig = c\n r = c + 1\n while (r < rows) {\n if (abs(A[r][c]) > ABig) {\n ABig = abs(A[r][c])\n rBig = r\n }\n r++\n }\n if (ABig === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n r = rBig\n if (r !== c) {\n temp = A[c]; A[c] = A[r]; A[r] = temp\n temp = B[c]; B[c] = B[r]; B[r] = temp\n }\n\n // eliminate non-zero values on the other rows at column c\n const Ac = A[c]\n const Bc = B[c]\n for (r = 0; r < rows; r++) {\n const Ar = A[r]\n const Br = B[r]\n if (r !== c) {\n // eliminate value at column c and row r\n if (Ar[c] !== 0) {\n f = divideScalar(unaryMinus(Ar[c]), Ac[c])\n\n // add (f * row c) to row r to eliminate the value\n // at column c\n for (s = c; s < cols; s++) {\n Ar[s] = addScalar(Ar[s], multiply(f, Ac[s]))\n }\n for (s = 0; s < cols; s++) {\n Br[s] = addScalar(Br[s], multiply(f, Bc[s]))\n }\n }\n } else {\n // normalize value at Acc to 1,\n // divide each value on row r with the value at Acc\n f = Ac[c]\n for (s = c; s < cols; s++) {\n Ar[s] = divideScalar(Ar[s], f)\n }\n for (s = 0; s < cols; s++) {\n Br[s] = divideScalar(Br[s], f)\n }\n }\n }\n }\n return B\n }\n }\n})\n","import { clone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\nimport { format } from '../../utils/string.js'\n\nconst name = 'eigs'\nconst dependencies = ['config', 'typed', 'matrix', 'addScalar', 'equal', 'subtract', 'abs', 'atan', 'cos', 'sin', 'multiplyScalar', 'inv', 'bignumber', 'multiply', 'add']\n\nexport const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, matrix, addScalar, subtract, equal, abs, atan, cos, sin, multiplyScalar, inv, bignumber, multiply, add }) => {\n /**\n * Compute eigenvalue and eigenvector of a real symmetric matrix.\n * Only applicable to two dimensional symmetric matrices. Uses Jacobi\n * Algorithm. Matrix containing mixed type ('number', 'bignumber', 'fraction')\n * of elements are not supported. Input matrix or 2D array should contain all elements\n * of either 'number', 'bignumber' or 'fraction' type. For 'number' and 'fraction', the\n * eigenvalues are of 'number' type. For 'bignumber' the eigenvalues are of ''bignumber' type.\n * Eigenvectors are always of 'number' type.\n *\n * Syntax:\n *\n * math.eigs(x)\n *\n * Examples:\n *\n * const H = [[5, 2.3], [2.3, 1]]\n * const ans = math.eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}\n * const E = ans.values\n * const U = ans.vectors\n * math.multiply(H, math.column(U, 0)) // returns math.multiply(E[0], math.column(U, 0))\n * const UTxHxU = math.multiply(math.transpose(U), H, U) // rotates H to the eigen-representation\n * E[0] == UTxHxU[0][0] // returns true\n * See also:\n *\n * inv\n *\n * @param {Array | Matrix} x Matrix to be diagonalized\n * @return {{values: Array, vectors: Array} | {values: Matrix, vectors: Matrix}} Object containing eigenvalues (Array or Matrix) and eigenvectors (2D Array/Matrix with eigenvectors as columns).\n */\n return typed('eigs', {\n\n Array: function (x) {\n // check array size\n const mat = matrix(x)\n const size = mat.size()\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n // use dense 2D matrix implementation\n const ans = checkAndSubmit(mat, size[0])\n return { values: ans[0], vectors: ans[1] }\n },\n\n Matrix: function (x) {\n // use dense 2D array implementation\n // dense matrix\n const size = x.size()\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n const ans = checkAndSubmit(x, size[0])\n return { values: matrix(ans[0]), vectors: matrix(ans[1]) }\n }\n })\n\n // Is the matrix\n // symmetric ?\n function isSymmetric (x, n) {\n for (let i = 0; i < n; i++) {\n for (let j = i; j < n; j++) {\n // not symmtric\n if (!equal(x[i][j], x[j][i])) {\n throw new TypeError('Input matrix is not symmetric')\n }\n }\n }\n }\n\n // check input for possible problems\n // and perform diagonalization efficiently for\n // specific type of number\n function checkAndSubmit (x, n) {\n let type = x.datatype()\n // type check\n if (type === undefined) {\n type = x.getDataType()\n }\n if (type !== 'number' && type !== 'BigNumber' && type !== 'Fraction') {\n if (type === 'mixed') {\n throw new TypeError('Mixed matrix element type is not supported')\n } else {\n throw new TypeError('Matrix element type not supported (' + type + ')')\n }\n } else {\n isSymmetric(x.toArray(), n)\n }\n\n // perform efficient calculation for 'numbers'\n if (type === 'number') {\n return diag(x.toArray())\n } else if (type === 'Fraction') {\n const xArr = x.toArray()\n // convert fraction to numbers\n for (let i = 0; i < n; i++) {\n for (let j = i; j < n; j++) {\n xArr[i][j] = xArr[i][j].valueOf()\n xArr[j][i] = xArr[i][j]\n }\n }\n return diag(x.toArray())\n } else if (type === 'BigNumber') {\n return diagBig(x.toArray())\n }\n }\n\n // diagonalization implementation for number (efficient)\n function diag (x) {\n const N = x.length\n const e0 = Math.abs(config.epsilon / N)\n let psi\n let Sij = new Array(N)\n // Sij is Identity Matrix\n for (let i = 0; i < N; i++) {\n Sij[i] = createArray(N, 0)\n Sij[i][i] = 1.0\n }\n // initial error\n let Vab = getAij(x)\n while (Math.abs(Vab[1]) >= Math.abs(e0)) {\n const i = Vab[0][0]\n const j = Vab[0][1]\n psi = getTheta(x[i][i], x[j][j], x[i][j])\n x = x1(x, psi, i, j)\n Sij = Sij1(Sij, psi, i, j)\n Vab = getAij(x)\n }\n const Ei = createArray(N, 0) // eigenvalues\n for (let i = 0; i < N; i++) {\n Ei[i] = x[i][i]\n }\n return sorting(clone(Ei), clone(Sij))\n }\n\n // diagonalization implementation for bigNumber\n function diagBig (x) {\n const N = x.length\n const e0 = abs(config.epsilon / N)\n let psi\n let Sij = new Array(N)\n // Sij is Identity Matrix\n for (let i = 0; i < N; i++) {\n Sij[i] = createArray(N, 0)\n Sij[i][i] = 1.0\n }\n // initial error\n let Vab = getAijBig(x)\n while (abs(Vab[1]) >= abs(e0)) {\n const i = Vab[0][0]\n const j = Vab[0][1]\n psi = getThetaBig(x[i][i], x[j][j], x[i][j])\n x = x1Big(x, psi, i, j)\n Sij = Sij1Big(Sij, psi, i, j)\n Vab = getAijBig(x)\n }\n const Ei = createArray(N, 0) // eigenvalues\n for (let i = 0; i < N; i++) {\n Ei[i] = x[i][i]\n }\n // return [clone(Ei), clone(Sij)]\n return sorting(clone(Ei), clone(Sij))\n }\n\n // get angle\n function getTheta (aii, ajj, aij) {\n const denom = (ajj - aii)\n if (Math.abs(denom) <= config.epsilon) {\n return Math.PI / 4\n } else {\n return 0.5 * Math.atan(2 * aij / (ajj - aii))\n }\n }\n\n // get angle\n function getThetaBig (aii, ajj, aij) {\n const denom = subtract(ajj, aii)\n if (abs(denom) <= config.epsilon) {\n return bignumber(-1).acos().div(4)\n } else {\n return multiplyScalar(0.5, atan(multiply(2, aij, inv(denom))))\n }\n }\n\n // update eigvec\n function Sij1 (Sij, theta, i, j) {\n const N = Sij.length\n const c = Math.cos(theta)\n const s = Math.sin(theta)\n const Ski = createArray(N, 0)\n const Skj = createArray(N, 0)\n for (let k = 0; k < N; k++) {\n Ski[k] = c * Sij[k][i] - s * Sij[k][j]\n Skj[k] = s * Sij[k][i] + c * Sij[k][j]\n }\n for (let k = 0; k < N; k++) {\n Sij[k][i] = Ski[k]\n Sij[k][j] = Skj[k]\n }\n return Sij\n }\n // update eigvec for overlap\n function Sij1Big (Sij, theta, i, j) {\n const N = Sij.length\n const c = cos(theta)\n const s = sin(theta)\n const Ski = createArray(N, bignumber(0))\n const Skj = createArray(N, bignumber(0))\n for (let k = 0; k < N; k++) {\n Ski[k] = subtract(multiplyScalar(c, Sij[k][i]), multiplyScalar(s, Sij[k][j]))\n Skj[k] = addScalar(multiplyScalar(s, Sij[k][i]), multiplyScalar(c, Sij[k][j]))\n }\n for (let k = 0; k < N; k++) {\n Sij[k][i] = Ski[k]\n Sij[k][j] = Skj[k]\n }\n return Sij\n }\n\n // update matrix\n function x1Big (Hij, theta, i, j) {\n const N = Hij.length\n const c = bignumber(cos(theta))\n const s = bignumber(sin(theta))\n const c2 = multiplyScalar(c, c)\n const s2 = multiplyScalar(s, s)\n const Aki = createArray(N, bignumber(0))\n const Akj = createArray(N, bignumber(0))\n // 2cs Hij\n const csHij = multiply(bignumber(2), c, s, Hij[i][j])\n // Aii\n const Aii = addScalar(subtract(multiplyScalar(c2, Hij[i][i]), csHij), multiplyScalar(s2, Hij[j][j]))\n const Ajj = add(multiplyScalar(s2, Hij[i][i]), csHij, multiplyScalar(c2, Hij[j][j]))\n // 0 to i\n for (let k = 0; k < N; k++) {\n Aki[k] = subtract(multiplyScalar(c, Hij[i][k]), multiplyScalar(s, Hij[j][k]))\n Akj[k] = addScalar(multiplyScalar(s, Hij[i][k]), multiplyScalar(c, Hij[j][k]))\n }\n // Modify Hij\n Hij[i][i] = Aii\n Hij[j][j] = Ajj\n Hij[i][j] = bignumber(0)\n Hij[j][i] = bignumber(0)\n // 0 to i\n for (let k = 0; k < N; k++) {\n if (k !== i && k !== j) {\n Hij[i][k] = Aki[k]\n Hij[k][i] = Aki[k]\n Hij[j][k] = Akj[k]\n Hij[k][j] = Akj[k]\n }\n }\n return Hij\n }\n\n // update matrix\n function x1 (Hij, theta, i, j) {\n const N = Hij.length\n const c = Math.cos(theta)\n const s = Math.sin(theta)\n const c2 = c * c\n const s2 = s * s\n const Aki = createArray(N, 0)\n const Akj = createArray(N, 0)\n // Aii\n const Aii = c2 * Hij[i][i] - 2 * c * s * Hij[i][j] + s2 * Hij[j][j]\n const Ajj = s2 * Hij[i][i] + 2 * c * s * Hij[i][j] + c2 * Hij[j][j]\n // 0 to i\n for (let k = 0; k < N; k++) {\n Aki[k] = c * Hij[i][k] - s * Hij[j][k]\n Akj[k] = s * Hij[i][k] + c * Hij[j][k]\n }\n // Modify Hij\n Hij[i][i] = Aii\n Hij[j][j] = Ajj\n Hij[i][j] = 0\n Hij[j][i] = 0\n // 0 to i\n for (let k = 0; k < N; k++) {\n if (k !== i && k !== j) {\n Hij[i][k] = Aki[k]\n Hij[k][i] = Aki[k]\n Hij[j][k] = Akj[k]\n Hij[k][j] = Akj[k]\n }\n }\n return Hij\n }\n\n // get max off-diagonal value from Upper Diagonal\n function getAij (Mij) {\n const N = Mij.length\n let maxMij = 0\n let maxIJ = [0, 1]\n for (let i = 0; i < N; i++) {\n for (let j = i + 1; j < N; j++) {\n if (Math.abs(maxMij) < Math.abs(Mij[i][j])) {\n maxMij = Math.abs(Mij[i][j])\n maxIJ = [i, j]\n }\n }\n }\n return [maxIJ, maxMij]\n }\n\n // get max off-diagonal value from Upper Diagonal\n function getAijBig (Mij) {\n const N = Mij.length\n let maxMij = 0\n let maxIJ = [0, 1]\n for (let i = 0; i < N; i++) {\n for (let j = i + 1; j < N; j++) {\n if (abs(maxMij) < abs(Mij[i][j])) {\n maxMij = abs(Mij[i][j])\n maxIJ = [i, j]\n }\n }\n }\n return [maxIJ, maxMij]\n }\n\n // sort results\n function sorting (E, S) {\n const N = E.length\n const Ef = Array(N)\n const Sf = Array(N)\n for (let k = 0; k < N; k++) {\n Sf[k] = Array(N)\n }\n for (let i = 0; i < N; i++) {\n let minID = 0\n let minE = E[0]\n for (let j = 0; j < E.length; j++) {\n if (E[j] < minE) {\n minID = j\n minE = E[minID]\n }\n }\n Ef[i] = E.splice(minID, 1)[0]\n for (let k = 0; k < N; k++) {\n Sf[k][i] = S[k][minID]\n S[k].splice(minID, 1)\n }\n }\n return [clone(Ef), clone(Sf)]\n }\n\n /**\n * Create an array of a certain size and fill all items with an initial value\n * @param {number} size\n * @param {number} value\n * @return {number[]}\n */\n function createArray (size, value) {\n // TODO: as soon as all browsers support Array.fill, use that instead (IE doesn't support it)\n const array = new Array(size)\n\n for (let i = 0; i < size; i++) {\n array[i] = value\n }\n\n return array\n }\n})\n","import { isSparseMatrix } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'expm'\nconst dependencies = ['typed', 'abs', 'add', 'identity', 'inv', 'multiply']\n\nexport const createExpm = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, identity, inv, multiply }) => {\n /**\n * Compute the matrix exponential, expm(A) = e^A. The matrix must be square.\n * Not to be confused with exp(a), which performs element-wise\n * exponentiation.\n *\n * The exponential is calculated using the Padé approximant with scaling and\n * squaring; see \"Nineteen Dubious Ways to Compute the Exponential of a\n * Matrix,\" by Moler and Van Loan.\n *\n * Syntax:\n *\n * math.expm(x)\n *\n * Examples:\n *\n * const A = [[0,2],[0,0]]\n * math.expm(A) // returns [[1,2],[0,1]]\n *\n * See also:\n *\n * exp\n *\n * @param {Matrix} x A square Matrix\n * @return {Matrix} The exponential of x\n */\n return typed(name, {\n\n Matrix: function (A) {\n // Check matrix size\n const size = A.size()\n\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n const n = size[0]\n\n // Desired accuracy of the approximant (The actual accuracy\n // will be affected by round-off error)\n const eps = 1e-15\n\n // The Padé approximant is not so accurate when the values of A\n // are \"large\", so scale A by powers of two. Then compute the\n // exponential, and square the result repeatedly according to\n // the identity e^A = (e^(A/m))^m\n\n // Compute infinity-norm of A, ||A||, to see how \"big\" it is\n const infNorm = infinityNorm(A)\n\n // Find the optimal scaling factor and number of terms in the\n // Padé approximant to reach the desired accuracy\n const params = findParams(infNorm, eps)\n const q = params.q\n const j = params.j\n\n // The Pade approximation to e^A is:\n // Rqq(A) = Dqq(A) ^ -1 * Nqq(A)\n // where\n // Nqq(A) = sum(i=0, q, (2q-i)!p! / [ (2q)!i!(q-i)! ] A^i\n // Dqq(A) = sum(i=0, q, (2q-i)!q! / [ (2q)!i!(q-i)! ] (-A)^i\n\n // Scale A by 1 / 2^j\n const Apos = multiply(A, Math.pow(2, -j))\n\n // The i=0 term is just the identity matrix\n let N = identity(n)\n let D = identity(n)\n\n // Initialization (i=0)\n let factor = 1\n\n // Initialization (i=1)\n let AposToI = Apos // Cloning not necessary\n let alternate = -1\n\n for (let i = 1; i <= q; i++) {\n if (i > 1) {\n AposToI = multiply(AposToI, Apos)\n alternate = -alternate\n }\n factor = factor * (q - i + 1) / ((2 * q - i + 1) * i)\n\n N = add(N, multiply(factor, AposToI))\n D = add(D, multiply(factor * alternate, AposToI))\n }\n\n let R = multiply(inv(D), N)\n\n // Square j times\n for (let i = 0; i < j; i++) {\n R = multiply(R, R)\n }\n\n return isSparseMatrix(A)\n ? A.createSparseMatrix(R)\n : R\n }\n\n })\n\n function infinityNorm (A) {\n const n = A.size()[0]\n let infNorm = 0\n for (let i = 0; i < n; i++) {\n let rowSum = 0\n for (let j = 0; j < n; j++) {\n rowSum += abs(A.get([i, j]))\n }\n infNorm = Math.max(rowSum, infNorm)\n }\n return infNorm\n }\n\n /**\n * Find the best parameters for the Pade approximant given\n * the matrix norm and desired accuracy. Returns the first acceptable\n * combination in order of increasing computational load.\n */\n function findParams (infNorm, eps) {\n const maxSearchSize = 30\n for (let k = 0; k < maxSearchSize; k++) {\n for (let q = 0; q <= k; q++) {\n const j = k - q\n if (errorEstimate(infNorm, q, j) < eps) {\n return { q: q, j: j }\n }\n }\n }\n throw new Error('Could not find acceptable parameters to compute the matrix exponential (try increasing maxSearchSize in expm.js)')\n }\n\n /**\n * Returns the estimated error of the Pade approximant for the given\n * parameters.\n */\n function errorEstimate (infNorm, q, j) {\n let qfac = 1\n for (let i = 2; i <= q; i++) {\n qfac *= i\n }\n let twoqfac = qfac\n for (let i = q + 1; i <= 2 * q; i++) {\n twoqfac *= i\n }\n const twoqp1fac = twoqfac * (2 * q + 1)\n\n return 8.0 *\n Math.pow(infNorm / Math.pow(2, j), 2 * q) *\n qfac * qfac / (twoqfac * twoqp1fac)\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'sqrtm'\nconst dependencies = ['typed', 'abs', 'add', 'multiply', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity']\n\nexport const createSqrtm = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, multiply, sqrt, subtract, inv, size, max, identity }) => {\n const _maxIterations = 1e3\n const _tolerance = 1e-6\n\n /**\n * Calculate the principal square root matrix using the Denman–Beavers iterative method\n *\n * https://en.wikipedia.org/wiki/Square_root_of_a_matrix#By_Denman–Beavers_iteration\n *\n * @param {Array | Matrix} A The square matrix `A`\n * @return {Array | Matrix} The principal square root of matrix `A`\n * @private\n */\n function _denmanBeavers (A) {\n let error\n let iterations = 0\n\n let Y = A\n let Z = identity(size(A))\n\n do {\n const Yk = Y\n Y = multiply(0.5, add(Yk, inv(Z)))\n Z = multiply(0.5, add(Z, inv(Yk)))\n\n error = max(abs(subtract(Y, Yk)))\n\n if (error > _tolerance && ++iterations > _maxIterations) {\n throw new Error('computing square root of matrix: iterative method could not converge')\n }\n } while (error > _tolerance)\n\n return Y\n }\n\n /**\n * Calculate the principal square root of a square matrix.\n * The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.\n *\n * https://en.wikipedia.org/wiki/Square_root_of_a_matrix\n *\n * Syntax:\n *\n * X = math.sqrtm(A)\n *\n * Examples:\n *\n * math.sqrtm([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]]\n *\n * See also:\n *\n * sqrt, pow\n *\n * @param {Array | Matrix} A The square matrix `A`\n * @return {Array | Matrix} The principal square root of matrix `A`\n */\n return typed(name, {\n 'Array | Matrix': function (A) {\n const size = isMatrix(A) ? A.size() : arraySize(A)\n switch (size.length) {\n case 1:\n // Single element Array | Matrix\n if (size[0] === 1) {\n return sqrt(A)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n {\n // Two-dimensional Array | Matrix\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n return _denmanBeavers(A)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n default:\n // Multi dimensional array\n throw new RangeError('Matrix must be at most two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { extend } from '../../utils/object.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'divide'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'multiply',\n 'equalScalar',\n 'divideScalar',\n 'inv'\n]\n\nexport const createDivide = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, multiply, equalScalar, divideScalar, inv }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Divide two values, `x / y`.\n * To divide matrices, `x` is multiplied with the inverse of `y`: `x * inv(y)`.\n *\n * Syntax:\n *\n * math.divide(x, y)\n *\n * Examples:\n *\n * math.divide(2, 3) // returns number 0.6666666666666666\n *\n * const a = math.complex(5, 14)\n * const b = math.complex(4, 1)\n * math.divide(a, b) // returns Complex 2 + 3i\n *\n * const c = [[7, -6], [13, -4]]\n * const d = [[1, 2], [4, 3]]\n * math.divide(c, d) // returns Array [[-9, 4], [-11, 6]]\n *\n * const e = math.unit('18 km')\n * math.divide(e, 4.5) // returns Unit 4 km\n *\n * See also:\n *\n * multiply\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Numerator\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Quotient, `x / y`\n */\n return typed('divide', extend({\n // we extend the signatures of divideScalar with signatures dealing with matrices\n\n 'Array | Matrix, Array | Matrix': function (x, y) {\n // TODO: implement matrix right division using pseudo inverse\n // https://www.mathworks.nl/help/matlab/ref/mrdivide.html\n // https://www.gnu.org/software/octave/doc/interpreter/Arithmetic-Ops.html\n // https://stackoverflow.com/questions/12263932/how-does-gnu-octave-matrix-division-work-getting-unexpected-behaviour\n return multiply(x, inv(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, divideScalar, false)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, divideScalar, false)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, divideScalar, false).valueOf()\n },\n\n 'any, Array | Matrix': function (x, y) {\n return multiply(x, inv(y))\n }\n }, divideScalar.signatures))\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'distance'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'subtract',\n 'divideScalar',\n 'multiplyScalar',\n 'unaryMinus',\n 'sqrt',\n 'abs'\n]\n\nexport const createDistance = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, subtract, multiplyScalar, divideScalar, unaryMinus, sqrt, abs }) => {\n /**\n * Calculates:\n * The eucledian distance between two points in N-dimensional spaces.\n * Distance between point and a line in 2 and 3 dimensional spaces.\n * Pairwise distance between a set of 2D or 3D points\n * NOTE:\n * When substituting coefficients of a line(a, b and c), use ax + by + c = 0 instead of ax + by = c\n * For parametric equation of a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b, c)\n *\n * Syntax:\n * math.distance([x1, y1], [x2, y2])\n *- math.distance({pointOneX: 4, pointOneY: 5}, {pointTwoX: 2, pointTwoY: 7})\n * math.distance([x1, y1, z1], [x2, y2, z2])\n * math.distance({pointOneX: 4, pointOneY: 5, pointOneZ: 8}, {pointTwoX: 2, pointTwoY: 7, pointTwoZ: 9})\n * math.distance([x1, y1, ... , N1], [x2, y2, ... , N2])\n * math.distance([[A], [B], [C]...])\n * math.distance([x1, y1], [LinePtX1, LinePtY1], [LinePtX2, LinePtY2])\n * math.distance({pointX: 1, pointY: 4}, {lineOnePtX: 6, lineOnePtY: 3}, {lineTwoPtX: 2, lineTwoPtY: 8})\n * math.distance([x1, y1, z1], [LinePtX1, LinePtY1, LinePtZ1], [LinePtX2, LinePtY2, LinePtZ2])\n * math.distance({pointX: 1, pointY: 4, pointZ: 7}, {lineOnePtX: 6, lineOnePtY: 3, lineOnePtZ: 4}, {lineTwoPtX: 2, lineTwoPtY: 8, lineTwoPtZ: 5})\n * math.distance([x1, y1], [xCoeffLine, yCoeffLine, constant])\n * math.distance({pointX: 10, pointY: 10}, {xCoeffLine: 8, yCoeffLine: 1, constant: 3})\n * math.distance([x1, y1, z1], [x0, y0, z0, a-tCoeff, b-tCoeff, c-tCoeff]) point and parametric equation of 3D line\n * math.distance([x, y, z], [x0, y0, z0, a, b, c])\n * math.distance({pointX: 2, pointY: 5, pointZ: 9}, {x0: 4, y0: 6, z0: 3, a: 4, b: 2, c: 0})\n *\n * Examples:\n * math.distance([0,0], [4,4]) // Returns 5.6569\n * math.distance(\n * {pointOneX: 0, pointOneY: 0},\n * {pointTwoX: 10, pointTwoY: 10}) // Returns 14.142135623730951\n * math.distance([1, 0, 1], [4, -2, 2]) // Returns 3.74166\n * math.distance(\n * {pointOneX: 4, pointOneY: 5, pointOneZ: 8},\n * {pointTwoX: 2, pointTwoY: 7, pointTwoZ: 9}) // Returns 3\n * math.distance([1, 0, 1, 0], [0, -1, 0, -1]) // Returns 2\n * math.distance([[1, 2], [1, 2], [1, 3]]) // Returns [0, 1, 1]\n * math.distance([[1,2,4], [1,2,6], [8,1,3]]) // Returns [2, 7.14142842854285, 7.681145747868608]\n * math.distance([10, 10], [8, 1, 3]) // Returns 11.535230316796387\n * math.distance([10, 10], [2, 3], [-8, 0]) // Returns 8.759953130362847\n * math.distance(\n * {pointX: 1, pointY: 4},\n * {lineOnePtX: 6, lineOnePtY: 3},\n * {lineTwoPtX: 2, lineTwoPtY: 8}) // Returns 2.720549372624744\n * math.distance([2, 3, 1], [1, 1, 2, 5, 0, 1]) // Returns 2.3204774044612857\n * math.distance(\n * {pointX: 2, pointY: 3, pointZ: 1},\n * {x0: 1, y0: 1, z0: 2, a: 5, b: 0, c: 1} // Returns 2.3204774044612857\n *\n * @param {Array | Matrix | Object} x Co-ordinates of first point\n * @param {Array | Matrix | Object} y Co-ordinates of second point\n * @return {Number | BigNumber} Returns the distance from two/three points\n */\n return typed(name, {\n 'Array, Array, Array': function (x, y, z) {\n // Point to Line 2D (x=Point, y=LinePoint1, z=LinePoint2)\n if (x.length === 2 && y.length === 2 && z.length === 2) {\n if (!_2d(x)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument') }\n if (!_2d(y)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument') }\n if (!_2d(z)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument') }\n const m = divideScalar(subtract(z[1], z[0]), subtract(y[1], y[0]))\n const xCoeff = multiplyScalar(multiplyScalar(m, m), y[0])\n const yCoeff = unaryMinus(multiplyScalar(m, y[0]))\n const constant = x[1]\n\n return _distancePointLine2D(x[0], x[1], xCoeff, yCoeff, constant)\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Object, Object, Object': function (x, y, z) {\n if (Object.keys(x).length === 2 && Object.keys(y).length === 2 && Object.keys(z).length === 2) {\n if (!_2d(x)) { throw new TypeError('Values of pointX and pointY should be numbers or BigNumbers') }\n if (!_2d(y)) { throw new TypeError('Values of lineOnePtX and lineOnePtY should be numbers or BigNumbers') }\n if (!_2d(z)) { throw new TypeError('Values of lineTwoPtX and lineTwoPtY should be numbers or BigNumbers') }\n if ('pointX' in x && 'pointY' in x && 'lineOnePtX' in y &&\n 'lineOnePtY' in y && 'lineTwoPtX' in z && 'lineTwoPtY' in z) {\n const m = divideScalar(subtract(z.lineTwoPtY, z.lineTwoPtX), subtract(y.lineOnePtY, y.lineOnePtX))\n const xCoeff = multiplyScalar(multiplyScalar(m, m), y.lineOnePtX)\n const yCoeff = unaryMinus(multiplyScalar(m, y.lineOnePtX))\n const constant = x.pointX\n\n return _distancePointLine2D(x.pointX, x.pointY, xCoeff, yCoeff, constant)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Array, Array': function (x, y) {\n // Point to Line 2D (x=[pointX, pointY], y=[x-coeff, y-coeff, const])\n if (x.length === 2 && y.length === 3) {\n if (!_2d(x)) {\n throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument')\n }\n if (!_3d(y)) {\n throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument')\n }\n\n return _distancePointLine2D(x[0], x[1], y[0], y[1], y[2])\n } else if (x.length === 3 && y.length === 6) {\n // Point to Line 3D\n if (!_3d(x)) {\n throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument')\n }\n if (!_parametricLine(y)) {\n throw new TypeError('Array with 6 numbers or BigNumbers expected for second argument')\n }\n\n return _distancePointLine3D(x[0], x[1], x[2], y[0], y[1], y[2], y[3], y[4], y[5])\n } else if (x.length === y.length && x.length > 0) {\n // Point to Point N-dimensions\n if (!_containsOnlyNumbers(x)) {\n throw new TypeError('All values of an array should be numbers or BigNumbers')\n }\n if (!_containsOnlyNumbers(y)) {\n throw new TypeError('All values of an array should be numbers or BigNumbers')\n }\n\n return _euclideanDistance(x, y)\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Object, Object': function (x, y) {\n if (Object.keys(x).length === 2 && Object.keys(y).length === 3) {\n if (!_2d(x)) {\n throw new TypeError('Values of pointX and pointY should be numbers or BigNumbers')\n }\n if (!_3d(y)) {\n throw new TypeError('Values of xCoeffLine, yCoeffLine and constant should be numbers or BigNumbers')\n }\n if ('pointX' in x && 'pointY' in x && 'xCoeffLine' in y && 'yCoeffLine' in y && 'constant' in y) {\n return _distancePointLine2D(x.pointX, x.pointY, y.xCoeffLine, y.yCoeffLine, y.constant)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 3 && Object.keys(y).length === 6) {\n // Point to Line 3D\n if (!_3d(x)) {\n throw new TypeError('Values of pointX, pointY and pointZ should be numbers or BigNumbers')\n }\n if (!_parametricLine(y)) {\n throw new TypeError('Values of x0, y0, z0, a, b and c should be numbers or BigNumbers')\n }\n if ('pointX' in x && 'pointY' in x && 'x0' in y && 'y0' in y && 'z0' in y && 'a' in y && 'b' in y && 'c' in y) {\n return _distancePointLine3D(x.pointX, x.pointY, x.pointZ, y.x0, y.y0, y.z0, y.a, y.b, y.c)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 2 && Object.keys(y).length === 2) {\n // Point to Point 2D\n if (!_2d(x)) {\n throw new TypeError('Values of pointOneX and pointOneY should be numbers or BigNumbers')\n }\n if (!_2d(y)) {\n throw new TypeError('Values of pointTwoX and pointTwoY should be numbers or BigNumbers')\n }\n if ('pointOneX' in x && 'pointOneY' in x && 'pointTwoX' in y && 'pointTwoY' in y) {\n return _euclideanDistance([x.pointOneX, x.pointOneY], [y.pointTwoX, y.pointTwoY])\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 3 && Object.keys(y).length === 3) {\n // Point to Point 3D\n if (!_3d(x)) {\n throw new TypeError('Values of pointOneX, pointOneY and pointOneZ should be numbers or BigNumbers')\n }\n if (!_3d(y)) {\n throw new TypeError('Values of pointTwoX, pointTwoY and pointTwoZ should be numbers or BigNumbers')\n }\n if ('pointOneX' in x && 'pointOneY' in x && 'pointOneZ' in x &&\n 'pointTwoX' in y && 'pointTwoY' in y && 'pointTwoZ' in y\n ) {\n return _euclideanDistance([x.pointOneX, x.pointOneY, x.pointOneZ], [y.pointTwoX, y.pointTwoY, y.pointTwoZ])\n } else {\n throw new TypeError('Key names do not match')\n }\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n Array: function (arr) {\n if (!_pairwise(arr)) { throw new TypeError('Incorrect array format entered for pairwise distance calculation') }\n\n return _distancePairwise(arr)\n }\n })\n\n function _isNumber (a) {\n // distance supports numbers and bignumbers\n return (typeof a === 'number' || isBigNumber(a))\n }\n\n function _2d (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1])\n }\n\n function _3d (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1]) && _isNumber(a[2])\n }\n\n function _containsOnlyNumbers (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (!Array.isArray(a)) {\n a = _objectToArray(a)\n }\n return a.every(_isNumber)\n }\n\n function _parametricLine (a) {\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1]) && _isNumber(a[2]) &&\n _isNumber(a[3]) && _isNumber(a[4]) && _isNumber(a[5])\n }\n\n function _objectToArray (o) {\n const keys = Object.keys(o)\n const a = []\n for (let i = 0; i < keys.length; i++) {\n a.push(o[keys[i]])\n }\n return a\n }\n\n function _pairwise (a) {\n // checks for valid arguments passed to _distancePairwise(Array)\n if (a[0].length === 2 && _isNumber(a[0][0]) && _isNumber(a[0][1])) {\n if (a.some(aI => aI.length !== 2 || !_isNumber(aI[0]) || !_isNumber(aI[1]))) {\n return false\n }\n } else if (a[0].length === 3 && _isNumber(a[0][0]) && _isNumber(a[0][1]) && _isNumber(a[0][2])) {\n if (a.some(aI => aI.length !== 3 || !_isNumber(aI[0]) || !_isNumber(aI[1]) || !_isNumber(aI[2]))) {\n return false\n }\n } else {\n return false\n }\n return true\n }\n\n function _distancePointLine2D (x, y, a, b, c) {\n const num = abs(addScalar(addScalar(multiplyScalar(a, x), multiplyScalar(b, y)), c))\n const den = sqrt(addScalar(multiplyScalar(a, a), multiplyScalar(b, b)))\n return divideScalar(num, den)\n }\n\n function _distancePointLine3D (x, y, z, x0, y0, z0, a, b, c) {\n let num = [subtract(multiplyScalar(subtract(y0, y), c), multiplyScalar(subtract(z0, z), b)),\n subtract(multiplyScalar(subtract(z0, z), a), multiplyScalar(subtract(x0, x), c)),\n subtract(multiplyScalar(subtract(x0, x), b), multiplyScalar(subtract(y0, y), a))]\n num = sqrt(addScalar(addScalar(multiplyScalar(num[0], num[0]), multiplyScalar(num[1], num[1])), multiplyScalar(num[2], num[2])))\n const den = sqrt(addScalar(addScalar(multiplyScalar(a, a), multiplyScalar(b, b)), multiplyScalar(c, c)))\n return divideScalar(num, den)\n }\n\n function _euclideanDistance (x, y) {\n const vectorSize = x.length\n let result = 0\n let diff = 0\n for (let i = 0; i < vectorSize; i++) {\n diff = subtract(x[i], y[i])\n result = addScalar(multiplyScalar(diff, diff), result)\n }\n return sqrt(result)\n }\n\n function _distancePairwise (a) {\n const result = []\n let pointA = []\n let pointB = []\n for (let i = 0; i < a.length - 1; i++) {\n for (let j = i + 1; j < a.length; j++) {\n if (a[0].length === 2) {\n pointA = [a[i][0], a[i][1]]\n pointB = [a[j][0], a[j][1]]\n } else if (a[0].length === 3) {\n pointA = [a[i][0], a[i][1], a[i][2]]\n pointB = [a[j][0], a[j][1], a[j][2]]\n }\n result.push(_euclideanDistance(pointA, pointB))\n }\n }\n return result\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'intersect'\nconst dependencies = [\n 'typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar'\n]\n\nexport const createIntersect = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, abs, add, addScalar, matrix, multiply, multiplyScalar, divideScalar, subtract, smaller, equalScalar }) => {\n /**\n * Calculates the point of intersection of two lines in two or three dimensions\n * and of a line and a plane in three dimensions. The inputs are in the form of\n * arrays or 1 dimensional matrices. The line intersection functions return null\n * if the lines do not meet.\n *\n * Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`.\n *\n * Syntax:\n *\n * math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)\n * math.intersect(endPoint1, endPoint2, planeCoefficients)\n *\n * Examples:\n *\n * math.intersect([0, 0], [10, 10], [10, 0], [0, 10]) // Returns [5, 5]\n * math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]) // Returns [5, 5, 0]\n * math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]) // Returns [7, -4, 3]\n *\n * @param {Array | Matrix} w Co-ordinates of first end-point of first line\n * @param {Array | Matrix} x Co-ordinates of second end-point of first line\n * @param {Array | Matrix} y Co-ordinates of first end-point of second line\n * OR Co-efficients of the plane's equation\n * @param {Array | Matrix} z Co-ordinates of second end-point of second line\n * OR null if the calculation is for line and plane\n * @return {Array} Returns the point of intersection of lines/lines-planes\n */\n return typed('intersect', {\n 'Array, Array, Array': function (x, y, plane) {\n if (!_3d(x)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument') }\n if (!_3d(y)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument') }\n if (!_4d(plane)) { throw new TypeError('Array with 4 numbers expected as third argument') }\n\n return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3])\n },\n\n 'Array, Array, Array, Array': function (w, x, y, z) {\n if (w.length === 2) {\n if (!_2d(w)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument') }\n if (!_2d(x)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument') }\n if (!_2d(y)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument') }\n if (!_2d(z)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument') }\n\n return _intersect2d(w, x, y, z)\n } else if (w.length === 3) {\n if (!_3d(w)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument') }\n if (!_3d(x)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument') }\n if (!_3d(y)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument') }\n if (!_3d(z)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument') }\n\n return _intersect3d(w[0], w[1], w[2], x[0], x[1], x[2], y[0], y[1], y[2], z[0], z[1], z[2])\n } else {\n throw new TypeError('Arrays with two or thee dimensional points expected')\n }\n },\n\n 'Matrix, Matrix, Matrix': function (x, y, plane) {\n return matrix(this(x.valueOf(), y.valueOf(), plane.valueOf()))\n },\n\n 'Matrix, Matrix, Matrix, Matrix': function (w, x, y, z) {\n // TODO: output matrix type should match input matrix type\n return matrix(this(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()))\n }\n })\n\n function _isNumeric (a) {\n // intersect supports numbers and bignumbers\n return (typeof a === 'number' || isBigNumber(a))\n }\n\n function _2d (x) {\n return x.length === 2 && _isNumeric(x[0]) && _isNumeric(x[1])\n }\n\n function _3d (x) {\n return x.length === 3 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2])\n }\n\n function _4d (x) {\n return x.length === 4 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2]) && _isNumeric(x[3])\n }\n\n function _intersect2d (p1a, p1b, p2a, p2b) {\n const o1 = p1a\n const o2 = p2a\n const d1 = subtract(o1, p1b)\n const d2 = subtract(o2, p2b)\n const det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]))\n if (smaller(abs(det), config.epsilon)) {\n return null\n }\n const d20o11 = multiplyScalar(d2[0], o1[1])\n const d21o10 = multiplyScalar(d2[1], o1[0])\n const d20o21 = multiplyScalar(d2[0], o2[1])\n const d21o20 = multiplyScalar(d2[1], o2[0])\n const t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det)\n return add(multiply(d1, t), o1)\n }\n\n function _intersect3dHelper (a, b, c, d, e, f, g, h, i, j, k, l) {\n // (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l)\n const add1 = multiplyScalar(subtract(a, b), subtract(c, d))\n const add2 = multiplyScalar(subtract(e, f), subtract(g, h))\n const add3 = multiplyScalar(subtract(i, j), subtract(k, l))\n return addScalar(addScalar(add1, add2), add3)\n }\n\n function _intersect3d (x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) {\n const d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3)\n const d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1)\n const d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1)\n const d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3)\n const d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1)\n const ta = divideScalar(\n subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)),\n subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)))\n const tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343)\n\n const pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)))\n const pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)))\n const paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)))\n const pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)))\n const pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)))\n const pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3)))\n if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) {\n return [pax, pay, paz]\n } else {\n return null\n }\n }\n\n function _intersectLinePlane (x1, y1, z1, x2, y2, z2, x, y, z, c) {\n const x1x = multiplyScalar(x1, x)\n const x2x = multiplyScalar(x2, x)\n const y1y = multiplyScalar(y1, y)\n const y2y = multiplyScalar(y2, y)\n const z1z = multiplyScalar(z1, z)\n const z2z = multiplyScalar(z2, z)\n const t = divideScalar(\n subtract(subtract(subtract(c, x1x), y1y), z1z),\n subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z))\n const px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)))\n const py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)))\n const pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1)))\n return [px, py, pz]\n // TODO: Add cases when line is parallel to the plane:\n // (a) no intersection,\n // (b) line contained in plane\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'sum'\nconst dependencies = ['typed', 'config', 'add', 'numeric']\n\nexport const createSum = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, add, numeric }) => {\n /**\n * Compute the sum of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the sum of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.sum(a, b, c, ...)\n * math.sum(A)\n *\n * Examples:\n *\n * math.sum(2, 1, 4, 3) // returns 10\n * math.sum([2, 1, 4, 3]) // returns 10\n * math.sum([[2, 5], [4, 3], [1, 7]]) // returns 22\n *\n * See also:\n *\n * mean, median, min, max, prod, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The sum of all values\n */\n return typed(name, {\n // sum([a, b, c, d, ...])\n 'Array | Matrix': _sum,\n\n // sum([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': _nsumDim,\n\n // sum(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function sum')\n }\n\n return _sum(args)\n }\n })\n\n /**\n * Recursively calculate the sum of an n-dimensional array\n * @param {Array | Matrix} array\n * @return {number} sum\n * @private\n */\n function _sum (array) {\n let sum\n\n deepForEach(array, function (value) {\n try {\n sum = (sum === undefined) ? value : add(sum, value)\n } catch (err) {\n throw improveErrorMessage(err, 'sum', value)\n }\n })\n\n // make sure returning numeric value: parse a string into a numeric value\n if (sum === undefined) {\n sum = numeric(0, config.number)\n }\n if (typeof sum === 'string') {\n sum = numeric(sum, config.number)\n }\n\n return sum\n }\n\n function _nsumDim (array, dim) {\n try {\n const sum = reduce(array, dim, add)\n return sum\n } catch (err) {\n throw improveErrorMessage(err, 'sum')\n }\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'mean'\nconst dependencies = ['typed', 'add', 'divide']\n\nexport const createMean = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide }) => {\n /**\n * Compute the mean value of matrix or a list with values.\n * In case of a multi dimensional array, the mean of the flattened array\n * will be calculated. When `dim` is provided, the maximum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.mean(a, b, c, ...)\n * math.mean(A)\n * math.mean(A, dim)\n *\n * Examples:\n *\n * math.mean(2, 1, 4, 3) // returns 2.5\n * math.mean([1, 2.7, 3.2, 4]) // returns 2.725\n *\n * math.mean([[2, 5], [6, 3], [1, 7]], 0) // returns [3, 5]\n * math.mean([[2, 5], [6, 3], [1, 7]], 1) // returns [3.5, 4.5, 4]\n *\n * See also:\n *\n * median, min, max, sum, prod, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The mean of all values\n */\n return typed(name, {\n // mean([a, b, c, d, ...])\n 'Array | Matrix': _mean,\n\n // mean([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': _nmeanDim,\n\n // mean(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function mean')\n }\n\n return _mean(args)\n }\n })\n\n /**\n * Calculate the mean value in an n-dimensional array, returning a\n * n-1 dimensional array\n * @param {Array} array\n * @param {number} dim\n * @return {number} mean\n * @private\n */\n function _nmeanDim (array, dim) {\n try {\n const sum = reduce(array, dim, add)\n const s = Array.isArray(array) ? arraySize(array) : array.size()\n return divide(sum, s[dim])\n } catch (err) {\n throw improveErrorMessage(err, 'mean')\n }\n }\n\n /**\n * Recursively calculate the mean value in an n-dimensional array\n * @param {Array} array\n * @return {number} mean\n * @private\n */\n function _mean (array) {\n let sum\n let num = 0\n\n deepForEach(array, function (value) {\n try {\n sum = sum === undefined ? value : add(sum, value)\n num++\n } catch (err) {\n throw improveErrorMessage(err, 'mean', value)\n }\n })\n\n if (num === 0) {\n throw new Error('Cannot calculate the mean of an empty array')\n }\n return divide(sum, num)\n }\n})\n","import { containsCollections } from '../../utils/collection.js'\nimport { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'median'\nconst dependencies = ['typed', 'add', 'divide', 'compare', 'partitionSelect']\n\nexport const createMedian = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, compare, partitionSelect }) => {\n /**\n * Recursively calculate the median of an n-dimensional array\n * @param {Array} array\n * @return {Number} median\n * @private\n */\n function _median (array) {\n try {\n array = flatten(array.valueOf())\n\n const num = array.length\n if (num === 0) {\n throw new Error('Cannot calculate median of an empty array')\n }\n\n if (num % 2 === 0) {\n // even: return the average of the two middle values\n const mid = num / 2 - 1\n const right = partitionSelect(array, mid + 1)\n\n // array now partitioned at mid + 1, take max of left part\n let left = array[mid]\n for (let i = 0; i < mid; ++i) {\n if (compare(array[i], left) > 0) {\n left = array[i]\n }\n }\n\n return middle2(left, right)\n } else {\n // odd: return the middle value\n const m = partitionSelect(array, (num - 1) / 2)\n\n return middle(m)\n }\n } catch (err) {\n throw improveErrorMessage(err, 'median')\n }\n }\n\n // helper function to type check the middle value of the array\n const middle = typed({\n 'number | BigNumber | Complex | Unit': function (value) {\n return value\n }\n })\n\n // helper function to type check the two middle value of the array\n const middle2 = typed({\n 'number | BigNumber | Complex | Unit, number | BigNumber | Complex | Unit': function (left, right) {\n return divide(add(left, right), 2)\n }\n })\n\n /**\n * Compute the median of a matrix or a list with values. The values are\n * sorted and the middle value is returned. In case of an even number of\n * values, the average of the two middle values is returned.\n * Supported types of values are: Number, BigNumber, Unit\n *\n * In case of a (multi dimensional) array or matrix, the median of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.median(a, b, c, ...)\n * math.median(A)\n *\n * Examples:\n *\n * math.median(5, 2, 7) // returns 5\n * math.median([3, -1, 5, 7]) // returns 4\n *\n * See also:\n *\n * mean, min, max, sum, prod, std, variance, quantileSeq\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The median\n */\n return typed(name, {\n // median([a, b, c, d, ...])\n 'Array | Matrix': _median,\n\n // median([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n // TODO: implement median(A, dim)\n throw new Error('median(A, dim) is not yet supported')\n // return reduce(arguments[0], arguments[1], ...)\n },\n\n // median(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function median')\n }\n\n return _median(args)\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'mad'\nconst dependencies = ['typed', 'abs', 'map', 'median', 'subtract']\n\nexport const createMad = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, map, median, subtract }) => {\n /**\n * Compute the median absolute deviation of a matrix or a list with values.\n * The median absolute deviation is defined as the median of the absolute\n * deviations from the median.\n *\n * Syntax:\n *\n * math.mad(a, b, c, ...)\n * math.mad(A)\n *\n * Examples:\n *\n * math.mad(10, 20, 30) // returns 10\n * math.mad([1, 2, 3]) // returns 1\n * math.mad([[1, 2, 3], [4, 5, 6]]) // returns 1.5\n *\n * See also:\n *\n * median, mean, std, abs\n *\n * @param {Array | Matrix} array\n * A single matrix or multiple scalar values.\n * @return {*} The median absolute deviation.\n */\n return typed(name, {\n // mad([a, b, c, d, ...])\n 'Array | Matrix': _mad,\n\n // mad(a, b, c, d, ...)\n '...': function (args) {\n return _mad(args)\n }\n })\n\n function _mad (array) {\n array = flatten(array.valueOf())\n\n if (array.length === 0) {\n throw new Error('Cannot calculate median absolute deviation (mad) of an empty array')\n }\n\n try {\n const med = median(array)\n return median(map(array, function (value) {\n return abs(subtract(value, med))\n }))\n } catch (err) {\n if (err instanceof TypeError && err.message.indexOf('median') !== -1) {\n throw new TypeError(err.message.replace('median', 'mad'))\n } else {\n throw improveErrorMessage(err, 'mad')\n }\n }\n }\n})\n","import { deepForEach } from '../../utils/collection.js'\nimport { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst DEFAULT_NORMALIZATION = 'unbiased'\n\nconst name = 'variance'\nconst dependencies = ['typed', 'add', 'subtract', 'multiply', 'divide', 'apply', 'isNaN']\n\nexport const createVariance = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, subtract, multiply, divide, apply, isNaN }) => {\n /**\n * Compute the variance of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the variance over all\n * elements will be calculated.\n *\n * Additionally, it is possible to compute the variance along the rows\n * or columns of a matrix by specifying the dimension as the second argument.\n *\n * Optionally, the type of normalization can be specified as the final\n * parameter. The parameter `normalization` can be one of the following values:\n *\n * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n *\n *\n * Note that older browser may not like the variable name `var`. In that\n * case, the function can be called as `math['var'](...)` instead of\n * `math.var(...)`.\n *\n * Syntax:\n *\n * math.variance(a, b, c, ...)\n * math.variance(A)\n * math.variance(A, normalization)\n * math.variance(A, dimension)\n * math.variance(A, dimension, normalization)\n *\n * Examples:\n *\n * math.variance(2, 4, 6) // returns 4\n * math.variance([2, 4, 6, 8]) // returns 6.666666666666667\n * math.variance([2, 4, 6, 8], 'uncorrected') // returns 5\n * math.variance([2, 4, 6, 8], 'biased') // returns 4\n *\n * math.variance([[1, 2, 3], [4, 5, 6]]) // returns 3.5\n * math.variance([[1, 2, 3], [4, 6, 8]], 0) // returns [4.5, 8, 12.5]\n * math.variance([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 4]\n * math.variance([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.5, 2]\n *\n * See also:\n *\n * mean, median, max, min, prod, std, sum\n *\n * @param {Array | Matrix} array\n * A single matrix or or multiple scalar values\n * @param {string} [normalization='unbiased']\n * Determines how to normalize the variance.\n * Choose 'unbiased' (default), 'uncorrected', or 'biased'.\n * @param dimension {number | BigNumber}\n * Determines the axis to compute the variance for a matrix\n * @return {*} The variance\n */\n return typed(name, {\n // variance([a, b, c, d, ...])\n 'Array | Matrix': function (array) {\n return _var(array, DEFAULT_NORMALIZATION)\n },\n\n // variance([a, b, c, d, ...], normalization)\n 'Array | Matrix, string': _var,\n\n // variance([a, b, c, c, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return _varDim(array, dim, DEFAULT_NORMALIZATION)\n },\n\n // variance([a, b, c, c, ...], dim, normalization)\n 'Array | Matrix, number | BigNumber, string': _varDim,\n\n // variance(a, b, c, d, ...)\n '...': function (args) {\n return _var(args, DEFAULT_NORMALIZATION)\n }\n })\n\n /**\n * Recursively calculate the variance of an n-dimensional array\n * @param {Array} array\n * @param {string} normalization\n * Determines how to normalize the variance:\n * - 'unbiased' The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n * @return {number | BigNumber} variance\n * @private\n */\n function _var (array, normalization) {\n let sum\n let num = 0\n\n if (array.length === 0) {\n throw new SyntaxError('Function variance requires one or more parameters (0 provided)')\n }\n\n // calculate the mean and number of elements\n deepForEach(array, function (value) {\n try {\n sum = sum === undefined ? value : add(sum, value)\n num++\n } catch (err) {\n throw improveErrorMessage(err, 'variance', value)\n }\n })\n if (num === 0) throw new Error('Cannot calculate variance of an empty array')\n\n const mean = divide(sum, num)\n\n // calculate the variance\n sum = undefined\n deepForEach(array, function (value) {\n const diff = subtract(value, mean)\n sum = sum === undefined ? multiply(diff, diff) : add(sum, multiply(diff, diff))\n })\n\n if (isNaN(sum)) {\n return sum\n }\n\n switch (normalization) {\n case 'uncorrected':\n return divide(sum, num)\n\n case 'biased':\n return divide(sum, num + 1)\n\n case 'unbiased':\n {\n const zero = isBigNumber(sum) ? sum.mul(0) : 0\n return (num === 1) ? zero : divide(sum, num - 1)\n }\n\n default:\n throw new Error('Unknown normalization \"' + normalization + '\". ' +\n 'Choose \"unbiased\" (default), \"uncorrected\", or \"biased\".')\n }\n }\n\n function _varDim (array, dim, normalization) {\n try {\n if (array.length === 0) {\n throw new SyntaxError('Function variance requires one or more parameters (0 provided)')\n }\n return apply(array, dim, (x) => _var(x, normalization))\n } catch (err) {\n throw improveErrorMessage(err, 'variance')\n }\n }\n})\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'quantileSeq'\nconst dependencies = ['typed', 'add', 'multiply', 'partitionSelect', 'compare']\n\nexport const createQuantileSeq = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, multiply, partitionSelect, compare }) => {\n /**\n * Compute the prob order quantile of a matrix or a list with values.\n * The sequence is sorted and the middle value is returned.\n * Supported types of sequence values are: Number, BigNumber, Unit\n * Supported types of probability are: Number, BigNumber\n *\n * In case of a (multi dimensional) array or matrix, the prob order quantile\n * of all elements will be calculated.\n *\n * Syntax:\n *\n * math.quantileSeq(A, prob[, sorted])\n * math.quantileSeq(A, [prob1, prob2, ...][, sorted])\n * math.quantileSeq(A, N[, sorted])\n *\n * Examples:\n *\n * math.quantileSeq([3, -1, 5, 7], 0.5) // returns 4\n * math.quantileSeq([3, -1, 5, 7], [1/3, 2/3]) // returns [3, 5]\n * math.quantileSeq([3, -1, 5, 7], 2) // returns [3, 5]\n * math.quantileSeq([-1, 3, 5, 7], 0.5, true) // returns 4\n *\n * See also:\n *\n * median, mean, min, max, sum, prod, std, variance\n *\n * @param {Array, Matrix} data A single matrix or Array\n * @param {Number, BigNumber, Array} probOrN prob is the order of the quantile, while N is\n * the amount of evenly distributed steps of\n * probabilities; only one of these options can\n * be provided\n * @param {Boolean} sorted=false is data sorted in ascending order\n * @return {Number, BigNumber, Unit, Array} Quantile(s)\n */\n function quantileSeq (data, probOrN, sorted) {\n let probArr, dataArr, one\n\n if (arguments.length < 2 || arguments.length > 3) {\n throw new SyntaxError('Function quantileSeq requires two or three parameters')\n }\n\n if (isCollection(data)) {\n sorted = sorted || false\n if (typeof sorted === 'boolean') {\n dataArr = data.valueOf()\n if (isNumber(probOrN)) {\n if (probOrN < 0) {\n throw new Error('N/prob must be non-negative')\n }\n\n if (probOrN <= 1) {\n // quantileSeq([a, b, c, d, ...], prob[,sorted])\n return _quantileSeq(dataArr, probOrN, sorted)\n }\n\n if (probOrN > 1) {\n // quantileSeq([a, b, c, d, ...], N[,sorted])\n if (!isInteger(probOrN)) {\n throw new Error('N must be a positive integer')\n }\n\n const nPlusOne = probOrN + 1\n probArr = new Array(probOrN)\n for (let i = 0; i < probOrN;) {\n probArr[i] = _quantileSeq(dataArr, (++i) / nPlusOne, sorted)\n }\n return probArr\n }\n }\n\n if (isBigNumber(probOrN)) {\n const BigNumber = probOrN.constructor\n\n if (probOrN.isNegative()) {\n throw new Error('N/prob must be non-negative')\n }\n\n one = new BigNumber(1)\n\n if (probOrN.lte(one)) {\n // quantileSeq([a, b, c, d, ...], prob[,sorted])\n return new BigNumber(_quantileSeq(dataArr, probOrN, sorted))\n }\n\n if (probOrN.gt(one)) {\n // quantileSeq([a, b, c, d, ...], N[,sorted])\n if (!probOrN.isInteger()) {\n throw new Error('N must be a positive integer')\n }\n\n // largest possible Array length is 2^32-1\n // 2^32 < 10^15, thus safe conversion guaranteed\n const intN = probOrN.toNumber()\n if (intN > 4294967295) {\n throw new Error('N must be less than or equal to 2^32-1, as that is the maximum length of an Array')\n }\n\n const nPlusOne = new BigNumber(intN + 1)\n probArr = new Array(intN)\n for (let i = 0; i < intN;) {\n probArr[i] = new BigNumber(_quantileSeq(dataArr, new BigNumber(++i).div(nPlusOne), sorted))\n }\n return probArr\n }\n }\n\n if (Array.isArray(probOrN)) {\n // quantileSeq([a, b, c, d, ...], [prob1, prob2, ...][,sorted])\n probArr = new Array(probOrN.length)\n for (let i = 0; i < probArr.length; ++i) {\n const currProb = probOrN[i]\n if (isNumber(currProb)) {\n if (currProb < 0 || currProb > 1) {\n throw new Error('Probability must be between 0 and 1, inclusive')\n }\n } else if (isBigNumber(currProb)) {\n one = new currProb.constructor(1)\n if (currProb.isNegative() || currProb.gt(one)) {\n throw new Error('Probability must be between 0 and 1, inclusive')\n }\n } else {\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n probArr[i] = _quantileSeq(dataArr, currProb, sorted)\n }\n return probArr\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n /**\n * Calculate the prob order quantile of an n-dimensional array.\n *\n * @param {Array} array\n * @param {Number, BigNumber} prob\n * @param {Boolean} sorted\n * @return {Number, BigNumber, Unit} prob order quantile\n * @private\n */\n function _quantileSeq (array, prob, sorted) {\n const flat = flatten(array)\n const len = flat.length\n if (len === 0) {\n throw new Error('Cannot calculate quantile of an empty sequence')\n }\n\n if (isNumber(prob)) {\n const index = prob * (len - 1)\n const fracPart = index % 1\n if (fracPart === 0) {\n const value = sorted ? flat[index] : partitionSelect(flat, index)\n\n validate(value)\n\n return value\n }\n\n const integerPart = Math.floor(index)\n\n let left\n let right\n if (sorted) {\n left = flat[integerPart]\n right = flat[integerPart + 1]\n } else {\n right = partitionSelect(flat, integerPart + 1)\n\n // max of partition is kth largest\n left = flat[integerPart]\n for (let i = 0; i < integerPart; ++i) {\n if (compare(flat[i], left) > 0) {\n left = flat[i]\n }\n }\n }\n\n validate(left)\n validate(right)\n\n // Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]\n return add(multiply(left, 1 - fracPart), multiply(right, fracPart))\n }\n\n // If prob is a BigNumber\n let index = prob.times(len - 1)\n if (index.isInteger()) {\n index = index.toNumber()\n const value = sorted ? flat[index] : partitionSelect(flat, index)\n\n validate(value)\n\n return value\n }\n\n const integerPart = index.floor()\n const fracPart = index.minus(integerPart)\n const integerPartNumber = integerPart.toNumber()\n\n let left\n let right\n if (sorted) {\n left = flat[integerPartNumber]\n right = flat[integerPartNumber + 1]\n } else {\n right = partitionSelect(flat, integerPartNumber + 1)\n\n // max of partition is kth largest\n left = flat[integerPartNumber]\n for (let i = 0; i < integerPartNumber; ++i) {\n if (compare(flat[i], left) > 0) {\n left = flat[i]\n }\n }\n }\n\n validate(left)\n validate(right)\n\n // Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]\n const one = new fracPart.constructor(1)\n return add(multiply(left, one.minus(fracPart)), multiply(right, fracPart))\n }\n\n /**\n * Check if array value types are valid, throw error otherwise.\n * @param {number | BigNumber | Unit} x\n * @param {number | BigNumber | Unit} x\n * @private\n */\n const validate = typed({\n 'number | BigNumber | Unit': function (x) {\n return x\n }\n })\n\n return quantileSeq\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'std'\nconst dependencies = ['typed', 'sqrt', 'variance']\n\nexport const createStd = /* #__PURE__ */ factory(name, dependencies, ({ typed, sqrt, variance }) => {\n /**\n * Compute the standard deviation of a matrix or a list with values.\n * The standard deviations is defined as the square root of the variance:\n * `std(A) = sqrt(variance(A))`.\n * In case of a (multi dimensional) array or matrix, the standard deviation\n * over all elements will be calculated by default, unless an axis is specified\n * in which case the standard deviation will be computed along that axis.\n *\n * Additionally, it is possible to compute the standard deviation along the rows\n * or columns of a matrix by specifying the dimension as the second argument.\n *\n * Optionally, the type of normalization can be specified as the final\n * parameter. The parameter `normalization` can be one of the following values:\n *\n * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n *\n *\n * Syntax:\n *\n * math.std(a, b, c, ...)\n * math.std(A)\n * math.std(A, normalization)\n * math.std(A, dimension)\n * math.std(A, dimension, normalization)\n *\n * Examples:\n *\n * math.std(2, 4, 6) // returns 2\n * math.std([2, 4, 6, 8]) // returns 2.581988897471611\n * math.std([2, 4, 6, 8], 'uncorrected') // returns 2.23606797749979\n * math.std([2, 4, 6, 8], 'biased') // returns 2\n *\n * math.std([[1, 2, 3], [4, 5, 6]]) // returns 1.8708286933869707\n * math.std([[1, 2, 3], [4, 6, 8]], 0) // returns [2.1213203435596424, 2.8284271247461903, 3.5355339059327378]\n * math.std([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 2]\n * math.std([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.7071067811865476, 1.4142135623730951]\n *\n * See also:\n *\n * mean, median, max, min, prod, sum, variance\n *\n * @param {Array | Matrix} array\n * A single matrix or or multiple scalar values\n * @param {string} [normalization='unbiased']\n * Determines how to normalize the variance.\n * Choose 'unbiased' (default), 'uncorrected', or 'biased'.\n * @param dimension {number | BigNumber}\n * Determines the axis to compute the standard deviation for a matrix\n * @return {*} The standard deviation\n */\n return typed(name, {\n // std([a, b, c, d, ...])\n 'Array | Matrix': _std,\n\n // std([a, b, c, d, ...], normalization)\n 'Array | Matrix, string': _std,\n\n // std([a, b, c, c, ...], dim)\n 'Array | Matrix, number | BigNumber': _std,\n\n // std([a, b, c, c, ...], dim, normalization)\n 'Array | Matrix, number | BigNumber, string': _std,\n\n // std(a, b, c, d, ...)\n '...': function (args) {\n return _std(args)\n }\n })\n\n function _std (array, normalization) {\n if (array.length === 0) {\n throw new SyntaxError('Function std requires one or more parameters (0 provided)')\n }\n\n try {\n return sqrt(variance.apply(null, arguments))\n } catch (err) {\n if (err instanceof TypeError && err.message.indexOf(' variance') !== -1) {\n throw new TypeError(err.message.replace(' variance', ' std'))\n } else {\n throw err\n }\n }\n }\n})\n","/** @param {number} i\n * @param {number} n\n * @returns {number} product of i to n\n */\nexport function product (i, n) {\n if (n < i) {\n return 1\n }\n\n if (n === i) {\n return n\n }\n\n const half = (n + i) >> 1 // divide (n + i) by 2 and truncate to integer\n return product(i, half) * product(half + 1, n)\n}\n","import { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nexport function combinationsNumber (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (k > n) {\n throw new TypeError('k must be less than or equal to n')\n }\n\n const nMinusk = n - k\n\n let prodrange\n if (k < nMinusk) {\n prodrange = product(nMinusk + 1, n)\n return prodrange / product(1, k)\n }\n prodrange = product(k + 1, n)\n return prodrange / product(1, nMinusk)\n}\ncombinationsNumber.signature = 'number, number'\n","import { factory } from '../../utils/factory.js'\nimport { combinationsNumber } from '../../plain/number/combinations.js'\n\nconst name = 'combinations'\nconst dependencies = ['typed']\n\nexport const createCombinations = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the number of ways of picking `k` unordered outcomes from `n`\n * possibilities.\n *\n * Combinations only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.combinations(n, k)\n *\n * Examples:\n *\n * math.combinations(7, 5) // returns 21\n *\n * See also:\n *\n * combinationsWithRep, permutations, factorial\n *\n * @param {number | BigNumber} n Total number of objects in the set\n * @param {number | BigNumber} k Number of objects in the subset\n * @return {number | BigNumber} Number of possible combinations.\n */\n return typed(name, {\n 'number, number': combinationsNumber,\n\n 'BigNumber, BigNumber': function (n, k) {\n const BigNumber = n.constructor\n let result, i\n const nMinusk = n.minus(k)\n const one = new BigNumber(1)\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (k.gt(n)) {\n throw new TypeError('k must be less than n in function combinations')\n }\n\n result = one\n if (k.lt(nMinusk)) {\n for (i = one; i.lte(nMinusk); i = i.plus(one)) {\n result = result.times(k.plus(i)).dividedBy(i)\n }\n } else {\n for (i = one; i.lte(k); i = i.plus(one)) {\n result = result.times(nMinusk.plus(i)).dividedBy(i)\n }\n }\n\n return result\n }\n\n // TODO: implement support for collection in combinations\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nconst name = 'combinationsWithRep'\nconst dependencies = ['typed']\n\nexport const createCombinationsWithRep = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the number of ways of picking `k` unordered outcomes from `n`\n * possibilities, allowing individual outcomes to be repeated more than once.\n *\n * CombinationsWithRep only takes integer arguments.\n * The following condition must be enforced: k <= n + k -1.\n *\n * Syntax:\n *\n * math.combinationsWithRep(n, k)\n *\n * Examples:\n *\n * math.combinationsWithRep(7, 5) // returns 462\n *\n * See also:\n *\n * combinations, permutations, factorial\n *\n * @param {number | BigNumber} n Total number of objects in the set\n * @param {number | BigNumber} k Number of objects in the subset\n * @return {number | BigNumber} Number of possible combinations with replacement.\n */\n return typed(name, {\n 'number, number': function (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (n < 1) {\n throw new TypeError('k must be less than or equal to n + k - 1')\n }\n\n if (k < n - 1) {\n const prodrange = product(n, n + k - 1)\n return prodrange / product(1, k)\n }\n const prodrange = product(k + 1, n + k - 1)\n return prodrange / product(1, n - 1)\n },\n\n 'BigNumber, BigNumber': function (n, k) {\n const BigNumber = n.constructor\n let result, i\n const one = new BigNumber(1)\n const nMinusOne = n.minus(one)\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (n.lt(one)) {\n throw new TypeError('k must be less than or equal to n + k - 1 in function combinationsWithRep')\n }\n\n result = one\n if (k.lt(nMinusOne)) {\n for (i = one; i.lte(nMinusOne); i = i.plus(one)) {\n result = result.times(k.plus(i)).dividedBy(i)\n }\n } else {\n for (i = one; i.lte(k); i = i.plus(one)) {\n result = result.times(nMinusOne.plus(i)).dividedBy(i)\n }\n }\n\n return result\n }\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","/* eslint-disable no-loss-of-precision */\n\nimport { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nexport function gammaNumber (n) {\n let x\n\n if (isInteger(n)) {\n if (n <= 0) {\n return isFinite(n) ? Infinity : NaN\n }\n\n if (n > 171) {\n return Infinity // Will overflow\n }\n\n return product(1, n - 1)\n }\n\n if (n < 0.5) {\n return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n))\n }\n\n if (n >= 171.35) {\n return Infinity // will overflow\n }\n\n if (n > 85.0) { // Extended Stirling Approx\n const twoN = n * n\n const threeN = twoN * n\n const fourN = threeN * n\n const fiveN = fourN * n\n return Math.sqrt(2 * Math.PI / n) * Math.pow((n / Math.E), n) *\n (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) -\n 571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) +\n 5246819 / (75246796800 * fiveN * n))\n }\n\n --n\n x = gammaP[0]\n for (let i = 1; i < gammaP.length; ++i) {\n x += gammaP[i] / (n + i)\n }\n\n const t = n + gammaG + 0.5\n return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x\n}\ngammaNumber.signature = 'number'\n\n// TODO: comment on the variables g and p\n\nexport const gammaG = 4.7421875\n\nexport const gammaP = [\n 0.99999999999999709182,\n 57.156235665862923517,\n -59.597960355475491248,\n 14.136097974741747174,\n -0.49191381609762019978,\n 0.33994649984811888699e-4,\n 0.46523628927048575665e-4,\n -0.98374475304879564677e-4,\n 0.15808870322491248884e-3,\n -0.21026444172410488319e-3,\n 0.21743961811521264320e-3,\n -0.16431810653676389022e-3,\n 0.84418223983852743293e-4,\n -0.26190838401581408670e-4,\n 0.36899182659531622704e-5\n]\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { gammaG, gammaNumber, gammaP } from '../../plain/number/index.js'\n\nconst name = 'gamma'\nconst dependencies = ['typed', 'config', 'multiplyScalar', 'pow', 'BigNumber', 'Complex']\n\nexport const createGamma = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, multiplyScalar, pow, BigNumber, Complex }) => {\n /**\n * Compute the gamma function of a value using Lanczos approximation for\n * small values, and an extended Stirling approximation for large values.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.gamma(n)\n *\n * Examples:\n *\n * math.gamma(5) // returns 24\n * math.gamma(-0.5) // returns -3.5449077018110335\n * math.gamma(math.i) // returns -0.15494982830180973 - 0.49801566811835596i\n *\n * See also:\n *\n * combinations, factorial, permutations\n *\n * @param {number | Array | Matrix} n A real or complex number\n * @return {number | Array | Matrix} The gamma of `n`\n */\n\n return typed(name, {\n\n number: gammaNumber,\n\n Complex: function (n) {\n if (n.im === 0) {\n return this(n.re)\n }\n\n n = new Complex(n.re - 1, n.im)\n const x = new Complex(gammaP[0], 0)\n for (let i = 1; i < gammaP.length; ++i) {\n const real = n.re + i // x += p[i]/(n+i)\n const den = real * real + n.im * n.im\n if (den !== 0) {\n x.re += gammaP[i] * real / den\n x.im += -(gammaP[i] * n.im) / den\n } else {\n x.re = gammaP[i] < 0\n ? -Infinity\n : Infinity\n }\n }\n\n const t = new Complex(n.re + gammaG + 0.5, n.im)\n const twoPiSqrt = Math.sqrt(2 * Math.PI)\n\n n.re += 0.5\n const result = pow(t, n)\n if (result.im === 0) { // sqrt(2*PI)*result\n result.re *= twoPiSqrt\n } else if (result.re === 0) {\n result.im *= twoPiSqrt\n } else {\n result.re *= twoPiSqrt\n result.im *= twoPiSqrt\n }\n\n const r = Math.exp(-t.re) // exp(-t)\n t.re = r * Math.cos(-t.im)\n t.im = r * Math.sin(-t.im)\n\n return multiplyScalar(multiplyScalar(result, t), x)\n },\n\n BigNumber: function (n) {\n if (n.isInteger()) {\n return (n.isNegative() || n.isZero())\n ? new BigNumber(Infinity)\n : bigFactorial(n.minus(1))\n }\n\n if (!n.isFinite()) {\n return new BigNumber(n.isNegative() ? NaN : Infinity)\n }\n\n throw new Error('Integer BigNumber expected')\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n })\n\n /**\n * Calculate factorial for a BigNumber\n * @param {BigNumber} n\n * @returns {BigNumber} Returns the factorial of n\n */\n function bigFactorial (n) {\n if (n < 8) {\n return new BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n])\n }\n\n const precision = config.precision + (Math.log(n.toNumber()) | 0)\n const Big = BigNumber.clone({ precision: precision })\n\n if (n % 2 === 1) {\n return n.times(bigFactorial(new BigNumber(n - 1)))\n }\n\n let p = n\n let prod = new Big(n)\n let sum = n.toNumber()\n\n while (p > 2) {\n p -= 2\n sum += p\n prod = prod.times(sum)\n }\n\n return new BigNumber(prod.toPrecision(BigNumber.precision))\n }\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'factorial'\nconst dependencies = ['typed', 'gamma']\n\nexport const createFactorial = /* #__PURE__ */ factory(name, dependencies, ({ typed, gamma }) => {\n /**\n * Compute the factorial of a value\n *\n * Factorial only supports an integer value as argument.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.factorial(n)\n *\n * Examples:\n *\n * math.factorial(5) // returns 120\n * math.factorial(3) // returns 6\n *\n * See also:\n *\n * combinations, combinationsWithRep, gamma, permutations\n *\n * @param {number | BigNumber | Array | Matrix} n An integer number\n * @return {number | BigNumber | Array | Matrix} The factorial of `n`\n */\n return typed(name, {\n number: function (n) {\n if (n < 0) {\n throw new Error('Value must be non-negative')\n }\n\n return gamma(n + 1)\n },\n\n BigNumber: function (n) {\n if (n.isNegative()) {\n throw new Error('Value must be non-negative')\n }\n\n return gamma(n.plus(1))\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'kldivergence'\nconst dependencies = ['typed', 'matrix', 'divide', 'sum', 'multiply', 'dotDivide', 'log', 'isNumeric']\n\nexport const createKldivergence = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divide, sum, multiply, dotDivide, log, isNumeric }) => {\n /**\n * Calculate the Kullback-Leibler (KL) divergence between two distributions\n *\n * Syntax:\n *\n * math.kldivergence(x, y)\n *\n * Examples:\n *\n * math.kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5]) //returns 0.24376698773121153\n *\n *\n * @param {Array | Matrix} q First vector\n * @param {Array | Matrix} p Second vector\n * @return {number} Returns distance between q and p\n */\n return typed(name, {\n 'Array, Array': function (q, p) {\n return _kldiv(matrix(q), matrix(p))\n },\n\n 'Matrix, Array': function (q, p) {\n return _kldiv(q, matrix(p))\n },\n\n 'Array, Matrix': function (q, p) {\n return _kldiv(matrix(q), p)\n },\n\n 'Matrix, Matrix': function (q, p) {\n return _kldiv(q, p)\n }\n\n })\n\n function _kldiv (q, p) {\n const plength = p.size().length\n const qlength = q.size().length\n if (plength > 1) {\n throw new Error('first object must be one dimensional')\n }\n\n if (qlength > 1) {\n throw new Error('second object must be one dimensional')\n }\n\n if (plength !== qlength) {\n throw new Error('Length of two vectors must be equal')\n }\n\n // Before calculation, apply normalization\n const sumq = sum(q)\n if (sumq === 0) {\n throw new Error('Sum of elements in first object must be non zero')\n }\n\n const sump = sum(p)\n if (sump === 0) {\n throw new Error('Sum of elements in second object must be non zero')\n }\n const qnorm = divide(q, sum(q))\n const pnorm = divide(p, sum(p))\n\n const result = sum(multiply(qnorm, log(dotDivide(qnorm, pnorm))))\n if (isNumeric(result)) {\n return result\n } else {\n return Number.NaN\n }\n }\n})\n","import { deepForEach } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'multinomial'\nconst dependencies = ['typed', 'add', 'divide', 'multiply', 'factorial', 'isInteger', 'isPositive']\n\nexport const createMultinomial = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, multiply, factorial, isInteger, isPositive }) => {\n /**\n * Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities.\n *\n * multinomial takes one array of integers as an argument.\n * The following condition must be enforced: every ai <= 0\n *\n * Syntax:\n *\n * math.multinomial(a) // a is an array type\n *\n * Examples:\n *\n * math.multinomial([1,2,1]) // returns 12\n *\n * See also:\n *\n * combinations, factorial\n *\n * @param {number[] | BigNumber[]} a Integer numbers of objects in the subset\n * @return {Number | BigNumber} Multinomial coefficient.\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n let sum = 0\n let denom = 1\n\n deepForEach(a, function (ai) {\n if (!isInteger(ai) || !isPositive(ai)) {\n throw new TypeError('Positive integer value expected in function multinomial')\n }\n sum = add(sum, ai)\n denom = multiply(denom, factorial(ai))\n })\n\n return divide(factorial(sum), denom)\n }\n })\n})\n","import { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'permutations'\nconst dependencies = ['typed', 'factorial']\n\nexport const createPermutations = /* #__PURE__ */ factory(name, dependencies, ({ typed, factorial }) => {\n /**\n * Compute the number of ways of obtaining an ordered subset of `k` elements\n * from a set of `n` elements.\n *\n * Permutations only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.permutations(n)\n * math.permutations(n, k)\n *\n * Examples:\n *\n * math.permutations(5) // 120\n * math.permutations(5, 3) // 60\n *\n * See also:\n *\n * combinations, combinationsWithRep, factorial\n *\n * @param {number | BigNumber} n The number of objects in total\n * @param {number | BigNumber} [k] The number of objects in the subset\n * @return {number | BigNumber} The number of permutations\n */\n return typed(name, {\n 'number | BigNumber': factorial,\n 'number, number': function (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (k > n) {\n throw new TypeError('second argument k must be less than or equal to first argument n')\n }\n // Permute n objects, k at a time\n return product((n - k) + 1, n)\n },\n\n 'BigNumber, BigNumber': function (n, k) {\n let result, i\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (k.gt(n)) {\n throw new TypeError('second argument k must be less than or equal to first argument n')\n }\n\n const one = n.mul(0).add(1)\n result = one\n for (i = n.minus(k).plus(1); i.lte(n); i = i.plus(1)) {\n result = result.times(i)\n }\n\n return result\n }\n\n // TODO: implement support for collection in permutations\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","import seedrandom from 'seedrandom'\n\nconst singletonRandom = /* #__PURE__ */ seedrandom(Date.now())\n\nexport function createRng (randomSeed) {\n let random\n\n // create a new random generator with given seed\n function setSeed (seed) {\n random = seed === null ? singletonRandom : seedrandom(String(seed))\n }\n\n // initialize a seeded pseudo random number generator with config's random seed\n setSeed(randomSeed)\n\n // wrapper function so the rng can be updated via generator\n function rng () {\n return random()\n }\n\n return rng\n}\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { isMatrix, isNumber } from '../../utils/is.js'\nimport { createRng } from './util/seededRNG.js'\n\nconst name = 'pickRandom'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createPickRandom = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Random pick one or more values from a one dimensional array.\n * Array elements are picked using a random function with uniform or weighted distribution.\n *\n * Syntax:\n *\n * math.pickRandom(array)\n * math.pickRandom(array, number)\n * math.pickRandom(array, weights)\n * math.pickRandom(array, number, weights)\n * math.pickRandom(array, weights, number)\n * math.pickRandom(array, { weights, number, elementWise })\n *\n * Examples:\n *\n * math.pickRandom([3, 6, 12, 2]) // returns one of the values in the array\n * math.pickRandom([3, 6, 12, 2], 2) // returns an array of two of the values in the array\n * math.pickRandom([3, 6, 12, 2], { number: 2 }) // returns an array of two of the values in the array\n * math.pickRandom([3, 6, 12, 2], [1, 3, 2, 1]) // returns one of the values in the array with weighted distribution\n * math.pickRandom([3, 6, 12, 2], 2, [1, 3, 2, 1]) // returns an array of two of the values in the array with weighted distribution\n * math.pickRandom([3, 6, 12, 2], [1, 3, 2, 1], 2) // returns an array of two of the values in the array with weighted distribution\n *\n * math.pickRandom([{x: 1.0, y: 2.0}, {x: 1.1, y: 2.0}], { elementWise: false })\n * // returns one of the items in the array\n *\n * See also:\n *\n * random, randomInt\n *\n * @param {Array | Matrix} array A one dimensional array\n * @param {Int} number An int or float\n * @param {Array | Matrix} weights An array of ints or floats\n * @return {number | Array} Returns a single random value from array when number is 1 or undefined.\n * Returns an array with the configured number of elements when number is > 1.\n */\n return typed({\n 'Array | Matrix': function (possibles) {\n return _pickRandom(possibles, {})\n },\n\n 'Array | Matrix, Object': function (possibles, options) {\n return _pickRandom(possibles, options)\n },\n\n 'Array | Matrix, number': function (possibles, number) {\n return _pickRandom(possibles, { number })\n },\n\n 'Array | Matrix, Array | Matrix': function (possibles, weights) {\n return _pickRandom(possibles, { weights })\n },\n\n 'Array | Matrix, Array | Matrix, number': function (possibles, weights, number) {\n return _pickRandom(possibles, { number, weights })\n },\n\n 'Array | Matrix, number, Array | Matrix': function (possibles, number, weights) {\n return _pickRandom(possibles, { number, weights })\n }\n })\n\n /**\n * @param {Array | Matrix} possibles\n * @param {{\n * number?: number,\n * weights?: Array | Matrix,\n * elementWise: boolean\n * }} options\n * @returns {number | Array}\n * @private\n */\n function _pickRandom (possibles, { number, weights, elementWise = true }) {\n const single = (typeof number === 'undefined')\n if (single) {\n number = 1\n }\n\n const createMatrix = isMatrix(possibles)\n ? possibles.create\n : isMatrix(weights)\n ? weights.create\n : null\n\n possibles = possibles.valueOf() // get Array\n if (weights) {\n weights = weights.valueOf() // get Array\n }\n\n if (elementWise === true) {\n possibles = flatten(possibles)\n weights = flatten(weights)\n }\n\n let totalWeights = 0\n\n if (typeof weights !== 'undefined') {\n if (weights.length !== possibles.length) {\n throw new Error('Weights must have the same length as possibles')\n }\n\n for (let i = 0, len = weights.length; i < len; i++) {\n if (!isNumber(weights[i]) || weights[i] < 0) {\n throw new Error('Weights must be an array of positive numbers')\n }\n\n totalWeights += weights[i]\n }\n }\n\n const length = possibles.length\n\n const result = []\n let pick\n\n while (result.length < number) {\n if (typeof weights === 'undefined') {\n pick = possibles[Math.floor(rng() * length)]\n } else {\n let randKey = rng() * totalWeights\n\n for (let i = 0, len = possibles.length; i < len; i++) {\n randKey -= weights[i]\n\n if (randKey < 0) {\n pick = possibles[i]\n break\n }\n }\n }\n\n result.push(pick)\n }\n\n return single\n ? result[0]\n : createMatrix\n ? createMatrix(result)\n : result\n }\n})\n","/**\n * This is a util function for generating a random matrix recursively.\n * @param {number[]} size\n * @param {function} random\n * @returns {Array}\n */\nexport function randomMatrix (size, random) {\n const data = []\n size = size.slice(0)\n\n if (size.length > 1) {\n for (let i = 0, length = size.shift(); i < length; i++) {\n data.push(randomMatrix(size, random))\n }\n } else {\n for (let i = 0, length = size.shift(); i < length; i++) {\n data.push(random())\n }\n }\n\n return data\n}\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { createRng } from './util/seededRNG.js'\nimport { randomMatrix } from './util/randomMatrix.js'\n\nconst name = 'random'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createRandom = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Return a random number larger or equal to `min` and smaller than `max`\n * using a uniform distribution.\n *\n * Syntax:\n *\n * math.random() // generate a random number between 0 and 1\n * math.random(max) // generate a random number between 0 and max\n * math.random(min, max) // generate a random number between min and max\n * math.random(size) // generate a matrix with random numbers between 0 and 1\n * math.random(size, max) // generate a matrix with random numbers between 0 and max\n * math.random(size, min, max) // generate a matrix with random numbers between min and max\n *\n * Examples:\n *\n * math.random() // returns a random number between 0 and 1\n * math.random(100) // returns a random number between 0 and 100\n * math.random(30, 40) // returns a random number between 30 and 40\n * math.random([2, 3]) // returns a 2x3 matrix with random numbers between 0 and 1\n *\n * See also:\n *\n * randomInt, pickRandom\n *\n * @param {Array | Matrix} [size] If provided, an array or matrix with given\n * size and filled with random values is returned\n * @param {number} [min] Minimum boundary for the random value, included\n * @param {number} [max] Maximum boundary for the random value, excluded\n * @return {number | Array | Matrix} A random number\n */\n return typed(name, {\n '': () => _random(0, 1),\n number: (max) => _random(0, max),\n 'number, number': (min, max) => _random(min, max),\n 'Array | Matrix': (size) => _randomMatrix(size, 0, 1),\n 'Array | Matrix, number': (size, max) => _randomMatrix(size, 0, max),\n 'Array | Matrix, number, number': (size, min, max) => _randomMatrix(size, min, max)\n })\n\n function _randomMatrix (size, min, max) {\n const res = randomMatrix(size.valueOf(), () => _random(min, max))\n return isMatrix(size) ? size.create(res) : res\n }\n\n function _random (min, max) {\n return min + rng() * (max - min)\n }\n})\n\n// number only implementation of random, no matrix support\n// TODO: there is quite some duplicate code in both createRandom and createRandomNumber, can we improve that?\nexport const createRandomNumber = /* #__PURE__ */ factory(name, ['typed', 'config', '?on'], ({ typed, config, on, matrix }) => {\n // seeded pseudo random number generator1\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n return typed(name, {\n '': () => _random(0, 1),\n number: (max) => _random(0, max),\n 'number, number': (min, max) => _random(min, max)\n })\n\n function _random (min, max) {\n return min + rng() * (max - min)\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { randomMatrix } from './util/randomMatrix.js'\nimport { createRng } from './util/seededRNG.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'randomInt'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createRandomInt = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Return a random integer number larger or equal to `min` and smaller than `max`\n * using a uniform distribution.\n *\n * Syntax:\n *\n * math.randomInt() // generate a random integer between 0 and 1\n * math.randomInt(max) // generate a random integer between 0 and max\n * math.randomInt(min, max) // generate a random integer between min and max\n * math.randomInt(size) // generate a matrix with random integer between 0 and 1\n * math.randomInt(size, max) // generate a matrix with random integer between 0 and max\n * math.randomInt(size, min, max) // generate a matrix with random integer between min and max\n *\n * Examples:\n *\n * math.randomInt(100) // returns a random integer between 0 and 100\n * math.randomInt(30, 40) // returns a random integer between 30 and 40\n * math.randomInt([2, 3]) // returns a 2x3 matrix with random integers between 0 and 1\n *\n * See also:\n *\n * random, pickRandom\n *\n * @param {Array | Matrix} [size] If provided, an array or matrix with given\n * size and filled with random values is returned\n * @param {number} [min] Minimum boundary for the random value, included\n * @param {number} [max] Maximum boundary for the random value, excluded\n * @return {number | Array | Matrix} A random integer value\n */\n return typed(name, {\n '': () => _randomInt(0, 1),\n number: (max) => _randomInt(0, max),\n 'number, number': (min, max) => _randomInt(min, max),\n 'Array | Matrix': (size) => _randomIntMatrix(size, 0, 1),\n 'Array | Matrix, number': (size, max) => _randomIntMatrix(size, 0, max),\n 'Array | Matrix, number, number': (size, min, max) => _randomIntMatrix(size, min, max)\n })\n\n function _randomIntMatrix (size, min, max) {\n const res = randomMatrix(size.valueOf(), () => _randomInt(min, max))\n return isMatrix(size) ? size.create(res) : res\n }\n\n function _randomInt (min, max) {\n return Math.floor(min + rng() * (max - min))\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'stirlingS2'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'subtract',\n 'multiplyScalar',\n 'divideScalar',\n 'pow',\n 'factorial',\n 'combinations',\n 'isNegative',\n 'isInteger',\n 'larger'\n]\n\nexport const createStirlingS2 = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n subtract,\n multiplyScalar,\n divideScalar,\n pow,\n factorial,\n combinations,\n isNegative,\n isInteger,\n larger\n }\n) => {\n /**\n * The Stirling numbers of the second kind, counts the number of ways to partition\n * a set of n labelled objects into k nonempty unlabelled subsets.\n * stirlingS2 only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * If n = k or k = 1, then s(n,k) = 1\n *\n * Syntax:\n *\n * math.stirlingS2(n, k)\n *\n * Examples:\n *\n * math.stirlingS2(5, 3) //returns 25\n *\n * See also:\n *\n * bellNumbers\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @param {Number | BigNumber} k Number of objects in the subset\n * @return {Number | BigNumber} S(n,k)\n */\n return typed(name, {\n 'number | BigNumber, number | BigNumber': function (n, k) {\n if (!isInteger(n) || isNegative(n) || !isInteger(k) || isNegative(k)) {\n throw new TypeError('Non-negative integer value expected in function stirlingS2')\n } else if (larger(k, n)) {\n throw new TypeError('k must be less than or equal to n in function stirlingS2')\n }\n\n // 1/k! Sum(i=0 -> k) [(-1)^(k-i)*C(k,j)* i^n]\n const kFactorial = factorial(k)\n let result = 0\n for (let i = 0; i <= k; i++) {\n const negativeOne = pow(-1, subtract(k, i))\n const kChooseI = combinations(k, i)\n const iPower = pow(i, n)\n\n result = addScalar(result, multiplyScalar(multiplyScalar(kChooseI, iPower), negativeOne))\n }\n\n return divideScalar(result, kFactorial)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'bellNumbers'\nconst dependencies = ['typed', 'addScalar', 'isNegative', 'isInteger', 'stirlingS2']\n\nexport const createBellNumbers = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, isNegative, isInteger, stirlingS2 }) => {\n /**\n * The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S.\n * bellNumbers only takes integer arguments.\n * The following condition must be enforced: n >= 0\n *\n * Syntax:\n *\n * math.bellNumbers(n)\n *\n * Examples:\n *\n * math.bellNumbers(3) // returns 5\n * math.bellNumbers(8) // returns 4140\n *\n * See also:\n *\n * stirlingS2\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @return {Number | BigNumber} B(n)\n */\n return typed(name, {\n 'number | BigNumber': function (n) {\n if (!isInteger(n) || isNegative(n)) {\n throw new TypeError('Non-negative integer value expected in function bellNumbers')\n }\n\n // Sum (k=0, n) S(n,k).\n let result = 0\n for (let i = 0; i <= n; i++) {\n result = addScalar(result, stirlingS2(n, i))\n }\n\n return result\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'catalan'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'combinations',\n 'isNegative',\n 'isInteger'\n]\n\nexport const createCatalan = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n divideScalar,\n multiplyScalar,\n combinations,\n isNegative,\n isInteger\n }\n) => {\n /**\n * The Catalan Numbers enumerate combinatorial structures of many different types.\n * catalan only takes integer arguments.\n * The following condition must be enforced: n >= 0\n *\n * Syntax:\n *\n * math.catalan(n)\n *\n * Examples:\n *\n * math.catalan(3) // returns 5\n * math.catalan(8) // returns 1430\n *\n * See also:\n *\n * bellNumbers\n *\n * @param {Number | BigNumber} n nth Catalan number\n * @return {Number | BigNumber} Cn(n)\n */\n return typed(name, {\n 'number | BigNumber': function (n) {\n if (!isInteger(n) || isNegative(n)) {\n throw new TypeError('Non-negative integer value expected in function catalan')\n }\n\n return divideScalar(combinations(multiplyScalar(n, 2), n), addScalar(n, 1))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'composition'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'combinations',\n 'isNegative',\n 'isPositive',\n 'isInteger',\n 'larger'\n]\n\nexport const createComposition = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n combinations,\n isPositive,\n isNegative,\n isInteger,\n larger\n }\n) => {\n /**\n * The composition counts of n into k parts.\n *\n * composition only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.composition(n, k)\n *\n * Examples:\n *\n * math.composition(5, 3) // returns 6\n *\n * See also:\n *\n * combinations\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @param {Number | BigNumber} k Number of objects in the subset\n * @return {Number | BigNumber} Returns the composition counts of n into k parts.\n */\n return typed(name, {\n 'number | BigNumber, number | BigNumber': function (n, k) {\n if (!isInteger(n) || !isPositive(n) || !isInteger(k) || !isPositive(k)) {\n throw new TypeError('Positive integer value expected in function composition')\n } else if (larger(k, n)) {\n throw new TypeError('k must be less than or equal to n in function composition')\n }\n\n return combinations(addScalar(n, -1), addScalar(k, -1))\n }\n })\n})\n","import { isOperatorNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { hasOwnProperty } from '../../../utils/object.js'\n\nconst name = 'simplifyUtil'\nconst dependencies = [\n 'FunctionNode',\n 'OperatorNode',\n 'SymbolNode'\n]\n\nexport const createUtil = /* #__PURE__ */ factory(name, dependencies, ({ FunctionNode, OperatorNode, SymbolNode }) => {\n // TODO commutative/associative properties rely on the arguments\n // e.g. multiply is not commutative for matrices\n // The properties should be calculated from an argument to simplify, or possibly something in math.config\n // the other option is for typed() to specify a return type so that we can evaluate the type of arguments\n const commutative = {\n add: true,\n multiply: true\n }\n const associative = {\n add: true,\n multiply: true\n }\n\n function isCommutative (node, context) {\n if (!isOperatorNode(node)) {\n return true\n }\n const name = node.fn.toString()\n if (context && hasOwnProperty(context, name) && hasOwnProperty(context[name], 'commutative')) {\n return context[name].commutative\n }\n return commutative[name] || false\n }\n\n function isAssociative (node, context) {\n if (!isOperatorNode(node)) {\n return false\n }\n const name = node.fn.toString()\n if (context && hasOwnProperty(context, name) && hasOwnProperty(context[name], 'associative')) {\n return context[name].associative\n }\n return associative[name] || false\n }\n\n /**\n * Flatten all associative operators in an expression tree.\n * Assumes parentheses have already been removed.\n */\n function flatten (node) {\n if (!node.args || node.args.length === 0) {\n return node\n }\n node.args = allChildren(node)\n for (let i = 0; i < node.args.length; i++) {\n flatten(node.args[i])\n }\n }\n\n /**\n * Get the children of a node as if it has been flattened.\n * TODO implement for FunctionNodes\n */\n function allChildren (node) {\n let op\n const children = []\n const findChildren = function (node) {\n for (let i = 0; i < node.args.length; i++) {\n const child = node.args[i]\n if (isOperatorNode(child) && op === child.op) {\n findChildren(child)\n } else {\n children.push(child)\n }\n }\n }\n\n if (isAssociative(node)) {\n op = node.op\n findChildren(node)\n return children\n } else {\n return node.args\n }\n }\n\n /**\n * Unflatten all flattened operators to a right-heavy binary tree.\n */\n function unflattenr (node) {\n if (!node.args || node.args.length === 0) {\n return\n }\n const makeNode = createMakeNodeFunction(node)\n const l = node.args.length\n for (let i = 0; i < l; i++) {\n unflattenr(node.args[i])\n }\n if (l > 2 && isAssociative(node)) {\n let curnode = node.args.pop()\n while (node.args.length > 0) {\n curnode = makeNode([node.args.pop(), curnode])\n }\n node.args = curnode.args\n }\n }\n\n /**\n * Unflatten all flattened operators to a left-heavy binary tree.\n */\n function unflattenl (node) {\n if (!node.args || node.args.length === 0) {\n return\n }\n const makeNode = createMakeNodeFunction(node)\n const l = node.args.length\n for (let i = 0; i < l; i++) {\n unflattenl(node.args[i])\n }\n if (l > 2 && isAssociative(node)) {\n let curnode = node.args.shift()\n while (node.args.length > 0) {\n curnode = makeNode([curnode, node.args.shift()])\n }\n node.args = curnode.args\n }\n }\n\n function createMakeNodeFunction (node) {\n if (isOperatorNode(node)) {\n return function (args) {\n try {\n return new OperatorNode(node.op, node.fn, args, node.implicit)\n } catch (err) {\n console.error(err)\n return []\n }\n }\n } else {\n return function (args) {\n return new FunctionNode(new SymbolNode(node.name), args)\n }\n }\n }\n\n return {\n createMakeNodeFunction,\n isCommutative,\n isAssociative,\n flatten,\n allChildren,\n unflattenr,\n unflattenl\n }\n})\n","import { isConstantNode, isFunctionNode, isOperatorNode, isParenthesisNode, isSymbolNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'simplifyCore'\nconst dependencies = [\n 'equal',\n 'isZero',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'ParenthesisNode'\n]\n\nexport const createSimplifyCore = /* #__PURE__ */ factory(name, dependencies, ({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n}) => {\n const node0 = new ConstantNode(0)\n const node1 = new ConstantNode(1)\n\n /**\n * simplifyCore() performs single pass simplification suitable for\n * applications requiring ultimate performance. In contrast, simplify()\n * extends simplifyCore() with additional passes to provide deeper\n * simplification.\n *\n * Syntax:\n *\n * simplify.simplifyCore(expr)\n *\n * Examples:\n *\n * const f = math.parse('2 * 1 * x ^ (2 - 1)')\n * math.simplify.simpifyCore(f) // Node {2 * x}\n * math.simplify('2 * 1 * x ^ (2 - 1)', [math.simplify.simpifyCore]) // Node {2 * x}\n *\n * See also:\n *\n * derivative\n *\n * @param {Node} node\n * The expression to be simplified\n */\n function simplifyCore (node) {\n if (isOperatorNode(node) && node.isUnary()) {\n const a0 = simplifyCore(node.args[0])\n\n if (node.op === '+') { // unary plus\n return a0\n }\n\n if (node.op === '-') { // unary minus\n if (isOperatorNode(a0)) {\n if (a0.isUnary() && a0.op === '-') {\n return a0.args[0]\n } else if (a0.isBinary() && a0.fn === 'subtract') {\n return new OperatorNode('-', 'subtract', [a0.args[1], a0.args[0]])\n }\n }\n return new OperatorNode(node.op, node.fn, [a0])\n }\n } else if (isOperatorNode(node) && node.isBinary()) {\n const a0 = simplifyCore(node.args[0])\n const a1 = simplifyCore(node.args[1])\n\n if (node.op === '+') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return a1\n } else if (isConstantNode(a1)) {\n return new ConstantNode(add(a0.value, a1.value))\n }\n }\n if (isConstantNode(a1) && isZero(a1.value)) {\n return a0\n }\n if (isOperatorNode(a1) && a1.isUnary() && a1.op === '-') {\n return new OperatorNode('-', 'subtract', [a0, a1.args[0]])\n }\n return new OperatorNode(node.op, node.fn, a1 ? [a0, a1] : [a0])\n } else if (node.op === '-') {\n if (isConstantNode(a0) && a1) {\n if (isConstantNode(a1)) {\n return new ConstantNode(subtract(a0.value, a1.value))\n } else if (isZero(a0.value)) {\n return new OperatorNode('-', 'unaryMinus', [a1])\n }\n }\n // if (node.fn === \"subtract\" && node.args.length === 2) {\n if (node.fn === 'subtract') {\n if (isConstantNode(a1) && isZero(a1.value)) {\n return a0\n }\n if (isOperatorNode(a1) && a1.isUnary() && a1.op === '-') {\n return simplifyCore(new OperatorNode('+', 'add', [a0, a1.args[0]]))\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n }\n } else if (node.op === '*') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return node0\n } else if (equal(a0.value, 1)) {\n return a1\n } else if (isConstantNode(a1)) {\n return new ConstantNode(multiply(a0.value, a1.value))\n }\n }\n if (isConstantNode(a1)) {\n if (isZero(a1.value)) {\n return node0\n } else if (equal(a1.value, 1)) {\n return a0\n } else if (isOperatorNode(a0) && a0.isBinary() && a0.op === node.op) {\n const a00 = a0.args[0]\n if (isConstantNode(a00)) {\n const a00a1 = new ConstantNode(multiply(a00.value, a1.value))\n return new OperatorNode(node.op, node.fn, [a00a1, a0.args[1]], node.implicit) // constants on left\n }\n }\n return new OperatorNode(node.op, node.fn, [a1, a0], node.implicit) // constants on left\n }\n return new OperatorNode(node.op, node.fn, [a0, a1], node.implicit)\n } else if (node.op === '/') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return node0\n } else if (isConstantNode(a1) &&\n (equal(a1.value, 1) || equal(a1.value, 2) || equal(a1.value, 4))) {\n return new ConstantNode(divide(a0.value, a1.value))\n }\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n } else if (node.op === '^') {\n if (isConstantNode(a1)) {\n if (isZero(a1.value)) {\n return node1\n } else if (equal(a1.value, 1)) {\n return a0\n } else {\n if (isConstantNode(a0)) {\n // fold constant\n return new ConstantNode(pow(a0.value, a1.value))\n } else if (isOperatorNode(a0) && a0.isBinary() && a0.op === '^') {\n const a01 = a0.args[1]\n if (isConstantNode(a01)) {\n return new OperatorNode(node.op, node.fn, [\n a0.args[0],\n new ConstantNode(multiply(a01.value, a1.value))\n ])\n }\n }\n }\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n }\n } else if (isParenthesisNode(node)) {\n const c = simplifyCore(node.content)\n if (isParenthesisNode(c) || isSymbolNode(c) || isConstantNode(c)) {\n return c\n }\n return new ParenthesisNode(c)\n } else if (isFunctionNode(node)) {\n const args = node.args\n .map(simplifyCore)\n .map(function (arg) {\n return isParenthesisNode(arg) ? arg.content : arg\n })\n return new FunctionNode(simplifyCore(node.fn), args)\n } else {\n // cannot simplify\n }\n return node\n }\n\n return simplifyCore\n})\n","// TODO this could be improved by simplifying seperated constants under associative and commutative operators\nimport { isFraction, isNode, isOperatorNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createUtil } from './util.js'\nimport { noBignumber, noFraction } from '../../../utils/noop.js'\n\nconst name = 'simplifyConstant'\nconst dependencies = [\n 'typed',\n 'config',\n 'mathWithTransform',\n '?fraction',\n '?bignumber',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'SymbolNode'\n]\n\nexport const createSimplifyConstant = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n}) => {\n const { isCommutative, isAssociative, allChildren, createMakeNodeFunction } =\n createUtil({ FunctionNode, OperatorNode, SymbolNode })\n\n function simplifyConstant (expr, options) {\n const res = foldFraction(expr, options)\n return isNode(res) ? res : _toNode(res)\n }\n\n function _eval (fnname, args, options) {\n try {\n return _toNumber(mathWithTransform[fnname].apply(null, args), options)\n } catch (ignore) {\n // sometimes the implicit type conversion causes the evaluation to fail, so we'll try again after removing Fractions\n args = args.map(function (x) {\n if (isFraction(x)) {\n return x.valueOf()\n }\n return x\n })\n return _toNumber(mathWithTransform[fnname].apply(null, args), options)\n }\n }\n\n const _toNode = typed({\n Fraction: _fractionToNode,\n number: function (n) {\n if (n < 0) {\n return unaryMinusNode(new ConstantNode(-n))\n }\n return new ConstantNode(n)\n },\n BigNumber: function (n) {\n if (n < 0) {\n return unaryMinusNode(new ConstantNode(-n))\n }\n return new ConstantNode(n) // old parameters: (n.toString(), 'number')\n },\n Complex: function (s) {\n throw new Error('Cannot convert Complex number to Node')\n }\n })\n\n // convert a number to a fraction only if it can be expressed exactly,\n // and when both numerator and denominator are small enough\n function _exactFraction (n, options) {\n const exactFractions = (options && options.exactFractions !== false)\n if (exactFractions && isFinite(n) && fraction) {\n const f = fraction(n)\n const fractionsLimit = (options && typeof options.fractionsLimit === 'number')\n ? options.fractionsLimit\n : Infinity // no limit by default\n\n if (f.valueOf() === n && f.n < fractionsLimit && f.d < fractionsLimit) {\n return f\n }\n }\n return n\n }\n\n // Convert numbers to a preferred number type in preference order: Fraction, number, Complex\n // BigNumbers are left alone\n const _toNumber = typed({\n 'string, Object': function (s, options) {\n if (config.number === 'BigNumber') {\n if (bignumber === undefined) {\n noBignumber()\n }\n return bignumber(s)\n } else if (config.number === 'Fraction') {\n if (fraction === undefined) {\n noFraction()\n }\n return fraction(s)\n } else {\n const n = parseFloat(s)\n return _exactFraction(n, options)\n }\n },\n\n 'Fraction, Object': function (s, options) { return s }, // we don't need options here\n\n 'BigNumber, Object': function (s, options) { return s }, // we don't need options here\n\n 'number, Object': function (s, options) {\n return _exactFraction(s, options)\n },\n\n 'Complex, Object': function (s, options) {\n if (s.im !== 0) {\n return s\n }\n return _exactFraction(s.re, options)\n }\n })\n\n function unaryMinusNode (n) {\n return new OperatorNode('-', 'unaryMinus', [n])\n }\n\n function _fractionToNode (f) {\n let n\n const vn = f.s * f.n\n if (vn < 0) {\n n = new OperatorNode('-', 'unaryMinus', [new ConstantNode(-vn)])\n } else {\n n = new ConstantNode(vn)\n }\n\n if (f.d === 1) {\n return n\n }\n return new OperatorNode('/', 'divide', [n, new ConstantNode(f.d)])\n }\n\n /*\n * Create a binary tree from a list of Fractions and Nodes.\n * Tries to fold Fractions by evaluating them until the first Node in the list is hit, so\n * `args` should be sorted to have the Fractions at the start (if the operator is commutative).\n * @param args - list of Fractions and Nodes\n * @param fn - evaluator for the binary operation evaluator that accepts two Fractions\n * @param makeNode - creates a binary OperatorNode/FunctionNode from a list of child Nodes\n * if args.length is 1, returns args[0]\n * @return - Either a Node representing a binary expression or Fraction\n */\n function foldOp (fn, args, makeNode, options) {\n return args.reduce(function (a, b) {\n if (!isNode(a) && !isNode(b)) {\n try {\n return _eval(fn, [a, b], options)\n } catch (ignoreandcontinue) {}\n a = _toNode(a)\n b = _toNode(b)\n } else if (!isNode(a)) {\n a = _toNode(a)\n } else if (!isNode(b)) {\n b = _toNode(b)\n }\n\n return makeNode([a, b])\n })\n }\n\n // destroys the original node and returns a folded one\n function foldFraction (node, options) {\n switch (node.type) {\n case 'SymbolNode':\n return node\n case 'ConstantNode':\n if (typeof node.value === 'number' || !isNaN(node.value)) {\n return _toNumber(node.value, options)\n }\n return node\n case 'FunctionNode':\n if (mathWithTransform[node.name] && mathWithTransform[node.name].rawArgs) {\n return node\n }\n {\n // Process operators as OperatorNode\n const operatorFunctions = ['add', 'multiply']\n if (operatorFunctions.indexOf(node.name) === -1) {\n let args = node.args.map(arg => foldFraction(arg, options))\n\n // If all args are numbers\n if (!args.some(isNode)) {\n try {\n return _eval(node.name, args, options)\n } catch (ignoreandcontine) {}\n }\n\n // Convert all args to nodes and construct a symbolic function call\n args = args.map(function (arg) {\n return isNode(arg) ? arg : _toNode(arg)\n })\n return new FunctionNode(node.name, args)\n } else {\n // treat as operator\n }\n }\n /* falls through */\n case 'OperatorNode':\n {\n const fn = node.fn.toString()\n let args\n let res\n const makeNode = createMakeNodeFunction(node)\n if (isOperatorNode(node) && node.isUnary()) {\n args = [foldFraction(node.args[0], options)]\n if (!isNode(args[0])) {\n res = _eval(fn, args, options)\n } else {\n res = makeNode(args)\n }\n } else if (isAssociative(node)) {\n args = allChildren(node)\n args = args.map(arg => foldFraction(arg, options))\n\n if (isCommutative(fn)) {\n // commutative binary operator\n const consts = []\n const vars = []\n\n for (let i = 0; i < args.length; i++) {\n if (!isNode(args[i])) {\n consts.push(args[i])\n } else {\n vars.push(args[i])\n }\n }\n\n if (consts.length > 1) {\n res = foldOp(fn, consts, makeNode, options)\n vars.unshift(res)\n res = foldOp(fn, vars, makeNode, options)\n } else {\n // we won't change the children order since it's not neccessary\n res = foldOp(fn, args, makeNode, options)\n }\n } else {\n // non-commutative binary operator\n res = foldOp(fn, args, makeNode, options)\n }\n } else {\n // non-associative binary operator\n args = node.args.map(arg => foldFraction(arg, options))\n res = foldOp(fn, args, makeNode, options)\n }\n return res\n }\n case 'ParenthesisNode':\n // remove the uneccessary parenthesis\n return foldFraction(node.content, options)\n case 'AccessorNode':\n /* falls through */\n case 'ArrayNode':\n /* falls through */\n case 'AssignmentNode':\n /* falls through */\n case 'BlockNode':\n /* falls through */\n case 'FunctionAssignmentNode':\n /* falls through */\n case 'IndexNode':\n /* falls through */\n case 'ObjectNode':\n /* falls through */\n case 'RangeNode':\n /* falls through */\n case 'ConditionalNode':\n /* falls through */\n default:\n throw new Error(`Unimplemented node type in simplifyConstant: ${node.type}`)\n }\n }\n\n return simplifyConstant\n})\n","import { isFunctionNode, isNode, isOperatorNode, isParenthesisNode, isSymbolNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'resolve'\nconst dependencies = [\n 'parse',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode'\n]\n\nexport const createResolve = /* #__PURE__ */ factory(name, dependencies, ({\n parse,\n FunctionNode,\n OperatorNode,\n ParenthesisNode\n}) => {\n /**\n * resolve(expr, scope) replaces variable nodes with their scoped values\n *\n * Syntax:\n *\n * simplify.resolve(expr, scope)\n *\n * Examples:\n *\n * math.simplify.resolve('x + y', {x:1, y:2}) // Node {1 + 2}\n * math.simplify.resolve(math.parse('x+y'), {x:1, y:2}) // Node {1 + 2}\n * math.simplify('x+y', {x:2, y:'x+x'}).toString() // \"6\"\n *\n * @param {Node} node\n * The expression tree to be simplified\n * @param {Object} scope with variables to be resolved\n */\n function resolve (node, scope) {\n if (!scope) {\n return node\n }\n if (isSymbolNode(node)) {\n const value = scope[node.name]\n if (isNode(value)) {\n return resolve(value, scope)\n } else if (typeof value === 'number') {\n return parse(String(value))\n }\n } else if (isOperatorNode(node)) {\n const args = node.args.map(function (arg) {\n return resolve(arg, scope)\n })\n return new OperatorNode(node.op, node.fn, args, node.implicit)\n } else if (isParenthesisNode(node)) {\n return new ParenthesisNode(resolve(node.content, scope))\n } else if (isFunctionNode(node)) {\n const args = node.args.map(function (arg) {\n return resolve(arg, scope)\n })\n return new FunctionNode(node.name, args)\n }\n return node\n }\n\n return resolve\n})\n","import { isConstantNode, isParenthesisNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { createUtil } from './simplify/util.js'\nimport { createSimplifyCore } from './simplify/simplifyCore.js'\nimport { createSimplifyConstant } from './simplify/simplifyConstant.js'\nimport { createResolve } from './simplify/resolve.js'\nimport { hasOwnProperty } from '../../utils/object.js'\n\nconst name = 'simplify'\nconst dependencies = [\n 'config',\n 'typed',\n 'parse',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'isZero',\n 'equal',\n '?fraction',\n '?bignumber',\n 'mathWithTransform',\n 'ConstantNode',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'SymbolNode'\n]\n\nexport const createSimplify = /* #__PURE__ */ factory(name, dependencies, (\n {\n config,\n typed,\n parse,\n add,\n subtract,\n multiply,\n divide,\n pow,\n isZero,\n equal,\n fraction,\n bignumber,\n mathWithTransform,\n ConstantNode,\n FunctionNode,\n OperatorNode,\n ParenthesisNode,\n SymbolNode\n }\n) => {\n const simplifyConstant = createSimplifyConstant({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n })\n const simplifyCore = createSimplifyCore({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n })\n const resolve = createResolve({\n parse,\n FunctionNode,\n OperatorNode,\n ParenthesisNode\n })\n\n const { isCommutative, isAssociative, flatten, unflattenr, unflattenl, createMakeNodeFunction } =\n createUtil({ FunctionNode, OperatorNode, SymbolNode })\n\n /**\n * Simplify an expression tree.\n *\n * A list of rules are applied to an expression, repeating over the list until\n * no further changes are made.\n * It's possible to pass a custom set of rules to the function as second\n * argument. A rule can be specified as an object, string, or function:\n *\n * const rules = [\n * { l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },\n * 'n1*n3 + n2*n3 -> (n1+n2)*n3',\n * function (node) {\n * // ... return a new node or return the node unchanged\n * return node\n * }\n * ]\n *\n * String and object rules consist of a left and right pattern. The left is\n * used to match against the expression and the right determines what matches\n * are replaced with. The main difference between a pattern and a normal\n * expression is that variables starting with the following characters are\n * interpreted as wildcards:\n *\n * - 'n' - matches any Node\n * - 'c' - matches any ConstantNode\n * - 'v' - matches any Node that is not a ConstantNode\n *\n * The default list of rules is exposed on the function as `simplify.rules`\n * and can be used as a basis to built a set of custom rules.\n *\n * For more details on the theory, see:\n *\n * - [Strategies for simplifying math expressions (Stackoverflow)](https://stackoverflow.com/questions/7540227/strategies-for-simplifying-math-expressions)\n * - [Symbolic computation - Simplification (Wikipedia)](https://en.wikipedia.org/wiki/Symbolic_computation#Simplification)\n *\n * An optional `options` argument can be passed as last argument of `simplify`.\n * There is currently one option available:\n * - `exactFractions`: a boolean which is `true` by default.\n * - `fractionsLimit`: when `exactFractions` is true, a fraction will be returned\n * only when both numerator and denominator are smaller than `fractionsLimit`.\n * Default value is 10000.\n *\n * Syntax:\n *\n * simplify(expr)\n * simplify(expr, rules)\n * simplify(expr, rules)\n * simplify(expr, rules, scope)\n * simplify(expr, rules, scope, options)\n * simplify(expr, scope)\n * simplify(expr, scope, options)\n *\n * Examples:\n *\n * math.simplify('2 * 1 * x ^ (2 - 1)') // Node \"2 * x\"\n * math.simplify('2 * 3 * x', {x: 4}) // Node \"24\"\n * const f = math.parse('2 * 1 * x ^ (2 - 1)')\n * math.simplify(f) // Node \"2 * x\"\n * math.simplify('0.4 * x', {}, {exactFractions: true}) // Node \"x * 2 / 5\"\n * math.simplify('0.4 * x', {}, {exactFractions: false}) // Node \"0.4 * x\"\n *\n * See also:\n *\n * derivative, parse, evaluate, rationalize\n *\n * @param {Node | string} expr\n * The expression to be simplified\n * @param {Array<{l:string, r: string} | string | function>} [rules]\n * Optional list with custom rules\n * @return {Node} Returns the simplified form of `expr`\n */\n const simplify = typed('simplify', {\n string: function (expr) {\n return this(parse(expr), this.rules, {}, {})\n },\n\n 'string, Object': function (expr, scope) {\n return this(parse(expr), this.rules, scope, {})\n },\n\n 'string, Object, Object': function (expr, scope, options) {\n return this(parse(expr), this.rules, scope, options)\n },\n\n 'string, Array': function (expr, rules) {\n return this(parse(expr), rules, {}, {})\n },\n\n 'string, Array, Object': function (expr, rules, scope) {\n return this(parse(expr), rules, scope, {})\n },\n\n 'string, Array, Object, Object': function (expr, rules, scope, options) {\n return this(parse(expr), rules, scope, options)\n },\n\n 'Node, Object': function (expr, scope) {\n return this(expr, this.rules, scope, {})\n },\n\n 'Node, Object, Object': function (expr, scope, options) {\n return this(expr, this.rules, scope, options)\n },\n\n Node: function (expr) {\n return this(expr, this.rules, {}, {})\n },\n\n 'Node, Array': function (expr, rules) {\n return this(expr, rules, {}, {})\n },\n\n 'Node, Array, Object': function (expr, rules, scope) {\n return this(expr, rules, scope, {})\n },\n\n 'Node, Array, Object, Object': function (expr, rules, scope, options) {\n rules = _buildRules(rules)\n let res = resolve(expr, scope)\n res = removeParens(res)\n const visited = {}\n let str = res.toString({ parenthesis: 'all' })\n while (!visited[str]) {\n visited[str] = true\n _lastsym = 0 // counter for placeholder symbols\n for (let i = 0; i < rules.length; i++) {\n if (typeof rules[i] === 'function') {\n res = rules[i](res, options)\n } else {\n flatten(res)\n res = applyRule(res, rules[i])\n }\n unflattenl(res) // using left-heavy binary tree here since custom rule functions may expect it\n }\n str = res.toString({ parenthesis: 'all' })\n }\n return res\n }\n })\n simplify.simplifyCore = simplifyCore\n simplify.resolve = resolve\n\n function removeParens (node) {\n return node.transform(function (node, path, parent) {\n return isParenthesisNode(node)\n ? removeParens(node.content)\n : node\n })\n }\n\n // All constants that are allowed in rules\n const SUPPORTED_CONSTANTS = {\n true: true,\n false: true,\n e: true,\n i: true,\n Infinity: true,\n LN2: true,\n LN10: true,\n LOG2E: true,\n LOG10E: true,\n NaN: true,\n phi: true,\n pi: true,\n SQRT1_2: true,\n SQRT2: true,\n tau: true\n // null: false,\n // undefined: false,\n // version: false,\n }\n\n // Array of strings, used to build the ruleSet.\n // Each l (left side) and r (right side) are parsed by\n // the expression parser into a node tree.\n // Left hand sides are matched to subtrees within the\n // expression to be parsed and replaced with the right\n // hand side.\n // TODO: Add support for constraints on constants (either in the form of a '=' expression or a callback [callback allows things like comparing symbols alphabetically])\n // To evaluate lhs constants for rhs constants, use: { l: 'c1+c2', r: 'c3', evaluate: 'c3 = c1 + c2' }. Multiple assignments are separated by ';' in block format.\n // It is possible to get into an infinite loop with conflicting rules\n simplify.rules = [\n simplifyCore,\n // { l: 'n+0', r: 'n' }, // simplifyCore\n // { l: 'n^0', r: '1' }, // simplifyCore\n // { l: '0*n', r: '0' }, // simplifyCore\n // { l: 'n/n', r: '1'}, // simplifyCore\n // { l: 'n^1', r: 'n' }, // simplifyCore\n // { l: '+n1', r:'n1' }, // simplifyCore\n // { l: 'n--n1', r:'n+n1' }, // simplifyCore\n { l: 'log(e)', r: '1' },\n\n // temporary rules\n { l: 'n-n1', r: 'n+-n1' }, // temporarily replace 'subtract' so we can further flatten the 'add' operator\n { l: '-(c*v)', r: '(-c) * v' }, // make non-constant terms positive\n { l: '-v', r: '(-1) * v' },\n { l: 'n/n1^n2', r: 'n*n1^-n2' }, // temporarily replace 'divide' so we can further flatten the 'multiply' operator\n { l: 'n/n1', r: 'n*n1^-1' },\n\n // expand nested exponentiation\n { l: '(n ^ n1) ^ n2', r: 'n ^ (n1 * n2)' },\n\n // collect like factors\n { l: 'n*n', r: 'n^2' },\n { l: 'n * n^n1', r: 'n^(n1+1)' },\n { l: 'n^n1 * n^n2', r: 'n^(n1+n2)' },\n\n // collect like terms\n { l: 'n+n', r: '2*n' },\n { l: 'n+-n', r: '0' },\n { l: 'n1*n2 + n2', r: '(n1+1)*n2' },\n { l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },\n\n // remove parenthesis in the case of negating a quantitiy\n { l: 'n1 + -1 * (n2 + n3)', r: 'n1 + -1 * n2 + -1 * n3' },\n\n simplifyConstant,\n\n { l: '(-n)*n1', r: '-(n*n1)' }, // make factors positive (and undo 'make non-constant terms positive')\n\n // ordering of constants\n { l: 'c+v', r: 'v+c', context: { add: { commutative: false } } },\n { l: 'v*c', r: 'c*v', context: { multiply: { commutative: false } } },\n\n // undo temporary rules\n // { l: '(-1) * n', r: '-n' }, // #811 added test which proved this is redundant\n { l: 'n+-n1', r: 'n-n1' }, // undo replace 'subtract'\n { l: 'n*(n1^-1)', r: 'n/n1' }, // undo replace 'divide'\n { l: 'n*n1^-n2', r: 'n/n1^n2' },\n { l: 'n1^-1', r: '1/n1' },\n\n { l: 'n*(n1/n2)', r: '(n*n1)/n2' }, // '*' before '/'\n { l: 'n-(n1+n2)', r: 'n-n1-n2' }, // '-' before '+'\n // { l: '(n1/n2)/n3', r: 'n1/(n2*n3)' },\n // { l: '(n*n1)/(n*n2)', r: 'n1/n2' },\n\n { l: '1*n', r: 'n' }, // this pattern can be produced by simplifyConstant\n\n { l: 'n1/(n2/n3)', r: '(n1*n3)/n2' }\n\n ]\n\n /**\n * Parse the string array of rules into nodes\n *\n * Example syntax for rules:\n *\n * Position constants to the left in a product:\n * { l: 'n1 * c1', r: 'c1 * n1' }\n * n1 is any Node, and c1 is a ConstantNode.\n *\n * Apply difference of squares formula:\n * { l: '(n1 - n2) * (n1 + n2)', r: 'n1^2 - n2^2' }\n * n1, n2 mean any Node.\n *\n * Short hand notation:\n * 'n1 * c1 -> c1 * n1'\n */\n function _buildRules (rules) {\n // Array of rules to be used to simplify expressions\n const ruleSet = []\n for (let i = 0; i < rules.length; i++) {\n let rule = rules[i]\n let newRule\n const ruleType = typeof rule\n switch (ruleType) {\n case 'string':\n {\n const lr = rule.split('->')\n if (lr.length === 2) {\n rule = { l: lr[0], r: lr[1] }\n } else {\n throw SyntaxError('Could not parse rule: ' + rule)\n }\n }\n /* falls through */\n case 'object':\n newRule = {\n l: removeParens(parse(rule.l)),\n r: removeParens(parse(rule.r))\n }\n if (rule.context) {\n newRule.evaluate = rule.context\n }\n if (rule.evaluate) {\n newRule.evaluate = parse(rule.evaluate)\n }\n\n if (isAssociative(newRule.l)) {\n const makeNode = createMakeNodeFunction(newRule.l)\n const expandsym = _getExpandPlaceholderSymbol()\n newRule.expanded = {}\n newRule.expanded.l = makeNode([newRule.l.clone(), expandsym])\n // Push the expandsym into the deepest possible branch.\n // This helps to match the newRule against nodes returned from getSplits() later on.\n flatten(newRule.expanded.l)\n unflattenr(newRule.expanded.l)\n newRule.expanded.r = makeNode([newRule.r, expandsym])\n }\n break\n case 'function':\n newRule = rule\n break\n default:\n throw TypeError('Unsupported type of rule: ' + ruleType)\n }\n // console.log('Adding rule: ' + rules[i])\n // console.log(newRule)\n ruleSet.push(newRule)\n }\n return ruleSet\n }\n\n let _lastsym = 0\n function _getExpandPlaceholderSymbol () {\n return new SymbolNode('_p' + _lastsym++)\n }\n\n /**\n * Returns a simplfied form of node, or the original node if no simplification was possible.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The simplified form of `expr`, or the original node if no simplification was possible.\n */\n const applyRule = typed('applyRule', {\n 'Node, Object': function (node, rule) {\n // console.log('Entering applyRule(' + node.toString() + ')')\n\n // Do not clone node unless we find a match\n let res = node\n\n // First replace our child nodes with their simplified versions\n // If a child could not be simplified, the assignments will have\n // no effect since the node is returned unchanged\n if (res instanceof OperatorNode || res instanceof FunctionNode) {\n if (res.args) {\n for (let i = 0; i < res.args.length; i++) {\n res.args[i] = applyRule(res.args[i], rule)\n }\n }\n } else if (res instanceof ParenthesisNode) {\n if (res.content) {\n res.content = applyRule(res.content, rule)\n }\n }\n\n // Try to match a rule against this node\n let repl = rule.r\n let matches = _ruleMatch(rule.l, res)[0]\n\n // If the rule is associative operator, we can try matching it while allowing additional terms.\n // This allows us to match rules like 'n+n' to the expression '(1+x)+x' or even 'x+1+x' if the operator is commutative.\n if (!matches && rule.expanded) {\n repl = rule.expanded.r\n matches = _ruleMatch(rule.expanded.l, res)[0]\n }\n\n if (matches) {\n // const before = res.toString({parenthesis: 'all'})\n\n // Create a new node by cloning the rhs of the matched rule\n // we keep any implicit multiplication state if relevant\n const implicit = res.implicit\n res = repl.clone()\n if (implicit && 'implicit' in repl) {\n res.implicit = true\n }\n\n // Replace placeholders with their respective nodes without traversing deeper into the replaced nodes\n res = res.transform(function (node) {\n if (node.isSymbolNode && hasOwnProperty(matches.placeholders, node.name)) {\n return matches.placeholders[node.name].clone()\n } else {\n return node\n }\n })\n\n // const after = res.toString({parenthesis: 'all'})\n // console.log('Simplified ' + before + ' to ' + after)\n }\n\n return res\n }\n })\n\n /**\n * Get (binary) combinations of a flattened binary node\n * e.g. +(node1, node2, node3) -> [\n * +(node1, +(node2, node3)),\n * +(node2, +(node1, node3)),\n * +(node3, +(node1, node2))]\n *\n */\n function getSplits (node, context) {\n const res = []\n let right, rightArgs\n const makeNode = createMakeNodeFunction(node)\n if (isCommutative(node, context)) {\n for (let i = 0; i < node.args.length; i++) {\n rightArgs = node.args.slice(0)\n rightArgs.splice(i, 1)\n right = (rightArgs.length === 1) ? rightArgs[0] : makeNode(rightArgs)\n res.push(makeNode([node.args[i], right]))\n }\n } else {\n rightArgs = node.args.slice(1)\n right = (rightArgs.length === 1) ? rightArgs[0] : makeNode(rightArgs)\n res.push(makeNode([node.args[0], right]))\n }\n return res\n }\n\n /**\n * Returns the set union of two match-placeholders or null if there is a conflict.\n */\n function mergeMatch (match1, match2) {\n const res = { placeholders: {} }\n\n // Some matches may not have placeholders; this is OK\n if (!match1.placeholders && !match2.placeholders) {\n return res\n } else if (!match1.placeholders) {\n return match2\n } else if (!match2.placeholders) {\n return match1\n }\n\n // Placeholders with the same key must match exactly\n for (const key in match1.placeholders) {\n if (hasOwnProperty(match1.placeholders, key)) {\n res.placeholders[key] = match1.placeholders[key]\n\n if (hasOwnProperty(match2.placeholders, key)) {\n if (!_exactMatch(match1.placeholders[key], match2.placeholders[key])) {\n return null\n }\n }\n }\n }\n\n for (const key in match2.placeholders) {\n if (hasOwnProperty(match2.placeholders, key)) {\n res.placeholders[key] = match2.placeholders[key]\n }\n }\n\n return res\n }\n\n /**\n * Combine two lists of matches by applying mergeMatch to the cartesian product of two lists of matches.\n * Each list represents matches found in one child of a node.\n */\n function combineChildMatches (list1, list2) {\n const res = []\n\n if (list1.length === 0 || list2.length === 0) {\n return res\n }\n\n let merged\n for (let i1 = 0; i1 < list1.length; i1++) {\n for (let i2 = 0; i2 < list2.length; i2++) {\n merged = mergeMatch(list1[i1], list2[i2])\n if (merged) {\n res.push(merged)\n }\n }\n }\n return res\n }\n\n /**\n * Combine multiple lists of matches by applying mergeMatch to the cartesian product of two lists of matches.\n * Each list represents matches found in one child of a node.\n * Returns a list of unique matches.\n */\n function mergeChildMatches (childMatches) {\n if (childMatches.length === 0) {\n return childMatches\n }\n\n const sets = childMatches.reduce(combineChildMatches)\n const uniqueSets = []\n const unique = {}\n for (let i = 0; i < sets.length; i++) {\n const s = JSON.stringify(sets[i])\n if (!unique[s]) {\n unique[s] = true\n uniqueSets.push(sets[i])\n }\n }\n return uniqueSets\n }\n\n /**\n * Determines whether node matches rule.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} rule\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @return {Object} Information about the match, if it exists.\n */\n function _ruleMatch (rule, node, isSplit) {\n // console.log('Entering _ruleMatch(' + JSON.stringify(rule) + ', ' + JSON.stringify(node) + ')')\n // console.log('rule = ' + rule)\n // console.log('node = ' + node)\n\n // console.log('Entering _ruleMatch(' + rule.toString() + ', ' + node.toString() + ')')\n let res = [{ placeholders: {} }]\n\n if ((rule instanceof OperatorNode && node instanceof OperatorNode) ||\n (rule instanceof FunctionNode && node instanceof FunctionNode)) {\n // If the rule is an OperatorNode or a FunctionNode, then node must match exactly\n if (rule instanceof OperatorNode) {\n if (rule.op !== node.op || rule.fn !== node.fn) {\n return []\n }\n } else if (rule instanceof FunctionNode) {\n if (rule.name !== node.name) {\n return []\n }\n }\n\n // rule and node match. Search the children of rule and node.\n if ((node.args.length === 1 && rule.args.length === 1) || !isAssociative(node) || isSplit) {\n // Expect non-associative operators to match exactly\n const childMatches = []\n for (let i = 0; i < rule.args.length; i++) {\n const childMatch = _ruleMatch(rule.args[i], node.args[i])\n if (childMatch.length === 0) {\n // Child did not match, so stop searching immediately\n return []\n }\n // The child matched, so add the information returned from the child to our result\n childMatches.push(childMatch)\n }\n res = mergeChildMatches(childMatches)\n } else if (node.args.length >= 2 && rule.args.length === 2) { // node is flattened, rule is not\n // Associative operators/functions can be split in different ways so we check if the rule matches each\n // them and return their union.\n const splits = getSplits(node, rule.context)\n let splitMatches = []\n for (let i = 0; i < splits.length; i++) {\n const matchSet = _ruleMatch(rule, splits[i], true) // recursing at the same tree depth here\n splitMatches = splitMatches.concat(matchSet)\n }\n return splitMatches\n } else if (rule.args.length > 2) {\n throw Error('Unexpected non-binary associative function: ' + rule.toString())\n } else {\n // Incorrect number of arguments in rule and node, so no match\n return []\n }\n } else if (rule instanceof SymbolNode) {\n // If the rule is a SymbolNode, then it carries a special meaning\n // according to the first character of the symbol node name.\n // c.* matches a ConstantNode\n // n.* matches any node\n if (rule.name.length === 0) {\n throw new Error('Symbol in rule has 0 length...!?')\n }\n if (SUPPORTED_CONSTANTS[rule.name]) {\n // built-in constant must match exactly\n if (rule.name !== node.name) {\n return []\n }\n } else if (rule.name[0] === 'n' || rule.name.substring(0, 2) === '_p') {\n // rule matches _anything_, so assign this node to the rule.name placeholder\n // Assign node to the rule.name placeholder.\n // Our parent will check for matches among placeholders.\n res[0].placeholders[rule.name] = node\n } else if (rule.name[0] === 'v') {\n // rule matches any variable thing (not a ConstantNode)\n if (!isConstantNode(node)) {\n res[0].placeholders[rule.name] = node\n } else {\n // Mis-match: rule was expecting something other than a ConstantNode\n return []\n }\n } else if (rule.name[0] === 'c') {\n // rule matches any ConstantNode\n if (node instanceof ConstantNode) {\n res[0].placeholders[rule.name] = node\n } else {\n // Mis-match: rule was expecting a ConstantNode\n return []\n }\n } else {\n throw new Error('Invalid symbol in rule: ' + rule.name)\n }\n } else if (rule instanceof ConstantNode) {\n // Literal constant must match exactly\n if (!equal(rule.value, node.value)) {\n return []\n }\n } else {\n // Some other node was encountered which we aren't prepared for, so no match\n return []\n }\n\n // It's a match!\n\n // console.log('_ruleMatch(' + rule.toString() + ', ' + node.toString() + ') found a match')\n return res\n }\n\n /**\n * Determines whether p and q (and all their children nodes) are identical.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} p\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} q\n * @return {Object} Information about the match, if it exists.\n */\n function _exactMatch (p, q) {\n if (p instanceof ConstantNode && q instanceof ConstantNode) {\n if (!equal(p.value, q.value)) {\n return false\n }\n } else if (p instanceof SymbolNode && q instanceof SymbolNode) {\n if (p.name !== q.name) {\n return false\n }\n } else if ((p instanceof OperatorNode && q instanceof OperatorNode) ||\n (p instanceof FunctionNode && q instanceof FunctionNode)) {\n if (p instanceof OperatorNode) {\n if (p.op !== q.op || p.fn !== q.fn) {\n return false\n }\n } else if (p instanceof FunctionNode) {\n if (p.name !== q.name) {\n return false\n }\n }\n\n if (p.args.length !== q.args.length) {\n return false\n }\n\n for (let i = 0; i < p.args.length; i++) {\n if (!_exactMatch(p.args[i], q.args[i])) {\n return false\n }\n }\n } else {\n return false\n }\n\n return true\n }\n\n return simplify\n})\n","import { isConstantNode, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'derivative'\nconst dependencies = [\n 'typed',\n 'config',\n 'parse',\n 'simplify',\n 'equal',\n 'isZero',\n 'numeric',\n 'ConstantNode',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'SymbolNode'\n]\n\nexport const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n config,\n parse,\n simplify,\n equal,\n isZero,\n numeric,\n ConstantNode,\n FunctionNode,\n OperatorNode,\n ParenthesisNode,\n SymbolNode\n}) => {\n /**\n * Takes the derivative of an expression expressed in parser Nodes.\n * The derivative will be taken over the supplied variable in the\n * second parameter. If there are multiple variables in the expression,\n * it will return a partial derivative.\n *\n * This uses rules of differentiation which can be found here:\n *\n * - [Differentiation rules (Wikipedia)](https://en.wikipedia.org/wiki/Differentiation_rules)\n *\n * Syntax:\n *\n * derivative(expr, variable)\n * derivative(expr, variable, options)\n *\n * Examples:\n *\n * math.derivative('x^2', 'x') // Node {2 * x}\n * math.derivative('x^2', 'x', {simplify: false}) // Node {2 * 1 * x ^ (2 - 1)\n * math.derivative('sin(2x)', 'x')) // Node {2 * cos(2 * x)}\n * math.derivative('2*x', 'x').evaluate() // number 2\n * math.derivative('x^2', 'x').evaluate({x: 4}) // number 8\n * const f = math.parse('x^2')\n * const x = math.parse('x')\n * math.derivative(f, x) // Node {2 * x}\n *\n * See also:\n *\n * simplify, parse, evaluate\n *\n * @param {Node | string} expr The expression to differentiate\n * @param {SymbolNode | string} variable The variable over which to differentiate\n * @param {{simplify: boolean}} [options]\n * There is one option available, `simplify`, which\n * is true by default. When false, output will not\n * be simplified.\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The derivative of `expr`\n */\n const derivative = typed('derivative', {\n 'Node, SymbolNode, Object': function (expr, variable, options) {\n const constNodes = {}\n constTag(constNodes, expr, variable.name)\n const res = _derivative(expr, constNodes)\n return options.simplify ? simplify(res) : res\n },\n 'Node, SymbolNode': function (expr, variable) {\n return this(expr, variable, { simplify: true })\n },\n\n 'string, SymbolNode': function (expr, variable) {\n return this(parse(expr), variable)\n },\n 'string, SymbolNode, Object': function (expr, variable, options) {\n return this(parse(expr), variable, options)\n },\n\n 'string, string': function (expr, variable) {\n return this(parse(expr), parse(variable))\n },\n 'string, string, Object': function (expr, variable, options) {\n return this(parse(expr), parse(variable), options)\n },\n\n 'Node, string': function (expr, variable) {\n return this(expr, parse(variable))\n },\n 'Node, string, Object': function (expr, variable, options) {\n return this(expr, parse(variable), options)\n }\n\n // TODO: replace the 8 signatures above with 4 as soon as typed-function supports optional arguments\n\n /* TODO: implement and test syntax with order of derivatives -> implement as an option {order: number}\n 'Node, SymbolNode, ConstantNode': function (expr, variable, {order}) {\n let res = expr\n for (let i = 0; i < order; i++) {\n let constNodes = {}\n constTag(constNodes, expr, variable.name)\n res = _derivative(res, constNodes)\n }\n return res\n }\n */\n })\n\n derivative._simplify = true\n\n derivative.toTex = function (deriv) {\n return _derivTex.apply(null, deriv.args)\n }\n\n // FIXME: move the toTex method of derivative to latex.js. Difficulty is that it relies on parse.\n // NOTE: the optional \"order\" parameter here is currently unused\n const _derivTex = typed('_derivTex', {\n 'Node, SymbolNode': function (expr, x) {\n if (isConstantNode(expr) && typeOf(expr.value) === 'string') {\n return _derivTex(parse(expr.value).toString(), x.toString(), 1)\n } else {\n return _derivTex(expr.toString(), x.toString(), 1)\n }\n },\n 'Node, ConstantNode': function (expr, x) {\n if (typeOf(x.value) === 'string') {\n return _derivTex(expr, parse(x.value))\n } else {\n throw new Error(\"The second parameter to 'derivative' is a non-string constant\")\n }\n },\n 'Node, SymbolNode, ConstantNode': function (expr, x, order) {\n return _derivTex(expr.toString(), x.name, order.value)\n },\n 'string, string, number': function (expr, x, order) {\n let d\n if (order === 1) {\n d = '{d\\\\over d' + x + '}'\n } else {\n d = '{d^{' + order + '}\\\\over d' + x + '^{' + order + '}}'\n }\n return d + `\\\\left[${expr}\\\\right]`\n }\n })\n\n /**\n * Does a depth-first search on the expression tree to identify what Nodes\n * are constants (e.g. 2 + 2), and stores the ones that are constants in\n * constNodes. Classification is done as follows:\n *\n * 1. ConstantNodes are constants.\n * 2. If there exists a SymbolNode, of which we are differentiating over,\n * in the subtree it is not constant.\n *\n * @param {Object} constNodes Holds the nodes that are constant\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @param {string} varName Variable that we are differentiating\n * @return {boolean} if node is constant\n */\n // TODO: can we rewrite constTag into a pure function?\n const constTag = typed('constTag', {\n 'Object, ConstantNode, string': function (constNodes, node) {\n constNodes[node] = true\n return true\n },\n\n 'Object, SymbolNode, string': function (constNodes, node, varName) {\n // Treat other variables like constants. For reasoning, see:\n // https://en.wikipedia.org/wiki/Partial_derivative\n if (node.name !== varName) {\n constNodes[node] = true\n return true\n }\n return false\n },\n\n 'Object, ParenthesisNode, string': function (constNodes, node, varName) {\n return constTag(constNodes, node.content, varName)\n },\n\n 'Object, FunctionAssignmentNode, string': function (constNodes, node, varName) {\n if (node.params.indexOf(varName) === -1) {\n constNodes[node] = true\n return true\n }\n return constTag(constNodes, node.expr, varName)\n },\n\n 'Object, FunctionNode | OperatorNode, string': function (constNodes, node, varName) {\n if (node.args.length > 0) {\n let isConst = constTag(constNodes, node.args[0], varName)\n for (let i = 1; i < node.args.length; ++i) {\n isConst = constTag(constNodes, node.args[i], varName) && isConst\n }\n\n if (isConst) {\n constNodes[node] = true\n return true\n }\n }\n return false\n }\n })\n\n /**\n * Applies differentiation rules.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @param {Object} constNodes Holds the nodes that are constant\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The derivative of `expr`\n */\n const _derivative = typed('_derivative', {\n 'ConstantNode, Object': function (node) {\n return createConstantNode(0)\n },\n\n 'SymbolNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n return createConstantNode(1)\n },\n\n 'ParenthesisNode, Object': function (node, constNodes) {\n return new ParenthesisNode(_derivative(node.content, constNodes))\n },\n\n 'FunctionAssignmentNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n return _derivative(node.expr, constNodes)\n },\n\n 'FunctionNode, Object': function (node, constNodes) {\n if (node.args.length !== 1) {\n funcArgsCheck(node)\n }\n\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n\n const arg0 = node.args[0]\n let arg1\n\n let div = false // is output a fraction?\n let negative = false // is output negative?\n\n let funcDerivative\n switch (node.name) {\n case 'cbrt':\n // d/dx(cbrt(x)) = 1 / (3x^(2/3))\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n createConstantNode(3),\n new OperatorNode('^', 'pow', [\n arg0,\n new OperatorNode('/', 'divide', [\n createConstantNode(2),\n createConstantNode(3)\n ])\n ])\n ])\n break\n case 'sqrt':\n case 'nthRoot':\n // d/dx(sqrt(x)) = 1 / (2*sqrt(x))\n if (node.args.length === 1) {\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n createConstantNode(2),\n new FunctionNode('sqrt', [arg0])\n ])\n } else if (node.args.length === 2) {\n // Rearrange from nthRoot(x, a) -> x^(1/a)\n arg1 = new OperatorNode('/', 'divide', [\n createConstantNode(1),\n node.args[1]\n ])\n\n // Is a variable?\n constNodes[arg1] = constNodes[node.args[1]]\n\n return _derivative(new OperatorNode('^', 'pow', [arg0, arg1]), constNodes)\n }\n break\n case 'log10':\n arg1 = createConstantNode(10)\n /* fall through! */\n case 'log':\n if (!arg1 && node.args.length === 1) {\n // d/dx(log(x)) = 1 / x\n funcDerivative = arg0.clone()\n div = true\n } else if ((node.args.length === 1 && arg1) ||\n (node.args.length === 2 && constNodes[node.args[1]] !== undefined)) {\n // d/dx(log(x, c)) = 1 / (x*ln(c))\n funcDerivative = new OperatorNode('*', 'multiply', [\n arg0.clone(),\n new FunctionNode('log', [arg1 || node.args[1]])\n ])\n div = true\n } else if (node.args.length === 2) {\n // d/dx(log(f(x), g(x))) = d/dx(log(f(x)) / log(g(x)))\n return _derivative(new OperatorNode('/', 'divide', [\n new FunctionNode('log', [arg0]),\n new FunctionNode('log', [node.args[1]])\n ]), constNodes)\n }\n break\n case 'pow':\n constNodes[arg1] = constNodes[node.args[1]]\n // Pass to pow operator node parser\n return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes)\n case 'exp':\n // d/dx(e^x) = e^x\n funcDerivative = new FunctionNode('exp', [arg0.clone()])\n break\n case 'sin':\n // d/dx(sin(x)) = cos(x)\n funcDerivative = new FunctionNode('cos', [arg0.clone()])\n break\n case 'cos':\n // d/dx(cos(x)) = -sin(x)\n funcDerivative = new OperatorNode('-', 'unaryMinus', [\n new FunctionNode('sin', [arg0.clone()])\n ])\n break\n case 'tan':\n // d/dx(tan(x)) = sec(x)^2\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('sec', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'sec':\n // d/dx(sec(x)) = sec(x)tan(x)\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('tan', [arg0.clone()])\n ])\n break\n case 'csc':\n // d/dx(csc(x)) = -csc(x)cot(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('cot', [arg0.clone()])\n ])\n break\n case 'cot':\n // d/dx(cot(x)) = -csc(x)^2\n negative = true\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('csc', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'asin':\n // d/dx(asin(x)) = 1 / sqrt(1 - x^2)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n break\n case 'acos':\n // d/dx(acos(x)) = -1 / sqrt(1 - x^2)\n div = true\n negative = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n break\n case 'atan':\n // d/dx(atan(x)) = 1 / (x^2 + 1)\n div = true\n funcDerivative = new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n break\n case 'asec':\n // d/dx(asec(x)) = 1 / (|x|*sqrt(x^2 - 1))\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acsc':\n // d/dx(acsc(x)) = -1 / (|x|*sqrt(x^2 - 1))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acot':\n // d/dx(acot(x)) = -1 / (x^2 + 1)\n div = true\n negative = true\n funcDerivative = new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n break\n case 'sinh':\n // d/dx(sinh(x)) = cosh(x)\n funcDerivative = new FunctionNode('cosh', [arg0.clone()])\n break\n case 'cosh':\n // d/dx(cosh(x)) = sinh(x)\n funcDerivative = new FunctionNode('sinh', [arg0.clone()])\n break\n case 'tanh':\n // d/dx(tanh(x)) = sech(x)^2\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('sech', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'sech':\n // d/dx(sech(x)) = -sech(x)tanh(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('tanh', [arg0.clone()])\n ])\n break\n case 'csch':\n // d/dx(csch(x)) = -csch(x)coth(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('coth', [arg0.clone()])\n ])\n break\n case 'coth':\n // d/dx(coth(x)) = -csch(x)^2\n negative = true\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('csch', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'asinh':\n // d/dx(asinh(x)) = 1 / sqrt(x^2 + 1)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n break\n case 'acosh':\n // d/dx(acosh(x)) = 1 / sqrt(x^2 - 1); XXX potentially only for x >= 1 (the real spectrum)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n break\n case 'atanh':\n // d/dx(atanh(x)) = 1 / (1 - x^2)\n div = true\n funcDerivative = new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n break\n case 'asech':\n // d/dx(asech(x)) = -1 / (x*sqrt(1 - x^2))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n arg0.clone(),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n ])\n break\n case 'acsch':\n // d/dx(acsch(x)) = -1 / (|x|*sqrt(x^2 + 1))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acoth':\n // d/dx(acoth(x)) = -1 / (1 - x^2)\n div = true\n negative = true\n funcDerivative = new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n break\n case 'abs':\n // d/dx(abs(x)) = abs(x)/x\n funcDerivative = new OperatorNode('/', 'divide', [\n new FunctionNode(new SymbolNode('abs'), [arg0.clone()]),\n arg0.clone()\n ])\n break\n case 'gamma': // Needs digamma function, d/dx(gamma(x)) = gamma(x)digamma(x)\n default: throw new Error('Function \"' + node.name + '\" is not supported by derivative, or a wrong number of arguments is passed')\n }\n\n let op, func\n if (div) {\n op = '/'\n func = 'divide'\n } else {\n op = '*'\n func = 'multiply'\n }\n\n /* Apply chain rule to all functions:\n F(x) = f(g(x))\n F'(x) = g'(x)*f'(g(x)) */\n let chainDerivative = _derivative(arg0, constNodes)\n if (negative) {\n chainDerivative = new OperatorNode('-', 'unaryMinus', [chainDerivative])\n }\n return new OperatorNode(op, func, [chainDerivative, funcDerivative])\n },\n\n 'OperatorNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n\n if (node.op === '+') {\n // d/dx(sum(f(x)) = sum(f'(x))\n return new OperatorNode(node.op, node.fn, node.args.map(function (arg) {\n return _derivative(arg, constNodes)\n }))\n }\n\n if (node.op === '-') {\n // d/dx(+/-f(x)) = +/-f'(x)\n if (node.isUnary()) {\n return new OperatorNode(node.op, node.fn, [\n _derivative(node.args[0], constNodes)\n ])\n }\n\n // Linearity of differentiation, d/dx(f(x) +/- g(x)) = f'(x) +/- g'(x)\n if (node.isBinary()) {\n return new OperatorNode(node.op, node.fn, [\n _derivative(node.args[0], constNodes),\n _derivative(node.args[1], constNodes)\n ])\n }\n }\n\n if (node.op === '*') {\n // d/dx(c*f(x)) = c*f'(x)\n const constantTerms = node.args.filter(function (arg) {\n return constNodes[arg] !== undefined\n })\n\n if (constantTerms.length > 0) {\n const nonConstantTerms = node.args.filter(function (arg) {\n return constNodes[arg] === undefined\n })\n\n const nonConstantNode = nonConstantTerms.length === 1\n ? nonConstantTerms[0]\n : new OperatorNode('*', 'multiply', nonConstantTerms)\n\n const newArgs = constantTerms.concat(_derivative(nonConstantNode, constNodes))\n\n return new OperatorNode('*', 'multiply', newArgs)\n }\n\n // Product Rule, d/dx(f(x)*g(x)) = f'(x)*g(x) + f(x)*g'(x)\n return new OperatorNode('+', 'add', node.args.map(function (argOuter) {\n return new OperatorNode('*', 'multiply', node.args.map(function (argInner) {\n return (argInner === argOuter)\n ? _derivative(argInner, constNodes)\n : argInner.clone()\n }))\n }))\n }\n\n if (node.op === '/' && node.isBinary()) {\n const arg0 = node.args[0]\n const arg1 = node.args[1]\n\n // d/dx(f(x) / c) = f'(x) / c\n if (constNodes[arg1] !== undefined) {\n return new OperatorNode('/', 'divide', [_derivative(arg0, constNodes), arg1])\n }\n\n // Reciprocal Rule, d/dx(c / f(x)) = -c(f'(x)/f(x)^2)\n if (constNodes[arg0] !== undefined) {\n return new OperatorNode('*', 'multiply', [\n new OperatorNode('-', 'unaryMinus', [arg0]),\n new OperatorNode('/', 'divide', [\n _derivative(arg1, constNodes),\n new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])\n ])\n ])\n }\n\n // Quotient rule, d/dx(f(x) / g(x)) = (f'(x)g(x) - f(x)g'(x)) / g(x)^2\n return new OperatorNode('/', 'divide', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('*', 'multiply', [_derivative(arg0, constNodes), arg1.clone()]),\n new OperatorNode('*', 'multiply', [arg0.clone(), _derivative(arg1, constNodes)])\n ]),\n new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])\n ])\n }\n\n if (node.op === '^' && node.isBinary()) {\n const arg0 = node.args[0]\n const arg1 = node.args[1]\n\n if (constNodes[arg0] !== undefined) {\n // If is secretly constant; 0^f(x) = 1 (in JS), 1^f(x) = 1\n if (isConstantNode(arg0) && (isZero(arg0.value) || equal(arg0.value, 1))) {\n return createConstantNode(0)\n }\n\n // d/dx(c^f(x)) = c^f(x)*ln(c)*f'(x)\n return new OperatorNode('*', 'multiply', [\n node,\n new OperatorNode('*', 'multiply', [\n new FunctionNode('log', [arg0.clone()]),\n _derivative(arg1.clone(), constNodes)\n ])\n ])\n }\n\n if (constNodes[arg1] !== undefined) {\n if (isConstantNode(arg1)) {\n // If is secretly constant; f(x)^0 = 1 -> d/dx(1) = 0\n if (isZero(arg1.value)) {\n return createConstantNode(0)\n }\n // Ignore exponent; f(x)^1 = f(x)\n if (equal(arg1.value, 1)) {\n return _derivative(arg0, constNodes)\n }\n }\n\n // Elementary Power Rule, d/dx(f(x)^c) = c*f'(x)*f(x)^(c-1)\n const powMinusOne = new OperatorNode('^', 'pow', [\n arg0.clone(),\n new OperatorNode('-', 'subtract', [\n arg1,\n createConstantNode(1)\n ])\n ])\n\n return new OperatorNode('*', 'multiply', [\n arg1.clone(),\n new OperatorNode('*', 'multiply', [\n _derivative(arg0, constNodes),\n powMinusOne\n ])\n ])\n }\n\n // Functional Power Rule, d/dx(f^g) = f^g*[f'*(g/f) + g'ln(f)]\n return new OperatorNode('*', 'multiply', [\n new OperatorNode('^', 'pow', [arg0.clone(), arg1.clone()]),\n new OperatorNode('+', 'add', [\n new OperatorNode('*', 'multiply', [\n _derivative(arg0, constNodes),\n new OperatorNode('/', 'divide', [arg1.clone(), arg0.clone()])\n ]),\n new OperatorNode('*', 'multiply', [\n _derivative(arg1, constNodes),\n new FunctionNode('log', [arg0.clone()])\n ])\n ])\n ])\n }\n\n throw new Error('Operator \"' + node.op + '\" is not supported by derivative, or a wrong number of arguments is passed')\n }\n })\n\n /**\n * Ensures the number of arguments for a function are correct,\n * and will throw an error otherwise.\n *\n * @param {FunctionNode} node\n */\n function funcArgsCheck (node) {\n // TODO add min, max etc\n if ((node.name === 'log' || node.name === 'nthRoot' || node.name === 'pow') && node.args.length === 2) {\n return\n }\n\n // There should be an incorrect number of arguments if we reach here\n\n // Change all args to constants to avoid unidentified\n // symbol error when compiling function\n for (let i = 0; i < node.args.length; ++i) {\n node.args[i] = createConstantNode(0)\n }\n\n node.compile().evaluate()\n throw new Error('Expected TypeError, but none found')\n }\n\n /**\n * Helper function to create a constant node with a specific type\n * (number, BigNumber, Fraction)\n * @param {number} value\n * @param {string} [valueType]\n * @return {ConstantNode}\n */\n function createConstantNode (value, valueType) {\n return new ConstantNode(numeric(value, valueType || config.number))\n }\n\n return derivative\n})\n","import { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createSimplifyConstant } from './simplify/simplifyConstant.js'\nimport { createSimplifyCore } from './simplify/simplifyCore.js'\n\nconst name = 'rationalize'\nconst dependencies = [\n 'config',\n 'typed',\n 'equal',\n 'isZero',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'parse',\n 'simplify',\n '?bignumber',\n '?fraction',\n 'mathWithTransform',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'SymbolNode',\n 'ParenthesisNode'\n]\n\nexport const createRationalize = /* #__PURE__ */ factory(name, dependencies, ({\n config,\n typed,\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n parse,\n simplify,\n fraction,\n bignumber,\n mathWithTransform,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode,\n ParenthesisNode\n}) => {\n const simplifyConstant = createSimplifyConstant({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n })\n const simplifyCore = createSimplifyCore({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n })\n\n /**\n * Transform a rationalizable expression in a rational fraction.\n * If rational fraction is one variable polynomial then converts\n * the numerator and denominator in canonical form, with decreasing\n * exponents, returning the coefficients of numerator.\n *\n * Syntax:\n *\n * rationalize(expr)\n * rationalize(expr, detailed)\n * rationalize(expr, scope)\n * rationalize(expr, scope, detailed)\n *\n * Examples:\n *\n * math.rationalize('sin(x)+y')\n * // Error: There is an unsolved function call\n * math.rationalize('2x/y - y/(x+1)')\n * // (2*x^2-y^2+2*x)/(x*y+y)\n * math.rationalize('(2x+1)^6')\n * // 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1\n * math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3')\n * // -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4)\n * math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') =\n * // (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/\n * // (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72)\n *\n * math.rationalize('x+x+x+y',{y:1}) // 3*x+1\n * math.rationalize('x+x+x+y',{}) // 3*x+y\n *\n * const ret = math.rationalize('x+x+x+y',{},true)\n * // ret.expression=3*x+y, ret.variables = [\"x\",\"y\"]\n * const ret = math.rationalize('-2+5x^2',{},true)\n * // ret.expression=5*x^2-2, ret.variables = [\"x\"], ret.coefficients=[-2,0,5]\n *\n * See also:\n *\n * simplify\n *\n * @param {Node|string} expr The expression to check if is a polynomial expression\n * @param {Object|boolean} optional scope of expression or true for already evaluated rational expression at input\n * @param {Boolean} detailed optional True if return an object, false if return expression node (default)\n *\n * @return {Object | Node} The rational polynomial of `expr` or na object\n * {Object}\n * {Expression Node} expression: node simplified expression\n * {Expression Node} numerator: simplified numerator of expression\n * {Expression Node | boolean} denominator: simplified denominator or false (if there is no denominator)\n * {Array} variables: variable names\n * {Array} coefficients: coefficients of numerator sorted by increased exponent\n * {Expression Node} node simplified expression\n *\n */\n return typed(name, {\n string: function (expr) {\n return this(parse(expr), {}, false)\n },\n\n 'string, boolean': function (expr, detailed) {\n return this(parse(expr), {}, detailed)\n },\n\n 'string, Object': function (expr, scope) {\n return this(parse(expr), scope, false)\n },\n\n 'string, Object, boolean': function (expr, scope, detailed) {\n return this(parse(expr), scope, detailed)\n },\n\n Node: function (expr) {\n return this(expr, {}, false)\n },\n\n 'Node, boolean': function (expr, detailed) {\n return this(expr, {}, detailed)\n },\n\n 'Node, Object': function (expr, scope) {\n return this(expr, scope, false)\n },\n\n 'Node, Object, boolean': function (expr, scope, detailed) {\n const setRules = rulesRationalize() // Rules for change polynomial in near canonical form\n const polyRet = polynomial(expr, scope, true, setRules.firstRules) // Check if expression is a rationalizable polynomial\n const nVars = polyRet.variables.length\n expr = polyRet.expression\n\n if (nVars >= 1) { // If expression in not a constant\n expr = expandPower(expr) // First expand power of polynomials (cannot be made from rules!)\n let sBefore // Previous expression\n let rules\n let eDistrDiv = true\n let redoInic = false\n expr = simplify(expr, setRules.firstRules, {}, { exactFractions: false }) // Apply the initial rules, including succ div rules\n let s\n while (true) { // Apply alternately successive division rules and distr.div.rules\n rules = eDistrDiv ? setRules.distrDivRules : setRules.sucDivRules\n expr = simplify(expr, rules) // until no more changes\n eDistrDiv = !eDistrDiv // Swap between Distr.Div and Succ. Div. Rules\n\n s = expr.toString()\n if (s === sBefore) {\n break // No changes : end of the loop\n }\n\n redoInic = true\n sBefore = s\n }\n\n if (redoInic) { // Apply first rules again without succ div rules (if there are changes)\n expr = simplify(expr, setRules.firstRulesAgain, {}, { exactFractions: false })\n }\n expr = simplify(expr, setRules.finalRules, {}, { exactFractions: false }) // Apply final rules\n } // NVars >= 1\n\n const coefficients = []\n const retRationalize = {}\n\n if (expr.type === 'OperatorNode' && expr.isBinary() && expr.op === '/') { // Separate numerator from denominator\n if (nVars === 1) {\n expr.args[0] = polyToCanonical(expr.args[0], coefficients)\n expr.args[1] = polyToCanonical(expr.args[1])\n }\n if (detailed) {\n retRationalize.numerator = expr.args[0]\n retRationalize.denominator = expr.args[1]\n }\n } else {\n if (nVars === 1) {\n expr = polyToCanonical(expr, coefficients)\n }\n if (detailed) {\n retRationalize.numerator = expr\n retRationalize.denominator = null\n }\n }\n // nVars\n\n if (!detailed) return expr\n retRationalize.coefficients = coefficients\n retRationalize.variables = polyRet.variables\n retRationalize.expression = expr\n return retRationalize\n } // ^^^^^^^ end of rationalize ^^^^^^^^\n }) // end of typed rationalize\n\n /**\n * Function to simplify an expression using an optional scope and\n * return it if the expression is a polynomial expression, i.e.\n * an expression with one or more variables and the operators\n * +, -, *, and ^, where the exponent can only be a positive integer.\n *\n * Syntax:\n *\n * polynomial(expr,scope,extended, rules)\n *\n * @param {Node | string} expr The expression to simplify and check if is polynomial expression\n * @param {object} scope Optional scope for expression simplification\n * @param {boolean} extended Optional. Default is false. When true allows divide operator.\n * @param {array} rules Optional. Default is no rule.\n *\n *\n * @return {Object}\n * {Object} node: node simplified expression\n * {Array} variables: variable names\n */\n function polynomial (expr, scope, extended, rules) {\n const variables = []\n const node = simplify(expr, rules, scope, { exactFractions: false }) // Resolves any variables and functions with all defined parameters\n extended = !!extended\n\n const oper = '+-*' + (extended ? '/' : '')\n recPoly(node)\n const retFunc = {}\n retFunc.expression = node\n retFunc.variables = variables\n return retFunc\n\n // -------------------------------------------------------------------------------------------------------\n\n /**\n * Function to simplify an expression using an optional scope and\n * return it if the expression is a polynomial expression, i.e.\n * an expression with one or more variables and the operators\n * +, -, *, and ^, where the exponent can only be a positive integer.\n *\n * Syntax:\n *\n * recPoly(node)\n *\n *\n * @param {Node} node The current sub tree expression in recursion\n *\n * @return nothing, throw an exception if error\n */\n function recPoly (node) {\n const tp = node.type // node type\n if (tp === 'FunctionNode') {\n // No function call in polynomial expression\n throw new Error('There is an unsolved function call')\n } else if (tp === 'OperatorNode') {\n if (node.op === '^') {\n // TODO: handle negative exponents like in '1/x^(-2)'\n if (node.args[1].type !== 'ConstantNode' || !isInteger(parseFloat(node.args[1].value))) {\n throw new Error('There is a non-integer exponent')\n } else {\n recPoly(node.args[0])\n }\n } else {\n if (oper.indexOf(node.op) === -1) {\n throw new Error('Operator ' + node.op + ' invalid in polynomial expression')\n }\n for (let i = 0; i < node.args.length; i++) {\n recPoly(node.args[i])\n }\n } // type of operator\n } else if (tp === 'SymbolNode') {\n const name = node.name // variable name\n const pos = variables.indexOf(name)\n if (pos === -1) {\n // new variable in expression\n variables.push(name)\n }\n } else if (tp === 'ParenthesisNode') {\n recPoly(node.content)\n } else if (tp !== 'ConstantNode') {\n throw new Error('type ' + tp + ' is not allowed in polynomial expression')\n }\n } // end of recPoly\n } // end of polynomial\n\n // ---------------------------------------------------------------------------------------\n /**\n * Return a rule set to rationalize an polynomial expression in rationalize\n *\n * Syntax:\n *\n * rulesRationalize()\n *\n * @return {array} rule set to rationalize an polynomial expression\n */\n function rulesRationalize () {\n const oldRules = [simplifyCore, // sCore\n { l: 'n+n', r: '2*n' },\n { l: 'n+-n', r: '0' },\n simplifyConstant, // sConstant\n { l: 'n*(n1^-1)', r: 'n/n1' },\n { l: 'n*n1^-n2', r: 'n/n1^n2' },\n { l: 'n1^-1', r: '1/n1' },\n { l: 'n*(n1/n2)', r: '(n*n1)/n2' },\n { l: '1*n', r: 'n' }]\n\n const rulesFirst = [\n { l: '(-n1)/(-n2)', r: 'n1/n2' }, // Unary division\n { l: '(-n1)*(-n2)', r: 'n1*n2' }, // Unary multiplication\n { l: 'n1--n2', r: 'n1+n2' }, // '--' elimination\n { l: 'n1-n2', r: 'n1+(-n2)' }, // Subtraction turn into add with un�ry minus\n { l: '(n1+n2)*n3', r: '(n1*n3 + n2*n3)' }, // Distributive 1\n { l: 'n1*(n2+n3)', r: '(n1*n2+n1*n3)' }, // Distributive 2\n { l: 'c1*n + c2*n', r: '(c1+c2)*n' }, // Joining constants\n { l: 'c1*n + n', r: '(c1+1)*n' }, // Joining constants\n { l: 'c1*n - c2*n', r: '(c1-c2)*n' }, // Joining constants\n { l: 'c1*n - n', r: '(c1-1)*n' }, // Joining constants\n { l: 'v/c', r: '(1/c)*v' }, // variable/constant (new!)\n { l: 'v/-c', r: '-(1/c)*v' }, // variable/constant (new!)\n { l: '-v*-c', r: 'c*v' }, // Inversion constant and variable 1\n { l: '-v*c', r: '-c*v' }, // Inversion constant and variable 2\n { l: 'v*-c', r: '-c*v' }, // Inversion constant and variable 3\n { l: 'v*c', r: 'c*v' }, // Inversion constant and variable 4\n { l: '-(-n1*n2)', r: '(n1*n2)' }, // Unary propagation\n { l: '-(n1*n2)', r: '(-n1*n2)' }, // Unary propagation\n { l: '-(-n1+n2)', r: '(n1-n2)' }, // Unary propagation\n { l: '-(n1+n2)', r: '(-n1-n2)' }, // Unary propagation\n { l: '(n1^n2)^n3', r: '(n1^(n2*n3))' }, // Power to Power\n { l: '-(-n1/n2)', r: '(n1/n2)' }, // Division and Unary\n { l: '-(n1/n2)', r: '(-n1/n2)' }] // Divisao and Unary\n\n const rulesDistrDiv = [\n { l: '(n1/n2 + n3/n4)', r: '((n1*n4 + n3*n2)/(n2*n4))' }, // Sum of fractions\n { l: '(n1/n2 + n3)', r: '((n1 + n3*n2)/n2)' }, // Sum fraction with number 1\n { l: '(n1 + n2/n3)', r: '((n1*n3 + n2)/n3)' }] // Sum fraction with number 1\n\n const rulesSucDiv = [\n { l: '(n1/(n2/n3))', r: '((n1*n3)/n2)' }, // Division simplification\n { l: '(n1/n2/n3)', r: '(n1/(n2*n3))' }]\n\n const setRules = {} // rules set in 4 steps.\n\n // All rules => infinite loop\n // setRules.allRules =oldRules.concat(rulesFirst,rulesDistrDiv,rulesSucDiv)\n\n setRules.firstRules = oldRules.concat(rulesFirst, rulesSucDiv) // First rule set\n setRules.distrDivRules = rulesDistrDiv // Just distr. div. rules\n setRules.sucDivRules = rulesSucDiv // Jus succ. div. rules\n setRules.firstRulesAgain = oldRules.concat(rulesFirst) // Last rules set without succ. div.\n\n // Division simplification\n\n // Second rule set.\n // There is no aggregate expression with parentesis, but the only variable can be scattered.\n setRules.finalRules = [simplifyCore, // simplify.rules[0]\n { l: 'n*-n', r: '-n^2' }, // Joining multiply with power 1\n { l: 'n*n', r: 'n^2' }, // Joining multiply with power 2\n simplifyConstant, // simplify.rules[14] old 3rd index in oldRules\n { l: 'n*-n^n1', r: '-n^(n1+1)' }, // Joining multiply with power 3\n { l: 'n*n^n1', r: 'n^(n1+1)' }, // Joining multiply with power 4\n { l: 'n^n1*-n^n2', r: '-n^(n1+n2)' }, // Joining multiply with power 5\n { l: 'n^n1*n^n2', r: 'n^(n1+n2)' }, // Joining multiply with power 6\n { l: 'n^n1*-n', r: '-n^(n1+1)' }, // Joining multiply with power 7\n { l: 'n^n1*n', r: 'n^(n1+1)' }, // Joining multiply with power 8\n { l: 'n^n1/-n', r: '-n^(n1-1)' }, // Joining multiply with power 8\n { l: 'n^n1/n', r: 'n^(n1-1)' }, // Joining division with power 1\n { l: 'n/-n^n1', r: '-n^(1-n1)' }, // Joining division with power 2\n { l: 'n/n^n1', r: 'n^(1-n1)' }, // Joining division with power 3\n { l: 'n^n1/-n^n2', r: 'n^(n1-n2)' }, // Joining division with power 4\n { l: 'n^n1/n^n2', r: 'n^(n1-n2)' }, // Joining division with power 5\n { l: 'n1+(-n2*n3)', r: 'n1-n2*n3' }, // Solving useless parenthesis 1\n { l: 'v*(-c)', r: '-c*v' }, // Solving useless unary 2\n { l: 'n1+-n2', r: 'n1-n2' }, // Solving +- together (new!)\n { l: 'v*c', r: 'c*v' }, // inversion constant with variable\n { l: '(n1^n2)^n3', r: '(n1^(n2*n3))' } // Power to Power\n\n ]\n return setRules\n } // End rulesRationalize\n\n // ---------------------------------------------------------------------------------------\n /**\n * Expand recursively a tree node for handling with expressions with exponents\n * (it's not for constants, symbols or functions with exponents)\n * PS: The other parameters are internal for recursion\n *\n * Syntax:\n *\n * expandPower(node)\n *\n * @param {Node} node Current expression node\n * @param {node} parent Parent current node inside the recursion\n * @param (int} Parent number of chid inside the rercursion\n *\n * @return {node} node expression with all powers expanded.\n */\n function expandPower (node, parent, indParent) {\n const tp = node.type\n const internal = (arguments.length > 1) // TRUE in internal calls\n\n if (tp === 'OperatorNode' && node.isBinary()) {\n let does = false\n let val\n if (node.op === '^') { // First operator: Parenthesis or UnaryMinus\n if ((node.args[0].type === 'ParenthesisNode' ||\n node.args[0].type === 'OperatorNode') &&\n (node.args[1].type === 'ConstantNode')) { // Second operator: Constant\n val = parseFloat(node.args[1].value)\n does = (val >= 2 && isInteger(val))\n }\n }\n\n if (does) { // Exponent >= 2\n // Before:\n // operator A --> Subtree\n // parent pow\n // constant\n //\n if (val > 2) { // Exponent > 2,\n // AFTER: (exponent > 2)\n // operator A --> Subtree\n // parent *\n // deep clone (operator A --> Subtree\n // pow\n // constant - 1\n //\n const nEsqTopo = node.args[0]\n const nDirTopo = new OperatorNode('^', 'pow', [node.args[0].cloneDeep(), new ConstantNode(val - 1)])\n node = new OperatorNode('*', 'multiply', [nEsqTopo, nDirTopo])\n } else { // Expo = 2 - no power\n // AFTER: (exponent = 2)\n // operator A --> Subtree\n // parent oper\n // deep clone (operator A --> Subtree)\n //\n node = new OperatorNode('*', 'multiply', [node.args[0], node.args[0].cloneDeep()])\n }\n\n if (internal) {\n // Change parent references in internal recursive calls\n if (indParent === 'content') { parent.content = node } else { parent.args[indParent] = node }\n }\n } // does\n } // binary OperatorNode\n\n if (tp === 'ParenthesisNode') {\n // Recursion\n expandPower(node.content, node, 'content')\n } else if (tp !== 'ConstantNode' && tp !== 'SymbolNode') {\n for (let i = 0; i < node.args.length; i++) {\n expandPower(node.args[i], node, i)\n }\n }\n\n if (!internal) {\n // return the root node\n return node\n }\n } // End expandPower\n\n // ---------------------------------------------------------------------------------------\n /**\n * Auxilary function for rationalize\n * Convert near canonical polynomial in one variable in a canonical polynomial\n * with one term for each exponent in decreasing order\n *\n * Syntax:\n *\n * polyToCanonical(node [, coefficients])\n *\n * @param {Node | string} expr The near canonical polynomial expression to convert in a a canonical polynomial expression\n *\n * The string or tree expression needs to be at below syntax, with free spaces:\n * ( (^(-)? | [+-]? )cte (*)? var (^expo)? | cte )+\n * Where 'var' is one variable with any valid name\n * 'cte' are real numeric constants with any value. It can be omitted if equal than 1\n * 'expo' are integers greater than 0. It can be omitted if equal than 1.\n *\n * @param {array} coefficients Optional returns coefficients sorted by increased exponent\n *\n *\n * @return {node} new node tree with one variable polynomial or string error.\n */\n function polyToCanonical (node, coefficients) {\n if (coefficients === undefined) { coefficients = [] } // coefficients.\n\n coefficients[0] = 0 // index is the exponent\n const o = {}\n o.cte = 1\n o.oper = '+'\n\n // fire: mark with * or ^ when finds * or ^ down tree, reset to \"\" with + and -.\n // It is used to deduce the exponent: 1 for *, 0 for \"\".\n o.fire = ''\n\n let maxExpo = 0 // maximum exponent\n let varname = '' // variable name\n\n recurPol(node, null, o)\n maxExpo = coefficients.length - 1\n let first = true\n let no\n\n for (let i = maxExpo; i >= 0; i--) {\n if (coefficients[i] === 0) continue\n let n1 = new ConstantNode(\n first ? coefficients[i] : Math.abs(coefficients[i]))\n const op = coefficients[i] < 0 ? '-' : '+'\n\n if (i > 0) { // Is not a constant without variable\n let n2 = new SymbolNode(varname)\n if (i > 1) {\n const n3 = new ConstantNode(i)\n n2 = new OperatorNode('^', 'pow', [n2, n3])\n }\n if (coefficients[i] === -1 && first) { n1 = new OperatorNode('-', 'unaryMinus', [n2]) } else if (Math.abs(coefficients[i]) === 1) { n1 = n2 } else { n1 = new OperatorNode('*', 'multiply', [n1, n2]) }\n }\n\n if (first) { no = n1 } else if (op === '+') { no = new OperatorNode('+', 'add', [no, n1]) } else { no = new OperatorNode('-', 'subtract', [no, n1]) }\n\n first = false\n } // for\n\n if (first) { return new ConstantNode(0) } else { return no }\n\n /**\n * Recursive auxilary function inside polyToCanonical for\n * converting expression in canonical form\n *\n * Syntax:\n *\n * recurPol(node, noPai, obj)\n *\n * @param {Node} node The current subpolynomial expression\n * @param {Node | Null} noPai The current parent node\n * @param {object} obj Object with many internal flags\n *\n * @return {} No return. If error, throws an exception\n */\n function recurPol (node, noPai, o) {\n const tp = node.type\n if (tp === 'FunctionNode') {\n // ***** FunctionName *****\n // No function call in polynomial expression\n throw new Error('There is an unsolved function call')\n } else if (tp === 'OperatorNode') {\n // ***** OperatorName *****\n if ('+-*^'.indexOf(node.op) === -1) throw new Error('Operator ' + node.op + ' invalid')\n\n if (noPai !== null) {\n // -(unary),^ : children of *,+,-\n if ((node.fn === 'unaryMinus' || node.fn === 'pow') && noPai.fn !== 'add' &&\n noPai.fn !== 'subtract' && noPai.fn !== 'multiply') { throw new Error('Invalid ' + node.op + ' placing') }\n\n // -,+,* : children of +,-\n if ((node.fn === 'subtract' || node.fn === 'add' || node.fn === 'multiply') &&\n noPai.fn !== 'add' && noPai.fn !== 'subtract') { throw new Error('Invalid ' + node.op + ' placing') }\n\n // -,+ : first child\n if ((node.fn === 'subtract' || node.fn === 'add' ||\n node.fn === 'unaryMinus') && o.noFil !== 0) { throw new Error('Invalid ' + node.op + ' placing') }\n } // Has parent\n\n // Firers: ^,* Old: ^,&,-(unary): firers\n if (node.op === '^' || node.op === '*') {\n o.fire = node.op\n }\n\n for (let i = 0; i < node.args.length; i++) {\n // +,-: reset fire\n if (node.fn === 'unaryMinus') o.oper = '-'\n if (node.op === '+' || node.fn === 'subtract') {\n o.fire = ''\n o.cte = 1 // default if there is no constant\n o.oper = (i === 0 ? '+' : node.op)\n }\n o.noFil = i // number of son\n recurPol(node.args[i], node, o)\n } // for in children\n } else if (tp === 'SymbolNode') { // ***** SymbolName *****\n if (node.name !== varname && varname !== '') { throw new Error('There is more than one variable') }\n varname = node.name\n if (noPai === null) {\n coefficients[1] = 1\n return\n }\n\n // ^: Symbol is First child\n if (noPai.op === '^' && o.noFil !== 0) { throw new Error('In power the variable should be the first parameter') }\n\n // *: Symbol is Second child\n if (noPai.op === '*' && o.noFil !== 1) { throw new Error('In multiply the variable should be the second parameter') }\n\n // Symbol: firers '',* => it means there is no exponent above, so it's 1 (cte * var)\n if (o.fire === '' || o.fire === '*') {\n if (maxExpo < 1) coefficients[1] = 0\n coefficients[1] += o.cte * (o.oper === '+' ? 1 : -1)\n maxExpo = Math.max(1, maxExpo)\n }\n } else if (tp === 'ConstantNode') {\n const valor = parseFloat(node.value)\n if (noPai === null) {\n coefficients[0] = valor\n return\n }\n if (noPai.op === '^') {\n // cte: second child of power\n if (o.noFil !== 1) throw new Error('Constant cannot be powered')\n\n if (!isInteger(valor) || valor <= 0) { throw new Error('Non-integer exponent is not allowed') }\n\n for (let i = maxExpo + 1; i < valor; i++) coefficients[i] = 0\n if (valor > maxExpo) coefficients[valor] = 0\n coefficients[valor] += o.cte * (o.oper === '+' ? 1 : -1)\n maxExpo = Math.max(valor, maxExpo)\n return\n }\n o.cte = valor\n\n // Cte: firer '' => There is no exponent and no multiplication, so the exponent is 0.\n if (o.fire === '') { coefficients[0] += o.cte * (o.oper === '+' ? 1 : -1) }\n } else { throw new Error('Type ' + tp + ' is not allowed') }\n } // End of recurPol\n } // End of polyToCanonical\n})\n","import { factory } from '../utils/factory.js'\n\nconst name = 'reviver'\nconst dependencies = [\n 'classes'\n]\n\nexport const createReviver = /* #__PURE__ */ factory(name, dependencies, ({ classes }) => {\n /**\n * Instantiate mathjs data types from their JSON representation\n * @param {string} key\n * @param {*} value\n * @returns {*} Returns the revived object\n */\n return function reviver (key, value) {\n const constructor = classes[value && value.mathjs]\n\n if (constructor && typeof constructor.fromJSON === 'function') {\n return constructor.fromJSON(value)\n }\n\n return value\n }\n})\n","import { factory } from '../utils/factory.js'\n\nconst name = 'replacer'\nconst dependencies = []\n\nexport const createReplacer = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Stringify data types into their JSON representation.\n * Most data types can be serialized using their `.toJSON` method,\n * but not all, for example the number `Infinity`. For these cases you have\n * to use the replacer. Example usage:\n *\n * JSON.stringify([2, Infinity], math.replacer)\n *\n * @param {string} key\n * @param {*} value\n * @returns {*} Returns the replaced object\n */\n return function replacer (key, value) {\n // the numeric values Infinitiy, -Infinity, and NaN cannot be serialized to JSON\n if (typeof value === 'number' && (!isFinite(value) || isNaN(value))) {\n return {\n mathjs: 'number',\n value: String(value)\n }\n }\n\n return value\n }\n})\n","\nexport const pi = Math.PI\nexport const tau = 2 * Math.PI\nexport const e = Math.E\nexport const phi = 1.6180339887498948 // eslint-disable-line no-loss-of-precision\n","import { factory } from './utils/factory.js'\nimport { version } from './version.js'\nimport {\n createBigNumberE,\n createBigNumberPhi,\n createBigNumberPi,\n createBigNumberTau\n} from './utils/bignumber/constants.js'\nimport { pi, tau, e, phi } from './plain/number/index.js'\n\nexport const createTrue = /* #__PURE__ */ factory('true', [], () => true)\nexport const createFalse = /* #__PURE__ */ factory('false', [], () => false)\nexport const createNull = /* #__PURE__ */ factory('null', [], () => null)\n\nexport const createInfinity = /* #__PURE__ */ recreateFactory(\n 'Infinity',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(Infinity)\n : Infinity\n)\n\nexport const createNaN = /* #__PURE__ */ recreateFactory(\n 'NaN',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(NaN)\n : NaN\n)\n\nexport const createPi = /* #__PURE__ */ recreateFactory(\n 'pi',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberPi(BigNumber)\n : pi\n)\n\nexport const createTau = /* #__PURE__ */ recreateFactory(\n 'tau',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberTau(BigNumber)\n : tau\n)\n\nexport const createE = /* #__PURE__ */ recreateFactory(\n 'e',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberE(BigNumber)\n : e\n)\n\n// golden ratio, (1+sqrt(5))/2\nexport const createPhi = /* #__PURE__ */ recreateFactory(\n 'phi',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberPhi(BigNumber)\n : phi\n)\n\nexport const createLN2 = /* #__PURE__ */ recreateFactory(\n 'LN2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(2).ln()\n : Math.LN2\n)\n\nexport const createLN10 = /* #__PURE__ */ recreateFactory(\n 'LN10',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(10).ln()\n : Math.LN10\n)\n\nexport const createLOG2E = /* #__PURE__ */ recreateFactory(\n 'LOG2E',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(1).div(new BigNumber(2).ln())\n : Math.LOG2E\n)\n\nexport const createLOG10E = /* #__PURE__ */ recreateFactory(\n 'LOG10E',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(1).div(new BigNumber(10).ln())\n : Math.LOG10E\n)\n\nexport const createSQRT1_2 = /* #__PURE__ */ recreateFactory( // eslint-disable-line camelcase\n 'SQRT1_2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber('0.5').sqrt()\n : Math.SQRT1_2\n)\n\nexport const createSQRT2 = /* #__PURE__ */ recreateFactory(\n 'SQRT2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(2).sqrt()\n : Math.SQRT2\n)\n\nexport const createI = /* #__PURE__ */ recreateFactory(\n 'i',\n ['Complex'],\n ({ Complex }) => Complex.I\n)\n\n// for backward compatibility with v5\nexport const createUppercasePi = /* #__PURE__ */ factory('PI', ['pi'], ({ pi }) => pi)\nexport const createUppercaseE = /* #__PURE__ */ factory('E', ['e'], ({ e }) => e)\n\nexport const createVersion = /* #__PURE__ */ factory('version', [], () => version)\n\n// helper function to create a factory with a flag recreateOnConfigChange\n// idea: allow passing optional properties to be attached to the factory function as 4th argument?\nfunction recreateFactory (name, dependencies, create) {\n return factory(name, dependencies, create, {\n recreateOnConfigChange: true\n })\n}\n","export const version = '8.1.1'\n// Note: This file is automatically generated when building math.js.\n// Changes made in this file will be overwritten.\n","import { factory } from '../../utils/factory.js'\n\n// Source: https://en.wikipedia.org/wiki/Physical_constant\n\n// Universal constants\nexport const createSpeedOfLight = /* #__PURE__ */ unitFactory('speedOfLight', '299792458', 'm s^-1')\nexport const createGravitationConstant = /* #__PURE__ */ unitFactory('gravitationConstant', '6.67430e-11', 'm^3 kg^-1 s^-2')\nexport const createPlanckConstant = /* #__PURE__ */ unitFactory('planckConstant', '6.62607015e-34', 'J s')\nexport const createReducedPlanckConstant = /* #__PURE__ */ unitFactory('reducedPlanckConstant', '1.0545718176461565e-34', 'J s')\n\n// Electromagnetic constants\nexport const createMagneticConstant = /* #__PURE__ */ unitFactory('magneticConstant', '1.25663706212e-6', 'N A^-2')\nexport const createElectricConstant = /* #__PURE__ */ unitFactory('electricConstant', '8.8541878128e-12', 'F m^-1')\nexport const createVacuumImpedance = /* #__PURE__ */ unitFactory('vacuumImpedance', '376.730313667', 'ohm')\nexport const createCoulomb = /* #__PURE__ */ unitFactory('coulomb', '8.987551792261171e9', 'N m^2 C^-2')\nexport const createElementaryCharge = /* #__PURE__ */ unitFactory('elementaryCharge', '1.602176634e-19', 'C')\nexport const createBohrMagneton = /* #__PURE__ */ unitFactory('bohrMagneton', '9.2740100783e-24', 'J T^-1')\nexport const createConductanceQuantum = /* #__PURE__ */ unitFactory('conductanceQuantum', '7.748091729863649e-5', 'S')\nexport const createInverseConductanceQuantum = /* #__PURE__ */ unitFactory('inverseConductanceQuantum', '12906.403729652257', 'ohm')\nexport const createMagneticFluxQuantum = /* #__PURE__ */ unitFactory('magneticFluxQuantum', '2.0678338484619295e-15', 'Wb')\nexport const createNuclearMagneton = /* #__PURE__ */ unitFactory('nuclearMagneton', '5.0507837461e-27', 'J T^-1')\nexport const createKlitzing = /* #__PURE__ */ unitFactory('klitzing', '25812.807459304513', 'ohm')\nexport const createJosephson = /* #__PURE__ */ unitFactory('josephson', '4.835978484169836e14 Hz V', 'Hz V^-1') // TODO: support for Hz needed\n\n// Atomic and nuclear constants\nexport const createBohrRadius = /* #__PURE__ */ unitFactory('bohrRadius', '5.29177210903e-11', 'm')\nexport const createClassicalElectronRadius = /* #__PURE__ */ unitFactory('classicalElectronRadius', '2.8179403262e-15', 'm')\nexport const createElectronMass = /* #__PURE__ */ unitFactory('electronMass', '9.1093837015e-31', 'kg')\nexport const createFermiCoupling = /* #__PURE__ */ unitFactory('fermiCoupling', '1.1663787e-5', 'GeV^-2')\nexport const createFineStructure = numberFactory('fineStructure', 7.2973525693e-3)\nexport const createHartreeEnergy = /* #__PURE__ */ unitFactory('hartreeEnergy', '4.3597447222071e-18', 'J')\nexport const createProtonMass = /* #__PURE__ */ unitFactory('protonMass', '1.67262192369e-27', 'kg')\nexport const createDeuteronMass = /* #__PURE__ */ unitFactory('deuteronMass', '3.3435830926e-27', 'kg')\nexport const createNeutronMass = /* #__PURE__ */ unitFactory('neutronMass', '1.6749271613e-27', 'kg')\nexport const createQuantumOfCirculation = /* #__PURE__ */ unitFactory('quantumOfCirculation', '3.6369475516e-4', 'm^2 s^-1')\nexport const createRydberg = /* #__PURE__ */ unitFactory('rydberg', '10973731.568160', 'm^-1')\nexport const createThomsonCrossSection = /* #__PURE__ */ unitFactory('thomsonCrossSection', '6.6524587321e-29', 'm^2')\nexport const createWeakMixingAngle = numberFactory('weakMixingAngle', 0.22290)\nexport const createEfimovFactor = numberFactory('efimovFactor', 22.7)\n\n// Physico-chemical constants\nexport const createAtomicMass = /* #__PURE__ */ unitFactory('atomicMass', '1.66053906660e-27', 'kg')\nexport const createAvogadro = /* #__PURE__ */ unitFactory('avogadro', '6.02214076e23', 'mol^-1')\nexport const createBoltzmann = /* #__PURE__ */ unitFactory('boltzmann', '1.380649e-23', 'J K^-1')\nexport const createFaraday = /* #__PURE__ */ unitFactory('faraday', '96485.33212331001', 'C mol^-1')\nexport const createFirstRadiation = /* #__PURE__ */ unitFactory('firstRadiation', '3.7417718521927573e-16', 'W m^2')\n// export const createSpectralRadiance = /* #__PURE__ */ unitFactory('spectralRadiance', '1.1910429723971881e-16', 'W m^2 sr^-1') // TODO spectralRadiance\nexport const createLoschmidt = /* #__PURE__ */ unitFactory('loschmidt', '2.686780111798444e25', 'm^-3')\nexport const createGasConstant = /* #__PURE__ */ unitFactory('gasConstant', '8.31446261815324', 'J K^-1 mol^-1')\nexport const createMolarPlanckConstant = /* #__PURE__ */ unitFactory('molarPlanckConstant', '3.990312712893431e-10', 'J s mol^-1')\nexport const createMolarVolume = /* #__PURE__ */ unitFactory('molarVolume', '0.022413969545014137', 'm^3 mol^-1')\nexport const createSackurTetrode = numberFactory('sackurTetrode', -1.16487052358)\nexport const createSecondRadiation = /* #__PURE__ */ unitFactory('secondRadiation', '0.014387768775039337', 'm K')\nexport const createStefanBoltzmann = /* #__PURE__ */ unitFactory('stefanBoltzmann', '5.67037441918443e-8', 'W m^-2 K^-4')\nexport const createWienDisplacement = /* #__PURE__ */ unitFactory('wienDisplacement', '2.897771955e-3', 'm K')\n\n// Adopted values\nexport const createMolarMass = /* #__PURE__ */ unitFactory('molarMass', '0.99999999965e-3', 'kg mol^-1')\nexport const createMolarMassC12 = /* #__PURE__ */ unitFactory('molarMassC12', '11.9999999958e-3', 'kg mol^-1')\nexport const createGravity = /* #__PURE__ */ unitFactory('gravity', '9.80665', 'm s^-2')\n// atm is defined in Unit.js\n\n// Natural units\nexport const createPlanckLength = /* #__PURE__ */ unitFactory('planckLength', '1.616255e-35', 'm')\nexport const createPlanckMass = /* #__PURE__ */ unitFactory('planckMass', '2.176435e-8', 'kg')\nexport const createPlanckTime = /* #__PURE__ */ unitFactory('planckTime', '5.391245e-44', 's')\nexport const createPlanckCharge = /* #__PURE__ */ unitFactory('planckCharge', '1.87554603778e-18', 'C')\nexport const createPlanckTemperature = /* #__PURE__ */ unitFactory('planckTemperature', '1.416785e+32', 'K')\n\n// helper function to create a factory function which creates a physical constant,\n// a Unit with either a number value or a BigNumber value depending on the configuration\nfunction unitFactory (name, valueStr, unitStr) {\n const dependencies = ['config', 'Unit', 'BigNumber']\n\n return factory(name, dependencies, ({ config, Unit, BigNumber }) => {\n // Note that we can parse into number or BigNumber.\n // We do not parse into Fractions as that doesn't make sense: we would lose precision of the values\n // Therefore we dont use Unit.parse()\n const value = config.number === 'BigNumber'\n ? new BigNumber(valueStr)\n : parseFloat(valueStr)\n\n const unit = new Unit(value, unitStr)\n unit.fixPrefix = true\n return unit\n })\n}\n\n// helper function to create a factory function which creates a numeric constant,\n// either a number or BigNumber depending on the configuration\nfunction numberFactory (name, value) {\n const dependencies = ['config', 'BigNumber']\n\n return factory(name, dependencies, ({ config, BigNumber }) => {\n return config.number === 'BigNumber'\n ? new BigNumber(value)\n : value\n })\n}\n","import { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createApply } from '../../function/matrix/apply.js'\nimport { isBigNumber, isNumber } from '../../utils/is.js'\n\nconst name = 'apply'\nconst dependencies = ['typed', 'isInteger']\n\n/**\n * Attach a transform function to math.apply\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function apply\n * from one-based to zero based\n */\nexport const createApplyTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger }) => {\n const apply = createApply({ typed, isInteger })\n\n // @see: comment of concat itself\n return typed('apply', {\n '...any': function (args) {\n // change dim from one-based to zero-based\n const dim = args[1]\n\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n\n try {\n return apply.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createColumn } from '../../function/matrix/column.js'\nimport { isNumber } from '../../utils/is.js'\n\nconst name = 'column'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\n/**\n * Attach a transform function to matrix.column\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `index` parameter of function column\n * from zero-based to one-based\n */\nexport const createColumnTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n const column = createColumn({ typed, Index, matrix, range })\n\n // @see: comment of column itself\n return typed('column', {\n '...any': function (args) {\n // change last argument from zero-based to one-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n }\n\n try {\n return column.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isSymbolNode } from '../../../utils/is.js'\n\n/**\n * Compile an inline expression like \"x > 0\"\n * @param {Node} expression\n * @param {Object} math\n * @param {Object} scope\n * @return {function} Returns a function with one argument which fills in the\n * undefined variable (like \"x\") and evaluates the expression\n */\nexport function compileInlineExpression (expression, math, scope) {\n // find an undefined symbol\n const symbol = expression.filter(function (node) {\n return isSymbolNode(node) &&\n !(node.name in math) &&\n !(node.name in scope)\n })[0]\n\n if (!symbol) {\n throw new Error('No undefined variable found in inline expression \"' + expression + '\"')\n }\n\n // create a test function for this equation\n const name = symbol.name // variable name\n const subScope = Object.create(scope)\n const eq = expression.compile()\n return function inlineExpression (x) {\n subScope[name] = x\n return eq.evaluate(subScope)\n }\n}\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { filter, filterRegExp } from '../../utils/array.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'filter'\nconst dependencies = ['typed']\n\nexport const createFilterTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.filter\n * Adds a property transform containing the transform function.\n *\n * This transform adds support for equations as test function for math.filter,\n * so you can do something like 'filter([3, -2, 5], x > 0)'.\n */\n function filterTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like filter([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like filter([3, -2, 5], x > 0)\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return filter(x, callback)\n }\n filterTransform.rawArgs = true\n\n // one based version of function filter\n const filter = typed('filter', {\n 'Array, function': _filter,\n\n 'Matrix, function': function (x, test) {\n return x.create(_filter(x.toArray(), test))\n },\n\n 'Array, RegExp': filterRegExp,\n\n 'Matrix, RegExp': function (x, test) {\n return x.create(filterRegExp(x.toArray(), test))\n }\n })\n\n return filterTransform\n}, { isTransformFunction: true })\n\n/**\n * Filter values in a callback given a callback function\n *\n * !!! Passes a one-based index !!!\n *\n * @param {Array} x\n * @param {Function} callback\n * @return {Array} Returns the filtered array\n * @private\n */\nfunction _filter (x, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n return filter(x, function (value, index, array) {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, [index + 1])\n } else { // 3 or -1\n return callback(value, [index + 1], array)\n }\n })\n}\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { forEach } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\n\nconst name = 'forEach'\nconst dependencies = ['typed']\n\nexport const createForEachTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.forEach\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n function forEachTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like forEach([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like forEach([3, -2, 5], x > 0 ? callback1(x) : callback2(x) )\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return _forEach(x, callback)\n }\n forEachTransform.rawArgs = true\n\n // one-based version of forEach\n const _forEach = typed('forEach', {\n 'Array | Matrix, function': function (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n forEach(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n recurse(child, index.concat(i + 1)) // one based index, hence i+1\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n callback(value)\n } else if (args === 2) {\n callback(value, index)\n } else { // 3 or -1\n callback(value, index, array)\n }\n }\n }\n recurse(array.valueOf(), []) // pass Array\n }\n })\n\n return forEachTransform\n}, { isTransformFunction: true })\n","import { isArray, isBigNumber, isMatrix, isNumber, isRange } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'index'\nconst dependencies = ['Index']\n\nexport const createIndexTransform = /* #__PURE__ */ factory(name, dependencies, ({ Index }) => {\n /**\n * Attach a transform function to math.index\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n return function indexTransform () {\n const args = []\n for (let i = 0, ii = arguments.length; i < ii; i++) {\n let arg = arguments[i]\n\n // change from one-based to zero based, and convert BigNumber to number\n if (isRange(arg)) {\n arg.start--\n arg.end -= (arg.step > 0 ? 0 : 2)\n } else if (arg && arg.isSet === true) {\n arg = arg.map(function (v) { return v - 1 })\n } else if (isArray(arg) || isMatrix(arg)) {\n arg = arg.map(function (v) { return v - 1 })\n } else if (isNumber(arg)) {\n arg--\n } else if (isBigNumber(arg)) {\n arg = arg.toNumber() - 1\n } else if (typeof arg === 'string') {\n // leave as is\n } else {\n throw new TypeError('Dimension must be an Array, Matrix, number, string, or Range')\n }\n\n args[i] = arg\n }\n\n const res = new Index()\n Index.apply(res, args)\n return res\n }\n}, { isTransformFunction: true })\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\n\nconst name = 'map'\nconst dependencies = ['typed']\n\nexport const createMapTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.map\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n function mapTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like filter([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like filter([3, -2, 5], x > 0)\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return map(x, callback)\n }\n mapTransform.rawArgs = true\n\n // one-based version of map function\n const map = typed('map', {\n 'Array, function': function (x, callback) {\n return _map(x, callback, x)\n },\n\n 'Matrix, function': function (x, callback) {\n return x.create(_map(x.valueOf(), callback, x))\n }\n })\n\n return mapTransform\n}, { isTransformFunction: true })\n\n/**\n * Map for a multi dimensional array. One-based indexes\n * @param {Array} array\n * @param {function} callback\n * @param {Array} orig\n * @return {Array}\n * @private\n */\nfunction _map (array, callback, orig) {\n // figure out what number of arguments the callback function expects\n const argsCount = maxArgumentCount(callback)\n\n function recurse (value, index) {\n if (Array.isArray(value)) {\n return map(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n return recurse(child, index.concat(i + 1)) // one based index, hence i + 1\n })\n } else {\n // invoke the (typed) callback function with the right number of arguments\n if (argsCount === 1) {\n return callback(value)\n } else if (argsCount === 2) {\n return callback(value, index)\n } else { // 3 or -1\n return callback(value, index, orig)\n }\n }\n }\n\n return recurse(array, [])\n}\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMax } from '../../function/statistics/max.js'\n\nconst name = 'max'\nconst dependencies = ['typed', 'config', 'numeric', 'larger']\n\nexport const createMaxTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, larger }) => {\n const max = createMax({ typed, config, numeric, larger })\n\n /**\n * Attach a transform function to math.max\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function max\n * from one-based to zero based\n */\n return typed('max', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return max.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMean } from '../../function/statistics/mean.js'\n\nconst name = 'mean'\nconst dependencies = ['typed', 'add', 'divide']\n\nexport const createMeanTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide }) => {\n const mean = createMean({ typed, add, divide })\n\n /**\n * Attach a transform function to math.mean\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function mean\n * from one-based to zero based\n */\n return typed('mean', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return mean.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMin } from '../../function/statistics/min.js'\n\nconst name = 'min'\nconst dependencies = ['typed', 'config', 'numeric', 'smaller']\n\nexport const createMinTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, smaller }) => {\n const min = createMin({ typed, config, numeric, smaller })\n\n /**\n * Attach a transform function to math.min\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function min\n * from one-based to zero based\n */\n return typed('min', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return min.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createRange } from '../../function/matrix/range.js'\n\nconst name = 'range'\nconst dependencies = ['typed', 'config', '?matrix', '?bignumber', 'smaller', 'smallerEq', 'larger', 'largerEq']\n\nexport const createRangeTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq }) => {\n const range = createRange({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq })\n\n /**\n * Attach a transform function to math.range\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed('range', {\n '...any': function (args) {\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (typeof last !== 'boolean') {\n // append a parameter includeEnd=true\n args.push(true)\n }\n\n return range.apply(null, args)\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createRow } from '../../function/matrix/row.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { isNumber } from '../../utils/is.js'\n\nconst name = 'row'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\n/**\n * Attach a transform function to matrix.column\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `index` parameter of function column\n * from zero-based to one-based\n */\nexport const createRowTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n const row = createRow({ typed, Index, matrix, range })\n\n // @see: comment of row itself\n return typed('row', {\n '...any': function (args) {\n // change last argument from zero-based to one-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n }\n\n try {\n return row.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createSubset } from '../../function/matrix/subset.js'\n\nconst name = 'subset'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSubsetTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const subset = createSubset({ typed, matrix })\n\n /**\n * Attach a transform function to math.subset\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed('subset', {\n '...any': function (args) {\n try {\n return subset.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isNumber } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createConcat } from '../../function/matrix/concat.js'\n\nconst name = 'concat'\nconst dependencies = ['typed', 'matrix', 'isInteger']\n\nexport const createConcatTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, isInteger }) => {\n const concat = createConcat({ typed, matrix, isInteger })\n\n /**\n * Attach a transform function to math.range\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function concat\n * from one-based to zero based\n */\n return typed('concat', {\n '...any': function (args) {\n // change last argument from one-based to zero-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n } else if (isBigNumber(last)) {\n args[lastIndex] = last.minus(1)\n }\n\n try {\n return concat.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createDiff } from '../../function/matrix/diff.js'\n\nconst name = 'diff'\nconst dependencies = ['typed', 'matrix', 'subtract', 'number', 'bignumber']\n\nexport const createDiffTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, number, bignumber }) => {\n const diff = createDiff({ typed, matrix, subtract, number, bignumber })\n\n /**\n * Attach a transform function to math.diff\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return diff.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createStd } from '../../function/statistics/std.js'\nimport { isBigNumber, isNumber, isCollection } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\n\nconst name = 'std'\nconst dependencies = ['typed', 'sqrt', 'variance']\n\n/**\n * Attach a transform function to math.std\n * Adds a property transform containing the transform function.\n *\n * This transform changed the `dim` parameter of function std\n * from one-based to zero based\n */\nexport const createStdTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, sqrt, variance }) => {\n const std = createStd({ typed, sqrt, variance })\n\n return typed('std', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length >= 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return std.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createSum } from '../../function/statistics/sum.js'\n\n/**\n * Attach a transform function to math.sum\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function mean\n * from one-based to zero based\n */\nconst name = 'sum'\nconst dependencies = ['typed', 'config', 'add', 'numeric']\n\nexport const createSumTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, add, numeric }) => {\n const sum = createSum({ typed, config, add, numeric })\n\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return sum.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createVariance } from '../../function/statistics/variance.js'\n\nconst name = 'variance'\nconst dependencies = ['typed', 'add', 'subtract', 'multiply', 'divide', 'apply', 'isNaN']\n\n/**\n * Attach a transform function to math.var\n * Adds a property transform containing the transform function.\n *\n * This transform changed the `dim` parameter of function var\n * from one-based to zero based\n */\nexport const createVarianceTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, subtract, multiply, divide, apply, isNaN }) => {\n const variance = createVariance({ typed, add, subtract, multiply, divide, apply, isNaN })\n\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length >= 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return variance.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isComplex, isFraction, isMatrix, isUnit } from '../../utils/is.js'\nimport { isFactory, stripOptionalNotation } from '../../utils/factory.js'\nimport { hasOwnProperty, lazy } from '../../utils/object.js'\nimport { contains } from '../../utils/array.js'\nimport { ArgumentsError } from '../../error/ArgumentsError.js'\n\nexport function importFactory (typed, load, math, importedFactories) {\n /**\n * Import functions from an object or a module.\n *\n * This function is only available on a mathjs instance created using `create`.\n *\n * Syntax:\n *\n * math.import(functions)\n * math.import(functions, options)\n *\n * Where:\n *\n * - `functions: Object`\n * An object with functions or factories to be imported.\n * - `options: Object` An object with import options. Available options:\n * - `override: boolean`\n * If true, existing functions will be overwritten. False by default.\n * - `silent: boolean`\n * If true, the function will not throw errors on duplicates or invalid\n * types. False by default.\n * - `wrap: boolean`\n * If true, the functions will be wrapped in a wrapper function\n * which converts data types like Matrix to primitive data types like Array.\n * The wrapper is needed when extending math.js with libraries which do not\n * support these data type. False by default.\n *\n * Examples:\n *\n * import { create, all } from 'mathjs'\n * import * as numbers from 'numbers'\n *\n * // create a mathjs instance\n * const math = create(all)\n *\n * // define new functions and variables\n * math.import({\n * myvalue: 42,\n * hello: function (name) {\n * return 'hello, ' + name + '!'\n * }\n * })\n *\n * // use the imported function and variable\n * math.myvalue * 2 // 84\n * math.hello('user') // 'hello, user!'\n *\n * // import the npm module 'numbers'\n * // (must be installed first with `npm install numbers`)\n * math.import(numbers, {wrap: true})\n *\n * math.fibonacci(7) // returns 13\n *\n * @param {Object | Array} functions Object with functions to be imported.\n * @param {Object} [options] Import options.\n */\n function mathImport (functions, options) {\n const num = arguments.length\n if (num !== 1 && num !== 2) {\n throw new ArgumentsError('import', num, 1, 2)\n }\n\n if (!options) {\n options = {}\n }\n\n function flattenImports (flatValues, value, name) {\n if (Array.isArray(value)) {\n value.forEach(item => flattenImports(flatValues, item))\n } else if (typeof value === 'object') {\n for (const name in value) {\n if (hasOwnProperty(value, name)) {\n flattenImports(flatValues, value[name], name)\n }\n }\n } else if (isFactory(value) || name !== undefined) {\n const flatName = isFactory(value)\n ? isTransformFunctionFactory(value)\n ? (value.fn + '.transform') // TODO: this is ugly\n : value.fn\n : name\n\n // we allow importing the same function twice if it points to the same implementation\n if (hasOwnProperty(flatValues, flatName) && flatValues[flatName] !== value && !options.silent) {\n throw new Error('Cannot import \"' + flatName + '\" twice')\n }\n\n flatValues[flatName] = value\n } else {\n if (!options.silent) {\n throw new TypeError('Factory, Object, or Array expected')\n }\n }\n }\n\n const flatValues = {}\n flattenImports(flatValues, functions)\n\n for (const name in flatValues) {\n if (hasOwnProperty(flatValues, name)) {\n // console.log('import', name)\n const value = flatValues[name]\n\n if (isFactory(value)) {\n // we ignore name here and enforce the name of the factory\n // maybe at some point we do want to allow overriding it\n // in that case we can implement an option overrideFactoryNames: true\n _importFactory(value, options)\n } else if (isSupportedType(value)) {\n _import(name, value, options)\n } else {\n if (!options.silent) {\n throw new TypeError('Factory, Object, or Array expected')\n }\n }\n }\n }\n }\n\n /**\n * Add a property to the math namespace\n * @param {string} name\n * @param {*} value\n * @param {Object} options See import for a description of the options\n * @private\n */\n function _import (name, value, options) {\n // TODO: refactor this function, it's to complicated and contains duplicate code\n if (options.wrap && typeof value === 'function') {\n // create a wrapper around the function\n value = _wrap(value)\n }\n\n // turn a plain function with a typed-function signature into a typed-function\n if (hasTypedFunctionSignature(value)) {\n value = typed(name, {\n [value.signature]: value\n })\n }\n\n if (isTypedFunction(math[name]) && isTypedFunction(value)) {\n if (options.override) {\n // give the typed function the right name\n value = typed(name, value.signatures)\n } else {\n // merge the existing and typed function\n value = typed(math[name], value)\n }\n\n math[name] = value\n delete importedFactories[name]\n\n _importTransform(name, value)\n math.emit('import', name, function resolver () {\n return value\n })\n return\n }\n\n if (math[name] === undefined || options.override) {\n math[name] = value\n delete importedFactories[name]\n\n _importTransform(name, value)\n math.emit('import', name, function resolver () {\n return value\n })\n return\n }\n\n if (!options.silent) {\n throw new Error('Cannot import \"' + name + '\": already exists')\n }\n }\n\n function _importTransform (name, value) {\n if (value && typeof value.transform === 'function') {\n math.expression.transform[name] = value.transform\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = value.transform\n }\n } else {\n // remove existing transform\n delete math.expression.transform[name]\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = value\n }\n }\n }\n\n function _deleteTransform (name) {\n delete math.expression.transform[name]\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = math[name]\n } else {\n delete math.expression.mathWithTransform[name]\n }\n }\n\n /**\n * Create a wrapper a round an function which converts the arguments\n * to their primitive values (like convert a Matrix to Array)\n * @param {Function} fn\n * @return {Function} Returns the wrapped function\n * @private\n */\n function _wrap (fn) {\n const wrapper = function wrapper () {\n const args = []\n for (let i = 0, len = arguments.length; i < len; i++) {\n const arg = arguments[i]\n args[i] = arg && arg.valueOf()\n }\n return fn.apply(math, args)\n }\n\n if (fn.transform) {\n wrapper.transform = fn.transform\n }\n\n return wrapper\n }\n\n /**\n * Import an instance of a factory into math.js\n * @param {function(scope: object)} factory\n * @param {Object} options See import for a description of the options\n * @param {string} [name=factory.name] Optional custom name\n * @private\n */\n function _importFactory (factory, options, name = factory.fn) {\n if (contains(name, '.')) {\n throw new Error('Factory name should not contain a nested path. ' +\n 'Name: ' + JSON.stringify(name))\n }\n\n const namespace = isTransformFunctionFactory(factory)\n ? math.expression.transform\n : math\n\n const existingTransform = name in math.expression.transform\n const existing = hasOwnProperty(namespace, name) ? namespace[name] : undefined\n\n const resolver = function () {\n // collect all dependencies, handle finding both functions and classes and other special cases\n const dependencies = {}\n factory.dependencies\n .map(stripOptionalNotation)\n .forEach(dependency => {\n if (contains(dependency, '.')) {\n throw new Error('Factory dependency should not contain a nested path. ' +\n 'Name: ' + JSON.stringify(dependency))\n }\n\n if (dependency === 'math') {\n dependencies.math = math\n } else if (dependency === 'mathWithTransform') {\n dependencies.mathWithTransform = math.expression.mathWithTransform\n } else if (dependency === 'classes') { // special case for json reviver\n dependencies.classes = math\n } else {\n dependencies[dependency] = math[dependency]\n }\n })\n\n const instance = /* #__PURE__ */ factory(dependencies)\n\n if (instance && typeof instance.transform === 'function') {\n throw new Error('Transforms cannot be attached to factory functions. ' +\n 'Please create a separate function for it with exports.path=\"expression.transform\"')\n }\n\n if (existing === undefined || options.override) {\n return instance\n }\n\n if (isTypedFunction(existing) && isTypedFunction(instance)) {\n // merge the existing and new typed function\n return typed(existing, instance)\n }\n\n if (options.silent) {\n // keep existing, ignore imported function\n return existing\n } else {\n throw new Error('Cannot import \"' + name + '\": already exists')\n }\n }\n\n // TODO: add unit test with non-lazy factory\n if (!factory.meta || factory.meta.lazy !== false) {\n lazy(namespace, name, resolver)\n\n // FIXME: remove the `if (existing &&` condition again. Can we make sure subset is loaded before subset.transform? (Name collision, and no dependencies between the two)\n if (existing && existingTransform) {\n _deleteTransform(name)\n } else {\n if (isTransformFunctionFactory(factory) || factoryAllowedInExpressions(factory)) {\n lazy(math.expression.mathWithTransform, name, () => namespace[name])\n }\n }\n } else {\n namespace[name] = resolver()\n\n // FIXME: remove the `if (existing &&` condition again. Can we make sure subset is loaded before subset.transform? (Name collision, and no dependencies between the two)\n if (existing && existingTransform) {\n _deleteTransform(name)\n } else {\n if (isTransformFunctionFactory(factory) || factoryAllowedInExpressions(factory)) {\n lazy(math.expression.mathWithTransform, name, () => namespace[name])\n }\n }\n }\n\n // TODO: improve factories, store a list with imports instead which can be re-played\n importedFactories[name] = factory\n\n math.emit('import', name, resolver)\n }\n\n /**\n * Check whether given object is a type which can be imported\n * @param {Function | number | string | boolean | null | Unit | Complex} object\n * @return {boolean}\n * @private\n */\n function isSupportedType (object) {\n return typeof object === 'function' ||\n typeof object === 'number' ||\n typeof object === 'string' ||\n typeof object === 'boolean' ||\n object === null ||\n isUnit(object) ||\n isComplex(object) ||\n isBigNumber(object) ||\n isFraction(object) ||\n isMatrix(object) ||\n Array.isArray(object)\n }\n\n /**\n * Test whether a given thing is a typed-function\n * @param {*} fn\n * @return {boolean} Returns true when `fn` is a typed-function\n */\n function isTypedFunction (fn) {\n return typeof fn === 'function' && typeof fn.signatures === 'object'\n }\n\n function hasTypedFunctionSignature (fn) {\n return typeof fn === 'function' && typeof fn.signature === 'string'\n }\n\n function allowedInExpressions (name) {\n return !hasOwnProperty(unsafe, name)\n }\n\n function factoryAllowedInExpressions (factory) {\n return factory.fn.indexOf('.') === -1 && // FIXME: make checking on path redundant, check on meta data instead\n !hasOwnProperty(unsafe, factory.fn) &&\n (!factory.meta || !factory.meta.isClass)\n }\n\n function isTransformFunctionFactory (factory) {\n return (factory !== undefined &&\n factory.meta !== undefined &&\n factory.meta.isTransformFunction === true) || false\n }\n\n // namespaces and functions not available in the parser for safety reasons\n const unsafe = {\n expression: true,\n type: true,\n docs: true,\n error: true,\n json: true,\n chain: true // chain method not supported. Note that there is a unit chain too.\n }\n\n return mathImport\n}\n","export const DEFAULT_CONFIG = {\n // minimum relative difference between two compared values,\n // used by all comparison functions\n epsilon: 1e-12,\n\n // type of default matrix output. Choose 'matrix' (default) or 'array'\n matrix: 'Matrix',\n\n // type of default number output. Choose 'number' (default) 'BigNumber', or 'Fraction\n number: 'number',\n\n // number of significant digits in BigNumbers\n precision: 64,\n\n // predictable output type of functions. When true, output type depends only\n // on the input types. When false (default), output type can vary depending\n // on input values. For example `math.sqrt(-4)` returns `complex('2i')` when\n // predictable is false, and returns `NaN` when true.\n predictable: false,\n\n // random seed for seeded pseudo random number generation\n // null = randomly seed\n randomSeed: null\n}\n","import { clone, mapObject, deepExtend } from '../../utils/object.js'\nimport { DEFAULT_CONFIG } from '../config.js'\n\nexport const MATRIX_OPTIONS = ['Matrix', 'Array'] // valid values for option matrix\nexport const NUMBER_OPTIONS = ['number', 'BigNumber', 'Fraction'] // valid values for option number\n\nexport function configFactory (config, emit) {\n /**\n * Set configuration options for math.js, and get current options.\n * Will emit a 'config' event, with arguments (curr, prev, changes).\n *\n * This function is only available on a mathjs instance created using `create`.\n *\n * Syntax:\n *\n * math.config(config: Object): Object\n *\n * Examples:\n *\n *\n * import { create, all } from 'mathjs'\n *\n * // create a mathjs instance\n * const math = create(all)\n *\n * math.config().number // outputs 'number'\n * math.evaluate('0.4') // outputs number 0.4\n * math.config({number: 'Fraction'})\n * math.evaluate('0.4') // outputs Fraction 2/5\n *\n * @param {Object} [options] Available options:\n * {number} epsilon\n * Minimum relative difference between two\n * compared values, used by all comparison functions.\n * {string} matrix\n * A string 'Matrix' (default) or 'Array'.\n * {string} number\n * A string 'number' (default), 'BigNumber', or 'Fraction'\n * {number} precision\n * The number of significant digits for BigNumbers.\n * Not applicable for Numbers.\n * {string} parenthesis\n * How to display parentheses in LaTeX and string\n * output.\n * {string} randomSeed\n * Random seed for seeded pseudo random number generator.\n * Set to null to randomly seed.\n * @return {Object} Returns the current configuration\n */\n function _config (options) {\n if (options) {\n const prev = mapObject(config, clone)\n\n // validate some of the options\n validateOption(options, 'matrix', MATRIX_OPTIONS)\n validateOption(options, 'number', NUMBER_OPTIONS)\n\n // merge options\n deepExtend(config, options)\n\n const curr = mapObject(config, clone)\n\n const changes = mapObject(options, clone)\n\n // emit 'config' event\n emit('config', curr, prev, changes)\n\n return curr\n } else {\n return mapObject(config, clone)\n }\n }\n\n // attach the valid options to the function so they can be extended\n _config.MATRIX_OPTIONS = MATRIX_OPTIONS\n _config.NUMBER_OPTIONS = NUMBER_OPTIONS\n\n // attach the config properties as readonly properties to the config function\n Object.keys(DEFAULT_CONFIG).forEach(key => {\n Object.defineProperty(_config, key, {\n get: () => config[key],\n enumerable: true,\n configurable: true\n })\n })\n\n return _config\n}\n\n/**\n * Test whether an Array contains a specific item.\n * @param {Array.} array\n * @param {string} item\n * @return {boolean}\n */\nfunction contains (array, item) {\n return array.indexOf(item) !== -1\n}\n\n/**\n * Validate an option\n * @param {Object} options Object with options\n * @param {string} name Name of the option to validate\n * @param {Array.} values Array with valid values for this option\n */\nfunction validateOption (options, name, values) {\n if (options[name] !== undefined && !contains(values, options[name])) {\n // unknown value\n console.warn('Warning: Unknown value \"' + options[name] + '\" for configuration option \"' + name + '\". ' +\n 'Available options: ' + values.map(value => JSON.stringify(value)).join(', ') + '.')\n }\n}\n","import * as all from './factoriesAny.js'\nimport { create } from './core/create.js'\n\nexport default create(all)\n","import './../utils/polyfills.js'\nimport { deepFlatten, isLegacyFactory, values } from '../utils/object.js'\nimport * as emitter from './../utils/emitter.js'\nimport { importFactory } from './function/import.js'\nimport { configFactory } from './function/config.js'\nimport { factory, isFactory } from '../utils/factory.js'\nimport {\n isAccessorNode,\n isArray,\n isArrayNode,\n isAssignmentNode,\n isBigNumber,\n isBlockNode,\n isBoolean,\n isChain,\n isCollection,\n isComplex,\n isConditionalNode,\n isConstantNode,\n isDate,\n isDenseMatrix,\n isFraction,\n isFunction,\n isFunctionAssignmentNode,\n isFunctionNode,\n isHelp,\n isIndex,\n isIndexNode,\n isMatrix,\n isNode,\n isNull,\n isNumber,\n isObject,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRange,\n isRangeNode,\n isRegExp,\n isResultSet,\n isSparseMatrix,\n isString,\n isSymbolNode,\n isUndefined,\n isUnit\n} from '../utils/is.js'\nimport { ArgumentsError } from '../error/ArgumentsError.js'\nimport { DimensionError } from '../error/DimensionError.js'\nimport { IndexError } from '../error/IndexError.js'\nimport { DEFAULT_CONFIG } from './config.js'\n\n/**\n * Create a mathjs instance from given factory functions and optionally config\n *\n * Usage:\n *\n * const mathjs1 = create({ createAdd, createMultiply, ...})\n * const config = { number: 'BigNumber' }\n * const mathjs2 = create(all, config)\n *\n * @param {Object} [factories] An object with factory functions\n * The object can contain nested objects,\n * all nested objects will be flattened.\n * @param {Object} [config] Available options:\n * {number} epsilon\n * Minimum relative difference between two\n * compared values, used by all comparison functions.\n * {string} matrix\n * A string 'Matrix' (default) or 'Array'.\n * {string} number\n * A string 'number' (default), 'BigNumber', or 'Fraction'\n * {number} precision\n * The number of significant digits for BigNumbers.\n * Not applicable for Numbers.\n * {boolean} predictable\n * Predictable output type of functions. When true,\n * output type depends only on the input types. When\n * false (default), output type can vary depending\n * on input values. For example `math.sqrt(-4)`\n * returns `complex('2i')` when predictable is false, and\n * returns `NaN` when true.\n * {string} randomSeed\n * Random seed for seeded pseudo random number generator.\n * Set to null to randomly seed.\n * @returns {Object} Returns a bare-bone math.js instance containing\n * functions:\n * - `import` to add new functions\n * - `config` to change configuration\n * - `on`, `off`, `once`, `emit` for events\n */\nexport function create (factories, config) {\n const configInternal = Object.assign({}, DEFAULT_CONFIG, config)\n\n // simple test for ES5 support\n if (typeof Object.create !== 'function') {\n throw new Error('ES5 not supported by this JavaScript engine. ' +\n 'Please load the es5-shim and es5-sham library for compatibility.')\n }\n\n // create the mathjs instance\n const math = emitter.mixin({\n // only here for backward compatibility for legacy factory functions\n isNumber,\n isComplex,\n isBigNumber,\n isFraction,\n isUnit,\n isString,\n isArray,\n isMatrix,\n isCollection,\n isDenseMatrix,\n isSparseMatrix,\n isRange,\n isIndex,\n isBoolean,\n isResultSet,\n isHelp,\n isFunction,\n isDate,\n isRegExp,\n isObject,\n isNull,\n isUndefined,\n\n isAccessorNode,\n isArrayNode,\n isAssignmentNode,\n isBlockNode,\n isConditionalNode,\n isConstantNode,\n isFunctionAssignmentNode,\n isFunctionNode,\n isIndexNode,\n isNode,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRangeNode,\n isSymbolNode,\n\n isChain\n })\n\n // load config function and apply provided config\n math.config = configFactory(configInternal, math.emit)\n\n math.expression = {\n transform: {},\n mathWithTransform: {\n config: math.config\n }\n }\n\n // cached factories and instances used by function load\n const legacyFactories = []\n const legacyInstances = []\n\n /**\n * Load a function or data type from a factory.\n * If the function or data type already exists, the existing instance is\n * returned.\n * @param {Function} factory\n * @returns {*}\n */\n function load (factory) {\n if (isFactory(factory)) {\n return factory(math)\n }\n\n const firstProperty = factory[Object.keys(factory)[0]]\n if (isFactory(firstProperty)) {\n return firstProperty(math)\n }\n\n if (!isLegacyFactory(factory)) {\n console.warn('Factory object with properties `type`, `name`, and `factory` expected', factory)\n throw new Error('Factory object with properties `type`, `name`, and `factory` expected')\n }\n\n const index = legacyFactories.indexOf(factory)\n let instance\n if (index === -1) {\n // doesn't yet exist\n if (factory.math === true) {\n // pass with math namespace\n instance = factory.factory(math.type, configInternal, load, math.typed, math)\n } else {\n instance = factory.factory(math.type, configInternal, load, math.typed)\n }\n\n // append to the cache\n legacyFactories.push(factory)\n legacyInstances.push(instance)\n } else {\n // already existing function, return the cached instance\n instance = legacyInstances[index]\n }\n\n return instance\n }\n\n const importedFactories = {}\n\n // load the import function\n function lazyTyped (...args) {\n return math.typed.apply(math.typed, args)\n }\n const internalImport = importFactory(lazyTyped, load, math, importedFactories)\n math.import = internalImport\n\n // listen for changes in config, import all functions again when changed\n // TODO: move this listener into the import function?\n math.on('config', () => {\n values(importedFactories).forEach(factory => {\n if (factory && factory.meta && factory.meta.recreateOnConfigChange) {\n // FIXME: only re-create when the current instance is the same as was initially created\n // FIXME: delete the functions/constants before importing them again?\n internalImport(factory, { override: true })\n }\n })\n })\n\n // the create function exposed on the mathjs instance is bound to\n // the factory functions passed before\n math.create = create.bind(null, factories)\n\n // export factory function\n math.factory = factory\n\n // import the factory functions like createAdd as an array instead of object,\n // else they will get a different naming (`createAdd` instead of `add`).\n math.import(values(deepFlatten(factories)))\n\n math.ArgumentsError = ArgumentsError\n math.DimensionError = DimensionError\n math.IndexError = IndexError\n\n return math\n}\n","import Emitter from 'tiny-emitter'\n\n/**\n * Extend given object with emitter functions `on`, `off`, `once`, `emit`\n * @param {Object} obj\n * @return {Object} obj\n */\nexport function mixin (obj) {\n // create event emitter\n const emitter = new Emitter()\n\n // bind methods to obj (we don't want to expose the emitter.e Array...)\n obj.on = emitter.on.bind(emitter)\n obj.off = 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modules\n \t__webpack_require__.n = function(module) {\n \t\tvar getter = module && module.__esModule ?\n \t\t\tfunction getDefault() { return module['default']; } :\n \t\t\tfunction getModuleExports() { return module; };\n \t\t__webpack_require__.d(getter, 'a', getter);\n \t\treturn getter;\n \t};\n\n \t// Object.prototype.hasOwnProperty.call\n \t__webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); };\n\n \t// __webpack_public_path__\n \t__webpack_require__.p = \"\";\n\n\n \t// Load entry module and return exports\n \treturn __webpack_require__(__webpack_require__.s = 20);\n","/**\n * @license Complex.js v2.0.11 11/02/2016\n *\n * Copyright (c) 2016, Robert Eisele (robert@xarg.org)\n * Dual licensed under the MIT or GPL Version 2 licenses.\n **/\n\n/**\n *\n * This class allows the manipulation of complex numbers.\n * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.\n *\n * Object form\n * { re: , im: }\n * { arg: , abs: }\n * { phi: , r: }\n *\n * Array / Vector form\n * [ real, imaginary ]\n *\n * Double form\n * 99.3 - Single double value\n *\n * String form\n * '23.1337' - Simple real number\n * '15+3i' - a simple complex number\n * '3-i' - a simple complex number\n *\n * Example:\n *\n * var c = new Complex('99.3+8i');\n * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);\n *\n */\n\n(function(root) {\n\n 'use strict';\n\n var cosh = function(x) {\n return (Math.exp(x) + Math.exp(-x)) * 0.5;\n };\n\n var sinh = function(x) {\n return (Math.exp(x) - Math.exp(-x)) * 0.5;\n };\n\n /**\n * Calculates cos(x) - 1 using Taylor series if x is small.\n *\n * @param {number} x\n * @returns {number} cos(x) - 1\n */\n\n var cosm1 = function(x) {\n var limit = Math.PI/4;\n if (x < -limit || x > limit) {\n return (Math.cos(x) - 1.0);\n }\n\n var xx = x * x;\n return xx *\n (-0.5 + xx *\n (1/24 + xx *\n (-1/720 + xx *\n (1/40320 + xx *\n (-1/3628800 + xx *\n (1/4790014600 + xx *\n (-1/87178291200 + xx *\n (1/20922789888000)\n )\n )\n )\n )\n )\n )\n )\n };\n\n var hypot = function(x, y) {\n\n var a = Math.abs(x);\n var b = Math.abs(y);\n\n if (a < 3000 && b < 3000) {\n return Math.sqrt(a * a + b * b);\n }\n\n if (a < b) {\n a = b;\n b = x / y;\n } else {\n b = y / x;\n }\n return a * Math.sqrt(1 + b * b);\n };\n\n var parser_exit = function() {\n throw SyntaxError('Invalid Param');\n };\n\n /**\n * Calculates log(sqrt(a^2+b^2)) in a way to avoid overflows\n *\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\n function logHypot(a, b) {\n\n var _a = Math.abs(a);\n var _b = Math.abs(b);\n\n if (a === 0) {\n return Math.log(_b);\n }\n\n if (b === 0) {\n return Math.log(_a);\n }\n\n if (_a < 3000 && _b < 3000) {\n return Math.log(a * a + b * b) * 0.5;\n }\n\n /* I got 4 ideas to compute this property without overflow:\n *\n * Testing 1000000 times with random samples for a,b ∈ [1, 1000000000] against a big decimal library to get an error estimate\n *\n * 1. Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)\n\n Math.log(a * a + b * b) / 2\n\n *\n *\n * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)\n\n var fn = function(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n var t = Math.min(a, b);\n a = Math.max(a, b);\n t = t / a;\n\n return Math.log(a) + Math.log(1 + t * t) / 2;\n };\n\n * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)\n\n Math.log(a / Math.cos(Math.atan2(b, a)))\n\n * 4. Use 3. and apply log rules: (OVERALL ERROR: 1.2014087502620896e-9)\n\n Math.log(a) - Math.log(Math.cos(Math.atan2(b, a)))\n\n */\n\n return Math.log(a / Math.cos(Math.atan2(b, a)));\n }\n\n var parse = function(a, b) {\n\n var z = {'re': 0, 'im': 0};\n\n if (a === undefined || a === null) {\n z['re'] =\n z['im'] = 0;\n } else if (b !== undefined) {\n z['re'] = a;\n z['im'] = b;\n } else\n switch (typeof a) {\n\n case 'object':\n\n if ('im' in a && 're' in a) {\n z['re'] = a['re'];\n z['im'] = a['im'];\n } else if ('abs' in a && 'arg' in a) {\n if (!Number.isFinite(a['abs']) && Number.isFinite(a['arg'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['abs'] * Math.cos(a['arg']);\n z['im'] = a['abs'] * Math.sin(a['arg']);\n } else if ('r' in a && 'phi' in a) {\n if (!Number.isFinite(a['r']) && Number.isFinite(a['phi'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['r'] * Math.cos(a['phi']);\n z['im'] = a['r'] * Math.sin(a['phi']);\n } else if (a.length === 2) { // Quick array check\n z['re'] = a[0];\n z['im'] = a[1];\n } else {\n parser_exit();\n }\n break;\n\n case 'string':\n\n z['im'] = /* void */\n z['re'] = 0;\n\n var tokens = a.match(/\\d+\\.?\\d*e[+-]?\\d+|\\d+\\.?\\d*|\\.\\d+|./g);\n var plus = 1;\n var minus = 0;\n\n if (tokens === null) {\n parser_exit();\n }\n\n for (var i = 0; i < tokens.length; i++) {\n\n var c = tokens[i];\n\n if (c === ' ' || c === '\\t' || c === '\\n') {\n /* void */\n } else if (c === '+') {\n plus++;\n } else if (c === '-') {\n minus++;\n } else if (c === 'i' || c === 'I') {\n\n if (plus + minus === 0) {\n parser_exit();\n }\n\n if (tokens[i + 1] !== ' ' && !isNaN(tokens[i + 1])) {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + tokens[i + 1]);\n i++;\n } else {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + '1');\n }\n plus = minus = 0;\n\n } else {\n\n if (plus + minus === 0 || isNaN(c)) {\n parser_exit();\n }\n\n if (tokens[i + 1] === 'i' || tokens[i + 1] === 'I') {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + c);\n i++;\n } else {\n z['re'] += parseFloat((minus % 2 ? '-' : '') + c);\n }\n plus = minus = 0;\n }\n }\n\n // Still something on the stack\n if (plus + minus > 0) {\n parser_exit();\n }\n break;\n\n case 'number':\n z['im'] = 0;\n z['re'] = a;\n break;\n\n default:\n parser_exit();\n }\n\n if (isNaN(z['re']) || isNaN(z['im'])) {\n // If a calculation is NaN, we treat it as NaN and don't throw\n //parser_exit();\n }\n\n return z;\n };\n\n /**\n * @constructor\n * @returns {Complex}\n */\n function Complex(a, b) {\n\n if (!(this instanceof Complex)) {\n return new Complex(a, b);\n }\n\n var z = parse(a, b);\n\n this['re'] = z['re'];\n this['im'] = z['im'];\n }\n\n Complex.prototype = {\n\n 're': 0,\n 'im': 0,\n\n /**\n * Calculates the sign of a complex number, which is a normalized complex\n *\n * @returns {Complex}\n */\n 'sign': function() {\n\n var abs = this['abs']();\n\n return new Complex(\n this['re'] / abs,\n this['im'] / abs);\n },\n\n /**\n * Adds two complex numbers\n *\n * @returns {Complex}\n */\n 'add': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity + Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity + z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] + z['re'],\n this['im'] + z['im']);\n },\n\n /**\n * Subtracts two complex numbers\n *\n * @returns {Complex}\n */\n 'sub': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity - Infinity = NaN\n if (this['isInfinite']() && z['isInfinite']()) {\n return Complex['NAN'];\n }\n\n // Infinity - z = Infinity { where z != Infinity }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] - z['re'],\n this['im'] - z['im']);\n },\n\n /**\n * Multiplies two complex numbers\n *\n * @returns {Complex}\n */\n 'mul': function(a, b) {\n\n var z = new Complex(a, b);\n\n // Infinity * 0 = NaN\n if ((this['isInfinite']() && z['isZero']()) || (this['isZero']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity * z = Infinity { where z != 0 }\n if (this['isInfinite']() || z['isInfinite']()) {\n return Complex['INFINITY'];\n }\n\n // Short circuit for real values\n if (z['im'] === 0 && this['im'] === 0) {\n return new Complex(this['re'] * z['re'], 0);\n }\n\n return new Complex(\n this['re'] * z['re'] - this['im'] * z['im'],\n this['re'] * z['im'] + this['im'] * z['re']);\n },\n\n /**\n * Divides two complex numbers\n *\n * @returns {Complex}\n */\n 'div': function(a, b) {\n\n var z = new Complex(a, b);\n\n // 0 / 0 = NaN and Infinity / Infinity = NaN\n if ((this['isZero']() && z['isZero']()) || (this['isInfinite']() && z['isInfinite']())) {\n return Complex['NAN'];\n }\n\n // Infinity / 0 = Infinity\n if (this['isInfinite']() || z['isZero']()) {\n return Complex['INFINITY'];\n }\n\n // 0 / Infinity = 0\n if (this['isZero']() || z['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n a = this['re'];\n b = this['im'];\n\n var c = z['re'];\n var d = z['im'];\n var t, x;\n\n if (0 === d) {\n // Divisor is real\n return new Complex(a / c, b / c);\n }\n\n if (Math.abs(c) < Math.abs(d)) {\n\n x = c / d;\n t = c * x + d;\n\n return new Complex(\n (a * x + b) / t,\n (b * x - a) / t);\n\n } else {\n\n x = d / c;\n t = d * x + c;\n\n return new Complex(\n (a + b * x) / t,\n (b - a * x) / t);\n }\n },\n\n /**\n * Calculate the power of two complex numbers\n *\n * @returns {Complex}\n */\n 'pow': function(a, b) {\n\n var z = new Complex(a, b);\n\n a = this['re'];\n b = this['im'];\n\n if (z['isZero']()) {\n return Complex['ONE'];\n }\n\n // If the exponent is real\n if (z['im'] === 0) {\n\n if (b === 0 && a >= 0) {\n\n return new Complex(Math.pow(a, z['re']), 0);\n\n } else if (a === 0) { // If base is fully imaginary\n\n switch ((z['re'] % 4 + 4) % 4) {\n case 0:\n return new Complex(Math.pow(b, z['re']), 0);\n case 1:\n return new Complex(0, Math.pow(b, z['re']));\n case 2:\n return new Complex(-Math.pow(b, z['re']), 0);\n case 3:\n return new Complex(0, -Math.pow(b, z['re']));\n }\n }\n }\n\n /* I couldn't find a good formula, so here is a derivation and optimization\n *\n * z_1^z_2 = (a + bi)^(c + di)\n * = exp((c + di) * log(a + bi)\n * = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))\n * =>...\n * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n *\n * =>...\n * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n *\n * =>\n * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))\n * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))\n *\n */\n\n if (a === 0 && b === 0 && z['re'] > 0 && z['im'] >= 0) {\n return Complex['ZERO'];\n }\n\n var arg = Math.atan2(b, a);\n var loh = logHypot(a, b);\n\n a = Math.exp(z['re'] * loh - z['im'] * arg);\n b = z['im'] * loh + z['re'] * arg;\n return new Complex(\n a * Math.cos(b),\n a * Math.sin(b));\n },\n\n /**\n * Calculate the complex square root\n *\n * @returns {Complex}\n */\n 'sqrt': function() {\n\n var a = this['re'];\n var b = this['im'];\n var r = this['abs']();\n\n var re, im;\n\n if (a >= 0) {\n\n if (b === 0) {\n return new Complex(Math.sqrt(a), 0);\n }\n\n re = 0.5 * Math.sqrt(2.0 * (r + a));\n } else {\n re = Math.abs(b) / Math.sqrt(2 * (r - a));\n }\n\n if (a <= 0) {\n im = 0.5 * Math.sqrt(2.0 * (r - a));\n } else {\n im = Math.abs(b) / Math.sqrt(2 * (r + a));\n }\n\n return new Complex(re, b < 0 ? -im : im);\n },\n\n /**\n * Calculate the complex exponent\n *\n * @returns {Complex}\n */\n 'exp': function() {\n\n var tmp = Math.exp(this['re']);\n\n if (this['im'] === 0) {\n //return new Complex(tmp, 0);\n }\n return new Complex(\n tmp * Math.cos(this['im']),\n tmp * Math.sin(this['im']));\n },\n\n /**\n * Calculate the complex exponent and subtracts one.\n *\n * This may be more accurate than `Complex(x).exp().sub(1)` if\n * `x` is small.\n *\n * @returns {Complex}\n */\n 'expm1': function() {\n\n /**\n * exp(a + i*b) - 1\n = exp(a) * (cos(b) + j*sin(b)) - 1\n = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)\n */\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.expm1(a) * Math.cos(b) + cosm1(b),\n Math.exp(a) * Math.sin(b));\n },\n\n /**\n * Calculate the natural log\n *\n * @returns {Complex}\n */\n 'log': function() {\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0 && a > 0) {\n //return new Complex(Math.log(a), 0);\n }\n\n return new Complex(\n logHypot(a, b),\n Math.atan2(b, a));\n },\n\n /**\n * Calculate the magnitude of the complex number\n *\n * @returns {number}\n */\n 'abs': function() {\n\n return hypot(this['re'], this['im']);\n },\n\n /**\n * Calculate the angle of the complex number\n *\n * @returns {number}\n */\n 'arg': function() {\n\n return Math.atan2(this['im'], this['re']);\n },\n\n /**\n * Calculate the sine of the complex number\n *\n * @returns {Complex}\n */\n 'sin': function() {\n\n // sin(c) = (e^b - e^(-b)) / (2i)\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.sin(a) * cosh(b),\n Math.cos(a) * sinh(b));\n },\n\n /**\n * Calculate the cosine\n *\n * @returns {Complex}\n */\n 'cos': function() {\n\n // cos(z) = (e^b + e^(-b)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n Math.cos(a) * cosh(b),\n -Math.sin(a) * sinh(b));\n },\n\n /**\n * Calculate the tangent\n *\n * @returns {Complex}\n */\n 'tan': function() {\n\n // tan(c) = (e^(ci) - e^(-ci)) / (i(e^(ci) + e^(-ci)))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) + cosh(b);\n\n return new Complex(\n Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the cotangent\n *\n * @returns {Complex}\n */\n 'cot': function() {\n\n // cot(c) = i(e^(ci) + e^(-ci)) / (e^(ci) - e^(-ci))\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = Math.cos(a) - cosh(b);\n\n return new Complex(\n -Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the secant\n *\n * @returns {Complex}\n */\n 'sec': function() {\n\n // sec(c) = 2 / (e^(ci) + e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) + 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.cos(a) * cosh(b) / d,\n Math.sin(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the cosecans\n *\n * @returns {Complex}\n */\n 'csc': function() {\n\n // csc(c) = 2i / (e^(ci) - e^(-ci))\n\n var a = this['re'];\n var b = this['im'];\n var d = 0.5 * cosh(2 * b) - 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.sin(a) * cosh(b) / d,\n -Math.cos(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the complex arcus sinus\n *\n * @returns {Complex}\n */\n 'asin': function() {\n\n // asin(c) = -i * log(ci + sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(t2['im'], -t2['re']);\n },\n\n /**\n * Calculate the complex arcus cosinus\n *\n * @returns {Complex}\n */\n 'acos': function() {\n\n // acos(c) = i * log(c - i * sqrt(1 - c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n var t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n var t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(Math.PI / 2 - t2['im'], t2['re']);\n },\n\n /**\n * Calculate the complex arcus tangent\n *\n * @returns {Complex}\n */\n 'atan': function() {\n\n // atan(c) = i / 2 log((i + x) / (i - x))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0) {\n\n if (b === 1) {\n return new Complex(0, Infinity);\n }\n\n if (b === -1) {\n return new Complex(0, -Infinity);\n }\n }\n\n var d = a * a + (1.0 - b) * (1.0 - b);\n\n var t1 = new Complex(\n (1 - b * b - a * a) / d,\n -2 * a / d).log();\n\n return new Complex(-0.5 * t1['im'], 0.5 * t1['re']);\n },\n\n /**\n * Calculate the complex arcus cotangent\n *\n * @returns {Complex}\n */\n 'acot': function() {\n\n // acot(c) = i / 2 log((c - i) / (c + i))\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n return new Complex(Math.atan2(1, a), 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atan()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atan();\n },\n\n /**\n * Calculate the complex arcus secant\n *\n * @returns {Complex}\n */\n 'asec': function() {\n\n // asec(c) = -i * log(1 / c + sqrt(1 - i / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acos()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acos();\n },\n\n /**\n * Calculate the complex arcus cosecans\n *\n * @returns {Complex}\n */\n 'acsc': function() {\n\n // acsc(c) = -i * log(i / c + sqrt(1 - 1 / c^2))\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(Math.PI / 2, Infinity);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asin()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asin();\n },\n\n /**\n * Calculate the complex sinh\n *\n * @returns {Complex}\n */\n 'sinh': function() {\n\n // sinh(c) = (e^c - e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n sinh(a) * Math.cos(b),\n cosh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex cosh\n *\n * @returns {Complex}\n */\n 'cosh': function() {\n\n // cosh(c) = (e^c + e^-c) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n return new Complex(\n cosh(a) * Math.cos(b),\n sinh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex tanh\n *\n * @returns {Complex}\n */\n 'tanh': function() {\n\n // tanh(c) = (e^c - e^-c) / (e^c + e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) + Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'coth': function() {\n\n // coth(c) = (e^c + e^-c) / (e^c - e^-c)\n\n var a = 2 * this['re'];\n var b = 2 * this['im'];\n var d = cosh(a) - Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n -Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'csch': function() {\n\n // csch(c) = 2 / (e^c - e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) - cosh(2 * a);\n\n return new Complex(\n -2 * sinh(a) * Math.cos(b) / d,\n 2 * cosh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex sech\n *\n * @returns {Complex}\n */\n 'sech': function() {\n\n // sech(c) = 2 / (e^c + e^-c)\n\n var a = this['re'];\n var b = this['im'];\n var d = Math.cos(2 * b) + cosh(2 * a);\n\n return new Complex(\n 2 * cosh(a) * Math.cos(b) / d,\n -2 * sinh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'asinh': function() {\n\n // asinh(c) = log(c + sqrt(c^2 + 1))\n\n var tmp = this['im'];\n this['im'] = -this['re'];\n this['re'] = tmp;\n var res = this['asin']();\n\n this['re'] = -this['im'];\n this['im'] = tmp;\n tmp = res['re'];\n\n res['re'] = -res['im'];\n res['im'] = tmp;\n return res;\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'acosh': function() {\n\n // acosh(c) = log(c + sqrt(c^2 - 1))\n\n var res = this['acos']();\n if (res['im'] <= 0) {\n var tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n } else {\n var tmp = res['im'];\n res['im'] = -res['re'];\n res['re'] = tmp;\n }\n return res;\n },\n\n /**\n * Calculate the complex atanh\n *\n * @returns {Complex}\n */\n 'atanh': function() {\n\n // atanh(c) = log((1+c) / (1-c)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n var noIM = a > 1 && b === 0;\n var oneMinus = 1 - a;\n var onePlus = 1 + a;\n var d = oneMinus * oneMinus + b * b;\n\n var x = (d !== 0)\n ? new Complex(\n (onePlus * oneMinus - b * b) / d,\n (b * oneMinus + onePlus * b) / d)\n : new Complex(\n (a !== -1) ? (a / 0) : 0,\n (b !== 0) ? (b / 0) : 0);\n\n var temp = x['re'];\n x['re'] = logHypot(x['re'], x['im']) / 2;\n x['im'] = Math.atan2(x['im'], temp) / 2;\n if (noIM) {\n x['im'] = -x['im'];\n }\n return x;\n },\n\n /**\n * Calculate the complex acoth\n *\n * @returns {Complex}\n */\n 'acoth': function() {\n\n // acoth(c) = log((c+1) / (c-1)) / 2\n\n var a = this['re'];\n var b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Math.PI / 2);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atanh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atanh();\n },\n\n /**\n * Calculate the complex acsch\n *\n * @returns {Complex}\n */\n 'acsch': function() {\n\n // acsch(c) = log((1+sqrt(1+c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (b === 0) {\n\n return new Complex(\n (a !== 0)\n ? Math.log(a + Math.sqrt(a * a + 1))\n : Infinity, 0);\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asinh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asinh();\n },\n\n /**\n * Calculate the complex asech\n *\n * @returns {Complex}\n */\n 'asech': function() {\n\n // asech(c) = log((1+sqrt(1-c^2))/c)\n\n var a = this['re'];\n var b = this['im'];\n\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n var d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acosh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acosh();\n },\n\n /**\n * Calculate the complex inverse 1/z\n *\n * @returns {Complex}\n */\n 'inverse': function() {\n\n // 1 / 0 = Infinity and 1 / Infinity = 0\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n if (this['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n var a = this['re'];\n var b = this['im'];\n\n var d = a * a + b * b;\n\n return new Complex(a / d, -b / d);\n },\n\n /**\n * Returns the complex conjugate\n *\n * @returns {Complex}\n */\n 'conjugate': function() {\n\n return new Complex(this['re'], -this['im']);\n },\n\n /**\n * Gets the negated complex number\n *\n * @returns {Complex}\n */\n 'neg': function() {\n\n return new Complex(-this['re'], -this['im']);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'ceil': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.ceil(this['re'] * places) / places,\n Math.ceil(this['im'] * places) / places);\n },\n\n /**\n * Floors the actual complex number\n *\n * @returns {Complex}\n */\n 'floor': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.floor(this['re'] * places) / places,\n Math.floor(this['im'] * places) / places);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'round': function(places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.round(this['re'] * places) / places,\n Math.round(this['im'] * places) / places);\n },\n\n /**\n * Compares two complex numbers\n *\n * **Note:** new Complex(Infinity).equals(Infinity) === false\n *\n * @returns {boolean}\n */\n 'equals': function(a, b) {\n\n var z = new Complex(a, b);\n\n return Math.abs(z['re'] - this['re']) <= Complex['EPSILON'] &&\n Math.abs(z['im'] - this['im']) <= Complex['EPSILON'];\n },\n\n /**\n * Clones the actual object\n *\n * @returns {Complex}\n */\n 'clone': function() {\n\n return new Complex(this['re'], this['im']);\n },\n\n /**\n * Gets a string of the actual complex number\n *\n * @returns {string}\n */\n 'toString': function() {\n\n var a = this['re'];\n var b = this['im'];\n var ret = '';\n\n if (this['isNaN']()) {\n return 'NaN';\n }\n\n if (this['isZero']()) {\n return '0';\n }\n\n if (this['isInfinite']()) {\n return 'Infinity';\n }\n\n if (a !== 0) {\n ret += a;\n }\n\n if (b !== 0) {\n\n if (a !== 0) {\n ret += b < 0 ? ' - ' : ' + ';\n } else if (b < 0) {\n ret += '-';\n }\n\n b = Math.abs(b);\n\n if (1 !== b) {\n ret += b;\n }\n ret += 'i';\n }\n\n if (!ret)\n return '0';\n\n return ret;\n },\n\n /**\n * Returns the actual number as a vector\n *\n * @returns {Array}\n */\n 'toVector': function() {\n\n return [this['re'], this['im']];\n },\n\n /**\n * Returns the actual real value of the current object\n *\n * @returns {number|null}\n */\n 'valueOf': function() {\n\n if (this['im'] === 0) {\n return this['re'];\n }\n return null;\n },\n\n /**\n * Determines whether a complex number is not on the Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isNaN': function() {\n return isNaN(this['re']) || isNaN(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the zero pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isZero': function() {\n return (\n (this['re'] === 0 || this['re'] === -0) &&\n (this['im'] === 0 || this['im'] === -0)\n );\n },\n\n /**\n * Determines whether a complex number is not at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isFinite': function() {\n return isFinite(this['re']) && isFinite(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isInfinite': function() {\n return !(this['isNaN']() || this['isFinite']());\n }\n };\n\n Complex['ZERO'] = new Complex(0, 0);\n Complex['ONE'] = new Complex(1, 0);\n Complex['I'] = new Complex(0, 1);\n Complex['PI'] = new Complex(Math.PI, 0);\n Complex['E'] = new Complex(Math.E, 0);\n Complex['INFINITY'] = new Complex(Infinity, Infinity);\n Complex['NAN'] = new Complex(NaN, NaN);\n Complex['EPSILON'] = 1e-16;\n\n if (typeof define === 'function' && define['amd']) {\n define([], function() {\n return Complex;\n });\n } else if (typeof exports === 'object') {\n Object.defineProperty(exports, \"__esModule\", {'value': true});\n Complex['default'] = Complex;\n Complex['Complex'] = Complex;\n module['exports'] = Complex;\n } else {\n root['Complex'] = Complex;\n }\n\n})(this);\n","module.exports = function() {\n\tthrow new Error(\"define cannot be used indirect\");\n};\n","/**\n * @license Fraction.js v4.0.12 09/09/2015\n * http://www.xarg.org/2014/03/rational-numbers-in-javascript/\n *\n * Copyright (c) 2015, Robert Eisele (robert@xarg.org)\n * Dual licensed under the MIT or GPL Version 2 licenses.\n **/\n\n\n/**\n *\n * This class offers the possibility to calculate fractions.\n * You can pass a fraction in different formats. Either as array, as double, as string or as an integer.\n *\n * Array/Object form\n * [ 0 => , 1 => ]\n * [ n => , d => ]\n *\n * Integer form\n * - Single integer value\n *\n * Double form\n * - Single double value\n *\n * String form\n * 123.456 - a simple double\n * 123/456 - a string fraction\n * 123.'456' - a double with repeating decimal places\n * 123.(456) - synonym\n * 123.45'6' - a double with repeating last place\n * 123.45(6) - synonym\n *\n * Example:\n *\n * var f = new Fraction(\"9.4'31'\");\n * f.mul([-4, 3]).div(4.9);\n *\n */\n\n(function(root) {\n\n \"use strict\";\n\n // Maximum search depth for cyclic rational numbers. 2000 should be more than enough.\n // Example: 1/7 = 0.(142857) has 6 repeating decimal places.\n // If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits\n var MAX_CYCLE_LEN = 2000;\n\n // Parsed data to avoid calling \"new\" all the time\n var P = {\n \"s\": 1,\n \"n\": 0,\n \"d\": 1\n };\n\n function createError(name) {\n\n function errorConstructor() {\n var temp = Error.apply(this, arguments);\n temp['name'] = this['name'] = name;\n this['stack'] = temp['stack'];\n this['message'] = temp['message'];\n }\n\n /**\n * Error constructor\n *\n * @constructor\n */\n function IntermediateInheritor() { }\n IntermediateInheritor.prototype = Error.prototype;\n errorConstructor.prototype = new IntermediateInheritor();\n\n return errorConstructor;\n }\n\n var DivisionByZero = Fraction['DivisionByZero'] = createError('DivisionByZero');\n var InvalidParameter = Fraction['InvalidParameter'] = createError('InvalidParameter');\n\n function assign(n, s) {\n\n if (isNaN(n = parseInt(n, 10))) {\n throwInvalidParam();\n }\n return n * s;\n }\n\n function throwInvalidParam() {\n throw new InvalidParameter();\n }\n\n var parse = function(p1, p2) {\n\n var n = 0, d = 1, s = 1;\n var v = 0, w = 0, x = 0, y = 1, z = 1;\n\n var A = 0, B = 1;\n var C = 1, D = 1;\n\n var N = 10000000;\n var M;\n\n if (p1 === undefined || p1 === null) {\n /* void */\n } else if (p2 !== undefined) {\n n = p1;\n d = p2;\n s = n * d;\n } else\n switch (typeof p1) {\n\n case \"object\":\n {\n if (\"d\" in p1 && \"n\" in p1) {\n n = p1[\"n\"];\n d = p1[\"d\"];\n if (\"s\" in p1)\n n *= p1[\"s\"];\n } else if (0 in p1) {\n n = p1[0];\n if (1 in p1)\n d = p1[1];\n } else {\n throwInvalidParam();\n }\n s = n * d;\n break;\n }\n case \"number\":\n {\n if (p1 < 0) {\n s = p1;\n p1 = -p1;\n }\n\n if (p1 % 1 === 0) {\n n = p1;\n } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow\n\n if (p1 >= 1) {\n z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10));\n p1 /= z;\n }\n\n // Using Farey Sequences\n // http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/\n\n while (B <= N && D <= N) {\n M = (A + C) / (B + D);\n\n if (p1 === M) {\n if (B + D <= N) {\n n = A + C;\n d = B + D;\n } else if (D > B) {\n n = C;\n d = D;\n } else {\n n = A;\n d = B;\n }\n break;\n\n } else {\n\n if (p1 > M) {\n A += C;\n B += D;\n } else {\n C += A;\n D += B;\n }\n\n if (B > N) {\n n = C;\n d = D;\n } else {\n n = A;\n d = B;\n }\n }\n }\n n *= z;\n } else if (isNaN(p1) || isNaN(p2)) {\n d = n = NaN;\n }\n break;\n }\n case \"string\":\n {\n B = p1.match(/\\d+|./g);\n\n if (B === null)\n throwInvalidParam();\n\n if (B[A] === '-') {// Check for minus sign at the beginning\n s = -1;\n A++;\n } else if (B[A] === '+') {// Check for plus sign at the beginning\n A++;\n }\n\n if (B.length === A + 1) { // Check if it's just a simple number \"1234\"\n w = assign(B[A++], s);\n } else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number\n\n if (B[A] !== '.') { // Handle 0.5 and .5\n v = assign(B[A++], s);\n }\n A++;\n\n // Check for decimal places\n if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === \"'\" && B[A + 3] === \"'\") {\n w = assign(B[A], s);\n y = Math.pow(10, B[A].length);\n A++;\n }\n\n // Check for repeating places\n if (B[A] === '(' && B[A + 2] === ')' || B[A] === \"'\" && B[A + 2] === \"'\") {\n x = assign(B[A + 1], s);\n z = Math.pow(10, B[A + 1].length) - 1;\n A += 3;\n }\n\n } else if (B[A + 1] === '/' || B[A + 1] === ':') { // Check for a simple fraction \"123/456\" or \"123:456\"\n w = assign(B[A], s);\n y = assign(B[A + 2], 1);\n A += 3;\n } else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction \"123 1/2\"\n v = assign(B[A], s);\n w = assign(B[A + 2], s);\n y = assign(B[A + 4], 1);\n A += 5;\n }\n\n if (B.length <= A) { // Check for more tokens on the stack\n d = y * z;\n s = /* void */\n n = x + d * v + z * w;\n break;\n }\n\n /* Fall through on error */\n }\n default:\n throwInvalidParam();\n }\n\n if (d === 0) {\n throw new DivisionByZero();\n }\n\n P[\"s\"] = s < 0 ? -1 : 1;\n P[\"n\"] = Math.abs(n);\n P[\"d\"] = Math.abs(d);\n };\n\n function modpow(b, e, m) {\n\n var r = 1;\n for (; e > 0; b = (b * b) % m, e >>= 1) {\n\n if (e & 1) {\n r = (r * b) % m;\n }\n }\n return r;\n }\n\n\n function cycleLen(n, d) {\n\n for (; d % 2 === 0;\n d /= 2) {\n }\n\n for (; d % 5 === 0;\n d /= 5) {\n }\n\n if (d === 1) // Catch non-cyclic numbers\n return 0;\n\n // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem:\n // 10^(d-1) % d == 1\n // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone,\n // as we want to translate the numbers to strings.\n\n var rem = 10 % d;\n var t = 1;\n\n for (; rem !== 1; t++) {\n rem = rem * 10 % d;\n\n if (t > MAX_CYCLE_LEN)\n return 0; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1`\n }\n return t;\n }\n\n\n function cycleStart(n, d, len) {\n\n var rem1 = 1;\n var rem2 = modpow(10, len, d);\n\n for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE)\n // Solve 10^s == 10^(s+t) (mod d)\n\n if (rem1 === rem2)\n return t;\n\n rem1 = rem1 * 10 % d;\n rem2 = rem2 * 10 % d;\n }\n return 0;\n }\n\n function gcd(a, b) {\n\n if (!a)\n return b;\n if (!b)\n return a;\n\n while (1) {\n a %= b;\n if (!a)\n return b;\n b %= a;\n if (!b)\n return a;\n }\n };\n\n /**\n * Module constructor\n *\n * @constructor\n * @param {number|Fraction=} a\n * @param {number=} b\n */\n function Fraction(a, b) {\n\n if (!(this instanceof Fraction)) {\n return new Fraction(a, b);\n }\n\n parse(a, b);\n\n if (Fraction['REDUCE']) {\n a = gcd(P[\"d\"], P[\"n\"]); // Abuse a\n } else {\n a = 1;\n }\n\n this[\"s\"] = P[\"s\"];\n this[\"n\"] = P[\"n\"] / a;\n this[\"d\"] = P[\"d\"] / a;\n }\n\n /**\n * Boolean global variable to be able to disable automatic reduction of the fraction\n *\n */\n Fraction['REDUCE'] = 1;\n\n Fraction.prototype = {\n\n \"s\": 1,\n \"n\": 0,\n \"d\": 1,\n\n /**\n * Calculates the absolute value\n *\n * Ex: new Fraction(-4).abs() => 4\n **/\n \"abs\": function() {\n\n return new Fraction(this[\"n\"], this[\"d\"]);\n },\n\n /**\n * Inverts the sign of the current fraction\n *\n * Ex: new Fraction(-4).neg() => 4\n **/\n \"neg\": function() {\n\n return new Fraction(-this[\"s\"] * this[\"n\"], this[\"d\"]);\n },\n\n /**\n * Adds two rational numbers\n *\n * Ex: new Fraction({n: 2, d: 3}).add(\"14.9\") => 467 / 30\n **/\n \"add\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * this[\"n\"] * P[\"d\"] + P[\"s\"] * this[\"d\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Subtracts two rational numbers\n *\n * Ex: new Fraction({n: 2, d: 3}).add(\"14.9\") => -427 / 30\n **/\n \"sub\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * this[\"n\"] * P[\"d\"] - P[\"s\"] * this[\"d\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Multiplies two rational numbers\n *\n * Ex: new Fraction(\"-17.(345)\").mul(3) => 5776 / 111\n **/\n \"mul\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * P[\"s\"] * this[\"n\"] * P[\"n\"],\n this[\"d\"] * P[\"d\"]\n );\n },\n\n /**\n * Divides two rational numbers\n *\n * Ex: new Fraction(\"-17.(345)\").inverse().div(3)\n **/\n \"div\": function(a, b) {\n\n parse(a, b);\n return new Fraction(\n this[\"s\"] * P[\"s\"] * this[\"n\"] * P[\"d\"],\n this[\"d\"] * P[\"n\"]\n );\n },\n\n /**\n * Clones the actual object\n *\n * Ex: new Fraction(\"-17.(345)\").clone()\n **/\n \"clone\": function() {\n return new Fraction(this);\n },\n\n /**\n * Calculates the modulo of two rational numbers - a more precise fmod\n *\n * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6)\n **/\n \"mod\": function(a, b) {\n\n if (isNaN(this['n']) || isNaN(this['d'])) {\n return new Fraction(NaN);\n }\n\n if (a === undefined) {\n return new Fraction(this[\"s\"] * this[\"n\"] % this[\"d\"], 1);\n }\n\n parse(a, b);\n if (0 === P[\"n\"] && 0 === this[\"d\"]) {\n Fraction(0, 0); // Throw DivisionByZero\n }\n\n /*\n * First silly attempt, kinda slow\n *\n return that[\"sub\"]({\n \"n\": num[\"n\"] * Math.floor((this.n / this.d) / (num.n / num.d)),\n \"d\": num[\"d\"],\n \"s\": this[\"s\"]\n });*/\n\n /*\n * New attempt: a1 / b1 = a2 / b2 * q + r\n * => b2 * a1 = a2 * b1 * q + b1 * b2 * r\n * => (b2 * a1 % a2 * b1) / (b1 * b2)\n */\n return new Fraction(\n this[\"s\"] * (P[\"d\"] * this[\"n\"]) % (P[\"n\"] * this[\"d\"]),\n P[\"d\"] * this[\"d\"]\n );\n },\n\n /**\n * Calculates the fractional gcd of two rational numbers\n *\n * Ex: new Fraction(5,8).gcd(3,7) => 1/56\n */\n \"gcd\": function(a, b) {\n\n parse(a, b);\n\n // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d)\n\n return new Fraction(gcd(P[\"n\"], this[\"n\"]) * gcd(P[\"d\"], this[\"d\"]), P[\"d\"] * this[\"d\"]);\n },\n\n /**\n * Calculates the fractional lcm of two rational numbers\n *\n * Ex: new Fraction(5,8).lcm(3,7) => 15\n */\n \"lcm\": function(a, b) {\n\n parse(a, b);\n\n // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d)\n\n if (P[\"n\"] === 0 && this[\"n\"] === 0) {\n return new Fraction;\n }\n return new Fraction(P[\"n\"] * this[\"n\"], gcd(P[\"n\"], this[\"n\"]) * gcd(P[\"d\"], this[\"d\"]));\n },\n\n /**\n * Calculates the ceil of a rational number\n *\n * Ex: new Fraction('4.(3)').ceil() => (5 / 1)\n **/\n \"ceil\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.ceil(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Calculates the floor of a rational number\n *\n * Ex: new Fraction('4.(3)').floor() => (4 / 1)\n **/\n \"floor\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.floor(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Rounds a rational numbers\n *\n * Ex: new Fraction('4.(3)').round() => (4 / 1)\n **/\n \"round\": function(places) {\n\n places = Math.pow(10, places || 0);\n\n if (isNaN(this[\"n\"]) || isNaN(this[\"d\"])) {\n return new Fraction(NaN);\n }\n return new Fraction(Math.round(places * this[\"s\"] * this[\"n\"] / this[\"d\"]), places);\n },\n\n /**\n * Gets the inverse of the fraction, means numerator and denominator are exchanged\n *\n * Ex: new Fraction([-3, 4]).inverse() => -4 / 3\n **/\n \"inverse\": function() {\n\n return new Fraction(this[\"s\"] * this[\"d\"], this[\"n\"]);\n },\n\n /**\n * Calculates the fraction to some integer exponent\n *\n * Ex: new Fraction(-1,2).pow(-3) => -8\n */\n \"pow\": function(m) {\n\n if (m < 0) {\n return new Fraction(Math.pow(this['s'] * this[\"d\"], -m), Math.pow(this[\"n\"], -m));\n } else {\n return new Fraction(Math.pow(this['s'] * this[\"n\"], m), Math.pow(this[\"d\"], m));\n }\n },\n\n /**\n * Check if two rational numbers are the same\n *\n * Ex: new Fraction(19.6).equals([98, 5]);\n **/\n \"equals\": function(a, b) {\n\n parse(a, b);\n return this[\"s\"] * this[\"n\"] * P[\"d\"] === P[\"s\"] * P[\"n\"] * this[\"d\"]; // Same as compare() === 0\n },\n\n /**\n * Check if two rational numbers are the same\n *\n * Ex: new Fraction(19.6).equals([98, 5]);\n **/\n \"compare\": function(a, b) {\n\n parse(a, b);\n var t = (this[\"s\"] * this[\"n\"] * P[\"d\"] - P[\"s\"] * P[\"n\"] * this[\"d\"]);\n return (0 < t) - (t < 0);\n },\n\n \"simplify\": function(eps) {\n\n // First naive implementation, needs improvement\n\n if (isNaN(this['n']) || isNaN(this['d'])) {\n return this;\n }\n\n var cont = this['abs']()['toContinued']();\n\n eps = eps || 0.001;\n\n function rec(a) {\n if (a.length === 1)\n return new Fraction(a[0]);\n return rec(a.slice(1))['inverse']()['add'](a[0]);\n }\n\n for (var i = 0; i < cont.length; i++) {\n var tmp = rec(cont.slice(0, i + 1));\n if (tmp['sub'](this['abs']())['abs']().valueOf() < eps) {\n return tmp['mul'](this['s']);\n }\n }\n return this;\n },\n\n /**\n * Check if two rational numbers are divisible\n *\n * Ex: new Fraction(19.6).divisible(1.5);\n */\n \"divisible\": function(a, b) {\n\n parse(a, b);\n return !(!(P[\"n\"] * this[\"d\"]) || ((this[\"n\"] * P[\"d\"]) % (P[\"n\"] * this[\"d\"])));\n },\n\n /**\n * Returns a decimal representation of the fraction\n *\n * Ex: new Fraction(\"100.'91823'\").valueOf() => 100.91823918239183\n **/\n 'valueOf': function() {\n\n return this[\"s\"] * this[\"n\"] / this[\"d\"];\n },\n\n /**\n * Returns a string-fraction representation of a Fraction object\n *\n * Ex: new Fraction(\"1.'3'\").toFraction() => \"4 1/3\"\n **/\n 'toFraction': function(excludeWhole) {\n\n var whole, str = \"\";\n var n = this[\"n\"];\n var d = this[\"d\"];\n if (this[\"s\"] < 0) {\n str += '-';\n }\n\n if (d === 1) {\n str += n;\n } else {\n\n if (excludeWhole && (whole = Math.floor(n / d)) > 0) {\n str += whole;\n str += \" \";\n n %= d;\n }\n\n str += n;\n str += '/';\n str += d;\n }\n return str;\n },\n\n /**\n * Returns a latex representation of a Fraction object\n *\n * Ex: new Fraction(\"1.'3'\").toLatex() => \"\\frac{4}{3}\"\n **/\n 'toLatex': function(excludeWhole) {\n\n var whole, str = \"\";\n var n = this[\"n\"];\n var d = this[\"d\"];\n if (this[\"s\"] < 0) {\n str += '-';\n }\n\n if (d === 1) {\n str += n;\n } else {\n\n if (excludeWhole && (whole = Math.floor(n / d)) > 0) {\n str += whole;\n n %= d;\n }\n\n str += \"\\\\frac{\";\n str += n;\n str += '}{';\n str += d;\n str += '}';\n }\n return str;\n },\n\n /**\n * Returns an array of continued fraction elements\n *\n * Ex: new Fraction(\"7/8\").toContinued() => [0,1,7]\n */\n 'toContinued': function() {\n\n var t;\n var a = this['n'];\n var b = this['d'];\n var res = [];\n\n if (isNaN(a) || isNaN(b)) {\n return res;\n }\n\n do {\n res.push(Math.floor(a / b));\n t = a % b;\n a = b;\n b = t;\n } while (a !== 1);\n\n return res;\n },\n\n /**\n * Creates a string representation of a fraction with all digits\n *\n * Ex: new Fraction(\"100.'91823'\").toString() => \"100.(91823)\"\n **/\n 'toString': function(dec) {\n\n var g;\n var N = this[\"n\"];\n var D = this[\"d\"];\n\n if (isNaN(N) || isNaN(D)) {\n return \"NaN\";\n }\n\n if (!Fraction['REDUCE']) {\n g = gcd(N, D);\n N /= g;\n D /= g;\n }\n\n dec = dec || 15; // 15 = decimal places when no repitation\n\n var cycLen = cycleLen(N, D); // Cycle length\n var cycOff = cycleStart(N, D, cycLen); // Cycle start\n\n var str = this['s'] === -1 ? \"-\" : \"\";\n\n str += N / D | 0;\n\n N %= D;\n N *= 10;\n\n if (N)\n str += \".\";\n\n if (cycLen) {\n\n for (var i = cycOff; i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n str += \"(\";\n for (var i = cycLen; i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n str += \")\";\n } else {\n for (var i = dec; N && i--;) {\n str += N / D | 0;\n N %= D;\n N *= 10;\n }\n }\n return str;\n }\n };\n\n if (typeof define === \"function\" && define[\"amd\"]) {\n define([], function() {\n return Fraction;\n });\n } else if (typeof exports === \"object\") {\n Object.defineProperty(Fraction, \"__esModule\", { 'value': true });\n Fraction['default'] = Fraction;\n Fraction['Fraction'] = Fraction;\n module['exports'] = Fraction;\n } else {\n root['Fraction'] = Fraction;\n }\n\n})(this);\n","/*\r\n * Natural Sort algorithm for Javascript - Version 0.7 - Released under MIT license\r\n * Author: Jim Palmer (based on chunking idea from Dave Koelle)\r\n */\r\n/*jshint unused:false */\r\nmodule.exports = function naturalSort (a, b) {\r\n\t\"use strict\";\r\n\tvar re = /(^([+\\-]?(?:0|[1-9]\\d*)(?:\\.\\d*)?(?:[eE][+\\-]?\\d+)?)?$|^0x[0-9a-f]+$|\\d+)/gi,\r\n\t\tsre = /(^[ ]*|[ ]*$)/g,\r\n\t\tdre = /(^([\\w ]+,?[\\w ]+)?[\\w ]+,?[\\w ]+\\d+:\\d+(:\\d+)?[\\w ]?|^\\d{1,4}[\\/\\-]\\d{1,4}[\\/\\-]\\d{1,4}|^\\w+, \\w+ \\d+, \\d{4})/,\r\n\t\thre = /^0x[0-9a-f]+$/i,\r\n\t\tore = /^0/,\r\n\t\ti = function(s) { return naturalSort.insensitive && ('' + s).toLowerCase() || '' + s; },\r\n\t\t// convert all to strings strip whitespace\r\n\t\tx = i(a).replace(sre, '') || '',\r\n\t\ty = i(b).replace(sre, '') || '',\r\n\t\t// chunk/tokenize\r\n\t\txN = x.replace(re, '\\0$1\\0').replace(/\\0$/,'').replace(/^\\0/,'').split('\\0'),\r\n\t\tyN = y.replace(re, '\\0$1\\0').replace(/\\0$/,'').replace(/^\\0/,'').split('\\0'),\r\n\t\t// numeric, hex or date detection\r\n\t\txD = parseInt(x.match(hre), 16) || (xN.length !== 1 && x.match(dre) && Date.parse(x)),\r\n\t\tyD = parseInt(y.match(hre), 16) || xD && y.match(dre) && Date.parse(y) || null,\r\n\t\toFxNcL, oFyNcL;\r\n\t// first try and sort Hex codes or Dates\r\n\tif (yD) {\r\n\t\tif ( xD < yD ) { return -1; }\r\n\t\telse if ( xD > yD ) { return 1; }\r\n\t}\r\n\t// natural sorting through split numeric strings and default strings\r\n\tfor(var cLoc=0, numS=Math.max(xN.length, yN.length); cLoc < numS; cLoc++) {\r\n\t\t// find floats not starting with '0', string or 0 if not defined (Clint Priest)\r\n\t\toFxNcL = !(xN[cLoc] || '').match(ore) && parseFloat(xN[cLoc]) || xN[cLoc] || 0;\r\n\t\toFyNcL = !(yN[cLoc] || '').match(ore) && parseFloat(yN[cLoc]) || yN[cLoc] || 0;\r\n\t\t// handle numeric vs string comparison - number < string - (Kyle Adams)\r\n\t\tif (isNaN(oFxNcL) !== isNaN(oFyNcL)) { return (isNaN(oFxNcL)) ? 1 : -1; }\r\n\t\t// rely on string comparison if different types - i.e. '02' < 2 != '02' < '2'\r\n\t\telse if (typeof oFxNcL !== typeof oFyNcL) {\r\n\t\t\toFxNcL += '';\r\n\t\t\toFyNcL += '';\r\n\t\t}\r\n\t\tif (oFxNcL < oFyNcL) { return -1; }\r\n\t\tif (oFxNcL > oFyNcL) { return 1; }\r\n\t}\r\n\treturn 0;\r\n};\r\n","module.exports = function(module) {\n\tif (!module.webpackPolyfill) {\n\t\tmodule.deprecate = function() {};\n\t\tmodule.paths = [];\n\t\t// module.parent = undefined by default\n\t\tif (!module.children) module.children = [];\n\t\tObject.defineProperty(module, \"loaded\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.l;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"id\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.i;\n\t\t\t}\n\t\t});\n\t\tmodule.webpackPolyfill = 1;\n\t}\n\treturn module;\n};\n","/* globals __webpack_amd_options__ */\nmodule.exports = __webpack_amd_options__;\n",";(function (globalScope) {\r\n 'use strict';\r\n\r\n\r\n /*\r\n * decimal.js v10.2.1\r\n * An arbitrary-precision Decimal type for JavaScript.\r\n * https://github.com/MikeMcl/decimal.js\r\n * Copyright (c) 2020 Michael Mclaughlin \r\n * MIT Licence\r\n */\r\n\r\n\r\n // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ //\r\n\r\n\r\n // The maximum exponent magnitude.\r\n // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.\r\n var EXP_LIMIT = 9e15, // 0 to 9e15\r\n\r\n // The limit on the value of `precision`, and on the value of the first argument to\r\n // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.\r\n MAX_DIGITS = 1e9, // 0 to 1e9\r\n\r\n // Base conversion alphabet.\r\n NUMERALS = '0123456789abcdef',\r\n\r\n // The natural logarithm of 10 (1025 digits).\r\n LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',\r\n\r\n // Pi (1025 digits).\r\n PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',\r\n\r\n\r\n // The initial configuration properties of the Decimal constructor.\r\n DEFAULTS = {\r\n\r\n // These values must be integers within the stated ranges (inclusive).\r\n // Most of these values can be changed at run-time using the `Decimal.config` method.\r\n\r\n // The maximum number of significant digits of the result of a calculation or base conversion.\r\n // E.g. `Decimal.config({ precision: 20 });`\r\n precision: 20, // 1 to MAX_DIGITS\r\n\r\n // The rounding mode used when rounding to `precision`.\r\n //\r\n // ROUND_UP 0 Away from zero.\r\n // ROUND_DOWN 1 Towards zero.\r\n // ROUND_CEIL 2 Towards +Infinity.\r\n // ROUND_FLOOR 3 Towards -Infinity.\r\n // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up.\r\n // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.\r\n // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.\r\n // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.\r\n // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.\r\n //\r\n // E.g.\r\n // `Decimal.rounding = 4;`\r\n // `Decimal.rounding = Decimal.ROUND_HALF_UP;`\r\n rounding: 4, // 0 to 8\r\n\r\n // The modulo mode used when calculating the modulus: a mod n.\r\n // The quotient (q = a / n) is calculated according to the corresponding rounding mode.\r\n // The remainder (r) is calculated as: r = a - n * q.\r\n //\r\n // UP 0 The remainder is positive if the dividend is negative, else is negative.\r\n // DOWN 1 The remainder has the same sign as the dividend (JavaScript %).\r\n // FLOOR 3 The remainder has the same sign as the divisor (Python %).\r\n // HALF_EVEN 6 The IEEE 754 remainder function.\r\n // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.\r\n //\r\n // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian\r\n // division (9) are commonly used for the modulus operation. The other rounding modes can also\r\n // be used, but they may not give useful results.\r\n modulo: 1, // 0 to 9\r\n\r\n // The exponent value at and beneath which `toString` returns exponential notation.\r\n // JavaScript numbers: -7\r\n toExpNeg: -7, // 0 to -EXP_LIMIT\r\n\r\n // The exponent value at and above which `toString` returns exponential notation.\r\n // JavaScript numbers: 21\r\n toExpPos: 21, // 0 to EXP_LIMIT\r\n\r\n // The minimum exponent value, beneath which underflow to zero occurs.\r\n // JavaScript numbers: -324 (5e-324)\r\n minE: -EXP_LIMIT, // -1 to -EXP_LIMIT\r\n\r\n // The maximum exponent value, above which overflow to Infinity occurs.\r\n // JavaScript numbers: 308 (1.7976931348623157e+308)\r\n maxE: EXP_LIMIT, // 1 to EXP_LIMIT\r\n\r\n // Whether to use cryptographically-secure random number generation, if available.\r\n crypto: false // true/false\r\n },\r\n\r\n\r\n // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //\r\n\r\n\r\n Decimal, inexact, noConflict, quadrant,\r\n external = true,\r\n\r\n decimalError = '[DecimalError] ',\r\n invalidArgument = decimalError + 'Invalid argument: ',\r\n precisionLimitExceeded = decimalError + 'Precision limit exceeded',\r\n cryptoUnavailable = decimalError + 'crypto unavailable',\r\n\r\n mathfloor = Math.floor,\r\n mathpow = Math.pow,\r\n\r\n isBinary = /^0b([01]+(\\.[01]*)?|\\.[01]+)(p[+-]?\\d+)?$/i,\r\n isHex = /^0x([0-9a-f]+(\\.[0-9a-f]*)?|\\.[0-9a-f]+)(p[+-]?\\d+)?$/i,\r\n isOctal = /^0o([0-7]+(\\.[0-7]*)?|\\.[0-7]+)(p[+-]?\\d+)?$/i,\r\n isDecimal = /^(\\d+(\\.\\d*)?|\\.\\d+)(e[+-]?\\d+)?$/i,\r\n\r\n BASE = 1e7,\r\n LOG_BASE = 7,\r\n MAX_SAFE_INTEGER = 9007199254740991,\r\n\r\n LN10_PRECISION = LN10.length - 1,\r\n PI_PRECISION = PI.length - 1,\r\n\r\n // Decimal.prototype object\r\n P = { name: '[object Decimal]' };\r\n\r\n\r\n // Decimal prototype methods\r\n\r\n\r\n /*\r\n * absoluteValue abs\r\n * ceil\r\n * comparedTo cmp\r\n * cosine cos\r\n * cubeRoot cbrt\r\n * decimalPlaces dp\r\n * dividedBy div\r\n * dividedToIntegerBy divToInt\r\n * equals eq\r\n * floor\r\n * greaterThan gt\r\n * greaterThanOrEqualTo gte\r\n * hyperbolicCosine cosh\r\n * hyperbolicSine sinh\r\n * hyperbolicTangent tanh\r\n * inverseCosine acos\r\n * inverseHyperbolicCosine acosh\r\n * inverseHyperbolicSine asinh\r\n * inverseHyperbolicTangent atanh\r\n * inverseSine asin\r\n * inverseTangent atan\r\n * isFinite\r\n * isInteger isInt\r\n * isNaN\r\n * isNegative isNeg\r\n * isPositive isPos\r\n * isZero\r\n * lessThan lt\r\n * lessThanOrEqualTo lte\r\n * logarithm log\r\n * [maximum] [max]\r\n * [minimum] [min]\r\n * minus sub\r\n * modulo mod\r\n * naturalExponential exp\r\n * naturalLogarithm ln\r\n * negated neg\r\n * plus add\r\n * precision sd\r\n * round\r\n * sine sin\r\n * squareRoot sqrt\r\n * tangent tan\r\n * times mul\r\n * toBinary\r\n * toDecimalPlaces toDP\r\n * toExponential\r\n * toFixed\r\n * toFraction\r\n * toHexadecimal toHex\r\n * toNearest\r\n * toNumber\r\n * toOctal\r\n * toPower pow\r\n * toPrecision\r\n * toSignificantDigits toSD\r\n * toString\r\n * truncated trunc\r\n * valueOf toJSON\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the absolute value of this Decimal.\r\n *\r\n */\r\n P.absoluteValue = P.abs = function () {\r\n var x = new this.constructor(this);\r\n if (x.s < 0) x.s = 1;\r\n return finalise(x);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of positive Infinity.\r\n *\r\n */\r\n P.ceil = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 2);\r\n };\r\n\r\n\r\n /*\r\n * Return\r\n * 1 if the value of this Decimal is greater than the value of `y`,\r\n * -1 if the value of this Decimal is less than the value of `y`,\r\n * 0 if they have the same value,\r\n * NaN if the value of either Decimal is NaN.\r\n *\r\n */\r\n P.comparedTo = P.cmp = function (y) {\r\n var i, j, xdL, ydL,\r\n x = this,\r\n xd = x.d,\r\n yd = (y = new x.constructor(y)).d,\r\n xs = x.s,\r\n ys = y.s;\r\n\r\n // Either NaN or ±Infinity?\r\n if (!xd || !yd) {\r\n return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;\r\n }\r\n\r\n // Either zero?\r\n if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;\r\n\r\n // Signs differ?\r\n if (xs !== ys) return xs;\r\n\r\n // Compare exponents.\r\n if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;\r\n\r\n xdL = xd.length;\r\n ydL = yd.length;\r\n\r\n // Compare digit by digit.\r\n for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {\r\n if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;\r\n }\r\n\r\n // Compare lengths.\r\n return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * cos(0) = 1\r\n * cos(-0) = 1\r\n * cos(Infinity) = NaN\r\n * cos(-Infinity) = NaN\r\n * cos(NaN) = NaN\r\n *\r\n */\r\n P.cosine = P.cos = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.d) return new Ctor(NaN);\r\n\r\n // cos(0) = cos(-0) = 1\r\n if (!x.d[0]) return new Ctor(1);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;\r\n Ctor.rounding = 1;\r\n\r\n x = cosine(Ctor, toLessThanHalfPi(Ctor, x));\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n *\r\n * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * cbrt(0) = 0\r\n * cbrt(-0) = -0\r\n * cbrt(1) = 1\r\n * cbrt(-1) = -1\r\n * cbrt(N) = N\r\n * cbrt(-I) = -I\r\n * cbrt(I) = I\r\n *\r\n * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))\r\n *\r\n */\r\n P.cubeRoot = P.cbrt = function () {\r\n var e, m, n, r, rep, s, sd, t, t3, t3plusx,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n external = false;\r\n\r\n // Initial estimate.\r\n s = x.s * mathpow(x.s * x, 1 / 3);\r\n\r\n // Math.cbrt underflow/overflow?\r\n // Pass x to Math.pow as integer, then adjust the exponent of the result.\r\n if (!s || Math.abs(s) == 1 / 0) {\r\n n = digitsToString(x.d);\r\n e = x.e;\r\n\r\n // Adjust n exponent so it is a multiple of 3 away from x exponent.\r\n if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');\r\n s = mathpow(n, 1 / 3);\r\n\r\n // Rarely, e may be one less than the result exponent value.\r\n e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));\r\n\r\n if (s == 1 / 0) {\r\n n = '5e' + e;\r\n } else {\r\n n = s.toExponential();\r\n n = n.slice(0, n.indexOf('e') + 1) + e;\r\n }\r\n\r\n r = new Ctor(n);\r\n r.s = x.s;\r\n } else {\r\n r = new Ctor(s.toString());\r\n }\r\n\r\n sd = (e = Ctor.precision) + 3;\r\n\r\n // Halley's method.\r\n // TODO? Compare Newton's method.\r\n for (;;) {\r\n t = r;\r\n t3 = t.times(t).times(t);\r\n t3plusx = t3.plus(x);\r\n r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);\r\n\r\n // TODO? Replace with for-loop and checkRoundingDigits.\r\n if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {\r\n n = n.slice(sd - 3, sd + 1);\r\n\r\n // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999\r\n // , i.e. approaching a rounding boundary, continue the iteration.\r\n if (n == '9999' || !rep && n == '4999') {\r\n\r\n // On the first iteration only, check to see if rounding up gives the exact result as the\r\n // nines may infinitely repeat.\r\n if (!rep) {\r\n finalise(t, e + 1, 0);\r\n\r\n if (t.times(t).times(t).eq(x)) {\r\n r = t;\r\n break;\r\n }\r\n }\r\n\r\n sd += 4;\r\n rep = 1;\r\n } else {\r\n\r\n // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.\r\n // If not, then there are further digits and m will be truthy.\r\n if (!+n || !+n.slice(1) && n.charAt(0) == '5') {\r\n\r\n // Truncate to the first rounding digit.\r\n finalise(r, e + 1, 1);\r\n m = !r.times(r).times(r).eq(x);\r\n }\r\n\r\n break;\r\n }\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, e, Ctor.rounding, m);\r\n };\r\n\r\n\r\n /*\r\n * Return the number of decimal places of the value of this Decimal.\r\n *\r\n */\r\n P.decimalPlaces = P.dp = function () {\r\n var w,\r\n d = this.d,\r\n n = NaN;\r\n\r\n if (d) {\r\n w = d.length - 1;\r\n n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;\r\n\r\n // Subtract the number of trailing zeros of the last word.\r\n w = d[w];\r\n if (w) for (; w % 10 == 0; w /= 10) n--;\r\n if (n < 0) n = 0;\r\n }\r\n\r\n return n;\r\n };\r\n\r\n\r\n /*\r\n * n / 0 = I\r\n * n / N = N\r\n * n / I = 0\r\n * 0 / n = 0\r\n * 0 / 0 = N\r\n * 0 / N = N\r\n * 0 / I = 0\r\n * N / n = N\r\n * N / 0 = N\r\n * N / N = N\r\n * N / I = N\r\n * I / n = I\r\n * I / 0 = I\r\n * I / N = N\r\n * I / I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.dividedBy = P.div = function (y) {\r\n return divide(this, new this.constructor(y));\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the integer part of dividing the value of this Decimal\r\n * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.dividedToIntegerBy = P.divToInt = function (y) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.\r\n *\r\n */\r\n P.equals = P.eq = function (y) {\r\n return this.cmp(y) === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the\r\n * direction of negative Infinity.\r\n *\r\n */\r\n P.floor = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 3);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is greater than the value of `y`, otherwise return\r\n * false.\r\n *\r\n */\r\n P.greaterThan = P.gt = function (y) {\r\n return this.cmp(y) > 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is greater than or equal to the value of `y`,\r\n * otherwise return false.\r\n *\r\n */\r\n P.greaterThanOrEqualTo = P.gte = function (y) {\r\n var k = this.cmp(y);\r\n return k == 1 || k === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [1, Infinity]\r\n *\r\n * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...\r\n *\r\n * cosh(0) = 1\r\n * cosh(-0) = 1\r\n * cosh(Infinity) = Infinity\r\n * cosh(-Infinity) = Infinity\r\n * cosh(NaN) = NaN\r\n *\r\n * x time taken (ms) result\r\n * 1000 9 9.8503555700852349694e+433\r\n * 10000 25 4.4034091128314607936e+4342\r\n * 100000 171 1.4033316802130615897e+43429\r\n * 1000000 3817 1.5166076984010437725e+434294\r\n * 10000000 abandoned after 2 minute wait\r\n *\r\n * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))\r\n *\r\n */\r\n P.hyperbolicCosine = P.cosh = function () {\r\n var k, n, pr, rm, len,\r\n x = this,\r\n Ctor = x.constructor,\r\n one = new Ctor(1);\r\n\r\n if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);\r\n if (x.isZero()) return one;\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n len = x.d.length;\r\n\r\n // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1\r\n // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n // TODO? Estimation reused from cosine() and may not be optimal here.\r\n if (len < 32) {\r\n k = Math.ceil(len / 3);\r\n n = (1 / tinyPow(4, k)).toString();\r\n } else {\r\n k = 16;\r\n n = '2.3283064365386962890625e-10';\r\n }\r\n\r\n x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);\r\n\r\n // Reverse argument reduction\r\n var cosh2_x,\r\n i = k,\r\n d8 = new Ctor(8);\r\n for (; i--;) {\r\n cosh2_x = x.times(x);\r\n x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));\r\n }\r\n\r\n return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...\r\n *\r\n * sinh(0) = 0\r\n * sinh(-0) = -0\r\n * sinh(Infinity) = Infinity\r\n * sinh(-Infinity) = -Infinity\r\n * sinh(NaN) = NaN\r\n *\r\n * x time taken (ms)\r\n * 10 2 ms\r\n * 100 5 ms\r\n * 1000 14 ms\r\n * 10000 82 ms\r\n * 100000 886 ms 1.4033316802130615897e+43429\r\n * 200000 2613 ms\r\n * 300000 5407 ms\r\n * 400000 8824 ms\r\n * 500000 13026 ms 8.7080643612718084129e+217146\r\n * 1000000 48543 ms\r\n *\r\n * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))\r\n *\r\n */\r\n P.hyperbolicSine = P.sinh = function () {\r\n var k, pr, rm, len,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n len = x.d.length;\r\n\r\n if (len < 3) {\r\n x = taylorSeries(Ctor, 2, x, x, true);\r\n } else {\r\n\r\n // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))\r\n // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))\r\n // 3 multiplications and 1 addition\r\n\r\n // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))\r\n // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))\r\n // 4 multiplications and 2 additions\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n k = 1.4 * Math.sqrt(len);\r\n k = k > 16 ? 16 : k | 0;\r\n\r\n x = x.times(1 / tinyPow(5, k));\r\n x = taylorSeries(Ctor, 2, x, x, true);\r\n\r\n // Reverse argument reduction\r\n var sinh2_x,\r\n d5 = new Ctor(5),\r\n d16 = new Ctor(16),\r\n d20 = new Ctor(20);\r\n for (; k--;) {\r\n sinh2_x = x.times(x);\r\n x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));\r\n }\r\n }\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * tanh(x) = sinh(x) / cosh(x)\r\n *\r\n * tanh(0) = 0\r\n * tanh(-0) = -0\r\n * tanh(Infinity) = 1\r\n * tanh(-Infinity) = -1\r\n * tanh(NaN) = NaN\r\n *\r\n */\r\n P.hyperbolicTangent = P.tanh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(x.s);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 7;\r\n Ctor.rounding = 1;\r\n\r\n return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of\r\n * this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [0, pi]\r\n *\r\n * acos(x) = pi/2 - asin(x)\r\n *\r\n * acos(0) = pi/2\r\n * acos(-0) = pi/2\r\n * acos(1) = 0\r\n * acos(-1) = pi\r\n * acos(1/2) = pi/3\r\n * acos(-1/2) = 2*pi/3\r\n * acos(|x| > 1) = NaN\r\n * acos(NaN) = NaN\r\n *\r\n */\r\n P.inverseCosine = P.acos = function () {\r\n var halfPi,\r\n x = this,\r\n Ctor = x.constructor,\r\n k = x.abs().cmp(1),\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding;\r\n\r\n if (k !== -1) {\r\n return k === 0\r\n // |x| is 1\r\n ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)\r\n // |x| > 1 or x is NaN\r\n : new Ctor(NaN);\r\n }\r\n\r\n if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3\r\n\r\n Ctor.precision = pr + 6;\r\n Ctor.rounding = 1;\r\n\r\n x = x.asin();\r\n halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return halfPi.minus(x);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [1, Infinity]\r\n * Range: [0, Infinity]\r\n *\r\n * acosh(x) = ln(x + sqrt(x^2 - 1))\r\n *\r\n * acosh(x < 1) = NaN\r\n * acosh(NaN) = NaN\r\n * acosh(Infinity) = Infinity\r\n * acosh(-Infinity) = NaN\r\n * acosh(0) = NaN\r\n * acosh(-0) = NaN\r\n * acosh(1) = 0\r\n * acosh(-1) = NaN\r\n *\r\n */\r\n P.inverseHyperbolicCosine = P.acosh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);\r\n if (!x.isFinite()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;\r\n Ctor.rounding = 1;\r\n external = false;\r\n\r\n x = x.times(x).minus(1).sqrt().plus(x);\r\n\r\n external = true;\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.ln();\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * asinh(x) = ln(x + sqrt(x^2 + 1))\r\n *\r\n * asinh(NaN) = NaN\r\n * asinh(Infinity) = Infinity\r\n * asinh(-Infinity) = -Infinity\r\n * asinh(0) = 0\r\n * asinh(-0) = -0\r\n *\r\n */\r\n P.inverseHyperbolicSine = P.asinh = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite() || x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;\r\n Ctor.rounding = 1;\r\n external = false;\r\n\r\n x = x.times(x).plus(1).sqrt().plus(x);\r\n\r\n external = true;\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.ln();\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the\r\n * value of this Decimal.\r\n *\r\n * Domain: [-1, 1]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * atanh(x) = 0.5 * ln((1 + x) / (1 - x))\r\n *\r\n * atanh(|x| > 1) = NaN\r\n * atanh(NaN) = NaN\r\n * atanh(Infinity) = NaN\r\n * atanh(-Infinity) = NaN\r\n * atanh(0) = 0\r\n * atanh(-0) = -0\r\n * atanh(1) = Infinity\r\n * atanh(-1) = -Infinity\r\n *\r\n */\r\n P.inverseHyperbolicTangent = P.atanh = function () {\r\n var pr, rm, wpr, xsd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n xsd = x.sd();\r\n\r\n if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);\r\n\r\n Ctor.precision = wpr = xsd - x.e;\r\n\r\n x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);\r\n\r\n Ctor.precision = pr + 4;\r\n Ctor.rounding = 1;\r\n\r\n x = x.ln();\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.times(0.5);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this\r\n * Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))\r\n *\r\n * asin(0) = 0\r\n * asin(-0) = -0\r\n * asin(1/2) = pi/6\r\n * asin(-1/2) = -pi/6\r\n * asin(1) = pi/2\r\n * asin(-1) = -pi/2\r\n * asin(|x| > 1) = NaN\r\n * asin(NaN) = NaN\r\n *\r\n * TODO? Compare performance of Taylor series.\r\n *\r\n */\r\n P.inverseSine = P.asin = function () {\r\n var halfPi, k,\r\n pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n k = x.abs().cmp(1);\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n if (k !== -1) {\r\n\r\n // |x| is 1\r\n if (k === 0) {\r\n halfPi = getPi(Ctor, pr + 4, rm).times(0.5);\r\n halfPi.s = x.s;\r\n return halfPi;\r\n }\r\n\r\n // |x| > 1 or x is NaN\r\n return new Ctor(NaN);\r\n }\r\n\r\n // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6\r\n\r\n Ctor.precision = pr + 6;\r\n Ctor.rounding = 1;\r\n\r\n x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return x.times(2);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value\r\n * of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi/2, pi/2]\r\n *\r\n * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n *\r\n * atan(0) = 0\r\n * atan(-0) = -0\r\n * atan(1) = pi/4\r\n * atan(-1) = -pi/4\r\n * atan(Infinity) = pi/2\r\n * atan(-Infinity) = -pi/2\r\n * atan(NaN) = NaN\r\n *\r\n */\r\n P.inverseTangent = P.atan = function () {\r\n var i, j, k, n, px, t, r, wpr, x2,\r\n x = this,\r\n Ctor = x.constructor,\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding;\r\n\r\n if (!x.isFinite()) {\r\n if (!x.s) return new Ctor(NaN);\r\n if (pr + 4 <= PI_PRECISION) {\r\n r = getPi(Ctor, pr + 4, rm).times(0.5);\r\n r.s = x.s;\r\n return r;\r\n }\r\n } else if (x.isZero()) {\r\n return new Ctor(x);\r\n } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {\r\n r = getPi(Ctor, pr + 4, rm).times(0.25);\r\n r.s = x.s;\r\n return r;\r\n }\r\n\r\n Ctor.precision = wpr = pr + 10;\r\n Ctor.rounding = 1;\r\n\r\n // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);\r\n\r\n // Argument reduction\r\n // Ensure |x| < 0.42\r\n // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))\r\n\r\n k = Math.min(28, wpr / LOG_BASE + 2 | 0);\r\n\r\n for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));\r\n\r\n external = false;\r\n\r\n j = Math.ceil(wpr / LOG_BASE);\r\n n = 1;\r\n x2 = x.times(x);\r\n r = new Ctor(x);\r\n px = x;\r\n\r\n // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...\r\n for (; i !== -1;) {\r\n px = px.times(x2);\r\n t = r.minus(px.div(n += 2));\r\n\r\n px = px.times(x2);\r\n r = t.plus(px.div(n += 2));\r\n\r\n if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);\r\n }\r\n\r\n if (k) r = r.times(2 << (k - 1));\r\n\r\n external = true;\r\n\r\n return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is a finite number, otherwise return false.\r\n *\r\n */\r\n P.isFinite = function () {\r\n return !!this.d;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is an integer, otherwise return false.\r\n *\r\n */\r\n P.isInteger = P.isInt = function () {\r\n return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is NaN, otherwise return false.\r\n *\r\n */\r\n P.isNaN = function () {\r\n return !this.s;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is negative, otherwise return false.\r\n *\r\n */\r\n P.isNegative = P.isNeg = function () {\r\n return this.s < 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is positive, otherwise return false.\r\n *\r\n */\r\n P.isPositive = P.isPos = function () {\r\n return this.s > 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is 0 or -0, otherwise return false.\r\n *\r\n */\r\n P.isZero = function () {\r\n return !!this.d && this.d[0] === 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is less than `y`, otherwise return false.\r\n *\r\n */\r\n P.lessThan = P.lt = function (y) {\r\n return this.cmp(y) < 0;\r\n };\r\n\r\n\r\n /*\r\n * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.\r\n *\r\n */\r\n P.lessThanOrEqualTo = P.lte = function (y) {\r\n return this.cmp(y) < 1;\r\n };\r\n\r\n\r\n /*\r\n * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * If no base is specified, return log[10](arg).\r\n *\r\n * log[base](arg) = ln(arg) / ln(base)\r\n *\r\n * The result will always be correctly rounded if the base of the log is 10, and 'almost always'\r\n * otherwise:\r\n *\r\n * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen\r\n * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error\r\n * between the result and the correctly rounded result will be one ulp (unit in the last place).\r\n *\r\n * log[-b](a) = NaN\r\n * log[0](a) = NaN\r\n * log[1](a) = NaN\r\n * log[NaN](a) = NaN\r\n * log[Infinity](a) = NaN\r\n * log[b](0) = -Infinity\r\n * log[b](-0) = -Infinity\r\n * log[b](-a) = NaN\r\n * log[b](1) = 0\r\n * log[b](Infinity) = Infinity\r\n * log[b](NaN) = NaN\r\n *\r\n * [base] {number|string|Decimal} The base of the logarithm.\r\n *\r\n */\r\n P.logarithm = P.log = function (base) {\r\n var isBase10, d, denominator, k, inf, num, sd, r,\r\n arg = this,\r\n Ctor = arg.constructor,\r\n pr = Ctor.precision,\r\n rm = Ctor.rounding,\r\n guard = 5;\r\n\r\n // Default base is 10.\r\n if (base == null) {\r\n base = new Ctor(10);\r\n isBase10 = true;\r\n } else {\r\n base = new Ctor(base);\r\n d = base.d;\r\n\r\n // Return NaN if base is negative, or non-finite, or is 0 or 1.\r\n if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);\r\n\r\n isBase10 = base.eq(10);\r\n }\r\n\r\n d = arg.d;\r\n\r\n // Is arg negative, non-finite, 0 or 1?\r\n if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {\r\n return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);\r\n }\r\n\r\n // The result will have a non-terminating decimal expansion if base is 10 and arg is not an\r\n // integer power of 10.\r\n if (isBase10) {\r\n if (d.length > 1) {\r\n inf = true;\r\n } else {\r\n for (k = d[0]; k % 10 === 0;) k /= 10;\r\n inf = k !== 1;\r\n }\r\n }\r\n\r\n external = false;\r\n sd = pr + guard;\r\n num = naturalLogarithm(arg, sd);\r\n denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n\r\n // The result will have 5 rounding digits.\r\n r = divide(num, denominator, sd, 1);\r\n\r\n // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,\r\n // calculate 10 further digits.\r\n //\r\n // If the result is known to have an infinite decimal expansion, repeat this until it is clear\r\n // that the result is above or below the boundary. Otherwise, if after calculating the 10\r\n // further digits, the last 14 are nines, round up and assume the result is exact.\r\n // Also assume the result is exact if the last 14 are zero.\r\n //\r\n // Example of a result that will be incorrectly rounded:\r\n // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...\r\n // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it\r\n // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so\r\n // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal\r\n // place is still 2.6.\r\n if (checkRoundingDigits(r.d, k = pr, rm)) {\r\n\r\n do {\r\n sd += 10;\r\n num = naturalLogarithm(arg, sd);\r\n denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);\r\n r = divide(num, denominator, sd, 1);\r\n\r\n if (!inf) {\r\n\r\n // Check for 14 nines from the 2nd rounding digit, as the first may be 4.\r\n if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {\r\n r = finalise(r, pr + 1, 0);\r\n }\r\n\r\n break;\r\n }\r\n } while (checkRoundingDigits(r.d, k += 10, rm));\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, pr, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n P.max = function () {\r\n Array.prototype.push.call(arguments, this);\r\n return maxOrMin(this.constructor, arguments, 'lt');\r\n };\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n P.min = function () {\r\n Array.prototype.push.call(arguments, this);\r\n return maxOrMin(this.constructor, arguments, 'gt');\r\n };\r\n */\r\n\r\n\r\n /*\r\n * n - 0 = n\r\n * n - N = N\r\n * n - I = -I\r\n * 0 - n = -n\r\n * 0 - 0 = 0\r\n * 0 - N = N\r\n * 0 - I = -I\r\n * N - n = N\r\n * N - 0 = N\r\n * N - N = N\r\n * N - I = N\r\n * I - n = I\r\n * I - 0 = I\r\n * I - N = N\r\n * I - I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.minus = P.sub = function (y) {\r\n var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // If either is not finite...\r\n if (!x.d || !y.d) {\r\n\r\n // Return NaN if either is NaN.\r\n if (!x.s || !y.s) y = new Ctor(NaN);\r\n\r\n // Return y negated if x is finite and y is ±Infinity.\r\n else if (x.d) y.s = -y.s;\r\n\r\n // Return x if y is finite and x is ±Infinity.\r\n // Return x if both are ±Infinity with different signs.\r\n // Return NaN if both are ±Infinity with the same sign.\r\n else y = new Ctor(y.d || x.s !== y.s ? x : NaN);\r\n\r\n return y;\r\n }\r\n\r\n // If signs differ...\r\n if (x.s != y.s) {\r\n y.s = -y.s;\r\n return x.plus(y);\r\n }\r\n\r\n xd = x.d;\r\n yd = y.d;\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n // If either is zero...\r\n if (!xd[0] || !yd[0]) {\r\n\r\n // Return y negated if x is zero and y is non-zero.\r\n if (yd[0]) y.s = -y.s;\r\n\r\n // Return x if y is zero and x is non-zero.\r\n else if (xd[0]) y = new Ctor(x);\r\n\r\n // Return zero if both are zero.\r\n // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.\r\n else return new Ctor(rm === 3 ? -0 : 0);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n }\r\n\r\n // x and y are finite, non-zero numbers with the same sign.\r\n\r\n // Calculate base 1e7 exponents.\r\n e = mathfloor(y.e / LOG_BASE);\r\n xe = mathfloor(x.e / LOG_BASE);\r\n\r\n xd = xd.slice();\r\n k = xe - e;\r\n\r\n // If base 1e7 exponents differ...\r\n if (k) {\r\n xLTy = k < 0;\r\n\r\n if (xLTy) {\r\n d = xd;\r\n k = -k;\r\n len = yd.length;\r\n } else {\r\n d = yd;\r\n e = xe;\r\n len = xd.length;\r\n }\r\n\r\n // Numbers with massively different exponents would result in a very high number of\r\n // zeros needing to be prepended, but this can be avoided while still ensuring correct\r\n // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.\r\n i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;\r\n\r\n if (k > i) {\r\n k = i;\r\n d.length = 1;\r\n }\r\n\r\n // Prepend zeros to equalise exponents.\r\n d.reverse();\r\n for (i = k; i--;) d.push(0);\r\n d.reverse();\r\n\r\n // Base 1e7 exponents equal.\r\n } else {\r\n\r\n // Check digits to determine which is the bigger number.\r\n\r\n i = xd.length;\r\n len = yd.length;\r\n xLTy = i < len;\r\n if (xLTy) len = i;\r\n\r\n for (i = 0; i < len; i++) {\r\n if (xd[i] != yd[i]) {\r\n xLTy = xd[i] < yd[i];\r\n break;\r\n }\r\n }\r\n\r\n k = 0;\r\n }\r\n\r\n if (xLTy) {\r\n d = xd;\r\n xd = yd;\r\n yd = d;\r\n y.s = -y.s;\r\n }\r\n\r\n len = xd.length;\r\n\r\n // Append zeros to `xd` if shorter.\r\n // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.\r\n for (i = yd.length - len; i > 0; --i) xd[len++] = 0;\r\n\r\n // Subtract yd from xd.\r\n for (i = yd.length; i > k;) {\r\n\r\n if (xd[--i] < yd[i]) {\r\n for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;\r\n --xd[j];\r\n xd[i] += BASE;\r\n }\r\n\r\n xd[i] -= yd[i];\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (; xd[--len] === 0;) xd.pop();\r\n\r\n // Remove leading zeros and adjust exponent accordingly.\r\n for (; xd[0] === 0; xd.shift()) --e;\r\n\r\n // Zero?\r\n if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);\r\n\r\n y.d = xd;\r\n y.e = getBase10Exponent(xd, e);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n };\r\n\r\n\r\n /*\r\n * n % 0 = N\r\n * n % N = N\r\n * n % I = n\r\n * 0 % n = 0\r\n * -0 % n = -0\r\n * 0 % 0 = N\r\n * 0 % N = N\r\n * 0 % I = 0\r\n * N % n = N\r\n * N % 0 = N\r\n * N % N = N\r\n * N % I = N\r\n * I % n = N\r\n * I % 0 = N\r\n * I % N = N\r\n * I % I = N\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * The result depends on the modulo mode.\r\n *\r\n */\r\n P.modulo = P.mod = function (y) {\r\n var q,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.\r\n if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);\r\n\r\n // Return x if y is ±Infinity or x is ±0.\r\n if (!y.d || x.d && !x.d[0]) {\r\n return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);\r\n }\r\n\r\n // Prevent rounding of intermediate calculations.\r\n external = false;\r\n\r\n if (Ctor.modulo == 9) {\r\n\r\n // Euclidian division: q = sign(y) * floor(x / abs(y))\r\n // result = x - q * y where 0 <= result < abs(y)\r\n q = divide(x, y.abs(), 0, 3, 1);\r\n q.s *= y.s;\r\n } else {\r\n q = divide(x, y, 0, Ctor.modulo, 1);\r\n }\r\n\r\n q = q.times(y);\r\n\r\n external = true;\r\n\r\n return x.minus(q);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of the value of this Decimal,\r\n * i.e. the base e raised to the power the value of this Decimal, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.naturalExponential = P.exp = function () {\r\n return naturalExponential(this);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,\r\n * rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.naturalLogarithm = P.ln = function () {\r\n return naturalLogarithm(this);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by\r\n * -1.\r\n *\r\n */\r\n P.negated = P.neg = function () {\r\n var x = new this.constructor(this);\r\n x.s = -x.s;\r\n return finalise(x);\r\n };\r\n\r\n\r\n /*\r\n * n + 0 = n\r\n * n + N = N\r\n * n + I = I\r\n * 0 + n = n\r\n * 0 + 0 = 0\r\n * 0 + N = N\r\n * 0 + I = I\r\n * N + n = N\r\n * N + 0 = N\r\n * N + N = N\r\n * N + I = N\r\n * I + n = I\r\n * I + 0 = I\r\n * I + N = N\r\n * I + I = I\r\n *\r\n * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.plus = P.add = function (y) {\r\n var carry, d, e, i, k, len, pr, rm, xd, yd,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n y = new Ctor(y);\r\n\r\n // If either is not finite...\r\n if (!x.d || !y.d) {\r\n\r\n // Return NaN if either is NaN.\r\n if (!x.s || !y.s) y = new Ctor(NaN);\r\n\r\n // Return x if y is finite and x is ±Infinity.\r\n // Return x if both are ±Infinity with the same sign.\r\n // Return NaN if both are ±Infinity with different signs.\r\n // Return y if x is finite and y is ±Infinity.\r\n else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);\r\n\r\n return y;\r\n }\r\n\r\n // If signs differ...\r\n if (x.s != y.s) {\r\n y.s = -y.s;\r\n return x.minus(y);\r\n }\r\n\r\n xd = x.d;\r\n yd = y.d;\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n // If either is zero...\r\n if (!xd[0] || !yd[0]) {\r\n\r\n // Return x if y is zero.\r\n // Return y if y is non-zero.\r\n if (!yd[0]) y = new Ctor(x);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n }\r\n\r\n // x and y are finite, non-zero numbers with the same sign.\r\n\r\n // Calculate base 1e7 exponents.\r\n k = mathfloor(x.e / LOG_BASE);\r\n e = mathfloor(y.e / LOG_BASE);\r\n\r\n xd = xd.slice();\r\n i = k - e;\r\n\r\n // If base 1e7 exponents differ...\r\n if (i) {\r\n\r\n if (i < 0) {\r\n d = xd;\r\n i = -i;\r\n len = yd.length;\r\n } else {\r\n d = yd;\r\n e = k;\r\n len = xd.length;\r\n }\r\n\r\n // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.\r\n k = Math.ceil(pr / LOG_BASE);\r\n len = k > len ? k + 1 : len + 1;\r\n\r\n if (i > len) {\r\n i = len;\r\n d.length = 1;\r\n }\r\n\r\n // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.\r\n d.reverse();\r\n for (; i--;) d.push(0);\r\n d.reverse();\r\n }\r\n\r\n len = xd.length;\r\n i = yd.length;\r\n\r\n // If yd is longer than xd, swap xd and yd so xd points to the longer array.\r\n if (len - i < 0) {\r\n i = len;\r\n d = yd;\r\n yd = xd;\r\n xd = d;\r\n }\r\n\r\n // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.\r\n for (carry = 0; i;) {\r\n carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;\r\n xd[i] %= BASE;\r\n }\r\n\r\n if (carry) {\r\n xd.unshift(carry);\r\n ++e;\r\n }\r\n\r\n // Remove trailing zeros.\r\n // No need to check for zero, as +x + +y != 0 && -x + -y != 0\r\n for (len = xd.length; xd[--len] == 0;) xd.pop();\r\n\r\n y.d = xd;\r\n y.e = getBase10Exponent(xd, e);\r\n\r\n return external ? finalise(y, pr, rm) : y;\r\n };\r\n\r\n\r\n /*\r\n * Return the number of significant digits of the value of this Decimal.\r\n *\r\n * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.\r\n *\r\n */\r\n P.precision = P.sd = function (z) {\r\n var k,\r\n x = this;\r\n\r\n if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);\r\n\r\n if (x.d) {\r\n k = getPrecision(x.d);\r\n if (z && x.e + 1 > k) k = x.e + 1;\r\n } else {\r\n k = NaN;\r\n }\r\n\r\n return k;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using\r\n * rounding mode `rounding`.\r\n *\r\n */\r\n P.round = function () {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n return finalise(new Ctor(x), x.e + 1, Ctor.rounding);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sine of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-1, 1]\r\n *\r\n * sin(x) = x - x^3/3! + x^5/5! - ...\r\n *\r\n * sin(0) = 0\r\n * sin(-0) = -0\r\n * sin(Infinity) = NaN\r\n * sin(-Infinity) = NaN\r\n * sin(NaN) = NaN\r\n *\r\n */\r\n P.sine = P.sin = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;\r\n Ctor.rounding = 1;\r\n\r\n x = sine(Ctor, toLessThanHalfPi(Ctor, x));\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * sqrt(-n) = N\r\n * sqrt(N) = N\r\n * sqrt(-I) = N\r\n * sqrt(I) = I\r\n * sqrt(0) = 0\r\n * sqrt(-0) = -0\r\n *\r\n */\r\n P.squareRoot = P.sqrt = function () {\r\n var m, n, sd, r, rep, t,\r\n x = this,\r\n d = x.d,\r\n e = x.e,\r\n s = x.s,\r\n Ctor = x.constructor;\r\n\r\n // Negative/NaN/Infinity/zero?\r\n if (s !== 1 || !d || !d[0]) {\r\n return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);\r\n }\r\n\r\n external = false;\r\n\r\n // Initial estimate.\r\n s = Math.sqrt(+x);\r\n\r\n // Math.sqrt underflow/overflow?\r\n // Pass x to Math.sqrt as integer, then adjust the exponent of the result.\r\n if (s == 0 || s == 1 / 0) {\r\n n = digitsToString(d);\r\n\r\n if ((n.length + e) % 2 == 0) n += '0';\r\n s = Math.sqrt(n);\r\n e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);\r\n\r\n if (s == 1 / 0) {\r\n n = '5e' + e;\r\n } else {\r\n n = s.toExponential();\r\n n = n.slice(0, n.indexOf('e') + 1) + e;\r\n }\r\n\r\n r = new Ctor(n);\r\n } else {\r\n r = new Ctor(s.toString());\r\n }\r\n\r\n sd = (e = Ctor.precision) + 3;\r\n\r\n // Newton-Raphson iteration.\r\n for (;;) {\r\n t = r;\r\n r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);\r\n\r\n // TODO? Replace with for-loop and checkRoundingDigits.\r\n if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {\r\n n = n.slice(sd - 3, sd + 1);\r\n\r\n // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or\r\n // 4999, i.e. approaching a rounding boundary, continue the iteration.\r\n if (n == '9999' || !rep && n == '4999') {\r\n\r\n // On the first iteration only, check to see if rounding up gives the exact result as the\r\n // nines may infinitely repeat.\r\n if (!rep) {\r\n finalise(t, e + 1, 0);\r\n\r\n if (t.times(t).eq(x)) {\r\n r = t;\r\n break;\r\n }\r\n }\r\n\r\n sd += 4;\r\n rep = 1;\r\n } else {\r\n\r\n // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.\r\n // If not, then there are further digits and m will be truthy.\r\n if (!+n || !+n.slice(1) && n.charAt(0) == '5') {\r\n\r\n // Truncate to the first rounding digit.\r\n finalise(r, e + 1, 1);\r\n m = !r.times(r).eq(x);\r\n }\r\n\r\n break;\r\n }\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return finalise(r, e, Ctor.rounding, m);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-Infinity, Infinity]\r\n *\r\n * tan(0) = 0\r\n * tan(-0) = -0\r\n * tan(Infinity) = NaN\r\n * tan(-Infinity) = NaN\r\n * tan(NaN) = NaN\r\n *\r\n */\r\n P.tangent = P.tan = function () {\r\n var pr, rm,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (!x.isFinite()) return new Ctor(NaN);\r\n if (x.isZero()) return new Ctor(x);\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n Ctor.precision = pr + 10;\r\n Ctor.rounding = 1;\r\n\r\n x = x.sin();\r\n x.s = 1;\r\n x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);\r\n\r\n Ctor.precision = pr;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);\r\n };\r\n\r\n\r\n /*\r\n * n * 0 = 0\r\n * n * N = N\r\n * n * I = I\r\n * 0 * n = 0\r\n * 0 * 0 = 0\r\n * 0 * N = N\r\n * 0 * I = N\r\n * N * n = N\r\n * N * 0 = N\r\n * N * N = N\r\n * N * I = N\r\n * I * n = I\r\n * I * 0 = N\r\n * I * N = N\r\n * I * I = I\r\n *\r\n * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n */\r\n P.times = P.mul = function (y) {\r\n var carry, e, i, k, r, rL, t, xdL, ydL,\r\n x = this,\r\n Ctor = x.constructor,\r\n xd = x.d,\r\n yd = (y = new Ctor(y)).d;\r\n\r\n y.s *= x.s;\r\n\r\n // If either is NaN, ±Infinity or ±0...\r\n if (!xd || !xd[0] || !yd || !yd[0]) {\r\n\r\n return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd\r\n\r\n // Return NaN if either is NaN.\r\n // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.\r\n ? NaN\r\n\r\n // Return ±Infinity if either is ±Infinity.\r\n // Return ±0 if either is ±0.\r\n : !xd || !yd ? y.s / 0 : y.s * 0);\r\n }\r\n\r\n e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);\r\n xdL = xd.length;\r\n ydL = yd.length;\r\n\r\n // Ensure xd points to the longer array.\r\n if (xdL < ydL) {\r\n r = xd;\r\n xd = yd;\r\n yd = r;\r\n rL = xdL;\r\n xdL = ydL;\r\n ydL = rL;\r\n }\r\n\r\n // Initialise the result array with zeros.\r\n r = [];\r\n rL = xdL + ydL;\r\n for (i = rL; i--;) r.push(0);\r\n\r\n // Multiply!\r\n for (i = ydL; --i >= 0;) {\r\n carry = 0;\r\n for (k = xdL + i; k > i;) {\r\n t = r[k] + yd[i] * xd[k - i - 1] + carry;\r\n r[k--] = t % BASE | 0;\r\n carry = t / BASE | 0;\r\n }\r\n\r\n r[k] = (r[k] + carry) % BASE | 0;\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (; !r[--rL];) r.pop();\r\n\r\n if (carry) ++e;\r\n else r.shift();\r\n\r\n y.d = r;\r\n y.e = getBase10Exponent(r, e);\r\n\r\n return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 2, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toBinary = function (sd, rm) {\r\n return toStringBinary(this, 2, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`\r\n * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.\r\n *\r\n * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toDecimalPlaces = P.toDP = function (dp, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n x = new Ctor(x);\r\n if (dp === void 0) return x;\r\n\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n return finalise(x, dp + x.e + 1, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in exponential notation rounded to\r\n * `dp` fixed decimal places using rounding mode `rounding`.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toExponential = function (dp, rm) {\r\n var str,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (dp === void 0) {\r\n str = finiteToString(x, true);\r\n } else {\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n x = finalise(new Ctor(x), dp + 1, rm);\r\n str = finiteToString(x, true, dp + 1);\r\n }\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in normal (fixed-point) notation to\r\n * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is\r\n * omitted.\r\n *\r\n * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.\r\n *\r\n * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.\r\n * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.\r\n * (-0).toFixed(3) is '0.000'.\r\n * (-0.5).toFixed(0) is '-0'.\r\n *\r\n */\r\n P.toFixed = function (dp, rm) {\r\n var str, y,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (dp === void 0) {\r\n str = finiteToString(x);\r\n } else {\r\n checkInt32(dp, 0, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n y = finalise(new Ctor(x), dp + x.e + 1, rm);\r\n str = finiteToString(y, false, dp + y.e + 1);\r\n }\r\n\r\n // To determine whether to add the minus sign look at the value before it was rounded,\r\n // i.e. look at `x` rather than `y`.\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return an array representing the value of this Decimal as a simple fraction with an integer\r\n * numerator and an integer denominator.\r\n *\r\n * The denominator will be a positive non-zero value less than or equal to the specified maximum\r\n * denominator. If a maximum denominator is not specified, the denominator will be the lowest\r\n * value necessary to represent the number exactly.\r\n *\r\n * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.\r\n *\r\n */\r\n P.toFraction = function (maxD) {\r\n var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,\r\n x = this,\r\n xd = x.d,\r\n Ctor = x.constructor;\r\n\r\n if (!xd) return new Ctor(x);\r\n\r\n n1 = d0 = new Ctor(1);\r\n d1 = n0 = new Ctor(0);\r\n\r\n d = new Ctor(d1);\r\n e = d.e = getPrecision(xd) - x.e - 1;\r\n k = e % LOG_BASE;\r\n d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);\r\n\r\n if (maxD == null) {\r\n\r\n // d is 10**e, the minimum max-denominator needed.\r\n maxD = e > 0 ? d : n1;\r\n } else {\r\n n = new Ctor(maxD);\r\n if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);\r\n maxD = n.gt(d) ? (e > 0 ? d : n1) : n;\r\n }\r\n\r\n external = false;\r\n n = new Ctor(digitsToString(xd));\r\n pr = Ctor.precision;\r\n Ctor.precision = e = xd.length * LOG_BASE * 2;\r\n\r\n for (;;) {\r\n q = divide(n, d, 0, 1, 1);\r\n d2 = d0.plus(q.times(d1));\r\n if (d2.cmp(maxD) == 1) break;\r\n d0 = d1;\r\n d1 = d2;\r\n d2 = n1;\r\n n1 = n0.plus(q.times(d2));\r\n n0 = d2;\r\n d2 = d;\r\n d = n.minus(q.times(d2));\r\n n = d2;\r\n }\r\n\r\n d2 = divide(maxD.minus(d0), d1, 0, 1, 1);\r\n n0 = n0.plus(d2.times(n1));\r\n d0 = d0.plus(d2.times(d1));\r\n n0.s = n1.s = x.s;\r\n\r\n // Determine which fraction is closer to x, n0/d0 or n1/d1?\r\n r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1\r\n ? [n1, d1] : [n0, d0];\r\n\r\n Ctor.precision = pr;\r\n external = true;\r\n\r\n return r;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 16, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toHexadecimal = P.toHex = function (sd, rm) {\r\n return toStringBinary(this, 16, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding\r\n * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.\r\n *\r\n * The return value will always have the same sign as this Decimal, unless either this Decimal\r\n * or `y` is NaN, in which case the return value will be also be NaN.\r\n *\r\n * The return value is not affected by the value of `precision`.\r\n *\r\n * y {number|string|Decimal} The magnitude to round to a multiple of.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * 'toNearest() rounding mode not an integer: {rm}'\r\n * 'toNearest() rounding mode out of range: {rm}'\r\n *\r\n */\r\n P.toNearest = function (y, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n x = new Ctor(x);\r\n\r\n if (y == null) {\r\n\r\n // If x is not finite, return x.\r\n if (!x.d) return x;\r\n\r\n y = new Ctor(1);\r\n rm = Ctor.rounding;\r\n } else {\r\n y = new Ctor(y);\r\n if (rm === void 0) {\r\n rm = Ctor.rounding;\r\n } else {\r\n checkInt32(rm, 0, 8);\r\n }\r\n\r\n // If x is not finite, return x if y is not NaN, else NaN.\r\n if (!x.d) return y.s ? x : y;\r\n\r\n // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.\r\n if (!y.d) {\r\n if (y.s) y.s = x.s;\r\n return y;\r\n }\r\n }\r\n\r\n // If y is not zero, calculate the nearest multiple of y to x.\r\n if (y.d[0]) {\r\n external = false;\r\n x = divide(x, y, 0, rm, 1).times(y);\r\n external = true;\r\n finalise(x);\r\n\r\n // If y is zero, return zero with the sign of x.\r\n } else {\r\n y.s = x.s;\r\n x = y;\r\n }\r\n\r\n return x;\r\n };\r\n\r\n\r\n /*\r\n * Return the value of this Decimal converted to a number primitive.\r\n * Zero keeps its sign.\r\n *\r\n */\r\n P.toNumber = function () {\r\n return +this;\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal in base 8, round to `sd` significant\r\n * digits using rounding mode `rm`.\r\n *\r\n * If the optional `sd` argument is present then return binary exponential notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toOctal = function (sd, rm) {\r\n return toStringBinary(this, 8, sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded\r\n * to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * ECMAScript compliant.\r\n *\r\n * pow(x, NaN) = NaN\r\n * pow(x, ±0) = 1\r\n\r\n * pow(NaN, non-zero) = NaN\r\n * pow(abs(x) > 1, +Infinity) = +Infinity\r\n * pow(abs(x) > 1, -Infinity) = +0\r\n * pow(abs(x) == 1, ±Infinity) = NaN\r\n * pow(abs(x) < 1, +Infinity) = +0\r\n * pow(abs(x) < 1, -Infinity) = +Infinity\r\n * pow(+Infinity, y > 0) = +Infinity\r\n * pow(+Infinity, y < 0) = +0\r\n * pow(-Infinity, odd integer > 0) = -Infinity\r\n * pow(-Infinity, even integer > 0) = +Infinity\r\n * pow(-Infinity, odd integer < 0) = -0\r\n * pow(-Infinity, even integer < 0) = +0\r\n * pow(+0, y > 0) = +0\r\n * pow(+0, y < 0) = +Infinity\r\n * pow(-0, odd integer > 0) = -0\r\n * pow(-0, even integer > 0) = +0\r\n * pow(-0, odd integer < 0) = -Infinity\r\n * pow(-0, even integer < 0) = +Infinity\r\n * pow(finite x < 0, finite non-integer) = NaN\r\n *\r\n * For non-integer or very large exponents pow(x, y) is calculated using\r\n *\r\n * x^y = exp(y*ln(x))\r\n *\r\n * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the\r\n * probability of an incorrectly rounded result\r\n * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14\r\n * i.e. 1 in 250,000,000,000,000\r\n *\r\n * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).\r\n *\r\n * y {number|string|Decimal} The power to which to raise this Decimal.\r\n *\r\n */\r\n P.toPower = P.pow = function (y) {\r\n var e, k, pr, r, rm, s,\r\n x = this,\r\n Ctor = x.constructor,\r\n yn = +(y = new Ctor(y));\r\n\r\n // Either ±Infinity, NaN or ±0?\r\n if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));\r\n\r\n x = new Ctor(x);\r\n\r\n if (x.eq(1)) return x;\r\n\r\n pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n\r\n if (y.eq(1)) return finalise(x, pr, rm);\r\n\r\n // y exponent\r\n e = mathfloor(y.e / LOG_BASE);\r\n\r\n // If y is a small integer use the 'exponentiation by squaring' algorithm.\r\n if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {\r\n r = intPow(Ctor, x, k, pr);\r\n return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);\r\n }\r\n\r\n s = x.s;\r\n\r\n // if x is negative\r\n if (s < 0) {\r\n\r\n // if y is not an integer\r\n if (e < y.d.length - 1) return new Ctor(NaN);\r\n\r\n // Result is positive if x is negative and the last digit of integer y is even.\r\n if ((y.d[e] & 1) == 0) s = 1;\r\n\r\n // if x.eq(-1)\r\n if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {\r\n x.s = s;\r\n return x;\r\n }\r\n }\r\n\r\n // Estimate result exponent.\r\n // x^y = 10^e, where e = y * log10(x)\r\n // log10(x) = log10(x_significand) + x_exponent\r\n // log10(x_significand) = ln(x_significand) / ln(10)\r\n k = mathpow(+x, yn);\r\n e = k == 0 || !isFinite(k)\r\n ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))\r\n : new Ctor(k + '').e;\r\n\r\n // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.\r\n\r\n // Overflow/underflow?\r\n if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);\r\n\r\n external = false;\r\n Ctor.rounding = x.s = 1;\r\n\r\n // Estimate the extra guard digits needed to ensure five correct rounding digits from\r\n // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):\r\n // new Decimal(2.32456).pow('2087987436534566.46411')\r\n // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815\r\n k = Math.min(12, (e + '').length);\r\n\r\n // r = x^y = exp(y*ln(x))\r\n r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);\r\n\r\n // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)\r\n if (r.d) {\r\n\r\n // Truncate to the required precision plus five rounding digits.\r\n r = finalise(r, pr + 5, 1);\r\n\r\n // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate\r\n // the result.\r\n if (checkRoundingDigits(r.d, pr, rm)) {\r\n e = pr + 10;\r\n\r\n // Truncate to the increased precision plus five rounding digits.\r\n r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);\r\n\r\n // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).\r\n if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {\r\n r = finalise(r, pr + 1, 0);\r\n }\r\n }\r\n }\r\n\r\n r.s = s;\r\n external = true;\r\n Ctor.rounding = rm;\r\n\r\n return finalise(r, pr, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal rounded to `sd` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * Return exponential notation if `sd` is less than the number of digits necessary to represent\r\n * the integer part of the value in normal notation.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n */\r\n P.toPrecision = function (sd, rm) {\r\n var str,\r\n x = this,\r\n Ctor = x.constructor;\r\n\r\n if (sd === void 0) {\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n } else {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n\r\n x = finalise(new Ctor(x), sd, rm);\r\n str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);\r\n }\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`\r\n * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if\r\n * omitted.\r\n *\r\n * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.\r\n * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.\r\n *\r\n * 'toSD() digits out of range: {sd}'\r\n * 'toSD() digits not an integer: {sd}'\r\n * 'toSD() rounding mode not an integer: {rm}'\r\n * 'toSD() rounding mode out of range: {rm}'\r\n *\r\n */\r\n P.toSignificantDigits = P.toSD = function (sd, rm) {\r\n var x = this,\r\n Ctor = x.constructor;\r\n\r\n if (sd === void 0) {\r\n sd = Ctor.precision;\r\n rm = Ctor.rounding;\r\n } else {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n }\r\n\r\n return finalise(new Ctor(x), sd, rm);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal.\r\n *\r\n * Return exponential notation if this Decimal has a positive exponent equal to or greater than\r\n * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.\r\n *\r\n */\r\n P.toString = function () {\r\n var x = this,\r\n Ctor = x.constructor,\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n\r\n return x.isNeg() && !x.isZero() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.\r\n *\r\n */\r\n P.truncated = P.trunc = function () {\r\n return finalise(new this.constructor(this), this.e + 1, 1);\r\n };\r\n\r\n\r\n /*\r\n * Return a string representing the value of this Decimal.\r\n * Unlike `toString`, negative zero will include the minus sign.\r\n *\r\n */\r\n P.valueOf = P.toJSON = function () {\r\n var x = this,\r\n Ctor = x.constructor,\r\n str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);\r\n\r\n return x.isNeg() ? '-' + str : str;\r\n };\r\n\r\n\r\n /*\r\n // Add aliases to match BigDecimal method names.\r\n // P.add = P.plus;\r\n P.subtract = P.minus;\r\n P.multiply = P.times;\r\n P.divide = P.div;\r\n P.remainder = P.mod;\r\n P.compareTo = P.cmp;\r\n P.negate = P.neg;\r\n */\r\n\r\n\r\n // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.\r\n\r\n\r\n /*\r\n * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,\r\n * finiteToString, naturalExponential, naturalLogarithm\r\n * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,\r\n * P.toPrecision, P.toSignificantDigits, toStringBinary, random\r\n * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm\r\n * convertBase toStringBinary, parseOther\r\n * cos P.cos\r\n * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,\r\n * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,\r\n * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,\r\n * taylorSeries, atan2, parseOther\r\n * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,\r\n * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,\r\n * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,\r\n * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,\r\n * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,\r\n * P.truncated, divide, getLn10, getPi, naturalExponential,\r\n * naturalLogarithm, ceil, floor, round, trunc\r\n * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,\r\n * toStringBinary\r\n * getBase10Exponent P.minus, P.plus, P.times, parseOther\r\n * getLn10 P.logarithm, naturalLogarithm\r\n * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2\r\n * getPrecision P.precision, P.toFraction\r\n * getZeroString digitsToString, finiteToString\r\n * intPow P.toPower, parseOther\r\n * isOdd toLessThanHalfPi\r\n * maxOrMin max, min\r\n * naturalExponential P.naturalExponential, P.toPower\r\n * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,\r\n * P.toPower, naturalExponential\r\n * nonFiniteToString finiteToString, toStringBinary\r\n * parseDecimal Decimal\r\n * parseOther Decimal\r\n * sin P.sin\r\n * taylorSeries P.cosh, P.sinh, cos, sin\r\n * toLessThanHalfPi P.cos, P.sin\r\n * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal\r\n * truncate intPow\r\n *\r\n * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,\r\n * naturalLogarithm, config, parseOther, random, Decimal\r\n */\r\n\r\n\r\n function digitsToString(d) {\r\n var i, k, ws,\r\n indexOfLastWord = d.length - 1,\r\n str = '',\r\n w = d[0];\r\n\r\n if (indexOfLastWord > 0) {\r\n str += w;\r\n for (i = 1; i < indexOfLastWord; i++) {\r\n ws = d[i] + '';\r\n k = LOG_BASE - ws.length;\r\n if (k) str += getZeroString(k);\r\n str += ws;\r\n }\r\n\r\n w = d[i];\r\n ws = w + '';\r\n k = LOG_BASE - ws.length;\r\n if (k) str += getZeroString(k);\r\n } else if (w === 0) {\r\n return '0';\r\n }\r\n\r\n // Remove trailing zeros of last w.\r\n for (; w % 10 === 0;) w /= 10;\r\n\r\n return str + w;\r\n }\r\n\r\n\r\n function checkInt32(i, min, max) {\r\n if (i !== ~~i || i < min || i > max) {\r\n throw Error(invalidArgument + i);\r\n }\r\n }\r\n\r\n\r\n /*\r\n * Check 5 rounding digits if `repeating` is null, 4 otherwise.\r\n * `repeating == null` if caller is `log` or `pow`,\r\n * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.\r\n */\r\n function checkRoundingDigits(d, i, rm, repeating) {\r\n var di, k, r, rd;\r\n\r\n // Get the length of the first word of the array d.\r\n for (k = d[0]; k >= 10; k /= 10) --i;\r\n\r\n // Is the rounding digit in the first word of d?\r\n if (--i < 0) {\r\n i += LOG_BASE;\r\n di = 0;\r\n } else {\r\n di = Math.ceil((i + 1) / LOG_BASE);\r\n i %= LOG_BASE;\r\n }\r\n\r\n // i is the index (0 - 6) of the rounding digit.\r\n // E.g. if within the word 3487563 the first rounding digit is 5,\r\n // then i = 4, k = 1000, rd = 3487563 % 1000 = 563\r\n k = mathpow(10, LOG_BASE - i);\r\n rd = d[di] % k | 0;\r\n\r\n if (repeating == null) {\r\n if (i < 3) {\r\n if (i == 0) rd = rd / 100 | 0;\r\n else if (i == 1) rd = rd / 10 | 0;\r\n r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;\r\n } else {\r\n r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&\r\n (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||\r\n (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;\r\n }\r\n } else {\r\n if (i < 4) {\r\n if (i == 0) rd = rd / 1000 | 0;\r\n else if (i == 1) rd = rd / 100 | 0;\r\n else if (i == 2) rd = rd / 10 | 0;\r\n r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;\r\n } else {\r\n r = ((repeating || rm < 4) && rd + 1 == k ||\r\n (!repeating && rm > 3) && rd + 1 == k / 2) &&\r\n (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;\r\n }\r\n }\r\n\r\n return r;\r\n }\r\n\r\n\r\n // Convert string of `baseIn` to an array of numbers of `baseOut`.\r\n // Eg. convertBase('255', 10, 16) returns [15, 15].\r\n // Eg. convertBase('ff', 16, 10) returns [2, 5, 5].\r\n function convertBase(str, baseIn, baseOut) {\r\n var j,\r\n arr = [0],\r\n arrL,\r\n i = 0,\r\n strL = str.length;\r\n\r\n for (; i < strL;) {\r\n for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;\r\n arr[0] += NUMERALS.indexOf(str.charAt(i++));\r\n for (j = 0; j < arr.length; j++) {\r\n if (arr[j] > baseOut - 1) {\r\n if (arr[j + 1] === void 0) arr[j + 1] = 0;\r\n arr[j + 1] += arr[j] / baseOut | 0;\r\n arr[j] %= baseOut;\r\n }\r\n }\r\n }\r\n\r\n return arr.reverse();\r\n }\r\n\r\n\r\n /*\r\n * cos(x) = 1 - x^2/2! + x^4/4! - ...\r\n * |x| < pi/2\r\n *\r\n */\r\n function cosine(Ctor, x) {\r\n var k, y,\r\n len = x.d.length;\r\n\r\n // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1\r\n // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n if (len < 32) {\r\n k = Math.ceil(len / 3);\r\n y = (1 / tinyPow(4, k)).toString();\r\n } else {\r\n k = 16;\r\n y = '2.3283064365386962890625e-10';\r\n }\r\n\r\n Ctor.precision += k;\r\n\r\n x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1));\r\n\r\n // Reverse argument reduction\r\n for (var i = k; i--;) {\r\n var cos2x = x.times(x);\r\n x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);\r\n }\r\n\r\n Ctor.precision -= k;\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Perform division in the specified base.\r\n */\r\n var divide = (function () {\r\n\r\n // Assumes non-zero x and k, and hence non-zero result.\r\n function multiplyInteger(x, k, base) {\r\n var temp,\r\n carry = 0,\r\n i = x.length;\r\n\r\n for (x = x.slice(); i--;) {\r\n temp = x[i] * k + carry;\r\n x[i] = temp % base | 0;\r\n carry = temp / base | 0;\r\n }\r\n\r\n if (carry) x.unshift(carry);\r\n\r\n return x;\r\n }\r\n\r\n function compare(a, b, aL, bL) {\r\n var i, r;\r\n\r\n if (aL != bL) {\r\n r = aL > bL ? 1 : -1;\r\n } else {\r\n for (i = r = 0; i < aL; i++) {\r\n if (a[i] != b[i]) {\r\n r = a[i] > b[i] ? 1 : -1;\r\n break;\r\n }\r\n }\r\n }\r\n\r\n return r;\r\n }\r\n\r\n function subtract(a, b, aL, base) {\r\n var i = 0;\r\n\r\n // Subtract b from a.\r\n for (; aL--;) {\r\n a[aL] -= i;\r\n i = a[aL] < b[aL] ? 1 : 0;\r\n a[aL] = i * base + a[aL] - b[aL];\r\n }\r\n\r\n // Remove leading zeros.\r\n for (; !a[0] && a.length > 1;) a.shift();\r\n }\r\n\r\n return function (x, y, pr, rm, dp, base) {\r\n var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,\r\n yL, yz,\r\n Ctor = x.constructor,\r\n sign = x.s == y.s ? 1 : -1,\r\n xd = x.d,\r\n yd = y.d;\r\n\r\n // Either NaN, Infinity or 0?\r\n if (!xd || !xd[0] || !yd || !yd[0]) {\r\n\r\n return new Ctor(// Return NaN if either NaN, or both Infinity or 0.\r\n !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :\r\n\r\n // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.\r\n xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);\r\n }\r\n\r\n if (base) {\r\n logBase = 1;\r\n e = x.e - y.e;\r\n } else {\r\n base = BASE;\r\n logBase = LOG_BASE;\r\n e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);\r\n }\r\n\r\n yL = yd.length;\r\n xL = xd.length;\r\n q = new Ctor(sign);\r\n qd = q.d = [];\r\n\r\n // Result exponent may be one less than e.\r\n // The digit array of a Decimal from toStringBinary may have trailing zeros.\r\n for (i = 0; yd[i] == (xd[i] || 0); i++);\r\n\r\n if (yd[i] > (xd[i] || 0)) e--;\r\n\r\n if (pr == null) {\r\n sd = pr = Ctor.precision;\r\n rm = Ctor.rounding;\r\n } else if (dp) {\r\n sd = pr + (x.e - y.e) + 1;\r\n } else {\r\n sd = pr;\r\n }\r\n\r\n if (sd < 0) {\r\n qd.push(1);\r\n more = true;\r\n } else {\r\n\r\n // Convert precision in number of base 10 digits to base 1e7 digits.\r\n sd = sd / logBase + 2 | 0;\r\n i = 0;\r\n\r\n // divisor < 1e7\r\n if (yL == 1) {\r\n k = 0;\r\n yd = yd[0];\r\n sd++;\r\n\r\n // k is the carry.\r\n for (; (i < xL || k) && sd--; i++) {\r\n t = k * base + (xd[i] || 0);\r\n qd[i] = t / yd | 0;\r\n k = t % yd | 0;\r\n }\r\n\r\n more = k || i < xL;\r\n\r\n // divisor >= 1e7\r\n } else {\r\n\r\n // Normalise xd and yd so highest order digit of yd is >= base/2\r\n k = base / (yd[0] + 1) | 0;\r\n\r\n if (k > 1) {\r\n yd = multiplyInteger(yd, k, base);\r\n xd = multiplyInteger(xd, k, base);\r\n yL = yd.length;\r\n xL = xd.length;\r\n }\r\n\r\n xi = yL;\r\n rem = xd.slice(0, yL);\r\n remL = rem.length;\r\n\r\n // Add zeros to make remainder as long as divisor.\r\n for (; remL < yL;) rem[remL++] = 0;\r\n\r\n yz = yd.slice();\r\n yz.unshift(0);\r\n yd0 = yd[0];\r\n\r\n if (yd[1] >= base / 2) ++yd0;\r\n\r\n do {\r\n k = 0;\r\n\r\n // Compare divisor and remainder.\r\n cmp = compare(yd, rem, yL, remL);\r\n\r\n // If divisor < remainder.\r\n if (cmp < 0) {\r\n\r\n // Calculate trial digit, k.\r\n rem0 = rem[0];\r\n if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);\r\n\r\n // k will be how many times the divisor goes into the current remainder.\r\n k = rem0 / yd0 | 0;\r\n\r\n // Algorithm:\r\n // 1. product = divisor * trial digit (k)\r\n // 2. if product > remainder: product -= divisor, k--\r\n // 3. remainder -= product\r\n // 4. if product was < remainder at 2:\r\n // 5. compare new remainder and divisor\r\n // 6. If remainder > divisor: remainder -= divisor, k++\r\n\r\n if (k > 1) {\r\n if (k >= base) k = base - 1;\r\n\r\n // product = divisor * trial digit.\r\n prod = multiplyInteger(yd, k, base);\r\n prodL = prod.length;\r\n remL = rem.length;\r\n\r\n // Compare product and remainder.\r\n cmp = compare(prod, rem, prodL, remL);\r\n\r\n // product > remainder.\r\n if (cmp == 1) {\r\n k--;\r\n\r\n // Subtract divisor from product.\r\n subtract(prod, yL < prodL ? yz : yd, prodL, base);\r\n }\r\n } else {\r\n\r\n // cmp is -1.\r\n // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1\r\n // to avoid it. If k is 1 there is a need to compare yd and rem again below.\r\n if (k == 0) cmp = k = 1;\r\n prod = yd.slice();\r\n }\r\n\r\n prodL = prod.length;\r\n if (prodL < remL) prod.unshift(0);\r\n\r\n // Subtract product from remainder.\r\n subtract(rem, prod, remL, base);\r\n\r\n // If product was < previous remainder.\r\n if (cmp == -1) {\r\n remL = rem.length;\r\n\r\n // Compare divisor and new remainder.\r\n cmp = compare(yd, rem, yL, remL);\r\n\r\n // If divisor < new remainder, subtract divisor from remainder.\r\n if (cmp < 1) {\r\n k++;\r\n\r\n // Subtract divisor from remainder.\r\n subtract(rem, yL < remL ? yz : yd, remL, base);\r\n }\r\n }\r\n\r\n remL = rem.length;\r\n } else if (cmp === 0) {\r\n k++;\r\n rem = [0];\r\n } // if cmp === 1, k will be 0\r\n\r\n // Add the next digit, k, to the result array.\r\n qd[i++] = k;\r\n\r\n // Update the remainder.\r\n if (cmp && rem[0]) {\r\n rem[remL++] = xd[xi] || 0;\r\n } else {\r\n rem = [xd[xi]];\r\n remL = 1;\r\n }\r\n\r\n } while ((xi++ < xL || rem[0] !== void 0) && sd--);\r\n\r\n more = rem[0] !== void 0;\r\n }\r\n\r\n // Leading zero?\r\n if (!qd[0]) qd.shift();\r\n }\r\n\r\n // logBase is 1 when divide is being used for base conversion.\r\n if (logBase == 1) {\r\n q.e = e;\r\n inexact = more;\r\n } else {\r\n\r\n // To calculate q.e, first get the number of digits of qd[0].\r\n for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;\r\n q.e = i + e * logBase - 1;\r\n\r\n finalise(q, dp ? pr + q.e + 1 : pr, rm, more);\r\n }\r\n\r\n return q;\r\n };\r\n })();\r\n\r\n\r\n /*\r\n * Round `x` to `sd` significant digits using rounding mode `rm`.\r\n * Check for over/under-flow.\r\n */\r\n function finalise(x, sd, rm, isTruncated) {\r\n var digits, i, j, k, rd, roundUp, w, xd, xdi,\r\n Ctor = x.constructor;\r\n\r\n // Don't round if sd is null or undefined.\r\n out: if (sd != null) {\r\n xd = x.d;\r\n\r\n // Infinity/NaN.\r\n if (!xd) return x;\r\n\r\n // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.\r\n // w: the word of xd containing rd, a base 1e7 number.\r\n // xdi: the index of w within xd.\r\n // digits: the number of digits of w.\r\n // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if\r\n // they had leading zeros)\r\n // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).\r\n\r\n // Get the length of the first word of the digits array xd.\r\n for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;\r\n i = sd - digits;\r\n\r\n // Is the rounding digit in the first word of xd?\r\n if (i < 0) {\r\n i += LOG_BASE;\r\n j = sd;\r\n w = xd[xdi = 0];\r\n\r\n // Get the rounding digit at index j of w.\r\n rd = w / mathpow(10, digits - j - 1) % 10 | 0;\r\n } else {\r\n xdi = Math.ceil((i + 1) / LOG_BASE);\r\n k = xd.length;\r\n if (xdi >= k) {\r\n if (isTruncated) {\r\n\r\n // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.\r\n for (; k++ <= xdi;) xd.push(0);\r\n w = rd = 0;\r\n digits = 1;\r\n i %= LOG_BASE;\r\n j = i - LOG_BASE + 1;\r\n } else {\r\n break out;\r\n }\r\n } else {\r\n w = k = xd[xdi];\r\n\r\n // Get the number of digits of w.\r\n for (digits = 1; k >= 10; k /= 10) digits++;\r\n\r\n // Get the index of rd within w.\r\n i %= LOG_BASE;\r\n\r\n // Get the index of rd within w, adjusted for leading zeros.\r\n // The number of leading zeros of w is given by LOG_BASE - digits.\r\n j = i - LOG_BASE + digits;\r\n\r\n // Get the rounding digit at index j of w.\r\n rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;\r\n }\r\n }\r\n\r\n // Are there any non-zero digits after the rounding digit?\r\n isTruncated = isTruncated || sd < 0 ||\r\n xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));\r\n\r\n // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right\r\n // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression\r\n // will give 714.\r\n\r\n roundUp = rm < 4\r\n ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))\r\n : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&\r\n\r\n // Check whether the digit to the left of the rounding digit is odd.\r\n ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||\r\n rm == (x.s < 0 ? 8 : 7));\r\n\r\n if (sd < 1 || !xd[0]) {\r\n xd.length = 0;\r\n if (roundUp) {\r\n\r\n // Convert sd to decimal places.\r\n sd -= x.e + 1;\r\n\r\n // 1, 0.1, 0.01, 0.001, 0.0001 etc.\r\n xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);\r\n x.e = -sd || 0;\r\n } else {\r\n\r\n // Zero.\r\n xd[0] = x.e = 0;\r\n }\r\n\r\n return x;\r\n }\r\n\r\n // Remove excess digits.\r\n if (i == 0) {\r\n xd.length = xdi;\r\n k = 1;\r\n xdi--;\r\n } else {\r\n xd.length = xdi + 1;\r\n k = mathpow(10, LOG_BASE - i);\r\n\r\n // E.g. 56700 becomes 56000 if 7 is the rounding digit.\r\n // j > 0 means i > number of leading zeros of w.\r\n xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;\r\n }\r\n\r\n if (roundUp) {\r\n for (;;) {\r\n\r\n // Is the digit to be rounded up in the first word of xd?\r\n if (xdi == 0) {\r\n\r\n // i will be the length of xd[0] before k is added.\r\n for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;\r\n j = xd[0] += k;\r\n for (k = 1; j >= 10; j /= 10) k++;\r\n\r\n // if i != k the length has increased.\r\n if (i != k) {\r\n x.e++;\r\n if (xd[0] == BASE) xd[0] = 1;\r\n }\r\n\r\n break;\r\n } else {\r\n xd[xdi] += k;\r\n if (xd[xdi] != BASE) break;\r\n xd[xdi--] = 0;\r\n k = 1;\r\n }\r\n }\r\n }\r\n\r\n // Remove trailing zeros.\r\n for (i = xd.length; xd[--i] === 0;) xd.pop();\r\n }\r\n\r\n if (external) {\r\n\r\n // Overflow?\r\n if (x.e > Ctor.maxE) {\r\n\r\n // Infinity.\r\n x.d = null;\r\n x.e = NaN;\r\n\r\n // Underflow?\r\n } else if (x.e < Ctor.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n // Ctor.underflow = true;\r\n } // else Ctor.underflow = false;\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n function finiteToString(x, isExp, sd) {\r\n if (!x.isFinite()) return nonFiniteToString(x);\r\n var k,\r\n e = x.e,\r\n str = digitsToString(x.d),\r\n len = str.length;\r\n\r\n if (isExp) {\r\n if (sd && (k = sd - len) > 0) {\r\n str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);\r\n } else if (len > 1) {\r\n str = str.charAt(0) + '.' + str.slice(1);\r\n }\r\n\r\n str = str + (x.e < 0 ? 'e' : 'e+') + x.e;\r\n } else if (e < 0) {\r\n str = '0.' + getZeroString(-e - 1) + str;\r\n if (sd && (k = sd - len) > 0) str += getZeroString(k);\r\n } else if (e >= len) {\r\n str += getZeroString(e + 1 - len);\r\n if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);\r\n } else {\r\n if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);\r\n if (sd && (k = sd - len) > 0) {\r\n if (e + 1 === len) str += '.';\r\n str += getZeroString(k);\r\n }\r\n }\r\n\r\n return str;\r\n }\r\n\r\n\r\n // Calculate the base 10 exponent from the base 1e7 exponent.\r\n function getBase10Exponent(digits, e) {\r\n var w = digits[0];\r\n\r\n // Add the number of digits of the first word of the digits array.\r\n for ( e *= LOG_BASE; w >= 10; w /= 10) e++;\r\n return e;\r\n }\r\n\r\n\r\n function getLn10(Ctor, sd, pr) {\r\n if (sd > LN10_PRECISION) {\r\n\r\n // Reset global state in case the exception is caught.\r\n external = true;\r\n if (pr) Ctor.precision = pr;\r\n throw Error(precisionLimitExceeded);\r\n }\r\n return finalise(new Ctor(LN10), sd, 1, true);\r\n }\r\n\r\n\r\n function getPi(Ctor, sd, rm) {\r\n if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);\r\n return finalise(new Ctor(PI), sd, rm, true);\r\n }\r\n\r\n\r\n function getPrecision(digits) {\r\n var w = digits.length - 1,\r\n len = w * LOG_BASE + 1;\r\n\r\n w = digits[w];\r\n\r\n // If non-zero...\r\n if (w) {\r\n\r\n // Subtract the number of trailing zeros of the last word.\r\n for (; w % 10 == 0; w /= 10) len--;\r\n\r\n // Add the number of digits of the first word.\r\n for (w = digits[0]; w >= 10; w /= 10) len++;\r\n }\r\n\r\n return len;\r\n }\r\n\r\n\r\n function getZeroString(k) {\r\n var zs = '';\r\n for (; k--;) zs += '0';\r\n return zs;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an\r\n * integer of type number.\r\n *\r\n * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.\r\n *\r\n */\r\n function intPow(Ctor, x, n, pr) {\r\n var isTruncated,\r\n r = new Ctor(1),\r\n\r\n // Max n of 9007199254740991 takes 53 loop iterations.\r\n // Maximum digits array length; leaves [28, 34] guard digits.\r\n k = Math.ceil(pr / LOG_BASE + 4);\r\n\r\n external = false;\r\n\r\n for (;;) {\r\n if (n % 2) {\r\n r = r.times(x);\r\n if (truncate(r.d, k)) isTruncated = true;\r\n }\r\n\r\n n = mathfloor(n / 2);\r\n if (n === 0) {\r\n\r\n // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.\r\n n = r.d.length - 1;\r\n if (isTruncated && r.d[n] === 0) ++r.d[n];\r\n break;\r\n }\r\n\r\n x = x.times(x);\r\n truncate(x.d, k);\r\n }\r\n\r\n external = true;\r\n\r\n return r;\r\n }\r\n\r\n\r\n function isOdd(n) {\r\n return n.d[n.d.length - 1] & 1;\r\n }\r\n\r\n\r\n /*\r\n * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.\r\n */\r\n function maxOrMin(Ctor, args, ltgt) {\r\n var y,\r\n x = new Ctor(args[0]),\r\n i = 0;\r\n\r\n for (; ++i < args.length;) {\r\n y = new Ctor(args[i]);\r\n if (!y.s) {\r\n x = y;\r\n break;\r\n } else if (x[ltgt](y)) {\r\n x = y;\r\n }\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant\r\n * digits.\r\n *\r\n * Taylor/Maclaurin series.\r\n *\r\n * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...\r\n *\r\n * Argument reduction:\r\n * Repeat x = x / 32, k += 5, until |x| < 0.1\r\n * exp(x) = exp(x / 2^k)^(2^k)\r\n *\r\n * Previously, the argument was initially reduced by\r\n * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10)\r\n * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was\r\n * found to be slower than just dividing repeatedly by 32 as above.\r\n *\r\n * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000\r\n * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000\r\n * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)\r\n *\r\n * exp(Infinity) = Infinity\r\n * exp(-Infinity) = 0\r\n * exp(NaN) = NaN\r\n * exp(±0) = 1\r\n *\r\n * exp(x) is non-terminating for any finite, non-zero x.\r\n *\r\n * The result will always be correctly rounded.\r\n *\r\n */\r\n function naturalExponential(x, sd) {\r\n var denominator, guard, j, pow, sum, t, wpr,\r\n rep = 0,\r\n i = 0,\r\n k = 0,\r\n Ctor = x.constructor,\r\n rm = Ctor.rounding,\r\n pr = Ctor.precision;\r\n\r\n // 0/NaN/Infinity?\r\n if (!x.d || !x.d[0] || x.e > 17) {\r\n\r\n return new Ctor(x.d\r\n ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0\r\n : x.s ? x.s < 0 ? 0 : x : 0 / 0);\r\n }\r\n\r\n if (sd == null) {\r\n external = false;\r\n wpr = pr;\r\n } else {\r\n wpr = sd;\r\n }\r\n\r\n t = new Ctor(0.03125);\r\n\r\n // while abs(x) >= 0.1\r\n while (x.e > -2) {\r\n\r\n // x = x / 2^5\r\n x = x.times(t);\r\n k += 5;\r\n }\r\n\r\n // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision\r\n // necessary to ensure the first 4 rounding digits are correct.\r\n guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;\r\n wpr += guard;\r\n denominator = pow = sum = new Ctor(1);\r\n Ctor.precision = wpr;\r\n\r\n for (;;) {\r\n pow = finalise(pow.times(x), wpr, 1);\r\n denominator = denominator.times(++i);\r\n t = sum.plus(divide(pow, denominator, wpr, 1));\r\n\r\n if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {\r\n j = k;\r\n while (j--) sum = finalise(sum.times(sum), wpr, 1);\r\n\r\n // Check to see if the first 4 rounding digits are [49]999.\r\n // If so, repeat the summation with a higher precision, otherwise\r\n // e.g. with precision: 18, rounding: 1\r\n // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)\r\n // `wpr - guard` is the index of first rounding digit.\r\n if (sd == null) {\r\n\r\n if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {\r\n Ctor.precision = wpr += 10;\r\n denominator = pow = t = new Ctor(1);\r\n i = 0;\r\n rep++;\r\n } else {\r\n return finalise(sum, Ctor.precision = pr, rm, external = true);\r\n }\r\n } else {\r\n Ctor.precision = pr;\r\n return sum;\r\n }\r\n }\r\n\r\n sum = t;\r\n }\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant\r\n * digits.\r\n *\r\n * ln(-n) = NaN\r\n * ln(0) = -Infinity\r\n * ln(-0) = -Infinity\r\n * ln(1) = 0\r\n * ln(Infinity) = Infinity\r\n * ln(-Infinity) = NaN\r\n * ln(NaN) = NaN\r\n *\r\n * ln(n) (n != 1) is non-terminating.\r\n *\r\n */\r\n function naturalLogarithm(y, sd) {\r\n var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,\r\n n = 1,\r\n guard = 10,\r\n x = y,\r\n xd = x.d,\r\n Ctor = x.constructor,\r\n rm = Ctor.rounding,\r\n pr = Ctor.precision;\r\n\r\n // Is x negative or Infinity, NaN, 0 or 1?\r\n if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {\r\n return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);\r\n }\r\n\r\n if (sd == null) {\r\n external = false;\r\n wpr = pr;\r\n } else {\r\n wpr = sd;\r\n }\r\n\r\n Ctor.precision = wpr += guard;\r\n c = digitsToString(xd);\r\n c0 = c.charAt(0);\r\n\r\n if (Math.abs(e = x.e) < 1.5e15) {\r\n\r\n // Argument reduction.\r\n // The series converges faster the closer the argument is to 1, so using\r\n // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b\r\n // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,\r\n // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can\r\n // later be divided by this number, then separate out the power of 10 using\r\n // ln(a*10^b) = ln(a) + b*ln(10).\r\n\r\n // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).\r\n //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {\r\n // max n is 6 (gives 0.7 - 1.3)\r\n while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {\r\n x = x.times(y);\r\n c = digitsToString(x.d);\r\n c0 = c.charAt(0);\r\n n++;\r\n }\r\n\r\n e = x.e;\r\n\r\n if (c0 > 1) {\r\n x = new Ctor('0.' + c);\r\n e++;\r\n } else {\r\n x = new Ctor(c0 + '.' + c.slice(1));\r\n }\r\n } else {\r\n\r\n // The argument reduction method above may result in overflow if the argument y is a massive\r\n // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this\r\n // function using ln(x*10^e) = ln(x) + e*ln(10).\r\n t = getLn10(Ctor, wpr + 2, pr).times(e + '');\r\n x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);\r\n Ctor.precision = pr;\r\n\r\n return sd == null ? finalise(x, pr, rm, external = true) : x;\r\n }\r\n\r\n // x1 is x reduced to a value near 1.\r\n x1 = x;\r\n\r\n // Taylor series.\r\n // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)\r\n // where x = (y - 1)/(y + 1) (|x| < 1)\r\n sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);\r\n x2 = finalise(x.times(x), wpr, 1);\r\n denominator = 3;\r\n\r\n for (;;) {\r\n numerator = finalise(numerator.times(x2), wpr, 1);\r\n t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));\r\n\r\n if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {\r\n sum = sum.times(2);\r\n\r\n // Reverse the argument reduction. Check that e is not 0 because, besides preventing an\r\n // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.\r\n if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));\r\n sum = divide(sum, new Ctor(n), wpr, 1);\r\n\r\n // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has\r\n // been repeated previously) and the first 4 rounding digits 9999?\r\n // If so, restart the summation with a higher precision, otherwise\r\n // e.g. with precision: 12, rounding: 1\r\n // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.\r\n // `wpr - guard` is the index of first rounding digit.\r\n if (sd == null) {\r\n if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {\r\n Ctor.precision = wpr += guard;\r\n t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);\r\n x2 = finalise(x.times(x), wpr, 1);\r\n denominator = rep = 1;\r\n } else {\r\n return finalise(sum, Ctor.precision = pr, rm, external = true);\r\n }\r\n } else {\r\n Ctor.precision = pr;\r\n return sum;\r\n }\r\n }\r\n\r\n sum = t;\r\n denominator += 2;\r\n }\r\n }\r\n\r\n\r\n // ±Infinity, NaN.\r\n function nonFiniteToString(x) {\r\n // Unsigned.\r\n return String(x.s * x.s / 0);\r\n }\r\n\r\n\r\n /*\r\n * Parse the value of a new Decimal `x` from string `str`.\r\n */\r\n function parseDecimal(x, str) {\r\n var e, i, len;\r\n\r\n // Decimal point?\r\n if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');\r\n\r\n // Exponential form?\r\n if ((i = str.search(/e/i)) > 0) {\r\n\r\n // Determine exponent.\r\n if (e < 0) e = i;\r\n e += +str.slice(i + 1);\r\n str = str.substring(0, i);\r\n } else if (e < 0) {\r\n\r\n // Integer.\r\n e = str.length;\r\n }\r\n\r\n // Determine leading zeros.\r\n for (i = 0; str.charCodeAt(i) === 48; i++);\r\n\r\n // Determine trailing zeros.\r\n for (len = str.length; str.charCodeAt(len - 1) === 48; --len);\r\n str = str.slice(i, len);\r\n\r\n if (str) {\r\n len -= i;\r\n x.e = e = e - i - 1;\r\n x.d = [];\r\n\r\n // Transform base\r\n\r\n // e is the base 10 exponent.\r\n // i is where to slice str to get the first word of the digits array.\r\n i = (e + 1) % LOG_BASE;\r\n if (e < 0) i += LOG_BASE;\r\n\r\n if (i < len) {\r\n if (i) x.d.push(+str.slice(0, i));\r\n for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));\r\n str = str.slice(i);\r\n i = LOG_BASE - str.length;\r\n } else {\r\n i -= len;\r\n }\r\n\r\n for (; i--;) str += '0';\r\n x.d.push(+str);\r\n\r\n if (external) {\r\n\r\n // Overflow?\r\n if (x.e > x.constructor.maxE) {\r\n\r\n // Infinity.\r\n x.d = null;\r\n x.e = NaN;\r\n\r\n // Underflow?\r\n } else if (x.e < x.constructor.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n // x.constructor.underflow = true;\r\n } // else x.constructor.underflow = false;\r\n }\r\n } else {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.\r\n */\r\n function parseOther(x, str) {\r\n var base, Ctor, divisor, i, isFloat, len, p, xd, xe;\r\n\r\n if (str === 'Infinity' || str === 'NaN') {\r\n if (!+str) x.s = NaN;\r\n x.e = NaN;\r\n x.d = null;\r\n return x;\r\n }\r\n\r\n if (isHex.test(str)) {\r\n base = 16;\r\n str = str.toLowerCase();\r\n } else if (isBinary.test(str)) {\r\n base = 2;\r\n } else if (isOctal.test(str)) {\r\n base = 8;\r\n } else {\r\n throw Error(invalidArgument + str);\r\n }\r\n\r\n // Is there a binary exponent part?\r\n i = str.search(/p/i);\r\n\r\n if (i > 0) {\r\n p = +str.slice(i + 1);\r\n str = str.substring(2, i);\r\n } else {\r\n str = str.slice(2);\r\n }\r\n\r\n // Convert `str` as an integer then divide the result by `base` raised to a power such that the\r\n // fraction part will be restored.\r\n i = str.indexOf('.');\r\n isFloat = i >= 0;\r\n Ctor = x.constructor;\r\n\r\n if (isFloat) {\r\n str = str.replace('.', '');\r\n len = str.length;\r\n i = len - i;\r\n\r\n // log[10](16) = 1.2041... , log[10](88) = 1.9444....\r\n divisor = intPow(Ctor, new Ctor(base), i, i * 2);\r\n }\r\n\r\n xd = convertBase(str, base, BASE);\r\n xe = xd.length - 1;\r\n\r\n // Remove trailing zeros.\r\n for (i = xe; xd[i] === 0; --i) xd.pop();\r\n if (i < 0) return new Ctor(x.s * 0);\r\n x.e = getBase10Exponent(xd, xe);\r\n x.d = xd;\r\n external = false;\r\n\r\n // At what precision to perform the division to ensure exact conversion?\r\n // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)\r\n // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412\r\n // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.\r\n // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount\r\n // Therefore using 4 * the number of digits of str will always be enough.\r\n if (isFloat) x = divide(x, divisor, len * 4);\r\n\r\n // Multiply by the binary exponent part if present.\r\n if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));\r\n external = true;\r\n\r\n return x;\r\n }\r\n\r\n\r\n /*\r\n * sin(x) = x - x^3/3! + x^5/5! - ...\r\n * |x| < pi/2\r\n *\r\n */\r\n function sine(Ctor, x) {\r\n var k,\r\n len = x.d.length;\r\n\r\n if (len < 3) return taylorSeries(Ctor, 2, x, x);\r\n\r\n // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)\r\n // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)\r\n // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))\r\n\r\n // Estimate the optimum number of times to use the argument reduction.\r\n k = 1.4 * Math.sqrt(len);\r\n k = k > 16 ? 16 : k | 0;\r\n\r\n x = x.times(1 / tinyPow(5, k));\r\n x = taylorSeries(Ctor, 2, x, x);\r\n\r\n // Reverse argument reduction\r\n var sin2_x,\r\n d5 = new Ctor(5),\r\n d16 = new Ctor(16),\r\n d20 = new Ctor(20);\r\n for (; k--;) {\r\n sin2_x = x.times(x);\r\n x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));\r\n }\r\n\r\n return x;\r\n }\r\n\r\n\r\n // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.\r\n function taylorSeries(Ctor, n, x, y, isHyperbolic) {\r\n var j, t, u, x2,\r\n i = 1,\r\n pr = Ctor.precision,\r\n k = Math.ceil(pr / LOG_BASE);\r\n\r\n external = false;\r\n x2 = x.times(x);\r\n u = new Ctor(y);\r\n\r\n for (;;) {\r\n t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);\r\n u = isHyperbolic ? y.plus(t) : y.minus(t);\r\n y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);\r\n t = u.plus(y);\r\n\r\n if (t.d[k] !== void 0) {\r\n for (j = k; t.d[j] === u.d[j] && j--;);\r\n if (j == -1) break;\r\n }\r\n\r\n j = u;\r\n u = y;\r\n y = t;\r\n t = j;\r\n i++;\r\n }\r\n\r\n external = true;\r\n t.d.length = k + 1;\r\n\r\n return t;\r\n }\r\n\r\n\r\n // Exponent e must be positive and non-zero.\r\n function tinyPow(b, e) {\r\n var n = b;\r\n while (--e) n *= b;\r\n return n;\r\n }\r\n\r\n\r\n // Return the absolute value of `x` reduced to less than or equal to half pi.\r\n function toLessThanHalfPi(Ctor, x) {\r\n var t,\r\n isNeg = x.s < 0,\r\n pi = getPi(Ctor, Ctor.precision, 1),\r\n halfPi = pi.times(0.5);\r\n\r\n x = x.abs();\r\n\r\n if (x.lte(halfPi)) {\r\n quadrant = isNeg ? 4 : 1;\r\n return x;\r\n }\r\n\r\n t = x.divToInt(pi);\r\n\r\n if (t.isZero()) {\r\n quadrant = isNeg ? 3 : 2;\r\n } else {\r\n x = x.minus(t.times(pi));\r\n\r\n // 0 <= x < pi\r\n if (x.lte(halfPi)) {\r\n quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);\r\n return x;\r\n }\r\n\r\n quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);\r\n }\r\n\r\n return x.minus(pi).abs();\r\n }\r\n\r\n\r\n /*\r\n * Return the value of Decimal `x` as a string in base `baseOut`.\r\n *\r\n * If the optional `sd` argument is present include a binary exponent suffix.\r\n */\r\n function toStringBinary(x, baseOut, sd, rm) {\r\n var base, e, i, k, len, roundUp, str, xd, y,\r\n Ctor = x.constructor,\r\n isExp = sd !== void 0;\r\n\r\n if (isExp) {\r\n checkInt32(sd, 1, MAX_DIGITS);\r\n if (rm === void 0) rm = Ctor.rounding;\r\n else checkInt32(rm, 0, 8);\r\n } else {\r\n sd = Ctor.precision;\r\n rm = Ctor.rounding;\r\n }\r\n\r\n if (!x.isFinite()) {\r\n str = nonFiniteToString(x);\r\n } else {\r\n str = finiteToString(x);\r\n i = str.indexOf('.');\r\n\r\n // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:\r\n // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))\r\n // minBinaryExponent = floor(decimalExponent * log[2](10))\r\n // log[2](10) = 3.321928094887362347870319429489390175864\r\n\r\n if (isExp) {\r\n base = 2;\r\n if (baseOut == 16) {\r\n sd = sd * 4 - 3;\r\n } else if (baseOut == 8) {\r\n sd = sd * 3 - 2;\r\n }\r\n } else {\r\n base = baseOut;\r\n }\r\n\r\n // Convert the number as an integer then divide the result by its base raised to a power such\r\n // that the fraction part will be restored.\r\n\r\n // Non-integer.\r\n if (i >= 0) {\r\n str = str.replace('.', '');\r\n y = new Ctor(1);\r\n y.e = str.length - i;\r\n y.d = convertBase(finiteToString(y), 10, base);\r\n y.e = y.d.length;\r\n }\r\n\r\n xd = convertBase(str, 10, base);\r\n e = len = xd.length;\r\n\r\n // Remove trailing zeros.\r\n for (; xd[--len] == 0;) xd.pop();\r\n\r\n if (!xd[0]) {\r\n str = isExp ? '0p+0' : '0';\r\n } else {\r\n if (i < 0) {\r\n e--;\r\n } else {\r\n x = new Ctor(x);\r\n x.d = xd;\r\n x.e = e;\r\n x = divide(x, y, sd, rm, 0, base);\r\n xd = x.d;\r\n e = x.e;\r\n roundUp = inexact;\r\n }\r\n\r\n // The rounding digit, i.e. the digit after the digit that may be rounded up.\r\n i = xd[sd];\r\n k = base / 2;\r\n roundUp = roundUp || xd[sd + 1] !== void 0;\r\n\r\n roundUp = rm < 4\r\n ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))\r\n : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||\r\n rm === (x.s < 0 ? 8 : 7));\r\n\r\n xd.length = sd;\r\n\r\n if (roundUp) {\r\n\r\n // Rounding up may mean the previous digit has to be rounded up and so on.\r\n for (; ++xd[--sd] > base - 1;) {\r\n xd[sd] = 0;\r\n if (!sd) {\r\n ++e;\r\n xd.unshift(1);\r\n }\r\n }\r\n }\r\n\r\n // Determine trailing zeros.\r\n for (len = xd.length; !xd[len - 1]; --len);\r\n\r\n // E.g. [4, 11, 15] becomes 4bf.\r\n for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);\r\n\r\n // Add binary exponent suffix?\r\n if (isExp) {\r\n if (len > 1) {\r\n if (baseOut == 16 || baseOut == 8) {\r\n i = baseOut == 16 ? 4 : 3;\r\n for (--len; len % i; len++) str += '0';\r\n xd = convertBase(str, base, baseOut);\r\n for (len = xd.length; !xd[len - 1]; --len);\r\n\r\n // xd[0] will always be be 1\r\n for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);\r\n } else {\r\n str = str.charAt(0) + '.' + str.slice(1);\r\n }\r\n }\r\n\r\n str = str + (e < 0 ? 'p' : 'p+') + e;\r\n } else if (e < 0) {\r\n for (; ++e;) str = '0' + str;\r\n str = '0.' + str;\r\n } else {\r\n if (++e > len) for (e -= len; e-- ;) str += '0';\r\n else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);\r\n }\r\n }\r\n\r\n str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;\r\n }\r\n\r\n return x.s < 0 ? '-' + str : str;\r\n }\r\n\r\n\r\n // Does not strip trailing zeros.\r\n function truncate(arr, len) {\r\n if (arr.length > len) {\r\n arr.length = len;\r\n return true;\r\n }\r\n }\r\n\r\n\r\n // Decimal methods\r\n\r\n\r\n /*\r\n * abs\r\n * acos\r\n * acosh\r\n * add\r\n * asin\r\n * asinh\r\n * atan\r\n * atanh\r\n * atan2\r\n * cbrt\r\n * ceil\r\n * clone\r\n * config\r\n * cos\r\n * cosh\r\n * div\r\n * exp\r\n * floor\r\n * hypot\r\n * ln\r\n * log\r\n * log2\r\n * log10\r\n * max\r\n * min\r\n * mod\r\n * mul\r\n * pow\r\n * random\r\n * round\r\n * set\r\n * sign\r\n * sin\r\n * sinh\r\n * sqrt\r\n * sub\r\n * tan\r\n * tanh\r\n * trunc\r\n */\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the absolute value of `x`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function abs(x) {\r\n return new this(x).abs();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arccosine in radians of `x`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function acos(x) {\r\n return new this(x).acos();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function acosh(x) {\r\n return new this(x).acosh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function add(x, y) {\r\n return new this(x).plus(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function asin(x) {\r\n return new this(x).asin();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function asinh(x) {\r\n return new this(x).asinh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function atan(x) {\r\n return new this(x).atan();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to\r\n * `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function atanh(x) {\r\n return new this(x).atanh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi\r\n * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * Domain: [-Infinity, Infinity]\r\n * Range: [-pi, pi]\r\n *\r\n * y {number|string|Decimal} The y-coordinate.\r\n * x {number|string|Decimal} The x-coordinate.\r\n *\r\n * atan2(±0, -0) = ±pi\r\n * atan2(±0, +0) = ±0\r\n * atan2(±0, -x) = ±pi for x > 0\r\n * atan2(±0, x) = ±0 for x > 0\r\n * atan2(-y, ±0) = -pi/2 for y > 0\r\n * atan2(y, ±0) = pi/2 for y > 0\r\n * atan2(±y, -Infinity) = ±pi for finite y > 0\r\n * atan2(±y, +Infinity) = ±0 for finite y > 0\r\n * atan2(±Infinity, x) = ±pi/2 for finite x\r\n * atan2(±Infinity, -Infinity) = ±3*pi/4\r\n * atan2(±Infinity, +Infinity) = ±pi/4\r\n * atan2(NaN, x) = NaN\r\n * atan2(y, NaN) = NaN\r\n *\r\n */\r\n function atan2(y, x) {\r\n y = new this(y);\r\n x = new this(x);\r\n var r,\r\n pr = this.precision,\r\n rm = this.rounding,\r\n wpr = pr + 4;\r\n\r\n // Either NaN\r\n if (!y.s || !x.s) {\r\n r = new this(NaN);\r\n\r\n // Both ±Infinity\r\n } else if (!y.d && !x.d) {\r\n r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);\r\n r.s = y.s;\r\n\r\n // x is ±Infinity or y is ±0\r\n } else if (!x.d || y.isZero()) {\r\n r = x.s < 0 ? getPi(this, pr, rm) : new this(0);\r\n r.s = y.s;\r\n\r\n // y is ±Infinity or x is ±0\r\n } else if (!y.d || x.isZero()) {\r\n r = getPi(this, wpr, 1).times(0.5);\r\n r.s = y.s;\r\n\r\n // Both non-zero and finite\r\n } else if (x.s < 0) {\r\n this.precision = wpr;\r\n this.rounding = 1;\r\n r = this.atan(divide(y, x, wpr, 1));\r\n x = getPi(this, wpr, 1);\r\n this.precision = pr;\r\n this.rounding = rm;\r\n r = y.s < 0 ? r.minus(x) : r.plus(x);\r\n } else {\r\n r = this.atan(divide(y, x, wpr, 1));\r\n }\r\n\r\n return r;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function cbrt(x) {\r\n return new this(x).cbrt();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function ceil(x) {\r\n return finalise(x = new this(x), x.e + 1, 2);\r\n }\r\n\r\n\r\n /*\r\n * Configure global settings for a Decimal constructor.\r\n *\r\n * `obj` is an object with one or more of the following properties,\r\n *\r\n * precision {number}\r\n * rounding {number}\r\n * toExpNeg {number}\r\n * toExpPos {number}\r\n * maxE {number}\r\n * minE {number}\r\n * modulo {number}\r\n * crypto {boolean|number}\r\n * defaults {true}\r\n *\r\n * E.g. Decimal.config({ precision: 20, rounding: 4 })\r\n *\r\n */\r\n function config(obj) {\r\n if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');\r\n var i, p, v,\r\n useDefaults = obj.defaults === true,\r\n ps = [\r\n 'precision', 1, MAX_DIGITS,\r\n 'rounding', 0, 8,\r\n 'toExpNeg', -EXP_LIMIT, 0,\r\n 'toExpPos', 0, EXP_LIMIT,\r\n 'maxE', 0, EXP_LIMIT,\r\n 'minE', -EXP_LIMIT, 0,\r\n 'modulo', 0, 9\r\n ];\r\n\r\n for (i = 0; i < ps.length; i += 3) {\r\n if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];\r\n if ((v = obj[p]) !== void 0) {\r\n if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;\r\n else throw Error(invalidArgument + p + ': ' + v);\r\n }\r\n }\r\n\r\n if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];\r\n if ((v = obj[p]) !== void 0) {\r\n if (v === true || v === false || v === 0 || v === 1) {\r\n if (v) {\r\n if (typeof crypto != 'undefined' && crypto &&\r\n (crypto.getRandomValues || crypto.randomBytes)) {\r\n this[p] = true;\r\n } else {\r\n throw Error(cryptoUnavailable);\r\n }\r\n } else {\r\n this[p] = false;\r\n }\r\n } else {\r\n throw Error(invalidArgument + p + ': ' + v);\r\n }\r\n }\r\n\r\n return this;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function cos(x) {\r\n return new this(x).cos();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function cosh(x) {\r\n return new this(x).cosh();\r\n }\r\n\r\n\r\n /*\r\n * Create and return a Decimal constructor with the same configuration properties as this Decimal\r\n * constructor.\r\n *\r\n */\r\n function clone(obj) {\r\n var i, p, ps;\r\n\r\n /*\r\n * The Decimal constructor and exported function.\r\n * Return a new Decimal instance.\r\n *\r\n * v {number|string|Decimal} A numeric value.\r\n *\r\n */\r\n function Decimal(v) {\r\n var e, i, t,\r\n x = this;\r\n\r\n // Decimal called without new.\r\n if (!(x instanceof Decimal)) return new Decimal(v);\r\n\r\n // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor\r\n // which points to Object.\r\n x.constructor = Decimal;\r\n\r\n // Duplicate.\r\n if (v instanceof Decimal) {\r\n x.s = v.s;\r\n\r\n if (external) {\r\n if (!v.d || v.e > Decimal.maxE) {\r\n\r\n // Infinity.\r\n x.e = NaN;\r\n x.d = null;\r\n } else if (v.e < Decimal.minE) {\r\n\r\n // Zero.\r\n x.e = 0;\r\n x.d = [0];\r\n } else {\r\n x.e = v.e;\r\n x.d = v.d.slice();\r\n }\r\n } else {\r\n x.e = v.e;\r\n x.d = v.d ? v.d.slice() : v.d;\r\n }\r\n\r\n return;\r\n }\r\n\r\n t = typeof v;\r\n\r\n if (t === 'number') {\r\n if (v === 0) {\r\n x.s = 1 / v < 0 ? -1 : 1;\r\n x.e = 0;\r\n x.d = [0];\r\n return;\r\n }\r\n\r\n if (v < 0) {\r\n v = -v;\r\n x.s = -1;\r\n } else {\r\n x.s = 1;\r\n }\r\n\r\n // Fast path for small integers.\r\n if (v === ~~v && v < 1e7) {\r\n for (e = 0, i = v; i >= 10; i /= 10) e++;\r\n\r\n if (external) {\r\n if (e > Decimal.maxE) {\r\n x.e = NaN;\r\n x.d = null;\r\n } else if (e < Decimal.minE) {\r\n x.e = 0;\r\n x.d = [0];\r\n } else {\r\n x.e = e;\r\n x.d = [v];\r\n }\r\n } else {\r\n x.e = e;\r\n x.d = [v];\r\n }\r\n\r\n return;\r\n\r\n // Infinity, NaN.\r\n } else if (v * 0 !== 0) {\r\n if (!v) x.s = NaN;\r\n x.e = NaN;\r\n x.d = null;\r\n return;\r\n }\r\n\r\n return parseDecimal(x, v.toString());\r\n\r\n } else if (t !== 'string') {\r\n throw Error(invalidArgument + v);\r\n }\r\n\r\n // Minus sign?\r\n if ((i = v.charCodeAt(0)) === 45) {\r\n v = v.slice(1);\r\n x.s = -1;\r\n } else {\r\n // Plus sign?\r\n if (i === 43) v = v.slice(1);\r\n x.s = 1;\r\n }\r\n\r\n return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);\r\n }\r\n\r\n Decimal.prototype = P;\r\n\r\n Decimal.ROUND_UP = 0;\r\n Decimal.ROUND_DOWN = 1;\r\n Decimal.ROUND_CEIL = 2;\r\n Decimal.ROUND_FLOOR = 3;\r\n Decimal.ROUND_HALF_UP = 4;\r\n Decimal.ROUND_HALF_DOWN = 5;\r\n Decimal.ROUND_HALF_EVEN = 6;\r\n Decimal.ROUND_HALF_CEIL = 7;\r\n Decimal.ROUND_HALF_FLOOR = 8;\r\n Decimal.EUCLID = 9;\r\n\r\n Decimal.config = Decimal.set = config;\r\n Decimal.clone = clone;\r\n Decimal.isDecimal = isDecimalInstance;\r\n\r\n Decimal.abs = abs;\r\n Decimal.acos = acos;\r\n Decimal.acosh = acosh; // ES6\r\n Decimal.add = add;\r\n Decimal.asin = asin;\r\n Decimal.asinh = asinh; // ES6\r\n Decimal.atan = atan;\r\n Decimal.atanh = atanh; // ES6\r\n Decimal.atan2 = atan2;\r\n Decimal.cbrt = cbrt; // ES6\r\n Decimal.ceil = ceil;\r\n Decimal.cos = cos;\r\n Decimal.cosh = cosh; // ES6\r\n Decimal.div = div;\r\n Decimal.exp = exp;\r\n Decimal.floor = floor;\r\n Decimal.hypot = hypot; // ES6\r\n Decimal.ln = ln;\r\n Decimal.log = log;\r\n Decimal.log10 = log10; // ES6\r\n Decimal.log2 = log2; // ES6\r\n Decimal.max = max;\r\n Decimal.min = min;\r\n Decimal.mod = mod;\r\n Decimal.mul = mul;\r\n Decimal.pow = pow;\r\n Decimal.random = random;\r\n Decimal.round = round;\r\n Decimal.sign = sign; // ES6\r\n Decimal.sin = sin;\r\n Decimal.sinh = sinh; // ES6\r\n Decimal.sqrt = sqrt;\r\n Decimal.sub = sub;\r\n Decimal.tan = tan;\r\n Decimal.tanh = tanh; // ES6\r\n Decimal.trunc = trunc; // ES6\r\n\r\n if (obj === void 0) obj = {};\r\n if (obj) {\r\n if (obj.defaults !== true) {\r\n ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];\r\n for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];\r\n }\r\n }\r\n\r\n Decimal.config(obj);\r\n\r\n return Decimal;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function div(x, y) {\r\n return new this(x).div(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} The power to which to raise the base of the natural log.\r\n *\r\n */\r\n function exp(x) {\r\n return new this(x).exp();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function floor(x) {\r\n return finalise(x = new this(x), x.e + 1, 3);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,\r\n * rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function hypot() {\r\n var i, n,\r\n t = new this(0);\r\n\r\n external = false;\r\n\r\n for (i = 0; i < arguments.length;) {\r\n n = new this(arguments[i++]);\r\n if (!n.d) {\r\n if (n.s) {\r\n external = true;\r\n return new this(1 / 0);\r\n }\r\n t = n;\r\n } else if (t.d) {\r\n t = t.plus(n.times(n));\r\n }\r\n }\r\n\r\n external = true;\r\n\r\n return t.sqrt();\r\n }\r\n\r\n\r\n /*\r\n * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),\r\n * otherwise return false.\r\n *\r\n */\r\n function isDecimalInstance(obj) {\r\n return obj instanceof Decimal || obj && obj.name === '[object Decimal]' || false;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function ln(x) {\r\n return new this(x).ln();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base\r\n * is specified, rounded to `precision` significant digits using rounding mode `rounding`.\r\n *\r\n * log[y](x)\r\n *\r\n * x {number|string|Decimal} The argument of the logarithm.\r\n * y {number|string|Decimal} The base of the logarithm.\r\n *\r\n */\r\n function log(x, y) {\r\n return new this(x).log(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function log2(x) {\r\n return new this(x).log(2);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function log10(x) {\r\n return new this(x).log(10);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the maximum of the arguments.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function max() {\r\n return maxOrMin(this, arguments, 'lt');\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the minimum of the arguments.\r\n *\r\n * arguments {number|string|Decimal}\r\n *\r\n */\r\n function min() {\r\n return maxOrMin(this, arguments, 'gt');\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function mod(x, y) {\r\n return new this(x).mod(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function mul(x, y) {\r\n return new this(x).mul(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} The base.\r\n * y {number|string|Decimal} The exponent.\r\n *\r\n */\r\n function pow(x, y) {\r\n return new this(x).pow(y);\r\n }\r\n\r\n\r\n /*\r\n * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with\r\n * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros\r\n * are produced).\r\n *\r\n * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.\r\n *\r\n */\r\n function random(sd) {\r\n var d, e, k, n,\r\n i = 0,\r\n r = new this(1),\r\n rd = [];\r\n\r\n if (sd === void 0) sd = this.precision;\r\n else checkInt32(sd, 1, MAX_DIGITS);\r\n\r\n k = Math.ceil(sd / LOG_BASE);\r\n\r\n if (!this.crypto) {\r\n for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;\r\n\r\n // Browsers supporting crypto.getRandomValues.\r\n } else if (crypto.getRandomValues) {\r\n d = crypto.getRandomValues(new Uint32Array(k));\r\n\r\n for (; i < k;) {\r\n n = d[i];\r\n\r\n // 0 <= n < 4294967296\r\n // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).\r\n if (n >= 4.29e9) {\r\n d[i] = crypto.getRandomValues(new Uint32Array(1))[0];\r\n } else {\r\n\r\n // 0 <= n <= 4289999999\r\n // 0 <= (n % 1e7) <= 9999999\r\n rd[i++] = n % 1e7;\r\n }\r\n }\r\n\r\n // Node.js supporting crypto.randomBytes.\r\n } else if (crypto.randomBytes) {\r\n\r\n // buffer\r\n d = crypto.randomBytes(k *= 4);\r\n\r\n for (; i < k;) {\r\n\r\n // 0 <= n < 2147483648\r\n n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);\r\n\r\n // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).\r\n if (n >= 2.14e9) {\r\n crypto.randomBytes(4).copy(d, i);\r\n } else {\r\n\r\n // 0 <= n <= 2139999999\r\n // 0 <= (n % 1e7) <= 9999999\r\n rd.push(n % 1e7);\r\n i += 4;\r\n }\r\n }\r\n\r\n i = k / 4;\r\n } else {\r\n throw Error(cryptoUnavailable);\r\n }\r\n\r\n k = rd[--i];\r\n sd %= LOG_BASE;\r\n\r\n // Convert trailing digits to zeros according to sd.\r\n if (k && sd) {\r\n n = mathpow(10, LOG_BASE - sd);\r\n rd[i] = (k / n | 0) * n;\r\n }\r\n\r\n // Remove trailing words which are zero.\r\n for (; rd[i] === 0; i--) rd.pop();\r\n\r\n // Zero?\r\n if (i < 0) {\r\n e = 0;\r\n rd = [0];\r\n } else {\r\n e = -1;\r\n\r\n // Remove leading words which are zero and adjust exponent accordingly.\r\n for (; rd[0] === 0; e -= LOG_BASE) rd.shift();\r\n\r\n // Count the digits of the first word of rd to determine leading zeros.\r\n for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;\r\n\r\n // Adjust the exponent for leading zeros of the first word of rd.\r\n if (k < LOG_BASE) e -= LOG_BASE - k;\r\n }\r\n\r\n r.e = e;\r\n r.d = rd;\r\n\r\n return r;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.\r\n *\r\n * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function round(x) {\r\n return finalise(x = new this(x), x.e + 1, this.rounding);\r\n }\r\n\r\n\r\n /*\r\n * Return\r\n * 1 if x > 0,\r\n * -1 if x < 0,\r\n * 0 if x is 0,\r\n * -0 if x is -0,\r\n * NaN otherwise\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function sign(x) {\r\n x = new this(x);\r\n return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function sin(x) {\r\n return new this(x).sin();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function sinh(x) {\r\n return new this(x).sinh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function sqrt(x) {\r\n return new this(x).sqrt();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits\r\n * using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal}\r\n * y {number|string|Decimal}\r\n *\r\n */\r\n function sub(x, y) {\r\n return new this(x).sub(y);\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant\r\n * digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function tan(x) {\r\n return new this(x).tan();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`\r\n * significant digits using rounding mode `rounding`.\r\n *\r\n * x {number|string|Decimal} A value in radians.\r\n *\r\n */\r\n function tanh(x) {\r\n return new this(x).tanh();\r\n }\r\n\r\n\r\n /*\r\n * Return a new Decimal whose value is `x` truncated to an integer.\r\n *\r\n * x {number|string|Decimal}\r\n *\r\n */\r\n function trunc(x) {\r\n return finalise(x = new this(x), x.e + 1, 1);\r\n }\r\n\r\n\r\n // Create and configure initial Decimal constructor.\r\n Decimal = clone(DEFAULTS);\r\n\r\n Decimal['default'] = Decimal.Decimal = Decimal;\r\n\r\n // Create the internal constants from their string values.\r\n LN10 = new Decimal(LN10);\r\n PI = new Decimal(PI);\r\n\r\n\r\n // Export.\r\n\r\n\r\n // AMD.\r\n if (typeof define == 'function' && define.amd) {\r\n define(function () {\r\n return Decimal;\r\n });\r\n\r\n // Node and other environments that support module.exports.\r\n } else if (typeof module != 'undefined' && module.exports) {\r\n if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {\r\n P[Symbol.for('nodejs.util.inspect.custom')] = P.toString;\r\n P[Symbol.toStringTag] = 'Decimal';\r\n }\r\n\r\n module.exports = Decimal;\r\n\r\n // Browser.\r\n } else {\r\n if (!globalScope) {\r\n globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;\r\n }\r\n\r\n noConflict = globalScope.Decimal;\r\n Decimal.noConflict = function () {\r\n globalScope.Decimal = noConflict;\r\n return Decimal;\r\n };\r\n\r\n globalScope.Decimal = Decimal;\r\n }\r\n})(this);\r\n","/**\n * typed-function\n *\n * Type checking for JavaScript functions\n *\n * https://github.com/josdejong/typed-function\n */\n'use strict';\n\n(function (root, factory) {\n if (typeof define === 'function' && define.amd) {\n // AMD. Register as an anonymous module.\n define([], factory);\n } else if (typeof exports === 'object') {\n // OldNode. Does not work with strict CommonJS, but\n // only CommonJS-like environments that support module.exports,\n // like OldNode.\n module.exports = factory();\n } else {\n // Browser globals (root is window)\n root.typed = factory();\n }\n}(this, function () {\n\n function ok () {\n return true;\n }\n\n function notOk () {\n return false;\n }\n\n function undef () {\n return undefined;\n }\n\n /**\n * @typedef {{\n * params: Param[],\n * fn: function\n * }} Signature\n *\n * @typedef {{\n * types: Type[],\n * restParam: boolean\n * }} Param\n *\n * @typedef {{\n * name: string,\n * typeIndex: number,\n * test: function,\n * conversion?: ConversionDef,\n * conversionIndex: number,\n * }} Type\n *\n * @typedef {{\n * from: string,\n * to: string,\n * convert: function (*) : *\n * }} ConversionDef\n *\n * @typedef {{\n * name: string,\n * test: function(*) : boolean\n * }} TypeDef\n */\n\n // create a new instance of typed-function\n function create () {\n // data type tests\n var _types = [\n { name: 'number', test: function (x) { return typeof x === 'number' } },\n { name: 'string', test: function (x) { return typeof x === 'string' } },\n { name: 'boolean', test: function (x) { return typeof x === 'boolean' } },\n { name: 'Function', test: function (x) { return typeof x === 'function'} },\n { name: 'Array', test: Array.isArray },\n { name: 'Date', test: function (x) { return x instanceof Date } },\n { name: 'RegExp', test: function (x) { return x instanceof RegExp } },\n { name: 'Object', test: function (x) {\n return typeof x === 'object' && x !== null && x.constructor === Object\n }},\n { name: 'null', test: function (x) { return x === null } },\n { name: 'undefined', test: function (x) { return x === undefined } }\n ];\n\n var anyType = {\n name: 'any',\n test: ok\n }\n\n // types which need to be ignored\n var _ignore = [];\n\n // type conversions\n var _conversions = [];\n\n // This is a temporary object, will be replaced with a typed function at the end\n var typed = {\n types: _types,\n conversions: _conversions,\n ignore: _ignore\n };\n\n /**\n * Find the test function for a type\n * @param {String} typeName\n * @return {TypeDef} Returns the type definition when found,\n * Throws a TypeError otherwise\n */\n function findTypeByName (typeName) {\n var entry = findInArray(typed.types, function (entry) {\n return entry.name === typeName;\n });\n\n if (entry) {\n return entry;\n }\n\n if (typeName === 'any') { // special baked-in case 'any'\n return anyType;\n }\n\n var hint = findInArray(typed.types, function (entry) {\n return entry.name.toLowerCase() === typeName.toLowerCase();\n });\n\n throw new TypeError('Unknown type \"' + typeName + '\"' +\n (hint ? ('. Did you mean \"' + hint.name + '\"?') : ''));\n }\n\n /**\n * Find the index of a type definition. Handles special case 'any'\n * @param {TypeDef} type\n * @return {number}\n */\n function findTypeIndex(type) {\n if (type === anyType) {\n return 999;\n }\n\n return typed.types.indexOf(type);\n }\n\n /**\n * Find a type that matches a value.\n * @param {*} value\n * @return {string} Returns the name of the first type for which\n * the type test matches the value.\n */\n function findTypeName(value) {\n var entry = findInArray(typed.types, function (entry) {\n return entry.test(value);\n });\n\n if (entry) {\n return entry.name;\n }\n\n throw new TypeError('Value has unknown type. Value: ' + value);\n }\n\n /**\n * Find a specific signature from a (composed) typed function, for example:\n *\n * typed.find(fn, ['number', 'string'])\n * typed.find(fn, 'number, string')\n *\n * Function find only only works for exact matches.\n *\n * @param {Function} fn A typed-function\n * @param {string | string[]} signature Signature to be found, can be\n * an array or a comma separated string.\n * @return {Function} Returns the matching signature, or\n * throws an error when no signature\n * is found.\n */\n function find (fn, signature) {\n if (!fn.signatures) {\n throw new TypeError('Function is no typed-function');\n }\n\n // normalize input\n var arr;\n if (typeof signature === 'string') {\n arr = signature.split(',');\n for (var i = 0; i < arr.length; i++) {\n arr[i] = arr[i].trim();\n }\n }\n else if (Array.isArray(signature)) {\n arr = signature;\n }\n else {\n throw new TypeError('String array or a comma separated string expected');\n }\n\n var str = arr.join(',');\n\n // find an exact match\n var match = fn.signatures[str];\n if (match) {\n return match;\n }\n\n // TODO: extend find to match non-exact signatures\n\n throw new TypeError('Signature not found (signature: ' + (fn.name || 'unnamed') + '(' + arr.join(', ') + '))');\n }\n\n /**\n * Convert a given value to another data type.\n * @param {*} value\n * @param {string} type\n */\n function convert (value, type) {\n var from = findTypeName(value);\n\n // check conversion is needed\n if (type === from) {\n return value;\n }\n\n for (var i = 0; i < typed.conversions.length; i++) {\n var conversion = typed.conversions[i];\n if (conversion.from === from && conversion.to === type) {\n return conversion.convert(value);\n }\n }\n\n throw new Error('Cannot convert from ' + from + ' to ' + type);\n }\n \n /**\n * Stringify parameters in a normalized way\n * @param {Param[]} params\n * @return {string}\n */\n function stringifyParams (params) {\n return params\n .map(function (param) {\n var typeNames = param.types.map(getTypeName);\n\n return (param.restParam ? '...' : '') + typeNames.join('|');\n })\n .join(',');\n }\n\n /**\n * Parse a parameter, like \"...number | boolean\"\n * @param {string} param\n * @param {ConversionDef[]} conversions\n * @return {Param} param\n */\n function parseParam (param, conversions) {\n var restParam = param.indexOf('...') === 0;\n var types = (!restParam)\n ? param\n : (param.length > 3)\n ? param.slice(3)\n : 'any';\n\n var typeNames = types.split('|').map(trim)\n .filter(notEmpty)\n .filter(notIgnore);\n\n var matchingConversions = filterConversions(conversions, typeNames);\n\n var exactTypes = typeNames.map(function (typeName) {\n var type = findTypeByName(typeName);\n\n return {\n name: typeName,\n typeIndex: findTypeIndex(type),\n test: type.test,\n conversion: null,\n conversionIndex: -1\n };\n });\n\n var convertibleTypes = matchingConversions.map(function (conversion) {\n var type = findTypeByName(conversion.from);\n\n return {\n name: conversion.from,\n typeIndex: findTypeIndex(type),\n test: type.test,\n conversion: conversion,\n conversionIndex: conversions.indexOf(conversion)\n };\n });\n\n return {\n types: exactTypes.concat(convertibleTypes),\n restParam: restParam\n };\n }\n\n /**\n * Parse a signature with comma separated parameters,\n * like \"number | boolean, ...string\"\n * @param {string} signature\n * @param {function} fn\n * @param {ConversionDef[]} conversions\n * @return {Signature | null} signature\n */\n function parseSignature (signature, fn, conversions) {\n var params = [];\n\n if (signature.trim() !== '') {\n params = signature\n .split(',')\n .map(trim)\n .map(function (param, index, array) {\n var parsedParam = parseParam(param, conversions);\n\n if (parsedParam.restParam && (index !== array.length - 1)) {\n throw new SyntaxError('Unexpected rest parameter \"' + param + '\": ' +\n 'only allowed for the last parameter');\n }\n\n return parsedParam;\n });\n }\n\n if (params.some(isInvalidParam)) {\n // invalid signature: at least one parameter has no types\n // (they may have been filtered)\n return null;\n }\n\n return {\n params: params,\n fn: fn\n };\n }\n\n /**\n * Test whether a set of params contains a restParam\n * @param {Param[]} params\n * @return {boolean} Returns true when the last parameter is a restParam\n */\n function hasRestParam(params) {\n var param = last(params)\n return param ? param.restParam : false;\n }\n\n /**\n * Test whether a parameter contains conversions\n * @param {Param} param\n * @return {boolean} Returns true when at least one of the parameters\n * contains a conversion.\n */\n function hasConversions(param) {\n return param.types.some(function (type) {\n return type.conversion != null;\n });\n }\n\n /**\n * Create a type test for a single parameter, which can have one or multiple\n * types.\n * @param {Param} param\n * @return {function(x: *) : boolean} Returns a test function\n */\n function compileTest(param) {\n if (!param || param.types.length === 0) {\n // nothing to do\n return ok;\n }\n else if (param.types.length === 1) {\n return findTypeByName(param.types[0].name).test;\n }\n else if (param.types.length === 2) {\n var test0 = findTypeByName(param.types[0].name).test;\n var test1 = findTypeByName(param.types[1].name).test;\n return function or(x) {\n return test0(x) || test1(x);\n }\n }\n else { // param.types.length > 2\n var tests = param.types.map(function (type) {\n return findTypeByName(type.name).test;\n })\n return function or(x) {\n for (var i = 0; i < tests.length; i++) {\n if (tests[i](x)) {\n return true;\n }\n }\n return false;\n }\n }\n }\n\n /**\n * Create a test for all parameters of a signature\n * @param {Param[]} params\n * @return {function(args: Array<*>) : boolean}\n */\n function compileTests(params) {\n var tests, test0, test1;\n\n if (hasRestParam(params)) {\n // variable arguments like '...number'\n tests = initial(params).map(compileTest);\n var varIndex = tests.length;\n var lastTest = compileTest(last(params));\n var testRestParam = function (args) {\n for (var i = varIndex; i < args.length; i++) {\n if (!lastTest(args[i])) {\n return false;\n }\n }\n return true;\n }\n\n return function testArgs(args) {\n for (var i = 0; i < tests.length; i++) {\n if (!tests[i](args[i])) {\n return false;\n }\n }\n return testRestParam(args) && (args.length >= varIndex + 1);\n };\n }\n else {\n // no variable arguments\n if (params.length === 0) {\n return function testArgs(args) {\n return args.length === 0;\n };\n }\n else if (params.length === 1) {\n test0 = compileTest(params[0]);\n return function testArgs(args) {\n return test0(args[0]) && args.length === 1;\n };\n }\n else if (params.length === 2) {\n test0 = compileTest(params[0]);\n test1 = compileTest(params[1]);\n return function testArgs(args) {\n return test0(args[0]) && test1(args[1]) && args.length === 2;\n };\n }\n else { // arguments.length > 2\n tests = params.map(compileTest);\n return function testArgs(args) {\n for (var i = 0; i < tests.length; i++) {\n if (!tests[i](args[i])) {\n return false;\n }\n }\n return args.length === tests.length;\n };\n }\n }\n }\n\n /**\n * Find the parameter at a specific index of a signature.\n * Handles rest parameters.\n * @param {Signature} signature\n * @param {number} index\n * @return {Param | null} Returns the matching parameter when found,\n * null otherwise.\n */\n function getParamAtIndex(signature, index) {\n return index < signature.params.length\n ? signature.params[index]\n : hasRestParam(signature.params)\n ? last(signature.params)\n : null\n }\n\n /**\n * Get all type names of a parameter\n * @param {Signature} signature\n * @param {number} index\n * @param {boolean} excludeConversions\n * @return {string[]} Returns an array with type names\n */\n function getExpectedTypeNames (signature, index, excludeConversions) {\n var param = getParamAtIndex(signature, index);\n var types = param\n ? excludeConversions\n ? param.types.filter(isExactType)\n : param.types\n : [];\n\n return types.map(getTypeName);\n }\n\n /**\n * Returns the name of a type\n * @param {Type} type\n * @return {string} Returns the type name\n */\n function getTypeName(type) {\n return type.name;\n }\n\n /**\n * Test whether a type is an exact type or conversion\n * @param {Type} type\n * @return {boolean} Returns true when\n */\n function isExactType(type) {\n return type.conversion === null || type.conversion === undefined;\n }\n\n /**\n * Helper function for creating error messages: create an array with\n * all available types on a specific argument index.\n * @param {Signature[]} signatures\n * @param {number} index\n * @return {string[]} Returns an array with available types\n */\n function mergeExpectedParams(signatures, index) {\n var typeNames = uniq(flatMap(signatures, function (signature) {\n return getExpectedTypeNames(signature, index, false);\n }));\n\n return (typeNames.indexOf('any') !== -1) ? ['any'] : typeNames;\n }\n\n /**\n * Create\n * @param {string} name The name of the function\n * @param {array.<*>} args The actual arguments passed to the function\n * @param {Signature[]} signatures A list with available signatures\n * @return {TypeError} Returns a type error with additional data\n * attached to it in the property `data`\n */\n function createError(name, args, signatures) {\n var err, expected;\n var _name = name || 'unnamed';\n\n // test for wrong type at some index\n var matchingSignatures = signatures;\n var index;\n for (index = 0; index < args.length; index++) {\n var nextMatchingDefs = matchingSignatures.filter(function (signature) {\n var test = compileTest(getParamAtIndex(signature, index));\n return (index < signature.params.length || hasRestParam(signature.params)) &&\n test(args[index]);\n });\n\n if (nextMatchingDefs.length === 0) {\n // no matching signatures anymore, throw error \"wrong type\"\n expected = mergeExpectedParams(matchingSignatures, index);\n if (expected.length > 0) {\n var actualType = findTypeName(args[index]);\n\n err = new TypeError('Unexpected type of argument in function ' + _name +\n ' (expected: ' + expected.join(' or ') +\n ', actual: ' + actualType + ', index: ' + index + ')');\n err.data = {\n category: 'wrongType',\n fn: _name,\n index: index,\n actual: actualType,\n expected: expected\n }\n return err;\n }\n }\n else {\n matchingSignatures = nextMatchingDefs;\n }\n }\n\n // test for too few arguments\n var lengths = matchingSignatures.map(function (signature) {\n return hasRestParam(signature.params) ? Infinity : signature.params.length;\n });\n if (args.length < Math.min.apply(null, lengths)) {\n expected = mergeExpectedParams(matchingSignatures, index);\n err = new TypeError('Too few arguments in function ' + _name +\n ' (expected: ' + expected.join(' or ') +\n ', index: ' + args.length + ')');\n err.data = {\n category: 'tooFewArgs',\n fn: _name,\n index: args.length,\n expected: expected\n }\n return err;\n }\n\n // test for too many arguments\n var maxLength = Math.max.apply(null, lengths);\n if (args.length > maxLength) {\n err = new TypeError('Too many arguments in function ' + _name +\n ' (expected: ' + maxLength + ', actual: ' + args.length + ')');\n err.data = {\n category: 'tooManyArgs',\n fn: _name,\n index: args.length,\n expectedLength: maxLength\n }\n return err;\n }\n\n err = new TypeError('Arguments of type \"' + args.join(', ') +\n '\" do not match any of the defined signatures of function ' + _name + '.');\n err.data = {\n category: 'mismatch',\n actual: args.map(findTypeName)\n }\n return err;\n }\n\n /**\n * Find the lowest index of all exact types of a parameter (no conversions)\n * @param {Param} param\n * @return {number} Returns the index of the lowest type in typed.types\n */\n function getLowestTypeIndex (param) {\n var min = 999;\n\n for (var i = 0; i < param.types.length; i++) {\n if (isExactType(param.types[i])) {\n min = Math.min(min, param.types[i].typeIndex);\n }\n }\n\n return min;\n }\n\n /**\n * Find the lowest index of the conversion of all types of the parameter\n * having a conversion\n * @param {Param} param\n * @return {number} Returns the lowest index of the conversions of this type\n */\n function getLowestConversionIndex (param) {\n var min = 999;\n\n for (var i = 0; i < param.types.length; i++) {\n if (!isExactType(param.types[i])) {\n min = Math.min(min, param.types[i].conversionIndex);\n }\n }\n\n return min;\n }\n\n /**\n * Compare two params\n * @param {Param} param1\n * @param {Param} param2\n * @return {number} returns a negative number when param1 must get a lower\n * index than param2, a positive number when the opposite,\n * or zero when both are equal\n */\n function compareParams (param1, param2) {\n var c;\n\n // compare having a rest parameter or not\n c = param1.restParam - param2.restParam;\n if (c !== 0) {\n return c;\n }\n\n // compare having conversions or not\n c = hasConversions(param1) - hasConversions(param2);\n if (c !== 0) {\n return c;\n }\n\n // compare the index of the types\n c = getLowestTypeIndex(param1) - getLowestTypeIndex(param2);\n if (c !== 0) {\n return c;\n }\n\n // compare the index of any conversion\n return getLowestConversionIndex(param1) - getLowestConversionIndex(param2);\n }\n\n /**\n * Compare two signatures\n * @param {Signature} signature1\n * @param {Signature} signature2\n * @return {number} returns a negative number when param1 must get a lower\n * index than param2, a positive number when the opposite,\n * or zero when both are equal\n */\n function compareSignatures (signature1, signature2) {\n var len = Math.min(signature1.params.length, signature2.params.length);\n var i;\n var c;\n\n // compare whether the params have conversions at all or not\n c = signature1.params.some(hasConversions) - signature2.params.some(hasConversions)\n if (c !== 0) {\n return c;\n }\n\n // next compare whether the params have conversions one by one\n for (i = 0; i < len; i++) {\n c = hasConversions(signature1.params[i]) - hasConversions(signature2.params[i]);\n if (c !== 0) {\n return c;\n }\n }\n\n // compare the types of the params one by one\n for (i = 0; i < len; i++) {\n c = compareParams(signature1.params[i], signature2.params[i]);\n if (c !== 0) {\n return c;\n }\n }\n\n // compare the number of params\n return signature1.params.length - signature2.params.length;\n }\n\n /**\n * Get params containing all types that can be converted to the defined types.\n *\n * @param {ConversionDef[]} conversions\n * @param {string[]} typeNames\n * @return {ConversionDef[]} Returns the conversions that are available\n * for every type (if any)\n */\n function filterConversions(conversions, typeNames) {\n var matches = {};\n\n conversions.forEach(function (conversion) {\n if (typeNames.indexOf(conversion.from) === -1 &&\n typeNames.indexOf(conversion.to) !== -1 &&\n !matches[conversion.from]) {\n matches[conversion.from] = conversion;\n }\n });\n\n return Object.keys(matches).map(function (from) {\n return matches[from];\n });\n }\n\n /**\n * Preprocess arguments before calling the original function:\n * - if needed convert the parameters\n * - in case of rest parameters, move the rest parameters into an Array\n * @param {Param[]} params\n * @param {function} fn\n * @return {function} Returns a wrapped function\n */\n function compileArgsPreprocessing(params, fn) {\n var fnConvert = fn;\n\n // TODO: can we make this wrapper function smarter/simpler?\n\n if (params.some(hasConversions)) {\n var restParam = hasRestParam(params);\n var compiledConversions = params.map(compileArgConversion)\n\n fnConvert = function convertArgs() {\n var args = [];\n var last = restParam ? arguments.length - 1 : arguments.length;\n for (var i = 0; i < last; i++) {\n args[i] = compiledConversions[i](arguments[i]);\n }\n if (restParam) {\n args[last] = arguments[last].map(compiledConversions[last]);\n }\n\n return fn.apply(this, args);\n }\n }\n\n var fnPreprocess = fnConvert;\n if (hasRestParam(params)) {\n var offset = params.length - 1;\n\n fnPreprocess = function preprocessRestParams () {\n return fnConvert.apply(this,\n slice(arguments, 0, offset).concat([slice(arguments, offset)]));\n }\n }\n\n return fnPreprocess;\n }\n\n /**\n * Compile conversion for a parameter to the right type\n * @param {Param} param\n * @return {function} Returns the wrapped function that will convert arguments\n *\n */\n function compileArgConversion(param) {\n var test0, test1, conversion0, conversion1;\n var tests = [];\n var conversions = [];\n\n param.types.forEach(function (type) {\n if (type.conversion) {\n tests.push(findTypeByName(type.conversion.from).test);\n conversions.push(type.conversion.convert);\n }\n });\n\n // create optimized conversion functions depending on the number of conversions\n switch (conversions.length) {\n case 0:\n return function convertArg(arg) {\n return arg;\n }\n\n case 1:\n test0 = tests[0]\n conversion0 = conversions[0];\n return function convertArg(arg) {\n if (test0(arg)) {\n return conversion0(arg)\n }\n return arg;\n }\n\n case 2:\n test0 = tests[0]\n test1 = tests[1]\n conversion0 = conversions[0];\n conversion1 = conversions[1];\n return function convertArg(arg) {\n if (test0(arg)) {\n return conversion0(arg)\n }\n if (test1(arg)) {\n return conversion1(arg)\n }\n return arg;\n }\n\n default:\n return function convertArg(arg) {\n for (var i = 0; i < conversions.length; i++) {\n if (tests[i](arg)) {\n return conversions[i](arg);\n }\n }\n return arg;\n }\n }\n }\n\n /**\n * Convert an array with signatures into a map with signatures,\n * where signatures with union types are split into separate signatures\n *\n * Throws an error when there are conflicting types\n *\n * @param {Signature[]} signatures\n * @return {Object.} Returns a map with signatures\n * as key and the original function\n * of this signature as value.\n */\n function createSignaturesMap(signatures) {\n var signaturesMap = {};\n signatures.forEach(function (signature) {\n if (!signature.params.some(hasConversions)) {\n splitParams(signature.params, true).forEach(function (params) {\n signaturesMap[stringifyParams(params)] = signature.fn;\n });\n }\n });\n\n return signaturesMap;\n }\n\n /**\n * Split params with union types in to separate params.\n *\n * For example:\n *\n * splitParams([['Array', 'Object'], ['string', 'RegExp'])\n * // returns:\n * // [\n * // ['Array', 'string'],\n * // ['Array', 'RegExp'],\n * // ['Object', 'string'],\n * // ['Object', 'RegExp']\n * // ]\n *\n * @param {Param[]} params\n * @param {boolean} ignoreConversionTypes\n * @return {Param[]}\n */\n function splitParams(params, ignoreConversionTypes) {\n function _splitParams(params, index, types) {\n if (index < params.length) {\n var param = params[index]\n var filteredTypes = ignoreConversionTypes\n ? param.types.filter(isExactType)\n : param.types;\n var typeGroups\n\n if (param.restParam) {\n // split the types of a rest parameter in two:\n // one with only exact types, and one with exact types and conversions\n var exactTypes = filteredTypes.filter(isExactType)\n typeGroups = exactTypes.length < filteredTypes.length\n ? [exactTypes, filteredTypes]\n : [filteredTypes]\n\n }\n else {\n // split all the types of a regular parameter into one type per group\n typeGroups = filteredTypes.map(function (type) {\n return [type]\n })\n }\n\n // recurse over the groups with types\n return flatMap(typeGroups, function (typeGroup) {\n return _splitParams(params, index + 1, types.concat([typeGroup]));\n });\n\n }\n else {\n // we've reached the end of the parameters. Now build a new Param\n var splittedParams = types.map(function (type, typeIndex) {\n return {\n types: type,\n restParam: (typeIndex === params.length - 1) && hasRestParam(params)\n }\n });\n\n return [splittedParams];\n }\n }\n\n return _splitParams(params, 0, []);\n }\n\n /**\n * Test whether two signatures have a conflicting signature\n * @param {Signature} signature1\n * @param {Signature} signature2\n * @return {boolean} Returns true when the signatures conflict, false otherwise.\n */\n function hasConflictingParams(signature1, signature2) {\n var ii = Math.max(signature1.params.length, signature2.params.length);\n\n for (var i = 0; i < ii; i++) {\n var typesNames1 = getExpectedTypeNames(signature1, i, true);\n var typesNames2 = getExpectedTypeNames(signature2, i, true);\n\n if (!hasOverlap(typesNames1, typesNames2)) {\n return false;\n }\n }\n\n var len1 = signature1.params.length;\n var len2 = signature2.params.length;\n var restParam1 = hasRestParam(signature1.params);\n var restParam2 = hasRestParam(signature2.params);\n\n return restParam1\n ? restParam2 ? (len1 === len2) : (len2 >= len1)\n : restParam2 ? (len1 >= len2) : (len1 === len2)\n }\n\n /**\n * Create a typed function\n * @param {String} name The name for the typed function\n * @param {Object.} signaturesMap\n * An object with one or\n * multiple signatures as key, and the\n * function corresponding to the\n * signature as value.\n * @return {function} Returns the created typed function.\n */\n function createTypedFunction(name, signaturesMap) {\n if (Object.keys(signaturesMap).length === 0) {\n throw new SyntaxError('No signatures provided');\n }\n\n // parse the signatures, and check for conflicts\n var parsedSignatures = [];\n Object.keys(signaturesMap)\n .map(function (signature) {\n return parseSignature(signature, signaturesMap[signature], typed.conversions);\n })\n .filter(notNull)\n .forEach(function (parsedSignature) {\n // check whether this parameter conflicts with already parsed signatures\n var conflictingSignature = findInArray(parsedSignatures, function (s) {\n return hasConflictingParams(s, parsedSignature)\n });\n if (conflictingSignature) {\n throw new TypeError('Conflicting signatures \"' +\n stringifyParams(conflictingSignature.params) + '\" and \"' +\n stringifyParams(parsedSignature.params) + '\".');\n }\n\n parsedSignatures.push(parsedSignature);\n });\n\n // split and filter the types of the signatures, and then order them\n var signatures = flatMap(parsedSignatures, function (parsedSignature) {\n var params = parsedSignature ? splitParams(parsedSignature.params, false) : []\n\n return params.map(function (params) {\n return {\n params: params,\n fn: parsedSignature.fn\n };\n });\n }).filter(notNull);\n\n signatures.sort(compareSignatures);\n\n // we create a highly optimized checks for the first couple of signatures with max 2 arguments\n var ok0 = signatures[0] && signatures[0].params.length <= 2 && !hasRestParam(signatures[0].params);\n var ok1 = signatures[1] && signatures[1].params.length <= 2 && !hasRestParam(signatures[1].params);\n var ok2 = signatures[2] && signatures[2].params.length <= 2 && !hasRestParam(signatures[2].params);\n var ok3 = signatures[3] && signatures[3].params.length <= 2 && !hasRestParam(signatures[3].params);\n var ok4 = signatures[4] && signatures[4].params.length <= 2 && !hasRestParam(signatures[4].params);\n var ok5 = signatures[5] && signatures[5].params.length <= 2 && !hasRestParam(signatures[5].params);\n var allOk = ok0 && ok1 && ok2 && ok3 && ok4 && ok5;\n\n // compile the tests\n var tests = signatures.map(function (signature) {\n return compileTests(signature.params);\n });\n\n var test00 = ok0 ? compileTest(signatures[0].params[0]) : notOk;\n var test10 = ok1 ? compileTest(signatures[1].params[0]) : notOk;\n var test20 = ok2 ? compileTest(signatures[2].params[0]) : notOk;\n var test30 = ok3 ? compileTest(signatures[3].params[0]) : notOk;\n var test40 = ok4 ? compileTest(signatures[4].params[0]) : notOk;\n var test50 = ok5 ? compileTest(signatures[5].params[0]) : notOk;\n\n var test01 = ok0 ? compileTest(signatures[0].params[1]) : notOk;\n var test11 = ok1 ? compileTest(signatures[1].params[1]) : notOk;\n var test21 = ok2 ? compileTest(signatures[2].params[1]) : notOk;\n var test31 = ok3 ? compileTest(signatures[3].params[1]) : notOk;\n var test41 = ok4 ? compileTest(signatures[4].params[1]) : notOk;\n var test51 = ok5 ? compileTest(signatures[5].params[1]) : notOk;\n\n // compile the functions\n var fns = signatures.map(function(signature) {\n return compileArgsPreprocessing(signature.params, signature.fn);\n });\n\n var fn0 = ok0 ? fns[0] : undef;\n var fn1 = ok1 ? fns[1] : undef;\n var fn2 = ok2 ? fns[2] : undef;\n var fn3 = ok3 ? fns[3] : undef;\n var fn4 = ok4 ? fns[4] : undef;\n var fn5 = ok5 ? fns[5] : undef;\n\n var len0 = ok0 ? signatures[0].params.length : -1;\n var len1 = ok1 ? signatures[1].params.length : -1;\n var len2 = ok2 ? signatures[2].params.length : -1;\n var len3 = ok3 ? signatures[3].params.length : -1;\n var len4 = ok4 ? signatures[4].params.length : -1;\n var len5 = ok5 ? signatures[5].params.length : -1;\n\n // simple and generic, but also slow\n var iStart = allOk ? 6 : 0;\n var iEnd = signatures.length;\n var generic = function generic() {\n 'use strict';\n\n for (var i = iStart; i < iEnd; i++) {\n if (tests[i](arguments)) {\n return fns[i].apply(this, arguments);\n }\n }\n\n throw createError(name, arguments, signatures);\n }\n\n // create the typed function\n // fast, specialized version. Falls back to the slower, generic one if needed\n var fn = function fn(arg0, arg1) {\n 'use strict';\n\n if (arguments.length === len0 && test00(arg0) && test01(arg1)) { return fn0.apply(fn, arguments); }\n if (arguments.length === len1 && test10(arg0) && test11(arg1)) { return fn1.apply(fn, arguments); }\n if (arguments.length === len2 && test20(arg0) && test21(arg1)) { return fn2.apply(fn, arguments); }\n if (arguments.length === len3 && test30(arg0) && test31(arg1)) { return fn3.apply(fn, arguments); }\n if (arguments.length === len4 && test40(arg0) && test41(arg1)) { return fn4.apply(fn, arguments); }\n if (arguments.length === len5 && test50(arg0) && test51(arg1)) { return fn5.apply(fn, arguments); }\n\n return generic.apply(fn, arguments);\n }\n\n // attach name the typed function\n try {\n Object.defineProperty(fn, 'name', {value: name});\n }\n catch (err) {\n // old browsers do not support Object.defineProperty and some don't support setting the name property\n // the function name is not essential for the functioning, it's mostly useful for debugging,\n // so it's fine to have unnamed functions.\n }\n\n // attach signatures to the function\n fn.signatures = createSignaturesMap(signatures);\n\n return fn;\n }\n\n /**\n * Test whether a type should be NOT be ignored\n * @param {string} typeName\n * @return {boolean}\n */\n function notIgnore(typeName) {\n return typed.ignore.indexOf(typeName) === -1;\n }\n\n /**\n * trim a string\n * @param {string} str\n * @return {string}\n */\n function trim(str) {\n return str.trim();\n }\n\n /**\n * Test whether a string is not empty\n * @param {string} str\n * @return {boolean}\n */\n function notEmpty(str) {\n return !!str;\n }\n\n /**\n * test whether a value is not strict equal to null\n * @param {*} value\n * @return {boolean}\n */\n function notNull(value) {\n return value !== null;\n }\n\n /**\n * Test whether a parameter has no types defined\n * @param {Param} param\n * @return {boolean}\n */\n function isInvalidParam (param) {\n return param.types.length === 0;\n }\n\n /**\n * Return all but the last items of an array\n * @param {Array} arr\n * @return {Array}\n */\n function initial(arr) {\n return arr.slice(0, arr.length - 1);\n }\n\n /**\n * return the last item of an array\n * @param {Array} arr\n * @return {*}\n */\n function last(arr) {\n return arr[arr.length - 1];\n }\n\n /**\n * Slice an array or function Arguments\n * @param {Array | Arguments | IArguments} arr\n * @param {number} start\n * @param {number} [end]\n * @return {Array}\n */\n function slice(arr, start, end) {\n return Array.prototype.slice.call(arr, start, end);\n }\n\n /**\n * Test whether an array contains some item\n * @param {Array} array\n * @param {*} item\n * @return {boolean} Returns true if array contains item, false if not.\n */\n function contains(array, item) {\n return array.indexOf(item) !== -1;\n }\n\n /**\n * Test whether two arrays have overlapping items\n * @param {Array} array1\n * @param {Array} array2\n * @return {boolean} Returns true when at least one item exists in both arrays\n */\n function hasOverlap(array1, array2) {\n for (var i = 0; i < array1.length; i++) {\n if (contains(array2, array1[i])) {\n return true;\n }\n }\n\n return false;\n }\n\n /**\n * Return the first item from an array for which test(arr[i]) returns true\n * @param {Array} arr\n * @param {function} test\n * @return {* | undefined} Returns the first matching item\n * or undefined when there is no match\n */\n function findInArray(arr, test) {\n for (var i = 0; i < arr.length; i++) {\n if (test(arr[i])) {\n return arr[i];\n }\n }\n return undefined;\n }\n\n /**\n * Filter unique items of an array with strings\n * @param {string[]} arr\n * @return {string[]}\n */\n function uniq(arr) {\n var entries = {}\n for (var i = 0; i < arr.length; i++) {\n entries[arr[i]] = true;\n }\n return Object.keys(entries);\n }\n\n /**\n * Flat map the result invoking a callback for every item in an array.\n * https://gist.github.com/samgiles/762ee337dff48623e729\n * @param {Array} arr\n * @param {function} callback\n * @return {Array}\n */\n function flatMap(arr, callback) {\n return Array.prototype.concat.apply([], arr.map(callback));\n }\n\n /**\n * Retrieve the function name from a set of typed functions,\n * and check whether the name of all functions match (if given)\n * @param {function[]} fns\n */\n function getName (fns) {\n var name = '';\n\n for (var i = 0; i < fns.length; i++) {\n var fn = fns[i];\n\n // check whether the names are the same when defined\n if ((typeof fn.signatures === 'object' || typeof fn.signature === 'string') && fn.name !== '') {\n if (name === '') {\n name = fn.name;\n }\n else if (name !== fn.name) {\n var err = new Error('Function names do not match (expected: ' + name + ', actual: ' + fn.name + ')');\n err.data = {\n actual: fn.name,\n expected: name\n };\n throw err;\n }\n }\n }\n\n return name;\n }\n\n // extract and merge all signatures of a list with typed functions\n function extractSignatures(fns) {\n var err;\n var signaturesMap = {};\n\n function validateUnique(_signature, _fn) {\n if (signaturesMap.hasOwnProperty(_signature) && _fn !== signaturesMap[_signature]) {\n err = new Error('Signature \"' + _signature + '\" is defined twice');\n err.data = {signature: _signature};\n throw err;\n // else: both signatures point to the same function, that's fine\n }\n }\n\n for (var i = 0; i < fns.length; i++) {\n var fn = fns[i];\n\n // test whether this is a typed-function\n if (typeof fn.signatures === 'object') {\n // merge the signatures\n for (var signature in fn.signatures) {\n if (fn.signatures.hasOwnProperty(signature)) {\n validateUnique(signature, fn.signatures[signature]);\n signaturesMap[signature] = fn.signatures[signature];\n }\n }\n }\n else if (typeof fn.signature === 'string') {\n validateUnique(fn.signature, fn);\n signaturesMap[fn.signature] = fn;\n }\n else {\n err = new TypeError('Function is no typed-function (index: ' + i + ')');\n err.data = {index: i};\n throw err;\n }\n }\n\n return signaturesMap;\n }\n\n typed = createTypedFunction('typed', {\n 'string, Object': createTypedFunction,\n 'Object': function (signaturesMap) {\n // find existing name\n var fns = [];\n for (var signature in signaturesMap) {\n if (signaturesMap.hasOwnProperty(signature)) {\n fns.push(signaturesMap[signature]);\n }\n }\n var name = getName(fns);\n return createTypedFunction(name, signaturesMap);\n },\n '...Function': function (fns) {\n return createTypedFunction(getName(fns), extractSignatures(fns));\n },\n 'string, ...Function': function (name, fns) {\n return createTypedFunction(name, extractSignatures(fns));\n }\n });\n\n typed.create = create;\n typed.types = _types;\n typed.conversions = _conversions;\n typed.ignore = _ignore;\n typed.convert = convert;\n typed.find = find;\n\n /**\n * add a type\n * @param {{name: string, test: function}} type\n * @param {boolean} [beforeObjectTest=true]\n * If true, the new test will be inserted before\n * the test with name 'Object' (if any), since\n * tests for Object match Array and classes too.\n */\n typed.addType = function (type, beforeObjectTest) {\n if (!type || typeof type.name !== 'string' || typeof type.test !== 'function') {\n throw new TypeError('Object with properties {name: string, test: function} expected');\n }\n\n if (beforeObjectTest !== false) {\n for (var i = 0; i < typed.types.length; i++) {\n if (typed.types[i].name === 'Object') {\n typed.types.splice(i, 0, type);\n return\n }\n }\n }\n\n typed.types.push(type);\n };\n\n // add a conversion\n typed.addConversion = function (conversion) {\n if (!conversion\n || typeof conversion.from !== 'string'\n || typeof conversion.to !== 'string'\n || typeof conversion.convert !== 'function') {\n throw new TypeError('Object with properties {from: string, to: string, convert: function} expected');\n }\n\n typed.conversions.push(conversion);\n };\n\n return typed;\n }\n\n return create();\n}));\n","// A library of seedable RNGs implemented in Javascript.\n//\n// Usage:\n//\n// var seedrandom = require('seedrandom');\n// var random = seedrandom(1); // or any seed.\n// var x = random(); // 0 <= x < 1. Every bit is random.\n// var x = random.quick(); // 0 <= x < 1. 32 bits of randomness.\n\n// alea, a 53-bit multiply-with-carry generator by Johannes Baagøe.\n// Period: ~2^116\n// Reported to pass all BigCrush tests.\nvar alea = require('./lib/alea');\n\n// xor128, a pure xor-shift generator by George Marsaglia.\n// Period: 2^128-1.\n// Reported to fail: MatrixRank and LinearComp.\nvar xor128 = require('./lib/xor128');\n\n// xorwow, George Marsaglia's 160-bit xor-shift combined plus weyl.\n// Period: 2^192-2^32\n// Reported to fail: CollisionOver, SimpPoker, and LinearComp.\nvar xorwow = require('./lib/xorwow');\n\n// xorshift7, by François Panneton and Pierre L'ecuyer, takes\n// a different approach: it adds robustness by allowing more shifts\n// than Marsaglia's original three. It is a 7-shift generator\n// with 256 bits, that passes BigCrush with no systmatic failures.\n// Period 2^256-1.\n// No systematic BigCrush failures reported.\nvar xorshift7 = require('./lib/xorshift7');\n\n// xor4096, by Richard Brent, is a 4096-bit xor-shift with a\n// very long period that also adds a Weyl generator. It also passes\n// BigCrush with no systematic failures. Its long period may\n// be useful if you have many generators and need to avoid\n// collisions.\n// Period: 2^4128-2^32.\n// No systematic BigCrush failures reported.\nvar xor4096 = require('./lib/xor4096');\n\n// Tyche-i, by Samuel Neves and Filipe Araujo, is a bit-shifting random\n// number generator derived from ChaCha, a modern stream cipher.\n// https://eden.dei.uc.pt/~sneves/pubs/2011-snfa2.pdf\n// Period: ~2^127\n// No systematic BigCrush failures reported.\nvar tychei = require('./lib/tychei');\n\n// The original ARC4-based prng included in this library.\n// Period: ~2^1600\nvar sr = require('./seedrandom');\n\nsr.alea = alea;\nsr.xor128 = xor128;\nsr.xorwow = xorwow;\nsr.xorshift7 = xorshift7;\nsr.xor4096 = xor4096;\nsr.tychei = tychei;\n\nmodule.exports = sr;\n","function E () {\n // Keep this empty so it's easier to inherit from\n // (via https://github.com/lipsmack from https://github.com/scottcorgan/tiny-emitter/issues/3)\n}\n\nE.prototype = {\n on: function (name, callback, ctx) {\n var e = this.e || (this.e = {});\n\n (e[name] || (e[name] = [])).push({\n fn: callback,\n ctx: ctx\n });\n\n return this;\n },\n\n once: function (name, callback, ctx) {\n var self = this;\n function listener () {\n self.off(name, listener);\n callback.apply(ctx, arguments);\n };\n\n listener._ = callback\n return this.on(name, listener, ctx);\n },\n\n emit: function (name) {\n var data = [].slice.call(arguments, 1);\n var evtArr = ((this.e || (this.e = {}))[name] || []).slice();\n var i = 0;\n var len = evtArr.length;\n\n for (i; i < len; i++) {\n evtArr[i].fn.apply(evtArr[i].ctx, data);\n }\n\n return this;\n },\n\n off: function (name, callback) {\n var e = this.e || (this.e = {});\n var evts = e[name];\n var liveEvents = [];\n\n if (evts && callback) {\n for (var i = 0, len = evts.length; i < len; i++) {\n if (evts[i].fn !== callback && evts[i].fn._ !== callback)\n liveEvents.push(evts[i]);\n }\n }\n\n // Remove event from queue to prevent memory leak\n // Suggested by https://github.com/lazd\n // Ref: https://github.com/scottcorgan/tiny-emitter/commit/c6ebfaa9bc973b33d110a84a307742b7cf94c953#commitcomment-5024910\n\n (liveEvents.length)\n ? e[name] = liveEvents\n : delete e[name];\n\n return this;\n }\n};\n\nmodule.exports = E;\nmodule.exports.TinyEmitter = E;\n","\"use strict\";\n\n// Map the characters to escape to their escaped values. The list is derived\n// from http://www.cespedes.org/blog/85/how-to-escape-latex-special-characters\n\nvar _extends = Object.assign || function (target) { for (var i = 1; i < arguments.length; i++) { var source = arguments[i]; for (var key in source) { if (Object.prototype.hasOwnProperty.call(source, key)) { target[key] = source[key]; } } } return target; };\n\nvar defaultEscapes = {\n \"{\": \"\\\\{\",\n \"}\": \"\\\\}\",\n \"\\\\\": \"\\\\textbackslash{}\",\n \"#\": \"\\\\#\",\n $: \"\\\\$\",\n \"%\": \"\\\\%\",\n \"&\": \"\\\\&\",\n \"^\": \"\\\\textasciicircum{}\",\n _: \"\\\\_\",\n \"~\": \"\\\\textasciitilde{}\"\n};\nvar formatEscapes = {\n \"\\u2013\": \"\\\\--\",\n \"\\u2014\": \"\\\\---\",\n \" \": \"~\",\n \"\\t\": \"\\\\qquad{}\",\n \"\\r\\n\": \"\\\\newline{}\",\n \"\\n\": \"\\\\newline{}\"\n};\n\nvar defaultEscapeMapFn = function defaultEscapeMapFn(defaultEscapes, formatEscapes) {\n return _extends({}, defaultEscapes, formatEscapes);\n};\n\n/**\n * Escape a string to be used in LaTeX documents.\n * @param {string} str the string to be escaped.\n * @param {boolean} params.preserveFormatting whether formatting escapes should\n * be performed (default: false).\n * @param {function} params.escapeMapFn the function to modify the escape maps.\n * @return {string} the escaped string, ready to be used in LaTeX.\n */\nmodule.exports = function (str) {\n var _ref = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {},\n _ref$preserveFormatti = _ref.preserveFormatting,\n preserveFormatting = _ref$preserveFormatti === undefined ? false : _ref$preserveFormatti,\n _ref$escapeMapFn = _ref.escapeMapFn,\n escapeMapFn = _ref$escapeMapFn === undefined ? defaultEscapeMapFn : _ref$escapeMapFn;\n\n var runningStr = String(str);\n var result = \"\";\n\n var escapes = escapeMapFn(_extends({}, defaultEscapes), preserveFormatting ? _extends({}, formatEscapes) : {});\n var escapeKeys = Object.keys(escapes); // as it is reused later on\n\n // Algorithm: Go through the string character by character, if it matches\n // with one of the special characters then we'll replace it with the escaped\n // version.\n\n var _loop = function _loop() {\n var specialCharFound = false;\n escapeKeys.forEach(function (key, index) {\n if (specialCharFound) {\n return;\n }\n if (runningStr.length >= key.length && runningStr.slice(0, key.length) === key) {\n result += escapes[escapeKeys[index]];\n runningStr = runningStr.slice(key.length, runningStr.length);\n specialCharFound = true;\n }\n });\n if (!specialCharFound) {\n result += runningStr.slice(0, 1);\n runningStr = runningStr.slice(1, runningStr.length);\n }\n };\n\n while (runningStr) {\n _loop();\n }\n return result;\n};","// A port of an algorithm by Johannes Baagøe , 2010\n// http://baagoe.com/en/RandomMusings/javascript/\n// https://github.com/nquinlan/better-random-numbers-for-javascript-mirror\n// Original work is under MIT license -\n\n// Copyright (C) 2010 by Johannes Baagøe \n//\n// Permission is hereby granted, free of charge, to any person obtaining a copy\n// of this software and associated documentation files (the \"Software\"), to deal\n// in the Software without restriction, including without limitation the rights\n// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n// copies of the Software, and to permit persons to whom the Software is\n// furnished to do so, subject to the following conditions:\n//\n// The above copyright notice and this permission notice shall be included in\n// all copies or substantial portions of the Software.\n//\n// THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n// THE SOFTWARE.\n\n\n\n(function(global, module, define) {\n\nfunction Alea(seed) {\n var me = this, mash = Mash();\n\n me.next = function() {\n var t = 2091639 * me.s0 + me.c * 2.3283064365386963e-10; // 2^-32\n me.s0 = me.s1;\n me.s1 = me.s2;\n return me.s2 = t - (me.c = t | 0);\n };\n\n // Apply the seeding algorithm from Baagoe.\n me.c = 1;\n me.s0 = mash(' ');\n me.s1 = mash(' ');\n me.s2 = mash(' ');\n me.s0 -= mash(seed);\n if (me.s0 < 0) { me.s0 += 1; }\n me.s1 -= mash(seed);\n if (me.s1 < 0) { me.s1 += 1; }\n me.s2 -= mash(seed);\n if (me.s2 < 0) { me.s2 += 1; }\n mash = null;\n}\n\nfunction copy(f, t) {\n t.c = f.c;\n t.s0 = f.s0;\n t.s1 = f.s1;\n t.s2 = f.s2;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new Alea(seed),\n state = opts && opts.state,\n prng = xg.next;\n prng.int32 = function() { return (xg.next() * 0x100000000) | 0; }\n prng.double = function() {\n return prng() + (prng() * 0x200000 | 0) * 1.1102230246251565e-16; // 2^-53\n };\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nfunction Mash() {\n var n = 0xefc8249d;\n\n var mash = function(data) {\n data = String(data);\n for (var i = 0; i < data.length; i++) {\n n += data.charCodeAt(i);\n var h = 0.02519603282416938 * n;\n n = h >>> 0;\n h -= n;\n h *= n;\n n = h >>> 0;\n h -= n;\n n += h * 0x100000000; // 2^32\n }\n return (n >>> 0) * 2.3283064365386963e-10; // 2^-32\n };\n\n return mash;\n}\n\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.alea = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xor128\" prng algorithm by\n// George Marsaglia. See http://www.jstatsoft.org/v08/i14/paper\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n me.x = 0;\n me.y = 0;\n me.z = 0;\n me.w = 0;\n\n // Set up generator function.\n me.next = function() {\n var t = me.x ^ (me.x << 11);\n me.x = me.y;\n me.y = me.z;\n me.z = me.w;\n return me.w ^= (me.w >>> 19) ^ t ^ (t >>> 8);\n };\n\n if (seed === (seed | 0)) {\n // Integer seed.\n me.x = seed;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 64; k++) {\n me.x ^= strseed.charCodeAt(k) | 0;\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.x = f.x;\n t.y = f.y;\n t.z = f.z;\n t.w = f.w;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xor128 = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xorwow\" prng algorithm by\n// George Marsaglia. See http://www.jstatsoft.org/v08/i14/paper\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n // Set up generator function.\n me.next = function() {\n var t = (me.x ^ (me.x >>> 2));\n me.x = me.y; me.y = me.z; me.z = me.w; me.w = me.v;\n return (me.d = (me.d + 362437 | 0)) +\n (me.v = (me.v ^ (me.v << 4)) ^ (t ^ (t << 1))) | 0;\n };\n\n me.x = 0;\n me.y = 0;\n me.z = 0;\n me.w = 0;\n me.v = 0;\n\n if (seed === (seed | 0)) {\n // Integer seed.\n me.x = seed;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 64; k++) {\n me.x ^= strseed.charCodeAt(k) | 0;\n if (k == strseed.length) {\n me.d = me.x << 10 ^ me.x >>> 4;\n }\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.x = f.x;\n t.y = f.y;\n t.z = f.z;\n t.w = f.w;\n t.v = f.v;\n t.d = f.d;\n return t;\n}\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xorwow = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","// A Javascript implementaion of the \"xorshift7\" algorithm by\n// François Panneton and Pierre L'ecuyer:\n// \"On the Xorgshift Random Number Generators\"\n// http://saluc.engr.uconn.edu/refs/crypto/rng/panneton05onthexorshift.pdf\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this;\n\n // Set up generator function.\n me.next = function() {\n // Update xor generator.\n var X = me.x, i = me.i, t, v, w;\n t = X[i]; t ^= (t >>> 7); v = t ^ (t << 24);\n t = X[(i + 1) & 7]; v ^= t ^ (t >>> 10);\n t = X[(i + 3) & 7]; v ^= t ^ (t >>> 3);\n t = X[(i + 4) & 7]; v ^= t ^ (t << 7);\n t = X[(i + 7) & 7]; t = t ^ (t << 13); v ^= t ^ (t << 9);\n X[i] = v;\n me.i = (i + 1) & 7;\n return v;\n };\n\n function init(me, seed) {\n var j, w, X = [];\n\n if (seed === (seed | 0)) {\n // Seed state array using a 32-bit integer.\n w = X[0] = seed;\n } else {\n // Seed state using a string.\n seed = '' + seed;\n for (j = 0; j < seed.length; ++j) {\n X[j & 7] = (X[j & 7] << 15) ^\n (seed.charCodeAt(j) + X[(j + 1) & 7] << 13);\n }\n }\n // Enforce an array length of 8, not all zeroes.\n while (X.length < 8) X.push(0);\n for (j = 0; j < 8 && X[j] === 0; ++j);\n if (j == 8) w = X[7] = -1; else w = X[j];\n\n me.x = X;\n me.i = 0;\n\n // Discard an initial 256 values.\n for (j = 256; j > 0; --j) {\n me.next();\n }\n }\n\n init(me, seed);\n}\n\nfunction copy(f, t) {\n t.x = f.x.slice();\n t.i = f.i;\n return t;\n}\n\nfunction impl(seed, opts) {\n if (seed == null) seed = +(new Date);\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (state.x) copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xorshift7 = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n","// A Javascript implementaion of Richard Brent's Xorgens xor4096 algorithm.\n//\n// This fast non-cryptographic random number generator is designed for\n// use in Monte-Carlo algorithms. It combines a long-period xorshift\n// generator with a Weyl generator, and it passes all common batteries\n// of stasticial tests for randomness while consuming only a few nanoseconds\n// for each prng generated. For background on the generator, see Brent's\n// paper: \"Some long-period random number generators using shifts and xors.\"\n// http://arxiv.org/pdf/1004.3115v1.pdf\n//\n// Usage:\n//\n// var xor4096 = require('xor4096');\n// random = xor4096(1); // Seed with int32 or string.\n// assert.equal(random(), 0.1520436450538547); // (0, 1) range, 53 bits.\n// assert.equal(random.int32(), 1806534897); // signed int32, 32 bits.\n//\n// For nonzero numeric keys, this impelementation provides a sequence\n// identical to that by Brent's xorgens 3 implementaion in C. This\n// implementation also provides for initalizing the generator with\n// string seeds, or for saving and restoring the state of the generator.\n//\n// On Chrome, this prng benchmarks about 2.1 times slower than\n// Javascript's built-in Math.random().\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this;\n\n // Set up generator function.\n me.next = function() {\n var w = me.w,\n X = me.X, i = me.i, t, v;\n // Update Weyl generator.\n me.w = w = (w + 0x61c88647) | 0;\n // Update xor generator.\n v = X[(i + 34) & 127];\n t = X[i = ((i + 1) & 127)];\n v ^= v << 13;\n t ^= t << 17;\n v ^= v >>> 15;\n t ^= t >>> 12;\n // Update Xor generator array state.\n v = X[i] = v ^ t;\n me.i = i;\n // Result is the combination.\n return (v + (w ^ (w >>> 16))) | 0;\n };\n\n function init(me, seed) {\n var t, v, i, j, w, X = [], limit = 128;\n if (seed === (seed | 0)) {\n // Numeric seeds initialize v, which is used to generates X.\n v = seed;\n seed = null;\n } else {\n // String seeds are mixed into v and X one character at a time.\n seed = seed + '\\0';\n v = 0;\n limit = Math.max(limit, seed.length);\n }\n // Initialize circular array and weyl value.\n for (i = 0, j = -32; j < limit; ++j) {\n // Put the unicode characters into the array, and shuffle them.\n if (seed) v ^= seed.charCodeAt((j + 32) % seed.length);\n // After 32 shuffles, take v as the starting w value.\n if (j === 0) w = v;\n v ^= v << 10;\n v ^= v >>> 15;\n v ^= v << 4;\n v ^= v >>> 13;\n if (j >= 0) {\n w = (w + 0x61c88647) | 0; // Weyl.\n t = (X[j & 127] ^= (v + w)); // Combine xor and weyl to init array.\n i = (0 == t) ? i + 1 : 0; // Count zeroes.\n }\n }\n // We have detected all zeroes; make the key nonzero.\n if (i >= 128) {\n X[(seed && seed.length || 0) & 127] = -1;\n }\n // Run the generator 512 times to further mix the state before using it.\n // Factoring this as a function slows the main generator, so it is just\n // unrolled here. The weyl generator is not advanced while warming up.\n i = 127;\n for (j = 4 * 128; j > 0; --j) {\n v = X[(i + 34) & 127];\n t = X[i = ((i + 1) & 127)];\n v ^= v << 13;\n t ^= t << 17;\n v ^= v >>> 15;\n t ^= t >>> 12;\n X[i] = v ^ t;\n }\n // Storing state as object members is faster than using closure variables.\n me.w = w;\n me.X = X;\n me.i = i;\n }\n\n init(me, seed);\n}\n\nfunction copy(f, t) {\n t.i = f.i;\n t.w = f.w;\n t.X = f.X.slice();\n return t;\n};\n\nfunction impl(seed, opts) {\n if (seed == null) seed = +(new Date);\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (state.X) copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.xor4096 = impl;\n}\n\n})(\n this, // window object or global\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n","// A Javascript implementaion of the \"Tyche-i\" prng algorithm by\n// Samuel Neves and Filipe Araujo.\n// See https://eden.dei.uc.pt/~sneves/pubs/2011-snfa2.pdf\n\n(function(global, module, define) {\n\nfunction XorGen(seed) {\n var me = this, strseed = '';\n\n // Set up generator function.\n me.next = function() {\n var b = me.b, c = me.c, d = me.d, a = me.a;\n b = (b << 25) ^ (b >>> 7) ^ c;\n c = (c - d) | 0;\n d = (d << 24) ^ (d >>> 8) ^ a;\n a = (a - b) | 0;\n me.b = b = (b << 20) ^ (b >>> 12) ^ c;\n me.c = c = (c - d) | 0;\n me.d = (d << 16) ^ (c >>> 16) ^ a;\n return me.a = (a - b) | 0;\n };\n\n /* The following is non-inverted tyche, which has better internal\n * bit diffusion, but which is about 25% slower than tyche-i in JS.\n me.next = function() {\n var a = me.a, b = me.b, c = me.c, d = me.d;\n a = (me.a + me.b | 0) >>> 0;\n d = me.d ^ a; d = d << 16 ^ d >>> 16;\n c = me.c + d | 0;\n b = me.b ^ c; b = b << 12 ^ d >>> 20;\n me.a = a = a + b | 0;\n d = d ^ a; me.d = d = d << 8 ^ d >>> 24;\n me.c = c = c + d | 0;\n b = b ^ c;\n return me.b = (b << 7 ^ b >>> 25);\n }\n */\n\n me.a = 0;\n me.b = 0;\n me.c = 2654435769 | 0;\n me.d = 1367130551;\n\n if (seed === Math.floor(seed)) {\n // Integer seed.\n me.a = (seed / 0x100000000) | 0;\n me.b = seed | 0;\n } else {\n // String seed.\n strseed += seed;\n }\n\n // Mix in string seed, then discard an initial batch of 64 values.\n for (var k = 0; k < strseed.length + 20; k++) {\n me.b ^= strseed.charCodeAt(k) | 0;\n me.next();\n }\n}\n\nfunction copy(f, t) {\n t.a = f.a;\n t.b = f.b;\n t.c = f.c;\n t.d = f.d;\n return t;\n};\n\nfunction impl(seed, opts) {\n var xg = new XorGen(seed),\n state = opts && opts.state,\n prng = function() { return (xg.next() >>> 0) / 0x100000000; };\n prng.double = function() {\n do {\n var top = xg.next() >>> 11,\n bot = (xg.next() >>> 0) / 0x100000000,\n result = (top + bot) / (1 << 21);\n } while (result === 0);\n return result;\n };\n prng.int32 = xg.next;\n prng.quick = prng;\n if (state) {\n if (typeof(state) == 'object') copy(state, xg);\n prng.state = function() { return copy(xg, {}); }\n }\n return prng;\n}\n\nif (module && module.exports) {\n module.exports = impl;\n} else if (define && define.amd) {\n define(function() { return impl; });\n} else {\n this.tychei = impl;\n}\n\n})(\n this,\n (typeof module) == 'object' && module, // present in node.js\n (typeof define) == 'function' && define // present with an AMD loader\n);\n\n\n","/*\nCopyright 2019 David Bau.\n\nPermission is hereby granted, free of charge, to any person obtaining\na copy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to\npermit persons to whom the Software is furnished to do so, subject to\nthe following conditions:\n\nThe above copyright notice and this permission notice shall be\nincluded in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.\nIN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY\nCLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,\nTORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE\nSOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n\n*/\n\n(function (global, pool, math) {\n//\n// The following constants are related to IEEE 754 limits.\n//\n\nvar width = 256, // each RC4 output is 0 <= x < 256\n chunks = 6, // at least six RC4 outputs for each double\n digits = 52, // there are 52 significant digits in a double\n rngname = 'random', // rngname: name for Math.random and Math.seedrandom\n startdenom = math.pow(width, chunks),\n significance = math.pow(2, digits),\n overflow = significance * 2,\n mask = width - 1,\n nodecrypto; // node.js crypto module, initialized at the bottom.\n\n//\n// seedrandom()\n// This is the seedrandom function described above.\n//\nfunction seedrandom(seed, options, callback) {\n var key = [];\n options = (options == true) ? { entropy: true } : (options || {});\n\n // Flatten the seed string or build one from local entropy if needed.\n var shortseed = mixkey(flatten(\n options.entropy ? [seed, tostring(pool)] :\n (seed == null) ? autoseed() : seed, 3), key);\n\n // Use the seed to initialize an ARC4 generator.\n var arc4 = new ARC4(key);\n\n // This function returns a random double in [0, 1) that contains\n // randomness in every bit of the mantissa of the IEEE 754 value.\n var prng = function() {\n var n = arc4.g(chunks), // Start with a numerator n < 2 ^ 48\n d = startdenom, // and denominator d = 2 ^ 48.\n x = 0; // and no 'extra last byte'.\n while (n < significance) { // Fill up all significant digits by\n n = (n + x) * width; // shifting numerator and\n d *= width; // denominator and generating a\n x = arc4.g(1); // new least-significant-byte.\n }\n while (n >= overflow) { // To avoid rounding up, before adding\n n /= 2; // last byte, shift everything\n d /= 2; // right using integer math until\n x >>>= 1; // we have exactly the desired bits.\n }\n return (n + x) / d; // Form the number within [0, 1).\n };\n\n prng.int32 = function() { return arc4.g(4) | 0; }\n prng.quick = function() { return arc4.g(4) / 0x100000000; }\n prng.double = prng;\n\n // Mix the randomness into accumulated entropy.\n mixkey(tostring(arc4.S), pool);\n\n // Calling convention: what to return as a function of prng, seed, is_math.\n return (options.pass || callback ||\n function(prng, seed, is_math_call, state) {\n if (state) {\n // Load the arc4 state from the given state if it has an S array.\n if (state.S) { copy(state, arc4); }\n // Only provide the .state method if requested via options.state.\n prng.state = function() { return copy(arc4, {}); }\n }\n\n // If called as a method of Math (Math.seedrandom()), mutate\n // Math.random because that is how seedrandom.js has worked since v1.0.\n if (is_math_call) { math[rngname] = prng; return seed; }\n\n // Otherwise, it is a newer calling convention, so return the\n // prng directly.\n else return prng;\n })(\n prng,\n shortseed,\n 'global' in options ? options.global : (this == math),\n options.state);\n}\n\n//\n// ARC4\n//\n// An ARC4 implementation. The constructor takes a key in the form of\n// an array of at most (width) integers that should be 0 <= x < (width).\n//\n// The g(count) method returns a pseudorandom integer that concatenates\n// the next (count) outputs from ARC4. Its return value is a number x\n// that is in the range 0 <= x < (width ^ count).\n//\nfunction ARC4(key) {\n var t, keylen = key.length,\n me = this, i = 0, j = me.i = me.j = 0, s = me.S = [];\n\n // The empty key [] is treated as [0].\n if (!keylen) { key = [keylen++]; }\n\n // Set up S using the standard key scheduling algorithm.\n while (i < width) {\n s[i] = i++;\n }\n for (i = 0; i < width; i++) {\n s[i] = s[j = mask & (j + key[i % keylen] + (t = s[i]))];\n s[j] = t;\n }\n\n // The \"g\" method returns the next (count) outputs as one number.\n (me.g = function(count) {\n // Using instance members instead of closure state nearly doubles speed.\n var t, r = 0,\n i = me.i, j = me.j, s = me.S;\n while (count--) {\n t = s[i = mask & (i + 1)];\n r = r * width + s[mask & ((s[i] = s[j = mask & (j + t)]) + (s[j] = t))];\n }\n me.i = i; me.j = j;\n return r;\n // For robust unpredictability, the function call below automatically\n // discards an initial batch of values. This is called RC4-drop[256].\n // See http://google.com/search?q=rsa+fluhrer+response&btnI\n })(width);\n}\n\n//\n// copy()\n// Copies internal state of ARC4 to or from a plain object.\n//\nfunction copy(f, t) {\n t.i = f.i;\n t.j = f.j;\n t.S = f.S.slice();\n return t;\n};\n\n//\n// flatten()\n// Converts an object tree to nested arrays of strings.\n//\nfunction flatten(obj, depth) {\n var result = [], typ = (typeof obj), prop;\n if (depth && typ == 'object') {\n for (prop in obj) {\n try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}\n }\n }\n return (result.length ? result : typ == 'string' ? obj : obj + '\\0');\n}\n\n//\n// mixkey()\n// Mixes a string seed into a key that is an array of integers, and\n// returns a shortened string seed that is equivalent to the result key.\n//\nfunction mixkey(seed, key) {\n var stringseed = seed + '', smear, j = 0;\n while (j < stringseed.length) {\n key[mask & j] =\n mask & ((smear ^= key[mask & j] * 19) + stringseed.charCodeAt(j++));\n }\n return tostring(key);\n}\n\n//\n// autoseed()\n// Returns an object for autoseeding, using window.crypto and Node crypto\n// module if available.\n//\nfunction autoseed() {\n try {\n var out;\n if (nodecrypto && (out = nodecrypto.randomBytes)) {\n // The use of 'out' to remember randomBytes makes tight minified code.\n out = out(width);\n } else {\n out = new Uint8Array(width);\n (global.crypto || global.msCrypto).getRandomValues(out);\n }\n return tostring(out);\n } catch (e) {\n var browser = global.navigator,\n plugins = browser && browser.plugins;\n return [+new Date, global, plugins, global.screen, tostring(pool)];\n }\n}\n\n//\n// tostring()\n// Converts an array of charcodes to a string\n//\nfunction tostring(a) {\n return String.fromCharCode.apply(0, a);\n}\n\n//\n// When seedrandom.js is loaded, we immediately mix a few bits\n// from the built-in RNG into the entropy pool. Because we do\n// not want to interfere with deterministic PRNG state later,\n// seedrandom will not call math.random on its own again after\n// initialization.\n//\nmixkey(math.random(), pool);\n\n//\n// Nodejs and AMD support: export the implementation as a module using\n// either convention.\n//\nif ((typeof module) == 'object' && module.exports) {\n module.exports = seedrandom;\n // When in node.js, try using crypto package for autoseeding.\n try {\n nodecrypto = require('crypto');\n } catch (ex) {}\n} else if ((typeof define) == 'function' && define.amd) {\n define(function() { return seedrandom; });\n} else {\n // When included as a plain script, set up Math.seedrandom global.\n math['seed' + rngname] = seedrandom;\n}\n\n\n// End anonymous scope, and pass initial values.\n})(\n // global: `self` in browsers (including strict mode and web workers),\n // otherwise `this` in Node and other environments\n (typeof self !== 'undefined') ? self : this,\n [], // pool: entropy pool starts empty\n Math // math: package containing random, pow, and seedrandom\n);\n","if(typeof __WEBPACK_EXTERNAL_MODULE__19__ === 'undefined') {var e = new Error(\"Cannot find module 'crypto'\"); e.code = 'MODULE_NOT_FOUND'; throw e;}\nmodule.exports = __WEBPACK_EXTERNAL_MODULE__19__;","// type checks for all known types\n//\n// note that:\n//\n// - check by duck-typing on a property like `isUnit`, instead of checking instanceof.\n// instanceof cannot be used because that would not allow to pass data from\n// one instance of math.js to another since each has it's own instance of Unit.\n// - check the `isUnit` property via the constructor, so there will be no\n// matches for \"fake\" instances like plain objects with a property `isUnit`.\n// That is important for security reasons.\n// - It must not be possible to override the type checks used internally,\n// for security reasons, so these functions are not exposed in the expression\n// parser.\n\nexport function isNumber (x) {\n return typeof x === 'number'\n}\n\nexport function isBigNumber (x) {\n return (x && x.constructor.prototype.isBigNumber === true) || false\n}\n\nexport function isComplex (x) {\n return (x && typeof x === 'object' && Object.getPrototypeOf(x).isComplex === true) || false\n}\n\nexport function isFraction (x) {\n return (x && typeof x === 'object' && Object.getPrototypeOf(x).isFraction === true) || false\n}\n\nexport function isUnit (x) {\n return (x && x.constructor.prototype.isUnit === true) || false\n}\n\nexport function isString (x) {\n return typeof x === 'string'\n}\n\nexport const isArray = Array.isArray\n\nexport function isMatrix (x) {\n return (x && x.constructor.prototype.isMatrix === true) || false\n}\n\n/**\n * Test whether a value is a collection: an Array or Matrix\n * @param {*} x\n * @returns {boolean} isCollection\n */\nexport function isCollection (x) {\n return Array.isArray(x) || isMatrix(x)\n}\n\nexport function isDenseMatrix (x) {\n return (x && x.isDenseMatrix && x.constructor.prototype.isMatrix === true) || false\n}\n\nexport function isSparseMatrix (x) {\n return (x && x.isSparseMatrix && x.constructor.prototype.isMatrix === true) || false\n}\n\nexport function isRange (x) {\n return (x && x.constructor.prototype.isRange === true) || false\n}\n\nexport function isIndex (x) {\n return (x && x.constructor.prototype.isIndex === true) || false\n}\n\nexport function isBoolean (x) {\n return typeof x === 'boolean'\n}\n\nexport function isResultSet (x) {\n return (x && x.constructor.prototype.isResultSet === true) || false\n}\n\nexport function isHelp (x) {\n return (x && x.constructor.prototype.isHelp === true) || false\n}\n\nexport function isFunction (x) {\n return typeof x === 'function'\n}\n\nexport function isDate (x) {\n return x instanceof Date\n}\n\nexport function isRegExp (x) {\n return x instanceof RegExp\n}\n\nexport function isObject (x) {\n return !!(x &&\n typeof x === 'object' &&\n x.constructor === Object &&\n !isComplex(x) &&\n !isFraction(x))\n}\n\nexport function isNull (x) {\n return x === null\n}\n\nexport function isUndefined (x) {\n return x === undefined\n}\n\nexport function isAccessorNode (x) {\n return (x && x.isAccessorNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isArrayNode (x) {\n return (x && x.isArrayNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isAssignmentNode (x) {\n return (x && x.isAssignmentNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isBlockNode (x) {\n return (x && x.isBlockNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isConditionalNode (x) {\n return (x && x.isConditionalNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isConstantNode (x) {\n return (x && x.isConstantNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isFunctionAssignmentNode (x) {\n return (x && x.isFunctionAssignmentNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isFunctionNode (x) {\n return (x && x.isFunctionNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isIndexNode (x) {\n return (x && x.isIndexNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isNode (x) {\n return (x && x.isNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isObjectNode (x) {\n return (x && x.isObjectNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isOperatorNode (x) {\n return (x && x.isOperatorNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isParenthesisNode (x) {\n return (x && x.isParenthesisNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isRangeNode (x) {\n return (x && x.isRangeNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isSymbolNode (x) {\n return (x && x.isSymbolNode === true && x.constructor.prototype.isNode === true) || false\n}\n\nexport function isChain (x) {\n return (x && x.constructor.prototype.isChain === true) || false\n}\n\nexport function typeOf (x) {\n const t = typeof x\n\n if (t === 'object') {\n // JavaScript types\n if (x === null) return 'null'\n if (Array.isArray(x)) return 'Array'\n if (x instanceof Date) return 'Date'\n if (x instanceof RegExp) return 'RegExp'\n\n // math.js types\n if (isBigNumber(x)) return 'BigNumber'\n if (isComplex(x)) return 'Complex'\n if (isFraction(x)) return 'Fraction'\n if (isMatrix(x)) return 'Matrix'\n if (isUnit(x)) return 'Unit'\n if (isIndex(x)) return 'Index'\n if (isRange(x)) return 'Range'\n if (isResultSet(x)) return 'ResultSet'\n if (isNode(x)) return x.type\n if (isChain(x)) return 'Chain'\n if (isHelp(x)) return 'Help'\n\n return 'Object'\n }\n\n if (t === 'function') return 'Function'\n\n return t // can be 'string', 'number', 'boolean', ...\n}\n","import { isNumber } from './is.js'\n\n/**\n * @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue\n */\n\n/**\n * Check if a number is integer\n * @param {number | boolean} value\n * @return {boolean} isInteger\n */\nexport function isInteger (value) {\n if (typeof value === 'boolean') {\n return true\n }\n\n return isFinite(value)\n ? (value === Math.round(value))\n : false\n // Note: we use ==, not ===, as we can have Booleans as well\n}\n\n/**\n * Calculate the sign of a number\n * @param {number} x\n * @returns {number}\n */\nexport const sign = /* #__PURE__ */ Math.sign || function (x) {\n if (x > 0) {\n return 1\n } else if (x < 0) {\n return -1\n } else {\n return 0\n }\n}\n\n/**\n * Calculate the base-2 logarithm of a number\n * @param {number} x\n * @returns {number}\n */\nexport const log2 = /* #__PURE__ */ Math.log2 || function log2 (x) {\n return Math.log(x) / Math.LN2\n}\n\n/**\n * Calculate the base-10 logarithm of a number\n * @param {number} x\n * @returns {number}\n */\nexport const log10 = /* #__PURE__ */ Math.log10 || function log10 (x) {\n return Math.log(x) / Math.LN10\n}\n\n/**\n * Calculate the natural logarithm of a number + 1\n * @param {number} x\n * @returns {number}\n */\nexport const log1p = /* #__PURE__ */ Math.log1p || function (x) {\n return Math.log(x + 1)\n}\n\n/**\n * Calculate cubic root for a number\n *\n * Code from es6-shim.js:\n * https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577\n *\n * @param {number} x\n * @returns {number} Returns the cubic root of x\n */\nexport const cbrt = /* #__PURE__ */ Math.cbrt || function cbrt (x) {\n if (x === 0) {\n return x\n }\n\n const negate = x < 0\n let result\n if (negate) {\n x = -x\n }\n\n if (isFinite(x)) {\n result = Math.exp(Math.log(x) / 3)\n // from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods\n result = (x / (result * result) + (2 * result)) / 3\n } else {\n result = x\n }\n\n return negate ? -result : result\n}\n\n/**\n * Calculates exponentiation minus 1\n * @param {number} x\n * @return {number} res\n */\nexport const expm1 = /* #__PURE__ */ Math.expm1 || function expm1 (x) {\n return (x >= 2e-4 || x <= -2e-4)\n ? Math.exp(x) - 1\n : x + x * x / 2 + x * x * x / 6\n}\n\n/**\n * Formats a number in a given base\n * @param {number} n\n * @param {number} base\n * @param {number} size\n * @returns {string}\n */\nfunction formatNumberToBase (n, base, size) {\n const prefixes = { 2: '0b', 8: '0o', 16: '0x' }\n const prefix = prefixes[base]\n let suffix = ''\n if (size) {\n if (size < 1) {\n throw new Error('size must be in greater than 0')\n }\n if (!isInteger(size)) {\n throw new Error('size must be an integer')\n }\n if (n > 2 ** (size - 1) - 1 || n < -(2 ** (size - 1))) {\n throw new Error(`Value must be in range [-2^${size - 1}, 2^${size - 1}-1]`)\n }\n if (!isInteger(n)) {\n throw new Error('Value must be an integer')\n }\n if (n < 0) {\n n = n + 2 ** size\n }\n suffix = `i${size}`\n }\n let sign = ''\n if (n < 0) {\n n = -n\n sign = '-'\n }\n return `${sign}${prefix}${n.toString(base)}${suffix}`\n}\n\n/**\n * Convert a number to a formatted string representation.\n *\n * Syntax:\n *\n * format(value)\n * format(value, options)\n * format(value, precision)\n * format(value, fn)\n *\n * Where:\n *\n * {number} value The value to be formatted\n * {Object} options An object with formatting options. Available options:\n * {string} notation\n * Number notation. Choose from:\n * 'fixed' Always use regular number notation.\n * For example '123.40' and '14000000'\n * 'exponential' Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * 'engineering' Always use engineering notation.\n * For example '123.4e+0' and '14.0e+6'\n * 'auto' (default) Regular number notation for numbers\n * having an absolute value between\n * `lowerExp` and `upperExp` bounds, and\n * uses exponential notation elsewhere.\n * Lower bound is included, upper bound\n * is excluded.\n * For example '123.4' and '1.4e7'.\n * 'bin', 'oct, or\n * 'hex' Format the number using binary, octal,\n * or hexadecimal notation.\n * For example '0b1101' and '0x10fe'.\n * {number} wordSize The word size in bits to use for formatting\n * in binary, octal, or hexadecimal notation.\n * To be used only with 'bin', 'oct', or 'hex'\n * values for 'notation' option. When this option\n * is defined the value is formatted as a signed\n * twos complement integer of the given word size\n * and the size suffix is appended to the output.\n * For example\n * format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'.\n * Default value is undefined.\n * {number} precision A number between 0 and 16 to round\n * the digits of the number.\n * In case of notations 'exponential',\n * 'engineering', and 'auto',\n * `precision` defines the total\n * number of significant digits returned.\n * In case of notation 'fixed',\n * `precision` defines the number of\n * significant digits after the decimal\n * point.\n * `precision` is undefined by default,\n * not rounding any digits.\n * {number} lowerExp Exponent determining the lower boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `-3`.\n * {number} upperExp Exponent determining the upper boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `5`.\n * {Function} fn A custom formatting function. Can be used to override the\n * built-in notations. Function `fn` is called with `value` as\n * parameter and must return a string. Is useful for example to\n * format all values inside a matrix in a particular way.\n *\n * Examples:\n *\n * format(6.4) // '6.4'\n * format(1240000) // '1.24e6'\n * format(1/3) // '0.3333333333333333'\n * format(1/3, 3) // '0.333'\n * format(21385, 2) // '21000'\n * format(12.071, {notation: 'fixed'}) // '12'\n * format(2.3, {notation: 'fixed', precision: 2}) // '2.30'\n * format(52.8, {notation: 'exponential'}) // '5.28e+1'\n * format(12345678, {notation: 'engineering'}) // '12.345678e+6'\n *\n * @param {number} value\n * @param {Object | Function | number} [options]\n * @return {string} str The formatted value\n */\nexport function format (value, options) {\n if (typeof options === 'function') {\n // handle format(value, fn)\n return options(value)\n }\n\n // handle special cases\n if (value === Infinity) {\n return 'Infinity'\n } else if (value === -Infinity) {\n return '-Infinity'\n } else if (isNaN(value)) {\n return 'NaN'\n }\n\n // default values for options\n let notation = 'auto'\n let precision\n let wordSize\n\n if (options) {\n // determine notation from options\n if (options.notation) {\n notation = options.notation\n }\n\n // determine precision from options\n if (isNumber(options)) {\n precision = options\n } else if (isNumber(options.precision)) {\n precision = options.precision\n }\n\n if (options.wordSize) {\n wordSize = options.wordSize\n if (typeof (wordSize) !== 'number') {\n throw new Error('Option \"wordSize\" must be a number')\n }\n }\n }\n\n // handle the various notations\n switch (notation) {\n case 'fixed':\n return toFixed(value, precision)\n\n case 'exponential':\n return toExponential(value, precision)\n\n case 'engineering':\n return toEngineering(value, precision)\n\n case 'bin':\n return formatNumberToBase(value, 2, wordSize)\n\n case 'oct':\n return formatNumberToBase(value, 8, wordSize)\n\n case 'hex':\n return formatNumberToBase(value, 16, wordSize)\n\n case 'auto':\n // remove trailing zeros after the decimal point\n return toPrecision(value, precision, options && options)\n .replace(/((\\.\\d*?)(0+))($|e)/, function () {\n const digits = arguments[2]\n const e = arguments[4]\n return (digits !== '.') ? digits + e : e\n })\n\n default:\n throw new Error('Unknown notation \"' + notation + '\". ' +\n 'Choose \"auto\", \"exponential\", \"fixed\", \"bin\", \"oct\", or \"hex.')\n }\n}\n\n/**\n * Split a number into sign, coefficients, and exponent\n * @param {number | string} value\n * @return {SplitValue}\n * Returns an object containing sign, coefficients, and exponent\n */\nexport function splitNumber (value) {\n // parse the input value\n const match = String(value).toLowerCase().match(/^0*?(-?)(\\d+\\.?\\d*)(e([+-]?\\d+))?$/)\n if (!match) {\n throw new SyntaxError('Invalid number ' + value)\n }\n\n const sign = match[1]\n const digits = match[2]\n let exponent = parseFloat(match[4] || '0')\n\n const dot = digits.indexOf('.')\n exponent += (dot !== -1) ? (dot - 1) : (digits.length - 1)\n\n const coefficients = digits\n .replace('.', '') // remove the dot (must be removed before removing leading zeros)\n .replace(/^0*/, function (zeros) {\n // remove leading zeros, add their count to the exponent\n exponent -= zeros.length\n return ''\n })\n .replace(/0*$/, '') // remove trailing zeros\n .split('')\n .map(function (d) {\n return parseInt(d)\n })\n\n if (coefficients.length === 0) {\n coefficients.push(0)\n exponent++\n }\n\n return {\n sign: sign,\n coefficients: coefficients,\n exponent: exponent\n }\n}\n\n/**\n * Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'\n * @param {number | string} value\n * @param {number} [precision] Optional number of significant figures to return.\n */\nexport function toEngineering (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n const split = splitNumber(value)\n const rounded = roundDigits(split, precision)\n\n const e = rounded.exponent\n const c = rounded.coefficients\n\n // find nearest lower multiple of 3 for exponent\n const newExp = e % 3 === 0 ? e : (e < 0 ? (e - 3) - (e % 3) : e - (e % 3))\n\n if (isNumber(precision)) {\n // add zeroes to give correct sig figs\n while (precision > c.length || (e - newExp) + 1 > c.length) {\n c.push(0)\n }\n } else {\n // concatenate coefficients with necessary zeros\n // add zeros if necessary (for example: 1e+8 -> 100e+6)\n const missingZeros = Math.abs(e - newExp) - (c.length - 1)\n for (let i = 0; i < missingZeros; i++) {\n c.push(0)\n }\n }\n\n // find difference in exponents\n let expDiff = Math.abs(e - newExp)\n let decimalIdx = 1\n\n // push decimal index over by expDiff times\n while (expDiff > 0) {\n decimalIdx++\n expDiff--\n }\n\n // if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.\n // otherwise concat with the rest of the coefficients\n const decimals = c.slice(decimalIdx).join('')\n const decimalVal = ((isNumber(precision) && decimals.length) || decimals.match(/[1-9]/)) ? ('.' + decimals) : ''\n\n const str = c.slice(0, decimalIdx).join('') +\n decimalVal +\n 'e' + (e >= 0 ? '+' : '') + newExp.toString()\n return rounded.sign + str\n}\n\n/**\n * Format a number with fixed notation.\n * @param {number | string} value\n * @param {number} [precision=undefined] Optional number of decimals after the\n * decimal point. null by default.\n */\nexport function toFixed (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n const splitValue = splitNumber(value)\n const rounded = (typeof precision === 'number')\n ? roundDigits(splitValue, splitValue.exponent + 1 + precision)\n : splitValue\n let c = rounded.coefficients\n let p = rounded.exponent + 1 // exponent may have changed\n\n // append zeros if needed\n const pp = p + (precision || 0)\n if (c.length < pp) {\n c = c.concat(zeros(pp - c.length))\n }\n\n // prepend zeros if needed\n if (p < 0) {\n c = zeros(-p + 1).concat(c)\n p = 1\n }\n\n // insert a dot if needed\n if (p < c.length) {\n c.splice(p, 0, (p === 0) ? '0.' : '.')\n }\n\n return rounded.sign + c.join('')\n}\n\n/**\n * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'\n * @param {number | string} value\n * @param {number} [precision] Number of digits in formatted output.\n * If not provided, the maximum available digits\n * is used.\n */\nexport function toExponential (value, precision) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n // round if needed, else create a clone\n const split = splitNumber(value)\n const rounded = precision ? roundDigits(split, precision) : split\n let c = rounded.coefficients\n const e = rounded.exponent\n\n // append zeros if needed\n if (c.length < precision) {\n c = c.concat(zeros(precision - c.length))\n }\n\n // format as `C.CCCe+EEE` or `C.CCCe-EEE`\n const first = c.shift()\n return rounded.sign + first + (c.length > 0 ? ('.' + c.join('')) : '') +\n 'e' + (e >= 0 ? '+' : '') + e\n}\n\n/**\n * Format a number with a certain precision\n * @param {number | string} value\n * @param {number} [precision=undefined] Optional number of digits.\n * @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]\n * By default:\n * lowerExp = -3 (incl)\n * upper = +5 (excl)\n * @return {string}\n */\nexport function toPrecision (value, precision, options) {\n if (isNaN(value) || !isFinite(value)) {\n return String(value)\n }\n\n // determine lower and upper bound for exponential notation.\n const lowerExp = (options && options.lowerExp !== undefined) ? options.lowerExp : -3\n const upperExp = (options && options.upperExp !== undefined) ? options.upperExp : 5\n\n const split = splitNumber(value)\n const rounded = precision ? roundDigits(split, precision) : split\n if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {\n // exponential notation\n return toExponential(value, precision)\n } else {\n let c = rounded.coefficients\n const e = rounded.exponent\n\n // append trailing zeros\n if (c.length < precision) {\n c = c.concat(zeros(precision - c.length))\n }\n\n // append trailing zeros\n // TODO: simplify the next statement\n c = c.concat(zeros(e - c.length + 1 +\n (c.length < precision ? precision - c.length : 0)))\n\n // prepend zeros\n c = zeros(-e).concat(c)\n\n const dot = e > 0 ? e : 0\n if (dot < c.length - 1) {\n c.splice(dot + 1, 0, '.')\n }\n\n return rounded.sign + c.join('')\n }\n}\n\n/**\n * Round the number of digits of a number *\n * @param {SplitValue} split A value split with .splitNumber(value)\n * @param {number} precision A positive integer\n * @return {SplitValue}\n * Returns an object containing sign, coefficients, and exponent\n * with rounded digits\n */\nexport function roundDigits (split, precision) {\n // create a clone\n const rounded = {\n sign: split.sign,\n coefficients: split.coefficients,\n exponent: split.exponent\n }\n const c = rounded.coefficients\n\n // prepend zeros if needed\n while (precision <= 0) {\n c.unshift(0)\n rounded.exponent++\n precision++\n }\n\n if (c.length > precision) {\n const removed = c.splice(precision, c.length - precision)\n\n if (removed[0] >= 5) {\n let i = precision - 1\n c[i]++\n while (c[i] === 10) {\n c.pop()\n if (i === 0) {\n c.unshift(0)\n rounded.exponent++\n i++\n }\n i--\n c[i]++\n }\n }\n }\n\n return rounded\n}\n\n/**\n * Create an array filled with zeros.\n * @param {number} length\n * @return {Array}\n */\nfunction zeros (length) {\n const arr = []\n for (let i = 0; i < length; i++) {\n arr.push(0)\n }\n return arr\n}\n\n/**\n * Count the number of significant digits of a number.\n *\n * For example:\n * 2.34 returns 3\n * 0.0034 returns 2\n * 120.5e+30 returns 4\n *\n * @param {number} value\n * @return {number} digits Number of significant digits\n */\nexport function digits (value) {\n return value\n .toExponential()\n .replace(/e.*$/, '') // remove exponential notation\n .replace(/^0\\.?0*|\\./, '') // remove decimal point and leading zeros\n .length\n}\n\n/**\n * Minimum number added to one that makes the result different than one\n */\nexport const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16\n\n/**\n * Compares two floating point numbers.\n * @param {number} x First value to compare\n * @param {number} y Second value to compare\n * @param {number} [epsilon] The maximum relative difference between x and y\n * If epsilon is undefined or null, the function will\n * test whether x and y are exactly equal.\n * @return {boolean} whether the two numbers are nearly equal\n*/\nexport function nearlyEqual (x, y, epsilon) {\n // if epsilon is null or undefined, test whether x and y are exactly equal\n if (epsilon === null || epsilon === undefined) {\n return x === y\n }\n\n if (x === y) {\n return true\n }\n\n // NaN\n if (isNaN(x) || isNaN(y)) {\n return false\n }\n\n // at this point x and y should be finite\n if (isFinite(x) && isFinite(y)) {\n // check numbers are very close, needed when comparing numbers near zero\n const diff = Math.abs(x - y)\n if (diff < DBL_EPSILON) {\n return true\n } else {\n // use relative error\n return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon\n }\n }\n\n // Infinite and Number or negative Infinite and positive Infinite cases\n return false\n}\n\n/**\n * Calculate the hyperbolic arccos of a number\n * @param {number} x\n * @return {number}\n */\nexport const acosh = Math.acosh || function (x) {\n return Math.log(Math.sqrt(x * x - 1) + x)\n}\n\nexport const asinh = Math.asinh || function (x) {\n return Math.log(Math.sqrt(x * x + 1) + x)\n}\n\n/**\n * Calculate the hyperbolic arctangent of a number\n * @param {number} x\n * @return {number}\n */\nexport const atanh = Math.atanh || function (x) {\n return Math.log((1 + x) / (1 - x)) / 2\n}\n\n/**\n * Calculate the hyperbolic cosine of a number\n * @param {number} x\n * @returns {number}\n */\nexport const cosh = Math.cosh || function (x) {\n return (Math.exp(x) + Math.exp(-x)) / 2\n}\n\n/**\n * Calculate the hyperbolic sine of a number\n * @param {number} x\n * @returns {number}\n */\nexport const sinh = Math.sinh || function (x) {\n return (Math.exp(x) - Math.exp(-x)) / 2\n}\n\n/**\n * Calculate the hyperbolic tangent of a number\n * @param {number} x\n * @returns {number}\n */\nexport const tanh = Math.tanh || function (x) {\n const e = Math.exp(2 * x)\n return (e - 1) / (e + 1)\n}\n","import { isInteger } from '../number.js'\n\n/**\n * Formats a BigNumber in a given base\n * @param {BigNumber} n\n * @param {number} base\n * @param {number} size\n * @returns {string}\n */\nfunction formatBigNumberToBase (n, base, size) {\n const BigNumberCtor = n.constructor\n const big2 = new BigNumberCtor(2)\n let suffix = ''\n if (size) {\n if (size < 1) {\n throw new Error('size must be in greater than 0')\n }\n if (!isInteger(size)) {\n throw new Error('size must be an integer')\n }\n if (n.greaterThan(big2.pow(size - 1).sub(1)) || n.lessThan(big2.pow(size - 1).mul(-1))) {\n throw new Error(`Value must be in range [-2^${size - 1}, 2^${size - 1}-1]`)\n }\n if (!n.isInteger()) {\n throw new Error('Value must be an integer')\n }\n if (n.lessThan(0)) {\n n = n.add(big2.pow(size))\n }\n suffix = `i${size}`\n }\n switch (base) {\n case 2: return `${n.toBinary()}${suffix}`\n case 8: return `${n.toOctal()}${suffix}`\n case 16: return `${n.toHexadecimal()}${suffix}`\n default: throw new Error(`Base ${base} not supported `)\n }\n}\n\n/**\n * Convert a BigNumber to a formatted string representation.\n *\n * Syntax:\n *\n * format(value)\n * format(value, options)\n * format(value, precision)\n * format(value, fn)\n *\n * Where:\n *\n * {number} value The value to be formatted\n * {Object} options An object with formatting options. Available options:\n * {string} notation\n * Number notation. Choose from:\n * 'fixed' Always use regular number notation.\n * For example '123.40' and '14000000'\n * 'exponential' Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * 'auto' (default) Regular number notation for numbers\n * having an absolute value between\n * `lower` and `upper` bounds, and uses\n * exponential notation elsewhere.\n * Lower bound is included, upper bound\n * is excluded.\n * For example '123.4' and '1.4e7'.\n * 'bin', 'oct, or\n * 'hex' Format the number using binary, octal,\n * or hexadecimal notation.\n * For example '0b1101' and '0x10fe'.\n * {number} wordSize The word size in bits to use for formatting\n * in binary, octal, or hexadecimal notation.\n * To be used only with 'bin', 'oct', or 'hex'\n * values for 'notation' option. When this option\n * is defined the value is formatted as a signed\n * twos complement integer of the given word size\n * and the size suffix is appended to the output.\n * For example\n * format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'.\n * Default value is undefined.\n * {number} precision A number between 0 and 16 to round\n * the digits of the number.\n * In case of notations 'exponential',\n * 'engineering', and 'auto',\n * `precision` defines the total\n * number of significant digits returned.\n * In case of notation 'fixed',\n * `precision` defines the number of\n * significant digits after the decimal\n * point.\n * `precision` is undefined by default.\n * {number} lowerExp Exponent determining the lower boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `-3`.\n * {number} upperExp Exponent determining the upper boundary\n * for formatting a value with an exponent\n * when `notation='auto`.\n * Default value is `5`.\n * {Function} fn A custom formatting function. Can be used to override the\n * built-in notations. Function `fn` is called with `value` as\n * parameter and must return a string. Is useful for example to\n * format all values inside a matrix in a particular way.\n *\n * Examples:\n *\n * format(6.4) // '6.4'\n * format(1240000) // '1.24e6'\n * format(1/3) // '0.3333333333333333'\n * format(1/3, 3) // '0.333'\n * format(21385, 2) // '21000'\n * format(12e8, {notation: 'fixed'}) // returns '1200000000'\n * format(2.3, {notation: 'fixed', precision: 4}) // returns '2.3000'\n * format(52.8, {notation: 'exponential'}) // returns '5.28e+1'\n * format(12400, {notation: 'engineering'}) // returns '12.400e+3'\n *\n * @param {BigNumber} value\n * @param {Object | Function | number} [options]\n * @return {string} str The formatted value\n */\nexport function format (value, options) {\n if (typeof options === 'function') {\n // handle format(value, fn)\n return options(value)\n }\n\n // handle special cases\n if (!value.isFinite()) {\n return value.isNaN() ? 'NaN' : (value.gt(0) ? 'Infinity' : '-Infinity')\n }\n\n // default values for options\n let notation = 'auto'\n let precision\n let wordSize\n\n if (options !== undefined) {\n // determine notation from options\n if (options.notation) {\n notation = options.notation\n }\n\n // determine precision from options\n if (typeof options === 'number') {\n precision = options\n } else if (options.precision) {\n precision = options.precision\n }\n\n if (options.wordSize) {\n wordSize = options.wordSize\n if (typeof (wordSize) !== 'number') {\n throw new Error('Option \"wordSize\" must be a number')\n }\n }\n }\n\n // handle the various notations\n switch (notation) {\n case 'fixed':\n return toFixed(value, precision)\n\n case 'exponential':\n return toExponential(value, precision)\n\n case 'engineering':\n return toEngineering(value, precision)\n\n case 'bin':\n return formatBigNumberToBase(value, 2, wordSize)\n\n case 'oct':\n return formatBigNumberToBase(value, 8, wordSize)\n\n case 'hex':\n return formatBigNumberToBase(value, 16, wordSize)\n\n case 'auto':\n {\n // determine lower and upper bound for exponential notation.\n // TODO: implement support for upper and lower to be BigNumbers themselves\n const lowerExp = (options && options.lowerExp !== undefined) ? options.lowerExp : -3\n const upperExp = (options && options.upperExp !== undefined) ? options.upperExp : 5\n\n // handle special case zero\n if (value.isZero()) return '0'\n\n // determine whether or not to output exponential notation\n let str\n const rounded = value.toSignificantDigits(precision)\n const exp = rounded.e\n if (exp >= lowerExp && exp < upperExp) {\n // normal number notation\n str = rounded.toFixed()\n } else {\n // exponential notation\n str = toExponential(value, precision)\n }\n\n // remove trailing zeros after the decimal point\n return str.replace(/((\\.\\d*?)(0+))($|e)/, function () {\n const digits = arguments[2]\n const e = arguments[4]\n return (digits !== '.') ? digits + e : e\n })\n }\n default:\n throw new Error('Unknown notation \"' + notation + '\". ' +\n 'Choose \"auto\", \"exponential\", \"fixed\", \"bin\", \"oct\", or \"hex.')\n }\n}\n\n/**\n * Format a BigNumber in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'\n * @param {BigNumber | string} value\n * @param {number} [precision] Optional number of significant figures to return.\n */\nexport function toEngineering (value, precision) {\n // find nearest lower multiple of 3 for exponent\n const e = value.e\n const newExp = e % 3 === 0 ? e : (e < 0 ? (e - 3) - (e % 3) : e - (e % 3))\n\n // find difference in exponents, and calculate the value without exponent\n const valueWithoutExp = value.mul(Math.pow(10, -newExp))\n\n let valueStr = valueWithoutExp.toPrecision(precision)\n if (valueStr.indexOf('e') !== -1) {\n valueStr = valueWithoutExp.toString()\n }\n\n return valueStr + 'e' + (e >= 0 ? '+' : '') + newExp.toString()\n}\n\n/**\n * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'\n * @param {BigNumber} value\n * @param {number} [precision] Number of digits in formatted output.\n * If not provided, the maximum available digits\n * is used.\n * @returns {string} str\n */\nexport function toExponential (value, precision) {\n if (precision !== undefined) {\n return value.toExponential(precision - 1) // Note the offset of one\n } else {\n return value.toExponential()\n }\n}\n\n/**\n * Format a number with fixed notation.\n * @param {BigNumber} value\n * @param {number} [precision=undefined] Optional number of decimals after the\n * decimal point. Undefined by default.\n */\nexport function toFixed (value, precision) {\n return value.toFixed(precision)\n}\n","import { isBigNumber, isString, typeOf } from './is.js'\nimport { format as formatNumber } from './number.js'\nimport { format as formatBigNumber } from './bignumber/formatter.js'\n\n/**\n * Check if a text ends with a certain string.\n * @param {string} text\n * @param {string} search\n */\nexport function endsWith (text, search) {\n const start = text.length - search.length\n const end = text.length\n return (text.substring(start, end) === search)\n}\n\n/**\n * Format a value of any type into a string.\n *\n * Usage:\n * math.format(value)\n * math.format(value, precision)\n *\n * When value is a function:\n *\n * - When the function has a property `syntax`, it returns this\n * syntax description.\n * - In other cases, a string `'function'` is returned.\n *\n * When `value` is an Object:\n *\n * - When the object contains a property `format` being a function, this\n * function is invoked as `value.format(options)` and the result is returned.\n * - When the object has its own `toString` method, this method is invoked\n * and the result is returned.\n * - In other cases the function will loop over all object properties and\n * return JSON object notation like '{\"a\": 2, \"b\": 3}'.\n *\n * Example usage:\n * math.format(2/7) // '0.2857142857142857'\n * math.format(math.pi, 3) // '3.14'\n * math.format(new Complex(2, 3)) // '2 + 3i'\n * math.format('hello') // '\"hello\"'\n *\n * @param {*} value Value to be stringified\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string} str\n */\nexport function format (value, options) {\n if (typeof value === 'number') {\n return formatNumber(value, options)\n }\n\n if (isBigNumber(value)) {\n return formatBigNumber(value, options)\n }\n\n // note: we use unsafe duck-typing here to check for Fractions, this is\n // ok here since we're only invoking toString or concatenating its values\n if (looksLikeFraction(value)) {\n if (!options || options.fraction !== 'decimal') {\n // output as ratio, like '1/3'\n return (value.s * value.n) + '/' + value.d\n } else {\n // output as decimal, like '0.(3)'\n return value.toString()\n }\n }\n\n if (Array.isArray(value)) {\n return formatArray(value, options)\n }\n\n if (isString(value)) {\n return '\"' + value + '\"'\n }\n\n if (typeof value === 'function') {\n return value.syntax ? String(value.syntax) : 'function'\n }\n\n if (value && typeof value === 'object') {\n if (typeof value.format === 'function') {\n return value.format(options)\n } else if (value && value.toString(options) !== {}.toString()) {\n // this object has a non-native toString method, use that one\n return value.toString(options)\n } else {\n const entries = Object.keys(value).map(key => {\n return '\"' + key + '\": ' + format(value[key], options)\n })\n\n return '{' + entries.join(', ') + '}'\n }\n }\n\n return String(value)\n}\n\n/**\n * Stringify a value into a string enclosed in double quotes.\n * Unescaped double quotes and backslashes inside the value are escaped.\n * @param {*} value\n * @return {string}\n */\nexport function stringify (value) {\n const text = String(value)\n let escaped = ''\n let i = 0\n while (i < text.length) {\n let c = text.charAt(i)\n\n if (c === '\\\\') {\n escaped += c\n i++\n\n c = text.charAt(i)\n if (c === '' || '\"\\\\/bfnrtu'.indexOf(c) === -1) {\n escaped += '\\\\' // no valid escape character -> escape it\n }\n escaped += c\n } else if (c === '\"') {\n escaped += '\\\\\"'\n } else {\n escaped += c\n }\n i++\n }\n\n return '\"' + escaped + '\"'\n}\n\n/**\n * Escape special HTML characters\n * @param {*} value\n * @return {string}\n */\nexport function escape (value) {\n let text = String(value)\n text = text.replace(/&/g, '&')\n .replace(/\"/g, '"')\n .replace(/'/g, ''')\n .replace(//g, '>')\n\n return text\n}\n\n/**\n * Recursively format an n-dimensional matrix\n * Example output: \"[[1, 2], [3, 4]]\"\n * @param {Array} array\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\nfunction formatArray (array, options) {\n if (Array.isArray(array)) {\n let str = '['\n const len = array.length\n for (let i = 0; i < len; i++) {\n if (i !== 0) {\n str += ', '\n }\n str += formatArray(array[i], options)\n }\n str += ']'\n return str\n } else {\n return format(array, options)\n }\n}\n\n/**\n * Check whether a value looks like a Fraction (unsafe duck-type check)\n * @param {*} value\n * @return {boolean}\n */\nfunction looksLikeFraction (value) {\n return (value &&\n typeof value === 'object' &&\n typeof value.s === 'number' &&\n typeof value.n === 'number' &&\n typeof value.d === 'number') || false\n}\n\n/**\n * Compare two strings\n * @param {string} x\n * @param {string} y\n * @returns {number}\n */\nexport function compareText (x, y) {\n // we don't want to convert numbers to string, only accept string input\n if (!isString(x)) {\n throw new TypeError('Unexpected type of argument in function compareText ' +\n '(expected: string or Array or Matrix, actual: ' + typeOf(x) + ', index: 0)')\n }\n if (!isString(y)) {\n throw new TypeError('Unexpected type of argument in function compareText ' +\n '(expected: string or Array or Matrix, actual: ' + typeOf(y) + ', index: 1)')\n }\n\n return (x === y)\n ? 0\n : (x > y ? 1 : -1)\n}\n","/**\n * Create a range error with the message:\n * 'Dimension mismatch ( != )'\n * @param {number | number[]} actual The actual size\n * @param {number | number[]} expected The expected size\n * @param {string} [relation='!='] Optional relation between actual\n * and expected size: '!=', '<', etc.\n * @extends RangeError\n */\nexport function DimensionError (actual, expected, relation) {\n if (!(this instanceof DimensionError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.actual = actual\n this.expected = expected\n this.relation = relation\n\n this.message = 'Dimension mismatch (' +\n (Array.isArray(actual) ? ('[' + actual.join(', ') + ']') : actual) +\n ' ' + (this.relation || '!=') + ' ' +\n (Array.isArray(expected) ? ('[' + expected.join(', ') + ']') : expected) +\n ')'\n\n this.stack = (new Error()).stack\n}\n\nDimensionError.prototype = new RangeError()\nDimensionError.prototype.constructor = RangeError\nDimensionError.prototype.name = 'DimensionError'\nDimensionError.prototype.isDimensionError = true\n","/**\n * Create a range error with the message:\n * 'Index out of range (index < min)'\n * 'Index out of range (index < max)'\n *\n * @param {number} index The actual index\n * @param {number} [min=0] Minimum index (included)\n * @param {number} [max] Maximum index (excluded)\n * @extends RangeError\n */\nexport function IndexError (index, min, max) {\n if (!(this instanceof IndexError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.index = index\n if (arguments.length < 3) {\n this.min = 0\n this.max = min\n } else {\n this.min = min\n this.max = max\n }\n\n if (this.min !== undefined && this.index < this.min) {\n this.message = 'Index out of range (' + this.index + ' < ' + this.min + ')'\n } else if (this.max !== undefined && this.index >= this.max) {\n this.message = 'Index out of range (' + this.index + ' > ' + (this.max - 1) + ')'\n } else {\n this.message = 'Index out of range (' + this.index + ')'\n }\n\n this.stack = (new Error()).stack\n}\n\nIndexError.prototype = new RangeError()\nIndexError.prototype.constructor = RangeError\nIndexError.prototype.name = 'IndexError'\nIndexError.prototype.isIndexError = true\n","import { isInteger } from './number.js'\nimport { isNumber } from './is.js'\nimport { format } from './string.js'\nimport { DimensionError } from '../error/DimensionError.js'\nimport { IndexError } from '../error/IndexError.js'\n\n/**\n * Calculate the size of a multi dimensional array.\n * This function checks the size of the first entry, it does not validate\n * whether all dimensions match. (use function `validate` for that)\n * @param {Array} x\n * @Return {Number[]} size\n */\nexport function arraySize (x) {\n const s = []\n\n while (Array.isArray(x)) {\n s.push(x.length)\n x = x[0]\n }\n\n return s\n}\n\n/**\n * Recursively validate whether each element in a multi dimensional array\n * has a size corresponding to the provided size array.\n * @param {Array} array Array to be validated\n * @param {number[]} size Array with the size of each dimension\n * @param {number} dim Current dimension\n * @throws DimensionError\n * @private\n */\nfunction _validate (array, size, dim) {\n let i\n const len = array.length\n\n if (len !== size[dim]) {\n throw new DimensionError(len, size[dim])\n }\n\n if (dim < size.length - 1) {\n // recursively validate each child array\n const dimNext = dim + 1\n for (i = 0; i < len; i++) {\n const child = array[i]\n if (!Array.isArray(child)) {\n throw new DimensionError(size.length - 1, size.length, '<')\n }\n _validate(array[i], size, dimNext)\n }\n } else {\n // last dimension. none of the childs may be an array\n for (i = 0; i < len; i++) {\n if (Array.isArray(array[i])) {\n throw new DimensionError(size.length + 1, size.length, '>')\n }\n }\n }\n}\n\n/**\n * Validate whether each element in a multi dimensional array has\n * a size corresponding to the provided size array.\n * @param {Array} array Array to be validated\n * @param {number[]} size Array with the size of each dimension\n * @throws DimensionError\n */\nexport function validate (array, size) {\n const isScalar = (size.length === 0)\n if (isScalar) {\n // scalar\n if (Array.isArray(array)) {\n throw new DimensionError(array.length, 0)\n }\n } else {\n // array\n _validate(array, size, 0)\n }\n}\n\n/**\n * Test whether index is an integer number with index >= 0 and index < length\n * when length is provided\n * @param {number} index Zero-based index\n * @param {number} [length] Length of the array\n */\nexport function validateIndex (index, length) {\n if (!isNumber(index) || !isInteger(index)) {\n throw new TypeError('Index must be an integer (value: ' + index + ')')\n }\n if (index < 0 || (typeof length === 'number' && index >= length)) {\n throw new IndexError(index, length)\n }\n}\n\n/**\n * Resize a multi dimensional array. The resized array is returned.\n * @param {Array} array Array to be resized\n * @param {Array.} size Array with the size of each dimension\n * @param {*} [defaultValue=0] Value to be filled in in new entries,\n * zero by default. Specify for example `null`,\n * to clearly see entries that are not explicitly\n * set.\n * @return {Array} array The resized array\n */\nexport function resize (array, size, defaultValue) {\n // TODO: add support for scalars, having size=[] ?\n\n // check the type of the arguments\n if (!Array.isArray(array) || !Array.isArray(size)) {\n throw new TypeError('Array expected')\n }\n if (size.length === 0) {\n throw new Error('Resizing to scalar is not supported')\n }\n\n // check whether size contains positive integers\n size.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n })\n\n // recursively resize the array\n const _defaultValue = (defaultValue !== undefined) ? defaultValue : 0\n _resize(array, size, 0, _defaultValue)\n\n return array\n}\n\n/**\n * Recursively resize a multi dimensional array\n * @param {Array} array Array to be resized\n * @param {number[]} size Array with the size of each dimension\n * @param {number} dim Current dimension\n * @param {*} [defaultValue] Value to be filled in in new entries,\n * undefined by default.\n * @private\n */\nfunction _resize (array, size, dim, defaultValue) {\n let i\n let elem\n const oldLen = array.length\n const newLen = size[dim]\n const minLen = Math.min(oldLen, newLen)\n\n // apply new length\n array.length = newLen\n\n if (dim < size.length - 1) {\n // non-last dimension\n const dimNext = dim + 1\n\n // resize existing child arrays\n for (i = 0; i < minLen; i++) {\n // resize child array\n elem = array[i]\n if (!Array.isArray(elem)) {\n elem = [elem] // add a dimension\n array[i] = elem\n }\n _resize(elem, size, dimNext, defaultValue)\n }\n\n // create new child arrays\n for (i = minLen; i < newLen; i++) {\n // get child array\n elem = []\n array[i] = elem\n\n // resize new child array\n _resize(elem, size, dimNext, defaultValue)\n }\n } else {\n // last dimension\n\n // remove dimensions of existing values\n for (i = 0; i < minLen; i++) {\n while (Array.isArray(array[i])) {\n array[i] = array[i][0]\n }\n }\n\n // fill new elements with the default value\n for (i = minLen; i < newLen; i++) {\n array[i] = defaultValue\n }\n }\n}\n\n/**\n * Re-shape a multi dimensional array to fit the specified dimensions\n * @param {Array} array Array to be reshaped\n * @param {Array.} sizes List of sizes for each dimension\n * @returns {Array} Array whose data has been formatted to fit the\n * specified dimensions\n *\n * @throws {DimensionError} If the product of the new dimension sizes does\n * not equal that of the old ones\n */\nexport function reshape (array, sizes) {\n const flatArray = flatten(array)\n let newArray\n\n function product (arr) {\n return arr.reduce((prev, curr) => prev * curr)\n }\n\n if (!Array.isArray(array) || !Array.isArray(sizes)) {\n throw new TypeError('Array expected')\n }\n\n if (sizes.length === 0) {\n throw new DimensionError(0, product(arraySize(array)), '!=')\n }\n\n let totalSize = 1\n for (let sizeIndex = 0; sizeIndex < sizes.length; sizeIndex++) {\n totalSize *= sizes[sizeIndex]\n }\n\n if (flatArray.length !== totalSize) {\n throw new DimensionError(\n product(sizes),\n product(arraySize(array)),\n '!='\n )\n }\n\n try {\n newArray = _reshape(flatArray, sizes)\n } catch (e) {\n if (e instanceof DimensionError) {\n throw new DimensionError(\n product(sizes),\n product(arraySize(array)),\n '!='\n )\n }\n throw e\n }\n\n return newArray\n}\n\n/**\n * Iteratively re-shape a multi dimensional array to fit the specified dimensions\n * @param {Array} array Array to be reshaped\n * @param {Array.} sizes List of sizes for each dimension\n * @returns {Array} Array whose data has been formatted to fit the\n * specified dimensions\n */\n\nfunction _reshape (array, sizes) {\n // testing if there are enough elements for the requested shape\n let tmpArray = array\n let tmpArray2\n // for each dimensions starting by the last one and ignoring the first one\n for (let sizeIndex = sizes.length - 1; sizeIndex > 0; sizeIndex--) {\n const size = sizes[sizeIndex]\n tmpArray2 = []\n\n // aggregate the elements of the current tmpArray in elements of the requested size\n const length = tmpArray.length / size\n for (let i = 0; i < length; i++) {\n tmpArray2.push(tmpArray.slice(i * size, (i + 1) * size))\n }\n // set it as the new tmpArray for the next loop turn or for return\n tmpArray = tmpArray2\n }\n\n return tmpArray\n}\n\n/**\n * Squeeze a multi dimensional array\n * @param {Array} array\n * @param {Array} [size]\n * @returns {Array} returns the array itself\n */\nexport function squeeze (array, size) {\n const s = size || arraySize(array)\n\n // squeeze outer dimensions\n while (Array.isArray(array) && array.length === 1) {\n array = array[0]\n s.shift()\n }\n\n // find the first dimension to be squeezed\n let dims = s.length\n while (s[dims - 1] === 1) {\n dims--\n }\n\n // squeeze inner dimensions\n if (dims < s.length) {\n array = _squeeze(array, dims, 0)\n s.length = dims\n }\n\n return array\n}\n\n/**\n * Recursively squeeze a multi dimensional array\n * @param {Array} array\n * @param {number} dims Required number of dimensions\n * @param {number} dim Current dimension\n * @returns {Array | *} Returns the squeezed array\n * @private\n */\nfunction _squeeze (array, dims, dim) {\n let i, ii\n\n if (dim < dims) {\n const next = dim + 1\n for (i = 0, ii = array.length; i < ii; i++) {\n array[i] = _squeeze(array[i], dims, next)\n }\n } else {\n while (Array.isArray(array)) {\n array = array[0]\n }\n }\n\n return array\n}\n\n/**\n * Unsqueeze a multi dimensional array: add dimensions when missing\n *\n * Paramter `size` will be mutated to match the new, unqueezed matrix size.\n *\n * @param {Array} array\n * @param {number} dims Desired number of dimensions of the array\n * @param {number} [outer] Number of outer dimensions to be added\n * @param {Array} [size] Current size of array.\n * @returns {Array} returns the array itself\n * @private\n */\nexport function unsqueeze (array, dims, outer, size) {\n const s = size || arraySize(array)\n\n // unsqueeze outer dimensions\n if (outer) {\n for (let i = 0; i < outer; i++) {\n array = [array]\n s.unshift(1)\n }\n }\n\n // unsqueeze inner dimensions\n array = _unsqueeze(array, dims, 0)\n while (s.length < dims) {\n s.push(1)\n }\n\n return array\n}\n\n/**\n * Recursively unsqueeze a multi dimensional array\n * @param {Array} array\n * @param {number} dims Required number of dimensions\n * @param {number} dim Current dimension\n * @returns {Array | *} Returns the squeezed array\n * @private\n */\nfunction _unsqueeze (array, dims, dim) {\n let i, ii\n\n if (Array.isArray(array)) {\n const next = dim + 1\n for (i = 0, ii = array.length; i < ii; i++) {\n array[i] = _unsqueeze(array[i], dims, next)\n }\n } else {\n for (let d = dim; d < dims; d++) {\n array = [array]\n }\n }\n\n return array\n}\n/**\n * Flatten a multi dimensional array, put all elements in a one dimensional\n * array\n * @param {Array} array A multi dimensional array\n * @return {Array} The flattened array (1 dimensional)\n */\nexport function flatten (array) {\n if (!Array.isArray(array)) {\n // if not an array, return as is\n return array\n }\n const flat = []\n\n array.forEach(function callback (value) {\n if (Array.isArray(value)) {\n value.forEach(callback) // traverse through sub-arrays recursively\n } else {\n flat.push(value)\n }\n })\n\n return flat\n}\n\n/**\n * A safe map\n * @param {Array} array\n * @param {function} callback\n */\nexport function map (array, callback) {\n return Array.prototype.map.call(array, callback)\n}\n\n/**\n * A safe forEach\n * @param {Array} array\n * @param {function} callback\n */\nexport function forEach (array, callback) {\n Array.prototype.forEach.call(array, callback)\n}\n\n/**\n * A safe filter\n * @param {Array} array\n * @param {function} callback\n */\nexport function filter (array, callback) {\n if (arraySize(array).length !== 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n\n return Array.prototype.filter.call(array, callback)\n}\n\n/**\n * Filter values in a callback given a regular expression\n * @param {Array} array\n * @param {RegExp} regexp\n * @return {Array} Returns the filtered array\n * @private\n */\nexport function filterRegExp (array, regexp) {\n if (arraySize(array).length !== 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n\n return Array.prototype.filter.call(array, (entry) => regexp.test(entry))\n}\n\n/**\n * A safe join\n * @param {Array} array\n * @param {string} separator\n */\nexport function join (array, separator) {\n return Array.prototype.join.call(array, separator)\n}\n\n/**\n * Assign a numeric identifier to every element of a sorted array\n * @param {Array} a An array\n * @return {Array} An array of objects containing the original value and its identifier\n */\nexport function identify (a) {\n if (!Array.isArray(a)) {\n throw new TypeError('Array input expected')\n }\n\n if (a.length === 0) {\n return a\n }\n\n const b = []\n let count = 0\n b[0] = { value: a[0], identifier: 0 }\n for (let i = 1; i < a.length; i++) {\n if (a[i] === a[i - 1]) {\n count++\n } else {\n count = 0\n }\n b.push({ value: a[i], identifier: count })\n }\n return b\n}\n\n/**\n * Remove the numeric identifier from the elements\n * @param {array} a An array\n * @return {array} An array of values without identifiers\n */\nexport function generalize (a) {\n if (!Array.isArray(a)) {\n throw new TypeError('Array input expected')\n }\n\n if (a.length === 0) {\n return a\n }\n\n const b = []\n for (let i = 0; i < a.length; i++) {\n b.push(a[i].value)\n }\n return b\n}\n\n/**\n * Check the datatype of a given object\n * This is a low level implementation that should only be used by\n * parent Matrix classes such as SparseMatrix or DenseMatrix\n * This method does not validate Array Matrix shape\n * @param {Array} array\n * @param {function} typeOf Callback function to use to determine the type of a value\n * @return string\n */\nexport function getArrayDataType (array, typeOf) {\n let type // to hold type info\n let length = 0 // to hold length value to ensure it has consistent sizes\n\n for (let i = 0; i < array.length; i++) {\n const item = array[i]\n const isArray = Array.isArray(item)\n\n // Saving the target matrix row size\n if (i === 0 && isArray) {\n length = item.length\n }\n\n // If the current item is an array but the length does not equal the targetVectorSize\n if (isArray && item.length !== length) {\n return undefined\n }\n\n const itemType = isArray\n ? getArrayDataType(item, typeOf) // recurse into a nested array\n : typeOf(item)\n\n if (type === undefined) {\n type = itemType // first item\n } else if (type !== itemType) {\n return 'mixed'\n } else {\n // we're good, everything has the same type so far\n }\n }\n\n return type\n}\n\n/**\n * Return the last item from an array\n * @param array\n * @returns {*}\n */\nexport function last (array) {\n return array[array.length - 1]\n}\n\n/**\n * Get all but the last element of array.\n */\nexport function initial (array) {\n return array.slice(0, array.length - 1)\n}\n\n/**\n * Test whether an array or string contains an item\n * @param {Array | string} array\n * @param {*} item\n * @return {boolean}\n */\nexport function contains (array, item) {\n return array.indexOf(item) !== -1\n}\n","import { isBigNumber } from './is.js'\n\n/**\n * Clone an object\n *\n * clone(x)\n *\n * Can clone any primitive type, array, and object.\n * If x has a function clone, this function will be invoked to clone the object.\n *\n * @param {*} x\n * @return {*} clone\n */\nexport function clone (x) {\n const type = typeof x\n\n // immutable primitive types\n if (type === 'number' || type === 'string' || type === 'boolean' ||\n x === null || x === undefined) {\n return x\n }\n\n // use clone function of the object when available\n if (typeof x.clone === 'function') {\n return x.clone()\n }\n\n // array\n if (Array.isArray(x)) {\n return x.map(function (value) {\n return clone(value)\n })\n }\n\n if (x instanceof Date) return new Date(x.valueOf())\n if (isBigNumber(x)) return x // bignumbers are immutable\n if (x instanceof RegExp) throw new TypeError('Cannot clone ' + x) // TODO: clone a RegExp\n\n // object\n return mapObject(x, clone)\n}\n\n/**\n * Apply map to all properties of an object\n * @param {Object} object\n * @param {function} callback\n * @return {Object} Returns a copy of the object with mapped properties\n */\nexport function mapObject (object, callback) {\n const clone = {}\n\n for (const key in object) {\n if (hasOwnProperty(object, key)) {\n clone[key] = callback(object[key])\n }\n }\n\n return clone\n}\n\n/**\n * Extend object a with the properties of object b\n * @param {Object} a\n * @param {Object} b\n * @return {Object} a\n */\nexport function extend (a, b) {\n for (const prop in b) {\n if (hasOwnProperty(b, prop)) {\n a[prop] = b[prop]\n }\n }\n return a\n}\n\n/**\n * Deep extend an object a with the properties of object b\n * @param {Object} a\n * @param {Object} b\n * @returns {Object}\n */\nexport function deepExtend (a, b) {\n // TODO: add support for Arrays to deepExtend\n if (Array.isArray(b)) {\n throw new TypeError('Arrays are not supported by deepExtend')\n }\n\n for (const prop in b) {\n // We check against prop not being in Object.prototype or Function.prototype\n // to prevent polluting for example Object.__proto__.\n if (hasOwnProperty(b, prop) && !(prop in Object.prototype) && !(prop in Function.prototype)) {\n if (b[prop] && b[prop].constructor === Object) {\n if (a[prop] === undefined) {\n a[prop] = {}\n }\n if (a[prop] && a[prop].constructor === Object) {\n deepExtend(a[prop], b[prop])\n } else {\n a[prop] = b[prop]\n }\n } else if (Array.isArray(b[prop])) {\n throw new TypeError('Arrays are not supported by deepExtend')\n } else {\n a[prop] = b[prop]\n }\n }\n }\n return a\n}\n\n/**\n * Deep test equality of all fields in two pairs of arrays or objects.\n * Compares values and functions strictly (ie. 2 is not the same as '2').\n * @param {Array | Object} a\n * @param {Array | Object} b\n * @returns {boolean}\n */\nexport function deepStrictEqual (a, b) {\n let prop, i, len\n if (Array.isArray(a)) {\n if (!Array.isArray(b)) {\n return false\n }\n\n if (a.length !== b.length) {\n return false\n }\n\n for (i = 0, len = a.length; i < len; i++) {\n if (!deepStrictEqual(a[i], b[i])) {\n return false\n }\n }\n return true\n } else if (typeof a === 'function') {\n return (a === b)\n } else if (a instanceof Object) {\n if (Array.isArray(b) || !(b instanceof Object)) {\n return false\n }\n\n for (prop in a) {\n // noinspection JSUnfilteredForInLoop\n if (!(prop in b) || !deepStrictEqual(a[prop], b[prop])) {\n return false\n }\n }\n for (prop in b) {\n // noinspection JSUnfilteredForInLoop\n if (!(prop in a) || !deepStrictEqual(a[prop], b[prop])) {\n return false\n }\n }\n return true\n } else {\n return (a === b)\n }\n}\n\n/**\n * Recursively flatten a nested object.\n * @param {Object} nestedObject\n * @return {Object} Returns the flattened object\n */\nexport function deepFlatten (nestedObject) {\n const flattenedObject = {}\n\n _deepFlatten(nestedObject, flattenedObject)\n\n return flattenedObject\n}\n\n// helper function used by deepFlatten\nfunction _deepFlatten (nestedObject, flattenedObject) {\n for (const prop in nestedObject) {\n if (hasOwnProperty(nestedObject, prop)) {\n const value = nestedObject[prop]\n if (typeof value === 'object' && value !== null) {\n _deepFlatten(value, flattenedObject)\n } else {\n flattenedObject[prop] = value\n }\n }\n }\n}\n\n/**\n * Test whether the current JavaScript engine supports Object.defineProperty\n * @returns {boolean} returns true if supported\n */\nexport function canDefineProperty () {\n // test needed for broken IE8 implementation\n try {\n if (Object.defineProperty) {\n Object.defineProperty({}, 'x', { get: function () {} })\n return true\n }\n } catch (e) {}\n\n return false\n}\n\n/**\n * Attach a lazy loading property to a constant.\n * The given function `fn` is called once when the property is first requested.\n *\n * @param {Object} object Object where to add the property\n * @param {string} prop Property name\n * @param {Function} valueResolver Function returning the property value. Called\n * without arguments.\n */\nexport function lazy (object, prop, valueResolver) {\n let _uninitialized = true\n let _value\n\n Object.defineProperty(object, prop, {\n get: function () {\n if (_uninitialized) {\n _value = valueResolver()\n _uninitialized = false\n }\n return _value\n },\n\n set: function (value) {\n _value = value\n _uninitialized = false\n },\n\n configurable: true,\n enumerable: true\n })\n}\n\n/**\n * Traverse a path into an object.\n * When a namespace is missing, it will be created\n * @param {Object} object\n * @param {string | string[]} path A dot separated string like 'name.space'\n * @return {Object} Returns the object at the end of the path\n */\nexport function traverse (object, path) {\n if (path && typeof path === 'string') {\n return traverse(object, path.split('.'))\n }\n\n let obj = object\n\n if (path) {\n for (let i = 0; i < path.length; i++) {\n const key = path[i]\n if (!(key in obj)) {\n obj[key] = {}\n }\n obj = obj[key]\n }\n }\n\n return obj\n}\n\n/**\n * A safe hasOwnProperty\n * @param {Object} object\n * @param {string} property\n */\nexport function hasOwnProperty (object, property) {\n return object && Object.hasOwnProperty.call(object, property)\n}\n\n/**\n * Test whether an object is a factory. a factory has fields:\n *\n * - factory: function (type: Object, config: Object, load: function, typed: function [, math: Object]) (required)\n * - name: string (optional)\n * - path: string A dot separated path (optional)\n * - math: boolean If true (false by default), the math namespace is passed\n * as fifth argument of the factory function\n *\n * @param {*} object\n * @returns {boolean}\n */\nexport function isLegacyFactory (object) {\n return object && typeof object.factory === 'function'\n}\n\n/**\n * Get a nested property from an object\n * @param {Object} object\n * @param {string | string[]} path\n * @returns {Object}\n */\nexport function get (object, path) {\n if (typeof path === 'string') {\n if (isPath(path)) {\n return get(object, path.split('.'))\n } else {\n return object[path]\n }\n }\n\n let child = object\n\n for (let i = 0; i < path.length; i++) {\n const key = path[i]\n child = child ? child[key] : undefined\n }\n\n return child\n}\n\n/**\n * Set a nested property in an object\n * Mutates the object itself\n * If the path doesn't exist, it will be created\n * @param {Object} object\n * @param {string | string[]} path\n * @param {*} value\n * @returns {Object}\n */\nexport function set (object, path, value) {\n if (typeof path === 'string') {\n if (isPath(path)) {\n return set(object, path.split('.'), value)\n } else {\n object[path] = value\n return object\n }\n }\n\n let child = object\n for (let i = 0; i < path.length - 1; i++) {\n const key = path[i]\n if (child[key] === undefined) {\n child[key] = {}\n }\n child = child[key]\n }\n\n if (path.length > 0) {\n const lastKey = path[path.length - 1]\n child[lastKey] = value\n }\n\n return object\n}\n\n/**\n * Create an object composed of the picked object properties\n * @param {Object} object\n * @param {string[]} properties\n * @param {function} [transform] Optional value to transform a value when picking it\n * @return {Object}\n */\nexport function pick (object, properties, transform) {\n const copy = {}\n\n for (let i = 0; i < properties.length; i++) {\n const key = properties[i]\n const value = get(object, key)\n if (value !== undefined) {\n set(copy, key, transform ? transform(value, key) : value)\n }\n }\n\n return copy\n}\n\n/**\n * Shallow version of pick, creating an object composed of the picked object properties\n * but not for nested properties\n * @param {Object} object\n * @param {string[]} properties\n * @return {Object}\n */\nexport function pickShallow (object, properties) {\n const copy = {}\n\n for (let i = 0; i < properties.length; i++) {\n const key = properties[i]\n const value = object[key]\n if (value !== undefined) {\n copy[key] = value\n }\n }\n\n return copy\n}\n\nexport function values (object) {\n return Object.keys(object).map(key => object[key])\n}\n\n// helper function to test whether a string contains a path like 'user.name'\nfunction isPath (str) {\n return str.indexOf('.') !== -1\n}\n","import { contains } from './array.js'\nimport { pickShallow } from './object.js'\n\n/**\n * Create a factory function, which can be used to inject dependencies.\n *\n * The created functions are memoized, a consecutive call of the factory\n * with the exact same inputs will return the same function instance.\n * The memoized cache is exposed on `factory.cache` and can be cleared\n * if needed.\n *\n * Example:\n *\n * const name = 'log'\n * const dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n *\n * export const createLog = factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n * // ... create the function log here and return it\n * }\n *\n * @param {string} name Name of the function to be created\n * @param {string[]} dependencies The names of all required dependencies\n * @param {function} create Callback function called with an object with all dependencies\n * @param {Object} [meta] Optional object with meta information that will be attached\n * to the created factory function as property `meta`.\n * @returns {function}\n */\nexport function factory (name, dependencies, create, meta) {\n function assertAndCreate (scope) {\n // we only pass the requested dependencies to the factory function\n // to prevent functions to rely on dependencies that are not explicitly\n // requested.\n const deps = pickShallow(scope, dependencies.map(stripOptionalNotation))\n\n assertDependencies(name, dependencies, scope)\n\n return create(deps)\n }\n\n assertAndCreate.isFactory = true\n assertAndCreate.fn = name\n assertAndCreate.dependencies = dependencies.slice().sort()\n if (meta) {\n assertAndCreate.meta = meta\n }\n\n return assertAndCreate\n}\n\n/**\n * Sort all factories such that when loading in order, the dependencies are resolved.\n *\n * @param {Array} factories\n * @returns {Array} Returns a new array with the sorted factories.\n */\nexport function sortFactories (factories) {\n const factoriesByName = {}\n\n factories.forEach(factory => {\n factoriesByName[factory.fn] = factory\n })\n\n function containsDependency (factory, dependency) {\n // TODO: detect circular references\n if (isFactory(factory)) {\n if (contains(factory.dependencies, dependency.fn || dependency.name)) {\n return true\n }\n\n if (factory.dependencies.some(d => containsDependency(factoriesByName[d], dependency))) {\n return true\n }\n }\n\n return false\n }\n\n const sorted = []\n\n function addFactory (factory) {\n let index = 0\n while (index < sorted.length && !containsDependency(sorted[index], factory)) {\n index++\n }\n\n sorted.splice(index, 0, factory)\n }\n\n // sort regular factory functions\n factories\n .filter(isFactory)\n .forEach(addFactory)\n\n // sort legacy factory functions AFTER the regular factory functions\n factories\n .filter(factory => !isFactory(factory))\n .forEach(addFactory)\n\n return sorted\n}\n\n// TODO: comment or cleanup if unused in the end\nexport function create (factories, scope = {}) {\n sortFactories(factories)\n .forEach(factory => factory(scope))\n\n return scope\n}\n\n/**\n * Test whether an object is a factory. This is the case when it has\n * properties name, dependencies, and a function create.\n * @param {*} obj\n * @returns {boolean}\n */\nexport function isFactory (obj) {\n return typeof obj === 'function' &&\n typeof obj.fn === 'string' &&\n Array.isArray(obj.dependencies)\n}\n\n/**\n * Assert that all dependencies of a list with dependencies are available in the provided scope.\n *\n * Will throw an exception when there are dependencies missing.\n *\n * @param {string} name Name for the function to be created. Used to generate a useful error message\n * @param {string[]} dependencies\n * @param {Object} scope\n */\nexport function assertDependencies (name, dependencies, scope) {\n const allDefined = dependencies\n .filter(dependency => !isOptionalDependency(dependency)) // filter optionals\n .every(dependency => scope[dependency] !== undefined)\n\n if (!allDefined) {\n const missingDependencies = dependencies.filter(dependency => scope[dependency] === undefined)\n\n // TODO: create a custom error class for this, a MathjsError or something like that\n throw new Error(`Cannot create function \"${name}\", ` +\n `some dependencies are missing: ${missingDependencies.map(d => `\"${d}\"`).join(', ')}.`)\n }\n}\n\nexport function isOptionalDependency (dependency) {\n return dependency && dependency[0] === '?'\n}\n\nexport function stripOptionalNotation (dependency) {\n return dependency && dependency[0] === '?'\n ? dependency.slice(1)\n : dependency\n}\n","/**\n * Create a typed-function which checks the types of the arguments and\n * can match them against multiple provided signatures. The typed-function\n * automatically converts inputs in order to find a matching signature.\n * Typed functions throw informative errors in case of wrong input arguments.\n *\n * See the library [typed-function](https://github.com/josdejong/typed-function)\n * for detailed documentation.\n *\n * Syntax:\n *\n * math.typed(name, signatures) : function\n * math.typed(signatures) : function\n *\n * Examples:\n *\n * // create a typed function with multiple types per argument (type union)\n * const fn2 = typed({\n * 'number | boolean': function (b) {\n * return 'b is a number or boolean'\n * },\n * 'string, number | boolean': function (a, b) {\n * return 'a is a string, b is a number or boolean'\n * }\n * })\n *\n * // create a typed function with an any type argument\n * const log = typed({\n * 'string, any': function (event, data) {\n * console.log('event: ' + event + ', data: ' + JSON.stringify(data))\n * }\n * })\n *\n * @param {string} [name] Optional name for the typed-function\n * @param {Object} signatures Object with one or multiple function signatures\n * @returns {function} The created typed-function.\n */\n\nimport {\n isAccessorNode,\n isArray,\n isArrayNode,\n isAssignmentNode,\n isBigNumber,\n isBlockNode,\n isBoolean,\n isChain,\n isComplex,\n isConditionalNode,\n isConstantNode,\n isDate,\n isDenseMatrix,\n isFraction,\n isFunction,\n isFunctionAssignmentNode,\n isFunctionNode,\n isHelp,\n isIndex,\n isIndexNode,\n isMatrix,\n isNode,\n isNull,\n isNumber,\n isObject,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRange,\n isRangeNode,\n isRegExp,\n isResultSet,\n isSparseMatrix,\n isString,\n isSymbolNode,\n isUndefined,\n isUnit\n} from '../../utils/is.js'\nimport typedFunction from 'typed-function'\nimport { digits } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\n// returns a new instance of typed-function\nlet _createTyped = function () {\n // initially, return the original instance of typed-function\n // consecutively, return a new instance from typed.create.\n _createTyped = typedFunction.create\n return typedFunction\n}\n\nconst dependencies = [\n '?BigNumber',\n '?Complex',\n '?DenseMatrix',\n '?Fraction'\n]\n\n/**\n * Factory function for creating a new typed instance\n * @param {Object} dependencies Object with data types like Complex and BigNumber\n * @returns {Function}\n */\nexport const createTyped = /* #__PURE__ */ factory('typed', dependencies, function createTyped ({ BigNumber, Complex, DenseMatrix, Fraction }) {\n // TODO: typed-function must be able to silently ignore signatures with unknown data types\n\n // get a new instance of typed-function\n const typed = _createTyped()\n\n // define all types. The order of the types determines in which order function\n // arguments are type-checked (so for performance it's important to put the\n // most used types first).\n typed.types = [\n { name: 'number', test: isNumber },\n { name: 'Complex', test: isComplex },\n { name: 'BigNumber', test: isBigNumber },\n { name: 'Fraction', test: isFraction },\n { name: 'Unit', test: isUnit },\n { name: 'string', test: isString },\n { name: 'Chain', test: isChain },\n { name: 'Array', test: isArray },\n { name: 'Matrix', test: isMatrix },\n { name: 'DenseMatrix', test: isDenseMatrix },\n { name: 'SparseMatrix', test: isSparseMatrix },\n { name: 'Range', test: isRange },\n { name: 'Index', test: isIndex },\n { name: 'boolean', test: isBoolean },\n { name: 'ResultSet', test: isResultSet },\n { name: 'Help', test: isHelp },\n { name: 'function', test: isFunction },\n { name: 'Date', test: isDate },\n { name: 'RegExp', test: isRegExp },\n { name: 'null', test: isNull },\n { name: 'undefined', test: isUndefined },\n\n { name: 'AccessorNode', test: isAccessorNode },\n { name: 'ArrayNode', test: isArrayNode },\n { name: 'AssignmentNode', test: isAssignmentNode },\n { name: 'BlockNode', test: isBlockNode },\n { name: 'ConditionalNode', test: isConditionalNode },\n { name: 'ConstantNode', test: isConstantNode },\n { name: 'FunctionNode', test: isFunctionNode },\n { name: 'FunctionAssignmentNode', test: isFunctionAssignmentNode },\n { name: 'IndexNode', test: isIndexNode },\n { name: 'Node', test: isNode },\n { name: 'ObjectNode', test: isObjectNode },\n { name: 'OperatorNode', test: isOperatorNode },\n { name: 'ParenthesisNode', test: isParenthesisNode },\n { name: 'RangeNode', test: isRangeNode },\n { name: 'SymbolNode', test: isSymbolNode },\n\n { name: 'Object', test: isObject } // order 'Object' last, it matches on other classes too\n ]\n\n typed.conversions = [\n {\n from: 'number',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n // note: conversion from number to BigNumber can fail if x has >15 digits\n if (digits(x) > 15) {\n throw new TypeError('Cannot implicitly convert a number with >15 significant digits to BigNumber ' +\n '(value: ' + x + '). ' +\n 'Use function bignumber(x) to convert to BigNumber.')\n }\n return new BigNumber(x)\n }\n }, {\n from: 'number',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x, 0)\n }\n }, {\n from: 'number',\n to: 'string',\n convert: function (x) {\n return x + ''\n }\n }, {\n from: 'BigNumber',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x.toNumber(), 0)\n }\n }, {\n from: 'Fraction',\n to: 'BigNumber',\n convert: function (x) {\n throw new TypeError('Cannot implicitly convert a Fraction to BigNumber or vice versa. ' +\n 'Use function bignumber(x) to convert to BigNumber or fraction(x) to convert to Fraction.')\n }\n }, {\n from: 'Fraction',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n return new Complex(x.valueOf(), 0)\n }\n }, {\n from: 'number',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n const f = new Fraction(x)\n if (f.valueOf() !== x) {\n throw new TypeError('Cannot implicitly convert a number to a Fraction when there will be a loss of precision ' +\n '(value: ' + x + '). ' +\n 'Use function fraction(x) to convert to Fraction.')\n }\n return f\n }\n }, {\n // FIXME: add conversion from Fraction to number, for example for `sqrt(fraction(1,3))`\n // from: 'Fraction',\n // to: 'number',\n // convert: function (x) {\n // return x.valueOf()\n // }\n // }, {\n from: 'string',\n to: 'number',\n convert: function (x) {\n const n = Number(x)\n if (isNaN(n)) {\n throw new Error('Cannot convert \"' + x + '\" to a number')\n }\n return n\n }\n }, {\n from: 'string',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n try {\n return new BigNumber(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to BigNumber')\n }\n }\n }, {\n from: 'string',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n try {\n return new Fraction(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to Fraction')\n }\n }\n }, {\n from: 'string',\n to: 'Complex',\n convert: function (x) {\n if (!Complex) {\n throwNoComplex(x)\n }\n\n try {\n return new Complex(x)\n } catch (err) {\n throw new Error('Cannot convert \"' + x + '\" to Complex')\n }\n }\n }, {\n from: 'boolean',\n to: 'number',\n convert: function (x) {\n return +x\n }\n }, {\n from: 'boolean',\n to: 'BigNumber',\n convert: function (x) {\n if (!BigNumber) {\n throwNoBignumber(x)\n }\n\n return new BigNumber(+x)\n }\n }, {\n from: 'boolean',\n to: 'Fraction',\n convert: function (x) {\n if (!Fraction) {\n throwNoFraction(x)\n }\n\n return new Fraction(+x)\n }\n }, {\n from: 'boolean',\n to: 'string',\n convert: function (x) {\n return String(x)\n }\n }, {\n from: 'Array',\n to: 'Matrix',\n convert: function (array) {\n if (!DenseMatrix) {\n throwNoMatrix()\n }\n\n return new DenseMatrix(array)\n }\n }, {\n from: 'Matrix',\n to: 'Array',\n convert: function (matrix) {\n return matrix.valueOf()\n }\n }\n ]\n\n return typed\n})\n\nfunction throwNoBignumber (x) {\n throw new Error(`Cannot convert value ${x} into a BigNumber: no class 'BigNumber' provided`)\n}\n\nfunction throwNoComplex (x) {\n throw new Error(`Cannot convert value ${x} into a Complex number: no class 'Complex' provided`)\n}\n\nfunction throwNoMatrix () {\n throw new Error('Cannot convert array into a Matrix: no class \\'DenseMatrix\\' provided')\n}\n\nfunction throwNoFraction (x) {\n throw new Error(`Cannot convert value ${x} into a Fraction, no class 'Fraction' provided.`)\n}\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'ResultSet'\nconst dependencies = []\n\nexport const createResultSet = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * A ResultSet contains a list or results\n * @class ResultSet\n * @param {Array} entries\n * @constructor ResultSet\n */\n function ResultSet (entries) {\n if (!(this instanceof ResultSet)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.entries = entries || []\n }\n\n /**\n * Attach type information\n */\n ResultSet.prototype.type = 'ResultSet'\n ResultSet.prototype.isResultSet = true\n\n /**\n * Returns the array with results hold by this ResultSet\n * @memberof ResultSet\n * @returns {Array} entries\n */\n ResultSet.prototype.valueOf = function () {\n return this.entries\n }\n\n /**\n * Returns the stringified results of the ResultSet\n * @memberof ResultSet\n * @returns {string} string\n */\n ResultSet.prototype.toString = function () {\n return '[' + this.entries.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the ResultSet\n * @memberof ResultSet\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"ResultSet\", \"entries\": [...]}`\n */\n ResultSet.prototype.toJSON = function () {\n return {\n mathjs: 'ResultSet',\n entries: this.entries\n }\n }\n\n /**\n * Instantiate a ResultSet from a JSON object\n * @memberof ResultSet\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"ResultSet\", \"entries\": [...]}`\n * @return {ResultSet}\n */\n ResultSet.fromJSON = function (json) {\n return new ResultSet(json.entries)\n }\n\n return ResultSet\n}, { isClass: true })\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'BigNumber'\nconst dependencies = ['?on', 'config']\n\nexport const createBigNumberClass = /* #__PURE__ */ factory(name, dependencies, ({ on, config }) => {\n const EUCLID = 9 // Use euclidian division for mod calculation\n const BigNumber = Decimal.clone({ precision: config.precision, modulo: EUCLID })\n\n /**\n * Attach type information\n */\n BigNumber.prototype.type = 'BigNumber'\n BigNumber.prototype.isBigNumber = true\n\n /**\n * Get a JSON representation of a BigNumber containing\n * type information\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"BigNumber\", \"value\": \"0.2\"}`\n */\n BigNumber.prototype.toJSON = function () {\n return {\n mathjs: 'BigNumber',\n value: this.toString()\n }\n }\n\n /**\n * Instantiate a BigNumber from a JSON object\n * @param {Object} json a JSON object structured as:\n * `{\"mathjs\": \"BigNumber\", \"value\": \"0.2\"}`\n * @return {BigNumber}\n */\n BigNumber.fromJSON = function (json) {\n return new BigNumber(json.value)\n }\n\n if (on) {\n // listen for changed in the configuration, automatically apply changed precision\n on('config', function (curr, prev) {\n if (curr.precision !== prev.precision) {\n BigNumber.config({ precision: curr.precision })\n }\n })\n }\n\n return BigNumber\n}, { isClass: true })\n","import Complex from 'complex.js'\nimport { format } from '../../utils/number.js'\nimport { isNumber, isUnit } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Complex'\nconst dependencies = []\n\nexport const createComplexClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Attach type information\n */\n Complex.prototype.type = 'Complex'\n Complex.prototype.isComplex = true\n\n /**\n * Get a JSON representation of the complex number\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Complex\", \"re\": 2, \"im\": 3}`\n */\n Complex.prototype.toJSON = function () {\n return {\n mathjs: 'Complex',\n re: this.re,\n im: this.im\n }\n }\n\n /*\n * Return the value of the complex number in polar notation\n * The angle phi will be set in the interval of [-pi, pi].\n * @return {{r: number, phi: number}} Returns and object with properties r and phi.\n */\n Complex.prototype.toPolar = function () {\n return {\n r: this.abs(),\n phi: this.arg()\n }\n }\n\n /**\n * Get a string representation of the complex number,\n * with optional formatting options.\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string} str\n */\n Complex.prototype.format = function (options) {\n let str = ''\n let im = this.im\n let re = this.re\n const strRe = format(this.re, options)\n const strIm = format(this.im, options)\n\n // round either re or im when smaller than the configured precision\n const precision = isNumber(options) ? options : options ? options.precision : null\n if (precision !== null) {\n const epsilon = Math.pow(10, -precision)\n if (Math.abs(re / im) < epsilon) {\n re = 0\n }\n if (Math.abs(im / re) < epsilon) {\n im = 0\n }\n }\n\n if (im === 0) {\n // real value\n str = strRe\n } else if (re === 0) {\n // purely complex value\n if (im === 1) {\n str = 'i'\n } else if (im === -1) {\n str = '-i'\n } else {\n str = strIm + 'i'\n }\n } else {\n // complex value\n if (im < 0) {\n if (im === -1) {\n str = strRe + ' - i'\n } else {\n str = strRe + ' - ' + strIm.substring(1) + 'i'\n }\n } else {\n if (im === 1) {\n str = strRe + ' + i'\n } else {\n str = strRe + ' + ' + strIm + 'i'\n }\n }\n }\n return str\n }\n\n /**\n * Create a complex number from polar coordinates\n *\n * Usage:\n *\n * Complex.fromPolar(r: number, phi: number) : Complex\n * Complex.fromPolar({r: number, phi: number}) : Complex\n *\n * @param {*} args...\n * @return {Complex}\n */\n Complex.fromPolar = function (args) {\n switch (arguments.length) {\n case 1:\n {\n const arg = arguments[0]\n if (typeof arg === 'object') {\n return Complex(arg)\n } else {\n throw new TypeError('Input has to be an object with r and phi keys.')\n }\n }\n case 2:\n {\n const r = arguments[0]\n let phi = arguments[1]\n if (isNumber(r)) {\n if (isUnit(phi) && phi.hasBase('ANGLE')) {\n // convert unit to a number in radians\n phi = phi.toNumber('rad')\n }\n\n if (isNumber(phi)) {\n return new Complex({ r: r, phi: phi })\n }\n\n throw new TypeError('Phi is not a number nor an angle unit.')\n } else {\n throw new TypeError('Radius r is not a number.')\n }\n }\n\n default:\n throw new SyntaxError('Wrong number of arguments in function fromPolar')\n }\n }\n\n Complex.prototype.valueOf = Complex.prototype.toString\n\n /**\n * Create a Complex number from a JSON object\n * @param {Object} json A JSON Object structured as\n * {\"mathjs\": \"Complex\", \"re\": 2, \"im\": 3}\n * All properties are optional, default values\n * for `re` and `im` are 0.\n * @return {Complex} Returns a new Complex number\n */\n Complex.fromJSON = function (json) {\n return new Complex(json)\n }\n\n /**\n * Compare two complex numbers, `a` and `b`:\n *\n * - Returns 1 when the real part of `a` is larger than the real part of `b`\n * - Returns -1 when the real part of `a` is smaller than the real part of `b`\n * - Returns 1 when the real parts are equal\n * and the imaginary part of `a` is larger than the imaginary part of `b`\n * - Returns -1 when the real parts are equal\n * and the imaginary part of `a` is smaller than the imaginary part of `b`\n * - Returns 0 when both real and imaginary parts are equal.\n *\n * @params {Complex} a\n * @params {Complex} b\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n Complex.compare = function (a, b) {\n if (a.re > b.re) { return 1 }\n if (a.re < b.re) { return -1 }\n\n if (a.im > b.im) { return 1 }\n if (a.im < b.im) { return -1 }\n\n return 0\n }\n\n return Complex\n}, { isClass: true })\n","import Fraction from 'fraction.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Fraction'\nconst dependencies = []\n\nexport const createFractionClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Attach type information\n */\n Fraction.prototype.type = 'Fraction'\n Fraction.prototype.isFraction = true\n\n /**\n * Get a JSON representation of a Fraction containing type information\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Fraction\", \"n\": 3, \"d\": 8}`\n */\n Fraction.prototype.toJSON = function () {\n return {\n mathjs: 'Fraction',\n n: this.s * this.n,\n d: this.d\n }\n }\n\n /**\n * Instantiate a Fraction from a JSON object\n * @param {Object} json a JSON object structured as:\n * `{\"mathjs\": \"Fraction\", \"n\": 3, \"d\": 8}`\n * @return {BigNumber}\n */\n Fraction.fromJSON = function (json) {\n return new Fraction(json)\n }\n\n return Fraction\n}, { isClass: true })\n","import { isBigNumber } from '../../utils/is.js'\nimport { format, sign } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Range'\nconst dependencies = []\n\nexport const createRangeClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Create a range. A range has a start, step, and end, and contains functions\n * to iterate over the range.\n *\n * A range can be constructed as:\n *\n * const range = new Range(start, end)\n * const range = new Range(start, end, step)\n *\n * To get the result of the range:\n * range.forEach(function (x) {\n * console.log(x)\n * })\n * range.map(function (x) {\n * return math.sin(x)\n * })\n * range.toArray()\n *\n * Example usage:\n *\n * const c = new Range(2, 6) // 2:1:5\n * c.toArray() // [2, 3, 4, 5]\n * const d = new Range(2, -3, -1) // 2:-1:-2\n * d.toArray() // [2, 1, 0, -1, -2]\n *\n * @class Range\n * @constructor Range\n * @param {number} start included lower bound\n * @param {number} end excluded upper bound\n * @param {number} [step] step size, default value is 1\n */\n function Range (start, end, step) {\n if (!(this instanceof Range)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n const hasStart = start !== null && start !== undefined\n const hasEnd = end !== null && end !== undefined\n const hasStep = step !== null && step !== undefined\n\n if (hasStart) {\n if (isBigNumber(start)) {\n start = start.toNumber()\n } else if (typeof start !== 'number') {\n throw new TypeError('Parameter start must be a number')\n }\n }\n if (hasEnd) {\n if (isBigNumber(end)) {\n end = end.toNumber()\n } else if (typeof end !== 'number') {\n throw new TypeError('Parameter end must be a number')\n }\n }\n if (hasStep) {\n if (isBigNumber(step)) {\n step = step.toNumber()\n } else if (typeof step !== 'number') {\n throw new TypeError('Parameter step must be a number')\n }\n }\n\n this.start = hasStart ? parseFloat(start) : 0\n this.end = hasEnd ? parseFloat(end) : 0\n this.step = hasStep ? parseFloat(step) : 1\n }\n\n /**\n * Attach type information\n */\n Range.prototype.type = 'Range'\n Range.prototype.isRange = true\n\n /**\n * Parse a string into a range,\n * The string contains the start, optional step, and end, separated by a colon.\n * If the string does not contain a valid range, null is returned.\n * For example str='0:2:11'.\n * @memberof Range\n * @param {string} str\n * @return {Range | null} range\n */\n Range.parse = function (str) {\n if (typeof str !== 'string') {\n return null\n }\n\n const args = str.split(':')\n const nums = args.map(function (arg) {\n return parseFloat(arg)\n })\n\n const invalid = nums.some(function (num) {\n return isNaN(num)\n })\n if (invalid) {\n return null\n }\n\n switch (nums.length) {\n case 2:\n return new Range(nums[0], nums[1])\n case 3:\n return new Range(nums[0], nums[2], nums[1])\n default:\n return null\n }\n }\n\n /**\n * Create a clone of the range\n * @return {Range} clone\n */\n Range.prototype.clone = function () {\n return new Range(this.start, this.end, this.step)\n }\n\n /**\n * Retrieve the size of the range.\n * Returns an array containing one number, the number of elements in the range.\n * @memberof Range\n * @returns {number[]} size\n */\n Range.prototype.size = function () {\n let len = 0\n const start = this.start\n const step = this.step\n const end = this.end\n const diff = end - start\n\n if (sign(step) === sign(diff)) {\n len = Math.ceil((diff) / step)\n } else if (diff === 0) {\n len = 0\n }\n\n if (isNaN(len)) {\n len = 0\n }\n return [len]\n }\n\n /**\n * Calculate the minimum value in the range\n * @memberof Range\n * @return {number | undefined} min\n */\n Range.prototype.min = function () {\n const size = this.size()[0]\n\n if (size > 0) {\n if (this.step > 0) {\n // positive step\n return this.start\n } else {\n // negative step\n return this.start + (size - 1) * this.step\n }\n } else {\n return undefined\n }\n }\n\n /**\n * Calculate the maximum value in the range\n * @memberof Range\n * @return {number | undefined} max\n */\n Range.prototype.max = function () {\n const size = this.size()[0]\n\n if (size > 0) {\n if (this.step > 0) {\n // positive step\n return this.start + (size - 1) * this.step\n } else {\n // negative step\n return this.start\n }\n } else {\n return undefined\n }\n }\n\n /**\n * Execute a callback function for each value in the range.\n * @memberof Range\n * @param {function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Range being traversed.\n */\n Range.prototype.forEach = function (callback) {\n let x = this.start\n const step = this.step\n const end = this.end\n let i = 0\n\n if (step > 0) {\n while (x < end) {\n callback(x, [i], this)\n x += step\n i++\n }\n } else if (step < 0) {\n while (x > end) {\n callback(x, [i], this)\n x += step\n i++\n }\n }\n }\n\n /**\n * Execute a callback function for each value in the Range, and return the\n * results as an array\n * @memberof Range\n * @param {function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @returns {Array} array\n */\n Range.prototype.map = function (callback) {\n const array = []\n this.forEach(function (value, index, obj) {\n array[index[0]] = callback(value, index, obj)\n })\n return array\n }\n\n /**\n * Create an Array with a copy of the Ranges data\n * @memberof Range\n * @returns {Array} array\n */\n Range.prototype.toArray = function () {\n const array = []\n this.forEach(function (value, index) {\n array[index[0]] = value\n })\n return array\n }\n\n /**\n * Get the primitive value of the Range, a one dimensional array\n * @memberof Range\n * @returns {Array} array\n */\n Range.prototype.valueOf = function () {\n // TODO: implement a caching mechanism for range.valueOf()\n return this.toArray()\n }\n\n /**\n * Get a string representation of the range, with optional formatting options.\n * Output is formatted as 'start:step:end', for example '2:6' or '0:0.2:11'\n * @memberof Range\n * @param {Object | number | function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n Range.prototype.format = function (options) {\n let str = format(this.start, options)\n\n if (this.step !== 1) {\n str += ':' + format(this.step, options)\n }\n str += ':' + format(this.end, options)\n return str\n }\n\n /**\n * Get a string representation of the range.\n * @memberof Range\n * @returns {string}\n */\n Range.prototype.toString = function () {\n return this.format()\n }\n\n /**\n * Get a JSON representation of the range\n * @memberof Range\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Range\", \"start\": 2, \"end\": 4, \"step\": 1}`\n */\n Range.prototype.toJSON = function () {\n return {\n mathjs: 'Range',\n start: this.start,\n end: this.end,\n step: this.step\n }\n }\n\n /**\n * Instantiate a Range from a JSON object\n * @memberof Range\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Range\", \"start\": 2, \"end\": 4, \"step\": 1}`\n * @return {Range}\n */\n Range.fromJSON = function (json) {\n return new Range(json.start, json.end, json.step)\n }\n\n return Range\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'Matrix'\nconst dependencies = []\n\nexport const createMatrixClass = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * @constructor Matrix\n *\n * A Matrix is a wrapper around an Array. A matrix can hold a multi dimensional\n * array. A matrix can be constructed as:\n *\n * let matrix = math.matrix(data)\n *\n * Matrix contains the functions to resize, get and set values, get the size,\n * clone the matrix and to convert the matrix to a vector, array, or scalar.\n * Furthermore, one can iterate over the matrix using map and forEach.\n * The internal Array of the Matrix can be accessed using the function valueOf.\n *\n * Example usage:\n *\n * let matrix = math.matrix([[1, 2], [3, 4]])\n * matix.size() // [2, 2]\n * matrix.resize([3, 2], 5)\n * matrix.valueOf() // [[1, 2], [3, 4], [5, 5]]\n * matrix.subset([1,2]) // 3 (indexes are zero-based)\n *\n */\n function Matrix () {\n if (!(this instanceof Matrix)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n }\n\n /**\n * Attach type information\n */\n Matrix.prototype.type = 'Matrix'\n Matrix.prototype.isMatrix = true\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @return {string} The storage format.\n */\n Matrix.prototype.storage = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke storage on a Matrix interface')\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @return {string} The datatype.\n */\n Matrix.prototype.datatype = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke datatype on a Matrix interface')\n }\n\n /**\n * Create a new Matrix With the type of the current matrix instance\n * @param {Array | Object} data\n * @param {string} [datatype]\n */\n Matrix.prototype.create = function (data, datatype) {\n throw new Error('Cannot invoke create on a Matrix interface')\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n Matrix.prototype.subset = function (index, replacement, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke subset on a Matrix interface')\n }\n\n /**\n * Get a single element from the matrix.\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n Matrix.prototype.get = function (index) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke get on a Matrix interface')\n }\n\n /**\n * Replace a single element in the matrix.\n * @param {number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {Matrix} self\n */\n Matrix.prototype.set = function (index, value, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke set on a Matrix interface')\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @param {number[]} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n Matrix.prototype.resize = function (size, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke resize on a Matrix interface')\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n Matrix.prototype.reshape = function (size, defaultValue) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke reshape on a Matrix interface')\n }\n\n /**\n * Create a clone of the matrix\n * @return {Matrix} clone\n */\n Matrix.prototype.clone = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke clone on a Matrix interface')\n }\n\n /**\n * Retrieve the size of the matrix.\n * @returns {number[]} size\n */\n Matrix.prototype.size = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke size on a Matrix interface')\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {Matrix} matrix\n */\n Matrix.prototype.map = function (callback, skipZeros) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke map on a Matrix interface')\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n */\n Matrix.prototype.forEach = function (callback) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke forEach on a Matrix interface')\n }\n\n /**\n * Create an Array with a copy of the data of the Matrix\n * @returns {Array} array\n */\n Matrix.prototype.toArray = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke toArray on a Matrix interface')\n }\n\n /**\n * Get the primitive value of the Matrix: a multidimensional array\n * @returns {Array} array\n */\n Matrix.prototype.valueOf = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke valueOf on a Matrix interface')\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n Matrix.prototype.format = function (options) {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke format on a Matrix interface')\n }\n\n /**\n * Get a string representation of the matrix\n * @returns {string} str\n */\n Matrix.prototype.toString = function () {\n // must be implemented by each of the Matrix implementations\n throw new Error('Cannot invoke toString on a Matrix interface')\n }\n\n return Matrix\n}, { isClass: true })\n","import { isArray, isBigNumber, isCollection, isIndex, isMatrix, isNumber, isString, typeOf } from '../../utils/is.js'\nimport { arraySize, getArrayDataType, reshape, resize, unsqueeze, validate, validateIndex } from '../../utils/array.js'\nimport { format } from '../../utils/string.js'\nimport { isInteger } from '../../utils/number.js'\nimport { clone, deepStrictEqual } from '../../utils/object.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'DenseMatrix'\nconst dependencies = [\n 'Matrix'\n]\n\nexport const createDenseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ Matrix }) => {\n /**\n * Dense Matrix implementation. A regular, dense matrix, supporting multi-dimensional matrices. This is the default matrix type.\n * @class DenseMatrix\n */\n function DenseMatrix (data, datatype) {\n if (!(this instanceof DenseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data)) {\n // check data is a DenseMatrix\n if (data.type === 'DenseMatrix') {\n // clone data & size\n this._data = clone(data._data)\n this._size = clone(data._size)\n this._datatype = datatype || data._datatype\n } else {\n // build data from existing matrix\n this._data = data.toArray()\n this._size = data.size()\n this._datatype = datatype || data._datatype\n }\n } else if (data && isArray(data.data) && isArray(data.size)) {\n // initialize fields from JSON representation\n this._data = data.data\n this._size = data.size\n // verify the dimensions of the array\n validate(this._data, this._size)\n this._datatype = datatype || data.datatype\n } else if (isArray(data)) {\n // replace nested Matrices with Arrays\n this._data = preprocess(data)\n // get the dimensions of the array\n this._size = arraySize(this._data)\n // verify the dimensions of the array, TODO: compute size while processing array\n validate(this._data, this._size)\n // data type unknown\n this._datatype = datatype\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._data = []\n this._size = [0]\n this._datatype = datatype\n }\n }\n\n DenseMatrix.prototype = new Matrix()\n\n /**\n * Create a new DenseMatrix\n */\n DenseMatrix.prototype.createDenseMatrix = function (data, datatype) {\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Attach type information\n */\n DenseMatrix.prototype.type = 'DenseMatrix'\n DenseMatrix.prototype.isDenseMatrix = true\n\n /**\n * Get the matrix type\n *\n * Usage:\n * const matrixType = matrix.getDataType() // retrieves the matrix type\n *\n * @memberOf DenseMatrix\n * @return {string} type information; if multiple types are found from the Matrix, it will return \"mixed\"\n */\n DenseMatrix.prototype.getDataType = function () {\n return getArrayDataType(this._data, typeOf)\n }\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @memberof DenseMatrix\n * @return {string} The storage format.\n */\n DenseMatrix.prototype.storage = function () {\n return 'dense'\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @memberof DenseMatrix\n * @return {string} The datatype.\n */\n DenseMatrix.prototype.datatype = function () {\n return this._datatype\n }\n\n /**\n * Create a new DenseMatrix\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {string} [datatype]\n */\n DenseMatrix.prototype.create = function (data, datatype) {\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @memberof DenseMatrix\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n DenseMatrix.prototype.subset = function (index, replacement, defaultValue) {\n switch (arguments.length) {\n case 1:\n return _get(this, index)\n\n // intentional fall through\n case 2:\n case 3:\n return _set(this, index, replacement, defaultValue)\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n /**\n * Get a single element from the matrix.\n * @memberof DenseMatrix\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n DenseMatrix.prototype.get = function (index) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check index\n for (let x = 0; x < index.length; x++) { validateIndex(index[x], this._size[x]) }\n\n let data = this._data\n for (let i = 0, ii = index.length; i < ii; i++) {\n const indexI = index[i]\n validateIndex(indexI, data.length)\n data = data[indexI]\n }\n\n return data\n }\n\n /**\n * Replace a single element in the matrix.\n * @memberof DenseMatrix\n * @param {number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {DenseMatrix} self\n */\n DenseMatrix.prototype.set = function (index, value, defaultValue) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length < this._size.length) { throw new DimensionError(index.length, this._size.length, '<') }\n\n let i, ii, indexI\n\n // enlarge matrix when needed\n const size = index.map(function (i) {\n return i + 1\n })\n _fit(this, size, defaultValue)\n\n // traverse over the dimensions\n let data = this._data\n for (i = 0, ii = index.length - 1; i < ii; i++) {\n indexI = index[i]\n validateIndex(indexI, data.length)\n data = data[indexI]\n }\n\n // set new value\n indexI = index[index.length - 1]\n validateIndex(indexI, data.length)\n data[indexI] = value\n\n return this\n }\n\n /**\n * Get a submatrix of this matrix\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix\n * @param {Index} index Zero-based index\n * @private\n */\n function _get (matrix, index) {\n if (!isIndex(index)) {\n throw new TypeError('Invalid index')\n }\n\n const isScalar = index.isScalar()\n if (isScalar) {\n // return a scalar\n return matrix.get(index.min())\n } else {\n // validate dimensions\n const size = index.size()\n if (size.length !== matrix._size.length) {\n throw new DimensionError(size.length, matrix._size.length)\n }\n\n // validate if any of the ranges in the index is out of range\n const min = index.min()\n const max = index.max()\n for (let i = 0, ii = matrix._size.length; i < ii; i++) {\n validateIndex(min[i], matrix._size[i])\n validateIndex(max[i], matrix._size[i])\n }\n\n // retrieve submatrix\n // TODO: more efficient when creating an empty matrix and setting _data and _size manually\n return new DenseMatrix(_getSubmatrix(matrix._data, index, size.length, 0), matrix._datatype)\n }\n }\n\n /**\n * Recursively get a submatrix of a multi dimensional matrix.\n * Index is not checked for correct number or length of dimensions.\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {Index} index\n * @param {number} dims Total number of dimensions\n * @param {number} dim Current dimension\n * @return {Array} submatrix\n * @private\n */\n function _getSubmatrix (data, index, dims, dim) {\n const last = (dim === dims - 1)\n const range = index.dimension(dim)\n\n if (last) {\n return range.map(function (i) {\n validateIndex(i, data.length)\n return data[i]\n }).valueOf()\n } else {\n return range.map(function (i) {\n validateIndex(i, data.length)\n const child = data[i]\n return _getSubmatrix(child, index, dims, dim + 1)\n }).valueOf()\n }\n }\n\n /**\n * Replace a submatrix in this matrix\n * Indexes are zero-based.\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix\n * @param {Index} index\n * @param {DenseMatrix | Array | *} submatrix\n * @param {*} defaultValue Default value, filled in on new entries when\n * the matrix is resized.\n * @return {DenseMatrix} matrix\n * @private\n */\n function _set (matrix, index, submatrix, defaultValue) {\n if (!index || index.isIndex !== true) {\n throw new TypeError('Invalid index')\n }\n\n // get index size and check whether the index contains a single value\n const iSize = index.size()\n const isScalar = index.isScalar()\n\n // calculate the size of the submatrix, and convert it into an Array if needed\n let sSize\n if (isMatrix(submatrix)) {\n sSize = submatrix.size()\n submatrix = submatrix.valueOf()\n } else {\n sSize = arraySize(submatrix)\n }\n\n if (isScalar) {\n // set a scalar\n\n // check whether submatrix is a scalar\n if (sSize.length !== 0) {\n throw new TypeError('Scalar expected')\n }\n\n matrix.set(index.min(), submatrix, defaultValue)\n } else {\n // set a submatrix\n\n // validate dimensions\n if (iSize.length < matrix._size.length) {\n throw new DimensionError(iSize.length, matrix._size.length, '<')\n }\n\n if (sSize.length < iSize.length) {\n // calculate number of missing outer dimensions\n let i = 0\n let outer = 0\n while (iSize[i] === 1 && sSize[i] === 1) {\n i++\n }\n while (iSize[i] === 1) {\n outer++\n i++\n }\n\n // unsqueeze both outer and inner dimensions\n submatrix = unsqueeze(submatrix, iSize.length, outer, sSize)\n }\n\n // check whether the size of the submatrix matches the index size\n if (!deepStrictEqual(iSize, sSize)) {\n throw new DimensionError(iSize, sSize, '>')\n }\n\n // enlarge matrix when needed\n const size = index.max().map(function (i) {\n return i + 1\n })\n _fit(matrix, size, defaultValue)\n\n // insert the sub matrix\n const dims = iSize.length\n const dim = 0\n _setSubmatrix(matrix._data, index, submatrix, dims, dim)\n }\n\n return matrix\n }\n\n /**\n * Replace a submatrix of a multi dimensional matrix.\n * @memberof DenseMatrix\n * @param {Array} data\n * @param {Index} index\n * @param {Array} submatrix\n * @param {number} dims Total number of dimensions\n * @param {number} dim\n * @private\n */\n function _setSubmatrix (data, index, submatrix, dims, dim) {\n const last = (dim === dims - 1)\n const range = index.dimension(dim)\n\n if (last) {\n range.forEach(function (dataIndex, subIndex) {\n validateIndex(dataIndex)\n data[dataIndex] = submatrix[subIndex[0]]\n })\n } else {\n range.forEach(function (dataIndex, subIndex) {\n validateIndex(dataIndex)\n _setSubmatrix(data[dataIndex], index, submatrix[subIndex[0]], dims, dim + 1)\n })\n }\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @memberof DenseMatrix\n * @param {number[] || Matrix} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n DenseMatrix.prototype.resize = function (size, defaultValue, copy) {\n // validate arguments\n if (!isCollection(size)) {\n throw new TypeError('Array or Matrix expected')\n }\n\n // SparseMatrix input is always 2d, flatten this into 1d if it's indeed a vector\n const sizeArray = size.valueOf().map(value => {\n return Array.isArray(value) && value.length === 1\n ? value[0]\n : value\n })\n\n // matrix to resize\n const m = copy ? this.clone() : this\n // resize matrix\n return _resize(m, sizeArray, defaultValue)\n }\n\n function _resize (matrix, size, defaultValue) {\n // check size\n if (size.length === 0) {\n // first value in matrix\n let v = matrix._data\n // go deep\n while (isArray(v)) {\n v = v[0]\n }\n return v\n }\n // resize matrix\n matrix._size = size.slice(0) // copy the array\n matrix._data = resize(matrix._data, matrix._size, defaultValue)\n // return matrix\n return matrix\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * NOTE: This might be better suited to copy by default, instead of modifying\n * in place. For now, it operates in place to remain consistent with\n * resize().\n *\n * @memberof DenseMatrix\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n DenseMatrix.prototype.reshape = function (size, copy) {\n const m = copy ? this.clone() : this\n\n m._data = reshape(m._data, size)\n m._size = size.slice(0)\n return m\n }\n\n /**\n * Enlarge the matrix when it is smaller than given size.\n * If the matrix is larger or equal sized, nothing is done.\n * @memberof DenseMatrix\n * @param {DenseMatrix} matrix The matrix to be resized\n * @param {number[]} size\n * @param {*} defaultValue Default value, filled in on new entries.\n * @private\n */\n function _fit (matrix, size, defaultValue) {\n const // copy the array\n newSize = matrix._size.slice(0)\n\n let changed = false\n\n // add dimensions when needed\n while (newSize.length < size.length) {\n newSize.push(0)\n changed = true\n }\n\n // enlarge size when needed\n for (let i = 0, ii = size.length; i < ii; i++) {\n if (size[i] > newSize[i]) {\n newSize[i] = size[i]\n changed = true\n }\n }\n\n if (changed) {\n // resize only when size is changed\n _resize(matrix, newSize, defaultValue)\n }\n }\n\n /**\n * Create a clone of the matrix\n * @memberof DenseMatrix\n * @return {DenseMatrix} clone\n */\n DenseMatrix.prototype.clone = function () {\n const m = new DenseMatrix({\n data: clone(this._data),\n size: clone(this._size),\n datatype: this._datatype\n })\n return m\n }\n\n /**\n * Retrieve the size of the matrix.\n * @memberof DenseMatrix\n * @returns {number[]} size\n */\n DenseMatrix.prototype.size = function () {\n return this._size.slice(0) // return a clone of _size\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @memberof DenseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n *\n * @return {DenseMatrix} matrix\n */\n DenseMatrix.prototype.map = function (callback) {\n // matrix instance\n const me = this\n const recurse = function (value, index) {\n if (isArray(value)) {\n return value.map(function (child, i) {\n return recurse(child, index.concat(i))\n })\n } else {\n return callback(value, index, me)\n }\n }\n\n // determine the new datatype when the original matrix has datatype defined\n // TODO: should be done in matrix constructor instead\n const data = recurse(this._data, [])\n const datatype = this._datatype !== undefined\n ? getArrayDataType(data, typeOf)\n : undefined\n return new DenseMatrix(data, datatype)\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @memberof DenseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n */\n DenseMatrix.prototype.forEach = function (callback) {\n // matrix instance\n const me = this\n const recurse = function (value, index) {\n if (isArray(value)) {\n value.forEach(function (child, i) {\n recurse(child, index.concat(i))\n })\n } else {\n callback(value, index, me)\n }\n }\n recurse(this._data, [])\n }\n\n /**\n * Create an Array with a copy of the data of the DenseMatrix\n * @memberof DenseMatrix\n * @returns {Array} array\n */\n DenseMatrix.prototype.toArray = function () {\n return clone(this._data)\n }\n\n /**\n * Get the primitive value of the DenseMatrix: a multidimensional array\n * @memberof DenseMatrix\n * @returns {Array} array\n */\n DenseMatrix.prototype.valueOf = function () {\n return this._data\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @memberof DenseMatrix\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n DenseMatrix.prototype.format = function (options) {\n return format(this._data, options)\n }\n\n /**\n * Get a string representation of the matrix\n * @memberof DenseMatrix\n * @returns {string} str\n */\n DenseMatrix.prototype.toString = function () {\n return format(this._data)\n }\n\n /**\n * Get a JSON representation of the matrix\n * @memberof DenseMatrix\n * @returns {Object}\n */\n DenseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'DenseMatrix',\n data: this._data,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Get the kth Matrix diagonal.\n *\n * @memberof DenseMatrix\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will retrieved.\n *\n * @returns {Matrix} The matrix with the diagonal values.\n */\n DenseMatrix.prototype.diagonal = function (k) {\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n\n // number diagonal values\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // x is a matrix get diagonal from matrix\n const data = []\n\n // loop rows\n for (let i = 0; i < n; i++) {\n data[i] = this._data[i + kSub][i + kSuper]\n }\n\n // create DenseMatrix\n return new DenseMatrix({\n data: data,\n size: [n],\n datatype: this._datatype\n })\n }\n\n /**\n * Create a diagonal matrix.\n *\n * @memberof DenseMatrix\n * @param {Array} size The matrix size.\n * @param {number | Matrix | Array } value The values for the diagonal.\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will be filled in.\n * @param {number} [defaultValue] The default value for non-diagonal\n * @param {string} [datatype] The datatype for the diagonal\n *\n * @returns {DenseMatrix}\n */\n DenseMatrix.diagonal = function (size, value, k, defaultValue) {\n if (!isArray(size)) { throw new TypeError('Array expected, size parameter') }\n if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // map size & validate\n size = size.map(function (s) {\n // check it is a big number\n if (isBigNumber(s)) {\n // convert it\n s = s.toNumber()\n }\n // validate arguments\n if (!isNumber(s) || !isInteger(s) || s < 1) {\n throw new Error('Size values must be positive integers')\n }\n return s\n })\n\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // number of non-zero items\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // value extraction function\n let _value\n\n // check value\n if (isArray(value)) {\n // validate array\n if (value.length !== n) {\n // number of values in array must be n\n throw new Error('Invalid value array length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value[i]\n }\n } else if (isMatrix(value)) {\n // matrix size\n const ms = value.size()\n // validate matrix\n if (ms.length !== 1 || ms[0] !== n) {\n // number of values in array must be n\n throw new Error('Invalid matrix length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value.get([i])\n }\n } else {\n // define function\n _value = function () {\n // return value\n return value\n }\n }\n\n // discover default value if needed\n if (!defaultValue) {\n // check first value in array\n defaultValue = isBigNumber(_value(0))\n ? _value(0).mul(0) // trick to create a BigNumber with value zero\n : 0\n }\n\n // empty array\n let data = []\n\n // check we need to resize array\n if (size.length > 0) {\n // resize array\n data = resize(data, size, defaultValue)\n // fill diagonal\n for (let d = 0; d < n; d++) {\n data[d + kSub][d + kSuper] = _value(d)\n }\n }\n\n // create DenseMatrix\n return new DenseMatrix({\n data: data,\n size: [rows, columns]\n })\n }\n\n /**\n * Generate a matrix from a JSON object\n * @memberof DenseMatrix\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"DenseMatrix\", data: [], size: []}`,\n * where mathjs is optional\n * @returns {DenseMatrix}\n */\n DenseMatrix.fromJSON = function (json) {\n return new DenseMatrix(json)\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @memberof DenseMatrix\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n DenseMatrix.prototype.swapRows = function (i, j) {\n // check index\n if (!isNumber(i) || !isInteger(i) || !isNumber(j) || !isInteger(j)) {\n throw new Error('Row index must be positive integers')\n }\n // check dimensions\n if (this._size.length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n // validate index\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[0])\n\n // swap rows\n DenseMatrix._swapRows(i, j, this._data)\n // return current instance\n return this\n }\n\n /**\n * Swap rows i and j in Dense Matrix data structure.\n *\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n * @param {Array} data Matrix data\n */\n DenseMatrix._swapRows = function (i, j, data) {\n // swap values i <-> j\n const vi = data[i]\n data[i] = data[j]\n data[j] = vi\n }\n\n /**\n * Preprocess data, which can be an Array or DenseMatrix with nested Arrays and\n * Matrices. Replaces all nested Matrices with Arrays\n * @memberof DenseMatrix\n * @param {Array} data\n * @return {Array} data\n */\n function preprocess (data) {\n for (let i = 0, ii = data.length; i < ii; i++) {\n const elem = data[i]\n if (isArray(elem)) {\n data[i] = preprocess(elem)\n } else if (elem && elem.isMatrix === true) {\n data[i] = preprocess(elem.valueOf())\n }\n }\n\n return data\n }\n\n return DenseMatrix\n}, { isClass: true })\n","import { clone as objectClone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'clone'\nconst dependencies = ['typed']\n\nexport const createClone = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Clone an object. Will make a deep copy of the data.\n *\n * Syntax:\n *\n * math.clone(x)\n *\n * Examples:\n *\n * math.clone(3.5) // returns number 3.5\n * math.clone(math.complex('2-4i') // returns Complex 2 - 4i\n * math.clone(math.unit(45, 'deg')) // returns Unit 45 deg\n * math.clone([[1, 2], [3, 4]]) // returns Array [[1, 2], [3, 4]]\n * math.clone(\"hello world\") // returns string \"hello world\"\n *\n * @param {*} x Object to be cloned\n * @return {*} A clone of object x\n */\n return typed(name, {\n any: objectClone\n })\n})\n","import { isCollection, isMatrix } from './is.js'\nimport { IndexError } from '../error/IndexError.js'\nimport { arraySize } from './array.js'\n\n/**\n * Test whether an array contains collections\n * @param {Array} array\n * @returns {boolean} Returns true when the array contains one or multiple\n * collections (Arrays or Matrices). Returns false otherwise.\n */\nexport function containsCollections (array) {\n for (let i = 0; i < array.length; i++) {\n if (isCollection(array[i])) {\n return true\n }\n }\n return false\n}\n\n/**\n * Recursively loop over all elements in a given multi dimensional array\n * and invoke the callback on each of the elements.\n * @param {Array | Matrix} array\n * @param {Function} callback The callback method is invoked with one\n * parameter: the current element in the array\n */\nexport function deepForEach (array, callback) {\n if (isMatrix(array)) {\n array = array.valueOf()\n }\n\n for (let i = 0, ii = array.length; i < ii; i++) {\n const value = array[i]\n\n if (Array.isArray(value)) {\n deepForEach(value, callback)\n } else {\n callback(value)\n }\n }\n}\n\n/**\n * Execute the callback function element wise for each element in array and any\n * nested array\n * Returns an array with the results\n * @param {Array | Matrix} array\n * @param {Function} callback The callback is called with two parameters:\n * value1 and value2, which contain the current\n * element of both arrays.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {Array | Matrix} res\n */\nexport function deepMap (array, callback, skipZeros) {\n if (array && (typeof array.map === 'function')) {\n // TODO: replace array.map with a for loop to improve performance\n return array.map(function (x) {\n return deepMap(x, callback, skipZeros)\n })\n } else {\n return callback(array)\n }\n}\n\n/**\n * Reduce a given matrix or array to a new matrix or\n * array with one less dimension, applying the given\n * callback in the selected dimension.\n * @param {Array | Matrix} mat\n * @param {number} dim\n * @param {Function} callback\n * @return {Array | Matrix} res\n */\nexport function reduce (mat, dim, callback) {\n const size = Array.isArray(mat) ? arraySize(mat) : mat.size()\n if (dim < 0 || (dim >= size.length)) {\n // TODO: would be more clear when throwing a DimensionError here\n throw new IndexError(dim, size.length)\n }\n\n if (isMatrix(mat)) {\n return mat.create(_reduce(mat.valueOf(), dim, callback))\n } else {\n return _reduce(mat, dim, callback)\n }\n}\n\n/**\n * Recursively reduce a matrix\n * @param {Array} mat\n * @param {number} dim\n * @param {Function} callback\n * @returns {Array} ret\n * @private\n */\nfunction _reduce (mat, dim, callback) {\n let i, ret, val, tran\n\n if (dim <= 0) {\n if (!Array.isArray(mat[0])) {\n val = mat[0]\n for (i = 1; i < mat.length; i++) {\n val = callback(val, mat[i])\n }\n return val\n } else {\n tran = _switch(mat)\n ret = []\n for (i = 0; i < tran.length; i++) {\n ret[i] = _reduce(tran[i], dim - 1, callback)\n }\n return ret\n }\n } else {\n ret = []\n for (i = 0; i < mat.length; i++) {\n ret[i] = _reduce(mat[i], dim - 1, callback)\n }\n return ret\n }\n}\n\n/**\n * Transpose a matrix\n * @param {Array} mat\n * @returns {Array} ret\n * @private\n */\nfunction _switch (mat) {\n const I = mat.length\n const J = mat[0].length\n let i, j\n const ret = []\n for (j = 0; j < J; j++) {\n const tmp = []\n for (i = 0; i < I; i++) {\n tmp.push(mat[i][j])\n }\n ret.push(tmp)\n }\n return ret\n}\n\n// TODO: document function scatter\nexport function scatter (a, j, w, x, u, mark, cindex, f, inverse, update, value) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n\n // vars\n let k, k0, k1, i\n\n // check we need to process values (pattern matrix)\n if (x) {\n // values in j\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check value exists in current j\n if (w[i] !== mark) {\n // i is new entry in j\n w[i] = mark\n // add i to pattern of C\n cindex.push(i)\n // x(i) = A, check we need to call function this time\n if (update) {\n // copy value to workspace calling callback function\n x[i] = inverse ? f(avalues[k], value) : f(value, avalues[k])\n // function was called on current row\n u[i] = mark\n } else {\n // copy value to workspace\n x[i] = avalues[k]\n }\n } else {\n // i exists in C already\n x[i] = inverse ? f(avalues[k], x[i]) : f(x[i], avalues[k])\n // function was called on current row\n u[i] = mark\n }\n }\n } else {\n // values in j\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check value exists in current j\n if (w[i] !== mark) {\n // i is new entry in j\n w[i] = mark\n // add i to pattern of C\n cindex.push(i)\n } else {\n // indicate function was called on current row\n u[i] = mark\n }\n }\n }\n}\n","import { deepMap } from '../../utils/collection.js'\nimport { isInteger as isIntegerNumber } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isInteger'\nconst dependencies = ['typed']\n\nexport const createIsInteger = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is an integer number.\n * The function supports `number`, `BigNumber`, and `Fraction`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isInteger(x)\n *\n * Examples:\n *\n * math.isInteger(2) // returns true\n * math.isInteger(0) // returns true\n * math.isInteger(0.5) // returns false\n * math.isInteger(math.bignumber(500)) // returns true\n * math.isInteger(math.fraction(4)) // returns true\n * math.isInteger('3') // returns true\n * math.isInteger([3, 0.5, -2]) // returns [true, false, true]\n * math.isInteger(math.complex('2-4i') // throws an error\n *\n * See also:\n *\n * isNumeric, isPositive, isNegative, isZero\n *\n * @param {number | BigNumber | Fraction | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` contains a numeric, integer value.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isIntegerNumber, // TODO: what to do with isInteger(add(0.1, 0.2)) ?\n\n BigNumber: function (x) {\n return x.isInt()\n },\n\n Fraction: function (x) {\n return x.d === 1 && isFinite(x.n)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { isInteger } from '../../utils/number.js'\n\nconst n1 = 'number'\n\nexport function isIntegerNumber (x) {\n return isInteger(x)\n}\nisIntegerNumber.signature = n1\n\nexport function isNegativeNumber (x) {\n return x < 0\n}\nisNegativeNumber.signature = n1\n\nexport function isPositiveNumber (x) {\n return x > 0\n}\nisPositiveNumber.signature = n1\n\nexport function isZeroNumber (x) {\n return x === 0\n}\nisZeroNumber.signature = n1\n\nexport function isNaNNumber (x) {\n return Number.isNaN(x)\n}\nisNaNNumber.signature = n1\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isNegativeNumber } from '../../plain/number/index.js'\n\nconst name = 'isNegative'\nconst dependencies = ['typed']\n\nexport const createIsNegative = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is negative: smaller than zero.\n * The function supports types `number`, `BigNumber`, `Fraction`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNegative(x)\n *\n * Examples:\n *\n * math.isNegative(3) // returns false\n * math.isNegative(-2) // returns true\n * math.isNegative(0) // returns false\n * math.isNegative(-0) // returns false\n * math.isNegative(math.bignumber(2)) // returns false\n * math.isNegative(math.fraction(-2, 5)) // returns true\n * math.isNegative('-2') // returns true\n * math.isNegative([2, 0, -3]') // returns [false, false, true]\n *\n * See also:\n *\n * isNumeric, isPositive, isZero, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isNegativeNumber,\n\n BigNumber: function (x) {\n return x.isNeg() && !x.isZero() && !x.isNaN()\n },\n\n Fraction: function (x) {\n return x.s < 0 // It's enough to decide on the sign\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isNumeric'\nconst dependencies = ['typed']\n\nexport const createIsNumeric = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is an numeric value.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNumeric(x)\n *\n * Examples:\n *\n * math.isNumeric(2) // returns true\n * math.isNumeric('2') // returns false\n * math.hasNumericValue('2') // returns true\n * math.isNumeric(0) // returns true\n * math.isNumeric(math.bignumber(500)) // returns true\n * math.isNumeric(math.fraction(4)) // returns true\n * math.isNumeric(math.complex('2-4i') // returns false\n * math.isNumeric([2.3, 'foo', false]) // returns [true, false, true]\n *\n * See also:\n *\n * isZero, isPositive, isNegative, isInteger, hasNumericValue\n *\n * @param {*} x Value to be tested\n * @return {boolean} Returns true when `x` is a `number`, `BigNumber`,\n * `Fraction`, or `boolean`. Returns false for other types.\n * Throws an error in case of unknown types.\n */\n return typed(name, {\n 'number | BigNumber | Fraction | boolean': function () {\n return true\n },\n\n 'Complex | Unit | string | null | undefined | Node': function () {\n return false\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'hasNumericValue'\nconst dependencies = ['typed', 'isNumeric']\n\nexport const createHasNumericValue = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNumeric }) => {\n /**\n * Test whether a value is an numeric value.\n *\n * In case of a string, true is returned if the string contains a numeric value.\n *\n * Syntax:\n *\n * math.hasNumericValue(x)\n *\n * Examples:\n *\n * math.hasNumericValue(2) // returns true\n * math.hasNumericValue('2') // returns true\n * math.isNumeric('2') // returns false\n * math.hasNumericValue(0) // returns true\n * math.hasNumericValue(math.bignumber(500)) // returns true\n * math.hasNumericValue(math.fraction(4)) // returns true\n * math.hasNumericValue(math.complex('2-4i') // returns false\n * math.hasNumericValue([2.3, 'foo', false]) // returns [true, false, true]\n *\n * See also:\n *\n * isZero, isPositive, isNegative, isInteger, isNumeric\n *\n * @param {*} x Value to be tested\n * @return {boolean} Returns true when `x` is a `number`, `BigNumber`,\n * `Fraction`, `Boolean`, or a `String` containing number. Returns false for other types.\n * Throws an error in case of unknown types.\n */\n return typed(name, {\n string: function (x) {\n return x.trim().length > 0 && !isNaN(Number(x))\n },\n any: function (x) {\n return isNumeric(x)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isPositiveNumber } from '../../plain/number/index.js'\n\nconst name = 'isPositive'\nconst dependencies = ['typed']\n\nexport const createIsPositive = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is positive: larger than zero.\n * The function supports types `number`, `BigNumber`, `Fraction`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isPositive(x)\n *\n * Examples:\n *\n * math.isPositive(3) // returns true\n * math.isPositive(-2) // returns false\n * math.isPositive(0) // returns false\n * math.isPositive(-0) // returns false\n * math.isPositive(0.5) // returns true\n * math.isPositive(math.bignumber(2)) // returns true\n * math.isPositive(math.fraction(-2, 5)) // returns false\n * math.isPositive(math.fraction(1,3)) // returns false\n * math.isPositive('2') // returns true\n * math.isPositive([2, 0, -3]) // returns [true, false, false]\n *\n * See also:\n *\n * isNumeric, isZero, isNegative, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isPositiveNumber,\n\n BigNumber: function (x) {\n return !x.isNeg() && !x.isZero() && !x.isNaN()\n },\n\n Fraction: function (x) {\n return x.s > 0 && x.n > 0\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isZeroNumber } from '../../plain/number/index.js'\n\nconst name = 'isZero'\nconst dependencies = ['typed']\n\nexport const createIsZero = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is zero.\n * The function can check for zero for types `number`, `BigNumber`, `Fraction`,\n * `Complex`, and `Unit`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isZero(x)\n *\n * Examples:\n *\n * math.isZero(0) // returns true\n * math.isZero(2) // returns false\n * math.isZero(0.5) // returns false\n * math.isZero(math.bignumber(0)) // returns true\n * math.isZero(math.fraction(0)) // returns true\n * math.isZero(math.fraction(1,3)) // returns false\n * math.isZero(math.complex('2 - 4i') // returns false\n * math.isZero(math.complex('0i') // returns true\n * math.isZero('0') // returns true\n * math.isZero('2') // returns false\n * math.isZero([2, 0, -3]') // returns [false, true, false]\n *\n * See also:\n *\n * isNumeric, isPositive, isNegative, isInteger\n *\n * @param {number | BigNumber | Complex | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isZeroNumber,\n\n BigNumber: function (x) {\n return x.isZero()\n },\n\n Complex: function (x) {\n return x.re === 0 && x.im === 0\n },\n\n Fraction: function (x) {\n return x.d === 1 && x.n === 0\n },\n\n Unit: function (x) {\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { isNaNNumber } from '../../plain/number/index.js'\n\nconst name = 'isNaN'\nconst dependencies = ['typed']\n\nexport const createIsNaN = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is NaN (not a number).\n * The function supports types `number`, `BigNumber`, `Fraction`, `Unit` and `Complex`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isNaN(x)\n *\n * Examples:\n *\n * math.isNaN(3) // returns false\n * math.isNaN(NaN) // returns true\n * math.isNaN(0) // returns false\n * math.isNaN(math.bignumber(NaN)) // returns true\n * math.isNaN(math.bignumber(0)) // returns false\n * math.isNaN(math.fraction(-2, 5)) // returns false\n * math.isNaN('-2') // returns false\n * math.isNaN([2, 0, -3, NaN]') // returns [false, false, false, true]\n *\n * See also:\n *\n * isNumeric, isNegative, isPositive, isZero, isInteger\n *\n * @param {number | BigNumber | Fraction | Unit | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is NaN.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: isNaNNumber,\n\n BigNumber: function (x) {\n return x.isNaN()\n },\n\n Fraction: function (x) {\n return false\n },\n\n Complex: function (x) {\n return x.isNaN()\n },\n\n Unit: function (x) {\n return Number.isNaN(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, Number.isNaN)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { typeOf as _typeOf } from '../../utils/is.js'\n\nconst name = 'typeOf'\nconst dependencies = ['typed']\n\nexport const createTypeOf = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Determine the type of a variable.\n *\n * Function `typeOf` recognizes the following types of objects:\n *\n * Object | Returns | Example\n * ---------------------- | ------------- | ------------------------------------------\n * null | `'null'` | `math.typeOf(null)`\n * number | `'number'` | `math.typeOf(3.5)`\n * boolean | `'boolean'` | `math.typeOf(true)`\n * string | `'string'` | `math.typeOf('hello world')`\n * Array | `'Array'` | `math.typeOf([1, 2, 3])`\n * Date | `'Date'` | `math.typeOf(new Date())`\n * Function | `'Function'` | `math.typeOf(function () {})`\n * Object | `'Object'` | `math.typeOf({a: 2, b: 3})`\n * RegExp | `'RegExp'` | `math.typeOf(/a regexp/)`\n * undefined | `'undefined'` | `math.typeOf(undefined)`\n * math.BigNumber | `'BigNumber'` | `math.typeOf(math.bignumber('2.3e500'))`\n * math.Chain | `'Chain'` | `math.typeOf(math.chain(2))`\n * math.Complex | `'Complex'` | `math.typeOf(math.complex(2, 3))`\n * math.Fraction | `'Fraction'` | `math.typeOf(math.fraction(1, 3))`\n * math.Help | `'Help'` | `math.typeOf(math.help('sqrt'))`\n * math.Help | `'Help'` | `math.typeOf(math.help('sqrt'))`\n * math.Index | `'Index'` | `math.typeOf(math.index(1, 3))`\n * math.Matrix | `'Matrix'` | `math.typeOf(math.matrix([[1,2], [3, 4]]))`\n * math.Range | `'Range'` | `math.typeOf(math.range(0, 10))`\n * math.ResultSet | `'ResultSet'` | `math.typeOf(math.evaluate('a=2\\nb=3'))`\n * math.Unit | `'Unit'` | `math.typeOf(math.unit('45 deg'))`\n * math.AccessorNode | `'AccessorNode'` | `math.typeOf(math.parse('A[2]'))`\n * math.ArrayNode | `'ArrayNode'` | `math.typeOf(math.parse('[1,2,3]'))`\n * math.AssignmentNode | `'AssignmentNode'` | `math.typeOf(math.parse('x=2'))`\n * math.BlockNode | `'BlockNode'` | `math.typeOf(math.parse('a=2; b=3'))`\n * math.ConditionalNode | `'ConditionalNode'` | `math.typeOf(math.parse('x<0 ? -x : x'))`\n * math.ConstantNode | `'ConstantNode'` | `math.typeOf(math.parse('2.3'))`\n * math.FunctionAssignmentNode | `'FunctionAssignmentNode'` | `math.typeOf(math.parse('f(x)=x^2'))`\n * math.FunctionNode | `'FunctionNode'` | `math.typeOf(math.parse('sqrt(4)'))`\n * math.IndexNode | `'IndexNode'` | `math.typeOf(math.parse('A[2]').index)`\n * math.ObjectNode | `'ObjectNode'` | `math.typeOf(math.parse('{a:2}'))`\n * math.ParenthesisNode | `'ParenthesisNode'` | `math.typeOf(math.parse('(2+3)'))`\n * math.RangeNode | `'RangeNode'` | `math.typeOf(math.parse('1:10'))`\n * math.SymbolNode | `'SymbolNode'` | `math.typeOf(math.parse('x'))`\n *\n * Syntax:\n *\n * math.typeOf(x)\n *\n * Examples:\n *\n * math.typeOf(3.5) // returns 'number'\n * math.typeOf(math.complex('2-4i')) // returns 'Complex'\n * math.typeOf(math.unit('45 deg')) // returns 'Unit'\n * math.typeOf('hello world') // returns 'string'\n *\n * @param {*} x The variable for which to test the type.\n * @return {string} Returns the name of the type. Primitive types are lower case,\n * non-primitive types are upper-camel-case.\n * For example 'number', 'string', 'Array', 'Date'.\n */\n return typed(name, {\n any: _typeOf\n })\n})\n","/**\n * Compares two BigNumbers.\n * @param {BigNumber} x First value to compare\n * @param {BigNumber} y Second value to compare\n * @param {number} [epsilon] The maximum relative difference between x and y\n * If epsilon is undefined or null, the function will\n * test whether x and y are exactly equal.\n * @return {boolean} whether the two numbers are nearly equal\n */\nexport function nearlyEqual (x, y, epsilon) {\n // if epsilon is null or undefined, test whether x and y are exactly equal\n if (epsilon === null || epsilon === undefined) {\n return x.eq(y)\n }\n\n // use \"==\" operator, handles infinities\n if (x.eq(y)) {\n return true\n }\n\n // NaN\n if (x.isNaN() || y.isNaN()) {\n return false\n }\n\n // at this point x and y should be finite\n if (x.isFinite() && y.isFinite()) {\n // check numbers are very close, needed when comparing numbers near zero\n const diff = x.minus(y).abs()\n if (diff.isZero()) {\n return true\n } else {\n // use relative error\n const max = x.constructor.max(x.abs(), y.abs())\n return diff.lte(max.times(epsilon))\n }\n }\n\n // Infinite and Number or negative Infinite and positive Infinite cases\n return false\n}\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { complexEquals } from '../../utils/complex.js'\n\nconst name = 'equalScalar'\nconst dependencies = ['typed', 'config']\n\nexport const createEqualScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed, config }) => {\n /**\n * Test whether two scalar values are nearly equal.\n *\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Complex} y Second value to compare\n * @return {boolean} Returns true when the compared values are equal, else returns false\n * @private\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x === y\n },\n\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.eq(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.equals(y)\n },\n\n 'Complex, Complex': function (x, y) {\n return complexEquals(x, y, config.epsilon)\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n }\n })\n})\n\nexport const createEqualScalarNumber = factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual } from './number.js'\n\n/**\n * Test whether two complex values are equal provided a given epsilon.\n * Does not use or change the global Complex.EPSILON setting\n * @param {Complex} x\n * @param {Complex} y\n * @param {number} epsilon\n * @returns {boolean}\n */\nexport function complexEquals (x, y, epsilon) {\n return nearlyEqual(x.re, y.re, epsilon) && nearlyEqual(x.im, y.im, epsilon)\n}\n","import { isArray, isBigNumber, isCollection, isIndex, isMatrix, isNumber, isString, typeOf } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { format } from '../../utils/string.js'\nimport { clone, deepStrictEqual } from '../../utils/object.js'\nimport { arraySize, getArrayDataType, unsqueeze, validateIndex } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { DimensionError } from '../../error/DimensionError.js'\n\nconst name = 'SparseMatrix'\nconst dependencies = [\n 'typed',\n 'equalScalar',\n 'Matrix'\n]\n\nexport const createSparseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar, Matrix }) => {\n /**\n * Sparse Matrix implementation. This type implements a Compressed Column Storage format\n * for sparse matrices.\n * @class SparseMatrix\n */\n function SparseMatrix (data, datatype) {\n if (!(this instanceof SparseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data)) {\n // create from matrix\n _createFromMatrix(this, data, datatype)\n } else if (data && isArray(data.index) && isArray(data.ptr) && isArray(data.size)) {\n // initialize fields\n this._values = data.values\n this._index = data.index\n this._ptr = data.ptr\n this._size = data.size\n this._datatype = datatype || data.datatype\n } else if (isArray(data)) {\n // create from array\n _createFromArray(this, data, datatype)\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._values = []\n this._index = []\n this._ptr = [0]\n this._size = [0, 0]\n this._datatype = datatype\n }\n }\n\n function _createFromMatrix (matrix, source, datatype) {\n // check matrix type\n if (source.type === 'SparseMatrix') {\n // clone arrays\n matrix._values = source._values ? clone(source._values) : undefined\n matrix._index = clone(source._index)\n matrix._ptr = clone(source._ptr)\n matrix._size = clone(source._size)\n matrix._datatype = datatype || source._datatype\n } else {\n // build from matrix data\n _createFromArray(matrix, source.valueOf(), datatype || source._datatype)\n }\n }\n\n function _createFromArray (matrix, data, datatype) {\n // initialize fields\n matrix._values = []\n matrix._index = []\n matrix._ptr = []\n matrix._datatype = datatype\n // discover rows & columns, do not use math.size() to avoid looping array twice\n const rows = data.length\n let columns = 0\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, datatype)\n }\n\n // check we have rows (empty array)\n if (rows > 0) {\n // column index\n let j = 0\n do {\n // store pointer to values index\n matrix._ptr.push(matrix._index.length)\n // loop rows\n for (let i = 0; i < rows; i++) {\n // current row\n const row = data[i]\n // check row is an array\n if (isArray(row)) {\n // update columns if needed (only on first column)\n if (j === 0 && columns < row.length) { columns = row.length }\n // check row has column\n if (j < row.length) {\n // value\n const v = row[j]\n // check value != 0\n if (!eq(v, zero)) {\n // store value\n matrix._values.push(v)\n // index\n matrix._index.push(i)\n }\n }\n } else {\n // update columns if needed (only on first column)\n if (j === 0 && columns < 1) { columns = 1 }\n // check value != 0 (row is a scalar)\n if (!eq(row, zero)) {\n // store value\n matrix._values.push(row)\n // index\n matrix._index.push(i)\n }\n }\n }\n // increment index\n j++\n }\n while (j < columns)\n }\n // store number of values in ptr\n matrix._ptr.push(matrix._index.length)\n // size\n matrix._size = [rows, columns]\n }\n\n SparseMatrix.prototype = new Matrix()\n\n /**\n * Create a new SparseMatrix\n */\n SparseMatrix.prototype.createSparseMatrix = function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n\n /**\n * Attach type information\n */\n SparseMatrix.prototype.type = 'SparseMatrix'\n SparseMatrix.prototype.isSparseMatrix = true\n\n /**\n * Get the matrix type\n *\n * Usage:\n * const matrixType = matrix.getDataType() // retrieves the matrix type\n *\n * @memberOf SparseMatrix\n * @return {string} type information; if multiple types are found from the Matrix, it will return \"mixed\"\n */\n SparseMatrix.prototype.getDataType = function () {\n return getArrayDataType(this._values, typeOf)\n }\n\n /**\n * Get the storage format used by the matrix.\n *\n * Usage:\n * const format = matrix.storage() // retrieve storage format\n *\n * @memberof SparseMatrix\n * @return {string} The storage format.\n */\n SparseMatrix.prototype.storage = function () {\n return 'sparse'\n }\n\n /**\n * Get the datatype of the data stored in the matrix.\n *\n * Usage:\n * const format = matrix.datatype() // retrieve matrix datatype\n *\n * @memberof SparseMatrix\n * @return {string} The datatype.\n */\n SparseMatrix.prototype.datatype = function () {\n return this._datatype\n }\n\n /**\n * Create a new SparseMatrix\n * @memberof SparseMatrix\n * @param {Array} data\n * @param {string} [datatype]\n */\n SparseMatrix.prototype.create = function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n\n /**\n * Get the matrix density.\n *\n * Usage:\n * const density = matrix.density() // retrieve matrix density\n *\n * @memberof SparseMatrix\n * @return {number} The matrix density.\n */\n SparseMatrix.prototype.density = function () {\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n // calculate density\n return rows !== 0 && columns !== 0 ? (this._index.length / (rows * columns)) : 0\n }\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @memberof SparseMatrix\n * @param {Index} index\n * @param {Array | Matrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n SparseMatrix.prototype.subset = function (index, replacement, defaultValue) { // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke subset on a Pattern only matrix') }\n\n // check arguments\n switch (arguments.length) {\n case 1:\n return _getsubset(this, index)\n\n // intentional fall through\n case 2:\n case 3:\n return _setsubset(this, index, replacement, defaultValue)\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n function _getsubset (matrix, idx) {\n // check idx\n if (!isIndex(idx)) {\n throw new TypeError('Invalid index')\n }\n\n const isScalar = idx.isScalar()\n if (isScalar) {\n // return a scalar\n return matrix.get(idx.min())\n }\n // validate dimensions\n const size = idx.size()\n if (size.length !== matrix._size.length) {\n throw new DimensionError(size.length, matrix._size.length)\n }\n\n // vars\n let i, ii, k, kk\n\n // validate if any of the ranges in the index is out of range\n const min = idx.min()\n const max = idx.max()\n for (i = 0, ii = matrix._size.length; i < ii; i++) {\n validateIndex(min[i], matrix._size[i])\n validateIndex(max[i], matrix._size[i])\n }\n\n // matrix arrays\n const mvalues = matrix._values\n const mindex = matrix._index\n const mptr = matrix._ptr\n\n // rows & columns dimensions for result matrix\n const rows = idx.dimension(0)\n const columns = idx.dimension(1)\n\n // workspace & permutation vector\n const w = []\n const pv = []\n\n // loop rows in resulting matrix\n rows.forEach(function (i, r) {\n // update permutation vector\n pv[i] = r[0]\n // mark i in workspace\n w[i] = true\n })\n\n // result matrix arrays\n const values = mvalues ? [] : undefined\n const index = []\n const ptr = []\n\n // loop columns in result matrix\n columns.forEach(function (j) {\n // update ptr\n ptr.push(index.length)\n // loop values in column j\n for (k = mptr[j], kk = mptr[j + 1]; k < kk; k++) {\n // row\n i = mindex[k]\n // check row is in result matrix\n if (w[i] === true) {\n // push index\n index.push(pv[i])\n // check we need to process values\n if (values) { values.push(mvalues[k]) }\n }\n }\n })\n // update ptr\n ptr.push(index.length)\n\n // return matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: size,\n datatype: matrix._datatype\n })\n }\n\n function _setsubset (matrix, index, submatrix, defaultValue) {\n // check index\n if (!index || index.isIndex !== true) {\n throw new TypeError('Invalid index')\n }\n\n // get index size and check whether the index contains a single value\n const iSize = index.size()\n const isScalar = index.isScalar()\n\n // calculate the size of the submatrix, and convert it into an Array if needed\n let sSize\n if (isMatrix(submatrix)) {\n // submatrix size\n sSize = submatrix.size()\n // use array representation\n submatrix = submatrix.toArray()\n } else {\n // get submatrix size (array, scalar)\n sSize = arraySize(submatrix)\n }\n\n // check index is a scalar\n if (isScalar) {\n // verify submatrix is a scalar\n if (sSize.length !== 0) {\n throw new TypeError('Scalar expected')\n }\n // set value\n matrix.set(index.min(), submatrix, defaultValue)\n } else {\n // validate dimensions, index size must be one or two dimensions\n if (iSize.length !== 1 && iSize.length !== 2) {\n throw new DimensionError(iSize.length, matrix._size.length, '<')\n }\n\n // check submatrix and index have the same dimensions\n if (sSize.length < iSize.length) {\n // calculate number of missing outer dimensions\n let i = 0\n let outer = 0\n while (iSize[i] === 1 && sSize[i] === 1) {\n i++\n }\n while (iSize[i] === 1) {\n outer++\n i++\n }\n // unsqueeze both outer and inner dimensions\n submatrix = unsqueeze(submatrix, iSize.length, outer, sSize)\n }\n\n // check whether the size of the submatrix matches the index size\n if (!deepStrictEqual(iSize, sSize)) {\n throw new DimensionError(iSize, sSize, '>')\n }\n\n // offsets\n const x0 = index.min()[0]\n const y0 = index.min()[1]\n\n // submatrix rows and columns\n const m = sSize[0]\n const n = sSize[1]\n\n // loop submatrix\n for (let x = 0; x < m; x++) {\n // loop columns\n for (let y = 0; y < n; y++) {\n // value at i, j\n const v = submatrix[x][y]\n // invoke set (zero value will remove entry from matrix)\n matrix.set([x + x0, y + y0], v, defaultValue)\n }\n }\n }\n return matrix\n }\n\n /**\n * Get a single element from the matrix.\n * @memberof SparseMatrix\n * @param {number[]} index Zero-based index\n * @return {*} value\n */\n SparseMatrix.prototype.get = function (index) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke get on a Pattern only matrix') }\n\n // row and column\n const i = index[0]\n const j = index[1]\n\n // check i, j are valid\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[1])\n\n // find value index\n const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)\n // check k is prior to next column k and it is in the correct row\n if (k < this._ptr[j + 1] && this._index[k] === i) { return this._values[k] }\n\n return 0\n }\n\n /**\n * Replace a single element in the matrix.\n * @memberof SparseMatrix\n * @param {number[]} index Zero-based index\n * @param {*} v\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be set to zero.\n * @return {SparseMatrix} self\n */\n SparseMatrix.prototype.set = function (index, v, defaultValue) {\n if (!isArray(index)) { throw new TypeError('Array expected') }\n if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }\n\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke set on a Pattern only matrix') }\n\n // row and column\n const i = index[0]\n const j = index[1]\n\n // rows & columns\n let rows = this._size[0]\n let columns = this._size[1]\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(this._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [this._datatype, this._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, this._datatype)\n }\n\n // check we need to resize matrix\n if (i > rows - 1 || j > columns - 1) {\n // resize matrix\n _resize(this, Math.max(i + 1, rows), Math.max(j + 1, columns), defaultValue)\n // update rows & columns\n rows = this._size[0]\n columns = this._size[1]\n }\n\n // check i, j are valid\n validateIndex(i, rows)\n validateIndex(j, columns)\n\n // find value index\n const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)\n // check k is prior to next column k and it is in the correct row\n if (k < this._ptr[j + 1] && this._index[k] === i) {\n // check value != 0\n if (!eq(v, zero)) {\n // update value\n this._values[k] = v\n } else {\n // remove value from matrix\n _remove(k, j, this._values, this._index, this._ptr)\n }\n } else {\n // insert value @ (i, j)\n _insert(k, i, j, v, this._values, this._index, this._ptr)\n }\n\n return this\n }\n\n function _getValueIndex (i, top, bottom, index) {\n // check row is on the bottom side\n if (bottom - top === 0) { return bottom }\n // loop rows [top, bottom[\n for (let r = top; r < bottom; r++) {\n // check we found value index\n if (index[r] === i) { return r }\n }\n // we did not find row\n return top\n }\n\n function _remove (k, j, values, index, ptr) {\n // remove value @ k\n values.splice(k, 1)\n index.splice(k, 1)\n // update pointers\n for (let x = j + 1; x < ptr.length; x++) { ptr[x]-- }\n }\n\n function _insert (k, i, j, v, values, index, ptr) {\n // insert value\n values.splice(k, 0, v)\n // update row for k\n index.splice(k, 0, i)\n // update column pointers\n for (let x = j + 1; x < ptr.length; x++) { ptr[x]++ }\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @memberof SparseMatrix\n * @param {number[] | Matrix} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n SparseMatrix.prototype.resize = function (size, defaultValue, copy) {\n // validate arguments\n if (!isCollection(size)) {\n throw new TypeError('Array or Matrix expected')\n }\n\n // SparseMatrix input is always 2d, flatten this into 1d if it's indeed a vector\n const sizeArray = size.valueOf().map(value => {\n return Array.isArray(value) && value.length === 1\n ? value[0]\n : value\n })\n\n if (sizeArray.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // check sizes\n sizeArray.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(sizeArray) + ')')\n }\n })\n\n // matrix to resize\n const m = copy ? this.clone() : this\n // resize matrix\n return _resize(m, sizeArray[0], sizeArray[1], defaultValue)\n }\n\n function _resize (matrix, rows, columns, defaultValue) {\n // value to insert at the time of growing matrix\n let value = defaultValue || 0\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(matrix._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, matrix._datatype)\n // convert value to the same datatype\n value = typed.convert(value, matrix._datatype)\n }\n\n // should we insert the value?\n const ins = !eq(value, zero)\n\n // old columns and rows\n const r = matrix._size[0]\n let c = matrix._size[1]\n\n let i, j, k\n\n // check we need to increase columns\n if (columns > c) {\n // loop new columns\n for (j = c; j < columns; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._values.length\n // check we need to insert matrix._values\n if (ins) {\n // loop rows\n for (i = 0; i < r; i++) {\n // add new matrix._values\n matrix._values.push(value)\n // update matrix._index\n matrix._index.push(i)\n }\n }\n }\n // store number of matrix._values in matrix._ptr\n matrix._ptr[columns] = matrix._values.length\n } else if (columns < c) {\n // truncate matrix._ptr\n matrix._ptr.splice(columns + 1, c - columns)\n // truncate matrix._values and matrix._index\n matrix._values.splice(matrix._ptr[columns], matrix._values.length)\n matrix._index.splice(matrix._ptr[columns], matrix._index.length)\n }\n // update columns\n c = columns\n\n // check we need to increase rows\n if (rows > r) {\n // check we have to insert values\n if (ins) {\n // inserts\n let n = 0\n // loop columns\n for (j = 0; j < c; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._ptr[j] + n\n // where to insert matrix._values\n k = matrix._ptr[j + 1] + n\n // pointer\n let p = 0\n // loop new rows, initialize pointer\n for (i = r; i < rows; i++, p++) {\n // add value\n matrix._values.splice(k + p, 0, value)\n // update matrix._index\n matrix._index.splice(k + p, 0, i)\n // increment inserts\n n++\n }\n }\n // store number of matrix._values in matrix._ptr\n matrix._ptr[c] = matrix._values.length\n }\n } else if (rows < r) {\n // deletes\n let d = 0\n // loop columns\n for (j = 0; j < c; j++) {\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._ptr[j] - d\n // where matrix._values start for next column\n const k0 = matrix._ptr[j]\n const k1 = matrix._ptr[j + 1] - d\n // loop matrix._index\n for (k = k0; k < k1; k++) {\n // row\n i = matrix._index[k]\n // check we need to delete value and matrix._index\n if (i > rows - 1) {\n // remove value\n matrix._values.splice(k, 1)\n // remove item from matrix._index\n matrix._index.splice(k, 1)\n // increase deletes\n d++\n }\n }\n }\n // update matrix._ptr for current column\n matrix._ptr[j] = matrix._values.length\n }\n // update matrix._size\n matrix._size[0] = rows\n matrix._size[1] = columns\n // return matrix\n return matrix\n }\n\n /**\n * Reshape the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (reshape in place).\n *\n * NOTE: This might be better suited to copy by default, instead of modifying\n * in place. For now, it operates in place to remain consistent with\n * resize().\n *\n * @memberof SparseMatrix\n * @param {number[]} size The new size the matrix should have.\n * @param {boolean} [copy] Return a reshaped copy of the matrix\n *\n * @return {Matrix} The reshaped matrix\n */\n SparseMatrix.prototype.reshape = function (size, copy) {\n // validate arguments\n if (!isArray(size)) { throw new TypeError('Array expected') }\n if (size.length !== 2) { throw new Error('Sparse matrices can only be reshaped in two dimensions') }\n\n // check sizes\n size.forEach(function (value) {\n if (!isNumber(value) || !isInteger(value) || value < 0) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n })\n\n // m * n must not change\n if (this._size[0] * this._size[1] !== size[0] * size[1]) {\n throw new Error('Reshaping sparse matrix will result in the wrong number of elements')\n }\n\n // matrix to reshape\n const m = copy ? this.clone() : this\n\n // return unchanged if the same shape\n if (this._size[0] === size[0] && this._size[1] === size[1]) {\n return m\n }\n\n // Convert to COO format (generate a column index)\n const colIndex = []\n for (let i = 0; i < m._ptr.length; i++) {\n for (let j = 0; j < m._ptr[i + 1] - m._ptr[i]; j++) {\n colIndex.push(i)\n }\n }\n\n // Clone the values array\n const values = m._values.slice()\n\n // Clone the row index array\n const rowIndex = m._index.slice()\n\n // Transform the (row, column) indices\n for (let i = 0; i < m._index.length; i++) {\n const r1 = rowIndex[i]\n const c1 = colIndex[i]\n const flat = r1 * m._size[1] + c1\n colIndex[i] = flat % size[1]\n rowIndex[i] = Math.floor(flat / size[1])\n }\n\n // Now reshaping is supposed to preserve the row-major order, BUT these sparse matrices are stored\n // in column-major order, so we have to reorder the value array now. One option is to use a multisort,\n // sorting several arrays based on some other array.\n\n // OR, we could easily just:\n\n // 1. Remove all values from the matrix\n m._values.length = 0\n m._index.length = 0\n m._ptr.length = size[1] + 1\n m._size = size.slice()\n for (let i = 0; i < m._ptr.length; i++) {\n m._ptr[i] = 0\n }\n\n // 2. Re-insert all elements in the proper order (simplified code from SparseMatrix.prototype.set)\n // This step is probably the most time-consuming\n for (let h = 0; h < values.length; h++) {\n const i = rowIndex[h]\n const j = colIndex[h]\n const v = values[h]\n const k = _getValueIndex(i, m._ptr[j], m._ptr[j + 1], m._index)\n _insert(k, i, j, v, m._values, m._index, m._ptr)\n }\n\n // The value indices are inserted out of order, but apparently that's... still OK?\n\n return m\n }\n\n /**\n * Create a clone of the matrix\n * @memberof SparseMatrix\n * @return {SparseMatrix} clone\n */\n SparseMatrix.prototype.clone = function () {\n const m = new SparseMatrix({\n values: this._values ? clone(this._values) : undefined,\n index: clone(this._index),\n ptr: clone(this._ptr),\n size: clone(this._size),\n datatype: this._datatype\n })\n return m\n }\n\n /**\n * Retrieve the size of the matrix.\n * @memberof SparseMatrix\n * @returns {number[]} size\n */\n SparseMatrix.prototype.size = function () {\n return this._size.slice(0) // copy the Array\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on\n * each entry of the matrix.\n * @memberof SparseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n *\n * @return {SparseMatrix} matrix\n */\n SparseMatrix.prototype.map = function (callback, skipZeros) {\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke map on a Pattern only matrix') }\n // matrix instance\n const me = this\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // invoke callback\n const invoke = function (v, i, j) {\n // invoke callback\n return callback(v, [i, j], me)\n }\n // invoke _map\n return _map(this, 0, rows - 1, 0, columns - 1, invoke, skipZeros)\n }\n\n /**\n * Create a new matrix with the results of the callback function executed on the interval\n * [minRow..maxRow, minColumn..maxColumn].\n */\n function _map (matrix, minRow, maxRow, minColumn, maxColumn, callback, skipZeros) {\n // result arrays\n const values = []\n const index = []\n const ptr = []\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(matrix._datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, matrix._datatype)\n }\n\n // invoke callback\n const invoke = function (v, x, y) {\n // invoke callback\n v = callback(v, x, y)\n // check value != 0\n if (!eq(v, zero)) {\n // store value\n values.push(v)\n // index\n index.push(x)\n }\n }\n // loop columns\n for (let j = minColumn; j <= maxColumn; j++) {\n // store pointer to values index\n ptr.push(values.length)\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = matrix._ptr[j]\n const k1 = matrix._ptr[j + 1]\n\n if (skipZeros) {\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = matrix._index[k]\n // check i is in range\n if (i >= minRow && i <= maxRow) {\n // value @ k\n invoke(matrix._values[k], i - minRow, j - minColumn)\n }\n }\n } else {\n // create a cache holding all defined values\n const values = {}\n for (let k = k0; k < k1; k++) {\n const i = matrix._index[k]\n values[i] = matrix._values[k]\n }\n\n // loop over all rows (indexes can be unordered so we can't use that),\n // and either read the value or zero\n for (let i = minRow; i <= maxRow; i++) {\n const value = (i in values) ? values[i] : 0\n invoke(value, i - minRow, j - minColumn)\n }\n }\n }\n\n // store number of values in ptr\n ptr.push(values.length)\n // return sparse matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [maxRow - minRow + 1, maxColumn - minColumn + 1]\n })\n }\n\n /**\n * Execute a callback function on each entry of the matrix.\n * @memberof SparseMatrix\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix being traversed.\n * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.\n */\n SparseMatrix.prototype.forEach = function (callback, skipZeros) {\n // check it is a pattern matrix\n if (!this._values) { throw new Error('Cannot invoke forEach on a Pattern only matrix') }\n // matrix instance\n const me = this\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n\n if (skipZeros) {\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = this._index[k]\n\n // value @ k\n callback(this._values[k], [i, j], me)\n }\n } else {\n // create a cache holding all defined values\n const values = {}\n for (let k = k0; k < k1; k++) {\n const i = this._index[k]\n values[i] = this._values[k]\n }\n\n // loop over all rows (indexes can be unordered so we can't use that),\n // and either read the value or zero\n for (let i = 0; i < rows; i++) {\n const value = (i in values) ? values[i] : 0\n callback(value, [i, j], me)\n }\n }\n }\n }\n\n /**\n * Create an Array with a copy of the data of the SparseMatrix\n * @memberof SparseMatrix\n * @returns {Array} array\n */\n SparseMatrix.prototype.toArray = function () {\n return _toArray(this._values, this._index, this._ptr, this._size, true)\n }\n\n /**\n * Get the primitive value of the SparseMatrix: a two dimensions array\n * @memberof SparseMatrix\n * @returns {Array} array\n */\n SparseMatrix.prototype.valueOf = function () {\n return _toArray(this._values, this._index, this._ptr, this._size, false)\n }\n\n function _toArray (values, index, ptr, size, copy) {\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n // result\n const a = []\n // vars\n let i, j\n // initialize array\n for (i = 0; i < rows; i++) {\n a[i] = []\n for (j = 0; j < columns; j++) { a[i][j] = 0 }\n }\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n i = index[k]\n // set value (use one for pattern matrix)\n a[i][j] = values ? (copy ? clone(values[k]) : values[k]) : 1\n }\n }\n return a\n }\n\n /**\n * Get a string representation of the matrix, with optional formatting options.\n * @memberof SparseMatrix\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @returns {string} str\n */\n SparseMatrix.prototype.format = function (options) {\n // rows and columns\n const rows = this._size[0]\n const columns = this._size[1]\n // density\n const density = this.density()\n // rows & columns\n let str = 'Sparse Matrix [' + format(rows, options) + ' x ' + format(columns, options) + '] density: ' + format(density, options) + '\\n'\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = this._index[k]\n // append value\n str += '\\n (' + format(i, options) + ', ' + format(j, options) + ') ==> ' + (this._values ? format(this._values[k], options) : 'X')\n }\n }\n return str\n }\n\n /**\n * Get a string representation of the matrix\n * @memberof SparseMatrix\n * @returns {string} str\n */\n SparseMatrix.prototype.toString = function () {\n return format(this.toArray())\n }\n\n /**\n * Get a JSON representation of the matrix\n * @memberof SparseMatrix\n * @returns {Object}\n */\n SparseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'SparseMatrix',\n values: this._values,\n index: this._index,\n ptr: this._ptr,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Get the kth Matrix diagonal.\n *\n * @memberof SparseMatrix\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will retrieved.\n *\n * @returns {Matrix} The matrix vector with the diagonal values.\n */\n SparseMatrix.prototype.diagonal = function (k) {\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows & columns\n const rows = this._size[0]\n const columns = this._size[1]\n\n // number diagonal values\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // diagonal arrays\n const values = []\n const index = []\n const ptr = []\n // initial ptr value\n ptr[0] = 0\n // loop columns\n for (let j = kSuper; j < columns && values.length < n; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = this._ptr[j]\n const k1 = this._ptr[j + 1]\n // loop x within [k0, k1[\n for (let x = k0; x < k1; x++) {\n // row index\n const i = this._index[x]\n // check row\n if (i === j - kSuper + kSub) {\n // value on this column\n values.push(this._values[x])\n // store row\n index[values.length - 1] = i - kSub\n // exit loop\n break\n }\n }\n }\n // close ptr\n ptr.push(values.length)\n // return matrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [n, 1]\n })\n }\n\n /**\n * Generate a matrix from a JSON object\n * @memberof SparseMatrix\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SparseMatrix\", \"values\": [], \"index\": [], \"ptr\": [], \"size\": []}`,\n * where mathjs is optional\n * @returns {SparseMatrix}\n */\n SparseMatrix.fromJSON = function (json) {\n return new SparseMatrix(json)\n }\n\n /**\n * Create a diagonal matrix.\n *\n * @memberof SparseMatrix\n * @param {Array} size The matrix size.\n * @param {number | Array | Matrix } value The values for the diagonal.\n * @param {number | BigNumber} [k=0] The kth diagonal where the vector will be filled in.\n * @param {number} [defaultValue] The default value for non-diagonal\n * @param {string} [datatype] The Matrix datatype, values must be of this datatype.\n *\n * @returns {SparseMatrix}\n */\n SparseMatrix.diagonal = function (size, value, k, defaultValue, datatype) {\n if (!isArray(size)) { throw new TypeError('Array expected, size parameter') }\n if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }\n\n // map size & validate\n size = size.map(function (s) {\n // check it is a big number\n if (isBigNumber(s)) {\n // convert it\n s = s.toNumber()\n }\n // validate arguments\n if (!isNumber(s) || !isInteger(s) || s < 1) {\n throw new Error('Size values must be positive integers')\n }\n return s\n })\n\n // validate k if any\n if (k) {\n // convert BigNumber to a number\n if (isBigNumber(k)) { k = k.toNumber() }\n // is must be an integer\n if (!isNumber(k) || !isInteger(k)) {\n throw new TypeError('The parameter k must be an integer number')\n }\n } else {\n // default value\n k = 0\n }\n\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n if (isString(datatype)) {\n // find signature that matches (datatype, datatype)\n eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar\n // convert 0 to the same datatype\n zero = typed.convert(0, datatype)\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // number of non-zero items\n const n = Math.min(rows - kSub, columns - kSuper)\n\n // value extraction function\n let _value\n\n // check value\n if (isArray(value)) {\n // validate array\n if (value.length !== n) {\n // number of values in array must be n\n throw new Error('Invalid value array length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value[i]\n }\n } else if (isMatrix(value)) {\n // matrix size\n const ms = value.size()\n // validate matrix\n if (ms.length !== 1 || ms[0] !== n) {\n // number of values in array must be n\n throw new Error('Invalid matrix length')\n }\n // define function\n _value = function (i) {\n // return value @ i\n return value.get([i])\n }\n } else {\n // define function\n _value = function () {\n // return value\n return value\n }\n }\n\n // create arrays\n const values = []\n const index = []\n const ptr = []\n\n // loop items\n for (let j = 0; j < columns; j++) {\n // number of rows with value\n ptr.push(values.length)\n // diagonal index\n const i = j - kSuper\n // check we need to set diagonal value\n if (i >= 0 && i < n) {\n // get value @ i\n const v = _value(i)\n // check for zero\n if (!eq(v, zero)) {\n // column\n index.push(i + kSub)\n // add value\n values.push(v)\n }\n }\n }\n // last value should be number of values\n ptr.push(values.length)\n // create SparseMatrix\n return new SparseMatrix({\n values: values,\n index: index,\n ptr: ptr,\n size: [rows, columns]\n })\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @memberof SparseMatrix\n * @param {number} i Matrix row index 1\n * @param {number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n SparseMatrix.prototype.swapRows = function (i, j) {\n // check index\n if (!isNumber(i) || !isInteger(i) || !isNumber(j) || !isInteger(j)) {\n throw new Error('Row index must be positive integers')\n }\n // check dimensions\n if (this._size.length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n // validate index\n validateIndex(i, this._size[0])\n validateIndex(j, this._size[0])\n\n // swap rows\n SparseMatrix._swapRows(i, j, this._size[1], this._values, this._index, this._ptr)\n // return current instance\n return this\n }\n\n /**\n * Loop rows with data in column j.\n *\n * @param {number} j Column\n * @param {Array} values Matrix values\n * @param {Array} index Matrix row indeces\n * @param {Array} ptr Matrix column pointers\n * @param {Function} callback Callback function invoked for every row in column j\n */\n SparseMatrix._forEachRow = function (j, values, index, ptr, callback) {\n // indeces for column j\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop\n for (let k = k0; k < k1; k++) {\n // invoke callback\n callback(index[k], values[k])\n }\n }\n\n /**\n * Swap rows x and y in Sparse Matrix data structures.\n *\n * @param {number} x Matrix row index 1\n * @param {number} y Matrix row index 2\n * @param {number} columns Number of columns in matrix\n * @param {Array} values Matrix values\n * @param {Array} index Matrix row indeces\n * @param {Array} ptr Matrix column pointers\n */\n SparseMatrix._swapRows = function (x, y, columns, values, index, ptr) {\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // find value index @ x\n const kx = _getValueIndex(x, k0, k1, index)\n // find value index @ x\n const ky = _getValueIndex(y, k0, k1, index)\n // check both rows exist in matrix\n if (kx < k1 && ky < k1 && index[kx] === x && index[ky] === y) {\n // swap values (check for pattern matrix)\n if (values) {\n const v = values[kx]\n values[kx] = values[ky]\n values[ky] = v\n }\n // next column\n continue\n }\n // check x row exist & no y row\n if (kx < k1 && index[kx] === x && (ky >= k1 || index[ky] !== y)) {\n // value @ x (check for pattern matrix)\n const vx = values ? values[kx] : undefined\n // insert value @ y\n index.splice(ky, 0, y)\n if (values) { values.splice(ky, 0, vx) }\n // remove value @ x (adjust array index if needed)\n index.splice(ky <= kx ? kx + 1 : kx, 1)\n if (values) { values.splice(ky <= kx ? kx + 1 : kx, 1) }\n // next column\n continue\n }\n // check y row exist & no x row\n if (ky < k1 && index[ky] === y && (kx >= k1 || index[kx] !== x)) {\n // value @ y (check for pattern matrix)\n const vy = values ? values[ky] : undefined\n // insert value @ x\n index.splice(kx, 0, x)\n if (values) { values.splice(kx, 0, vy) }\n // remove value @ y (adjust array index if needed)\n index.splice(kx <= ky ? ky + 1 : ky, 1)\n if (values) { values.splice(kx <= ky ? ky + 1 : ky, 1) }\n }\n }\n }\n\n return SparseMatrix\n}, { isClass: true })\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\n\nconst name = 'number'\nconst dependencies = ['typed']\n\nexport const createNumber = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a number or convert a string, boolean, or unit to a number.\n * When value is a matrix, all elements will be converted to number.\n *\n * Syntax:\n *\n * math.number(value)\n * math.number(unit, valuelessUnit)\n *\n * Examples:\n *\n * math.number(2) // returns number 2\n * math.number('7.2') // returns number 7.2\n * math.number(true) // returns number 1\n * math.number([true, false, true, true]) // returns [1, 0, 1, 1]\n * math.number(math.unit('52cm'), 'm') // returns 0.52\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, string, unit\n *\n * @param {string | number | BigNumber | Fraction | boolean | Array | Matrix | Unit | null} [value] Value to be converted\n * @param {Unit | string} [valuelessUnit] A valueless unit, used to convert a unit to a number\n * @return {number | Array | Matrix} The created number\n */\n const number = typed('number', {\n '': function () {\n return 0\n },\n\n number: function (x) {\n return x\n },\n\n string: function (x) {\n if (x === 'NaN') return NaN\n let size = 0\n const boxMatch = x.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/)\n if (boxMatch) {\n // x includes a size suffix like 0xffffi32, so we extract\n // the suffix and remove it from x\n size = Number(boxMatch[2])\n x = boxMatch[1]\n }\n let num = Number(x)\n if (isNaN(num)) {\n throw new SyntaxError('String \"' + x + '\" is no valid number')\n }\n if (boxMatch) {\n // x is a signed bin, oct, or hex literal\n // num is the value of string x if x is interpreted as unsigned\n if (num > 2 ** size - 1) {\n // literal is too large for size suffix\n throw new SyntaxError(`String \"${x}\" is out of range`)\n }\n // check if the bit at index size - 1 is set and if so do the twos complement\n if (num >= 2 ** (size - 1)) {\n num = num - 2 ** size\n }\n }\n return num\n },\n\n BigNumber: function (x) {\n return x.toNumber()\n },\n\n Fraction: function (x) {\n return x.valueOf()\n },\n\n Unit: function (x) {\n throw new Error('Second argument with valueless unit expected')\n },\n\n null: function (x) {\n return 0\n },\n\n 'Unit, string | Unit': function (unit, valuelessUnit) {\n return unit.toNumber(valuelessUnit)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n\n // reviver function to parse a JSON object like:\n //\n // {\"mathjs\":\"number\",\"value\":\"2.3\"}\n //\n // into a number 2.3\n number.fromJSON = function (json) {\n return parseFloat(json.value)\n }\n\n return number\n})\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\nimport { format } from '../utils/number.js'\n\nconst name = 'string'\nconst dependencies = ['typed']\n\nexport const createString = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a string or convert any object into a string.\n * Elements of Arrays and Matrices are processed element wise.\n *\n * Syntax:\n *\n * math.string(value)\n *\n * Examples:\n *\n * math.string(4.2) // returns string '4.2'\n * math.string(math.complex(3, 2) // returns string '3 + 2i'\n *\n * const u = math.unit(5, 'km')\n * math.string(u.to('m')) // returns string '5000 m'\n *\n * math.string([true, false]) // returns ['true', 'false']\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, number, unit\n *\n * @param {* | Array | Matrix | null} [value] A value to convert to a string\n * @return {string | Array | Matrix} The created string\n */\n return typed(name, {\n '': function () {\n return ''\n },\n\n number: format,\n\n null: function (x) {\n return 'null'\n },\n\n boolean: function (x) {\n return x + ''\n },\n\n string: function (x) {\n return x\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n any: function (x) {\n return String(x)\n }\n })\n})\n","import { factory } from '../utils/factory.js'\nimport { deepMap } from '../utils/collection.js'\n\nconst name = 'boolean'\nconst dependencies = ['typed']\n\nexport const createBoolean = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a boolean or convert a string or number to a boolean.\n * In case of a number, `true` is returned for non-zero numbers, and `false` in\n * case of zero.\n * Strings can be `'true'` or `'false'`, or can contain a number.\n * When value is a matrix, all elements will be converted to boolean.\n *\n * Syntax:\n *\n * math.boolean(x)\n *\n * Examples:\n *\n * math.boolean(0) // returns false\n * math.boolean(1) // returns true\n * math.boolean(-3) // returns true\n * math.boolean('true') // returns true\n * math.boolean('false') // returns false\n * math.boolean([1, 0, 1, 1]) // returns [true, false, true, true]\n *\n * See also:\n *\n * bignumber, complex, index, matrix, string, unit\n *\n * @param {string | number | boolean | Array | Matrix | null} value A value of any type\n * @return {boolean | Array | Matrix} The boolean value\n */\n return typed(name, {\n '': function () {\n return false\n },\n\n boolean: function (x) {\n return x\n },\n\n number: function (x) {\n return !!x\n },\n\n null: function (x) {\n return false\n },\n\n BigNumber: function (x) {\n return !x.isZero()\n },\n\n string: function (x) {\n // try case insensitive\n const lcase = x.toLowerCase()\n if (lcase === 'true') {\n return true\n } else if (lcase === 'false') {\n return false\n }\n\n // test whether value is a valid number\n const num = Number(x)\n if (x !== '' && !isNaN(num)) {\n return !!num\n }\n\n throw new Error('Cannot convert \"' + x + '\" to a boolean')\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'bignumber'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createBignumber = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Create a BigNumber, which can store numbers with arbitrary precision.\n * When a matrix is provided, all elements will be converted to BigNumber.\n *\n * Syntax:\n *\n * math.bignumber(x)\n *\n * Examples:\n *\n * 0.1 + 0.2 // returns number 0.30000000000000004\n * math.bignumber(0.1) + math.bignumber(0.2) // returns BigNumber 0.3\n *\n *\n * 7.2e500 // returns number Infinity\n * math.bignumber('7.2e500') // returns BigNumber 7.2e500\n *\n * See also:\n *\n * boolean, complex, index, matrix, string, unit\n *\n * @param {number | string | Fraction | BigNumber | Array | Matrix | boolean | null} [value] Value for the big number,\n * 0 by default.\n * @returns {BigNumber} The created bignumber\n */\n return typed('bignumber', {\n '': function () {\n return new BigNumber(0)\n },\n\n number: function (x) {\n // convert to string to prevent errors in case of >15 digits\n return new BigNumber(x + '')\n },\n\n string: function (x) {\n const match = x.match(/(0[box][0-9a-fA-F]*)i([0-9]*)/)\n if (match) {\n // x has a word size suffix\n const size = match[2]\n const n = BigNumber(match[1])\n const twoPowSize = new BigNumber(2).pow(Number(size))\n if (n.gt(twoPowSize.sub(1))) {\n throw new SyntaxError(`String \"${x}\" is out of range`)\n }\n const twoPowSizeSubOne = new BigNumber(2).pow(Number(size) - 1)\n if (n.gte(twoPowSizeSubOne)) {\n return n.sub(twoPowSize)\n } else {\n return n\n }\n }\n return new BigNumber(x)\n },\n\n BigNumber: function (x) {\n // we assume a BigNumber is immutable\n return x\n },\n\n Fraction: function (x) {\n return new BigNumber(x.n).div(x.d).times(x.s)\n },\n\n null: function (x) {\n return new BigNumber(0)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'complex'\nconst dependencies = ['typed', 'Complex']\n\nexport const createComplex = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex }) => {\n /**\n * Create a complex value or convert a value to a complex value.\n *\n * Syntax:\n *\n * math.complex() // creates a complex value with zero\n * // as real and imaginary part.\n * math.complex(re : number, im : string) // creates a complex value with provided\n * // values for real and imaginary part.\n * math.complex(re : number) // creates a complex value with provided\n * // real value and zero imaginary part.\n * math.complex(complex : Complex) // clones the provided complex value.\n * math.complex(arg : string) // parses a string into a complex value.\n * math.complex(array : Array) // converts the elements of the array\n * // or matrix element wise into a\n * // complex value.\n * math.complex({re: number, im: number}) // creates a complex value with provided\n * // values for real an imaginary part.\n * math.complex({r: number, phi: number}) // creates a complex value with provided\n * // polar coordinates\n *\n * Examples:\n *\n * const a = math.complex(3, -4) // a = Complex 3 - 4i\n * a.re = 5 // a = Complex 5 - 4i\n * const i = a.im // Number -4\n * const b = math.complex('2 + 6i') // Complex 2 + 6i\n * const c = math.complex() // Complex 0 + 0i\n * const d = math.add(a, b) // Complex 5 + 2i\n *\n * See also:\n *\n * bignumber, boolean, index, matrix, number, string, unit\n *\n * @param {* | Array | Matrix} [args]\n * Arguments specifying the real and imaginary part of the complex number\n * @return {Complex | Array | Matrix} Returns a complex value\n */\n return typed('complex', {\n '': function () {\n return Complex.ZERO\n },\n\n number: function (x) {\n return new Complex(x, 0)\n },\n\n 'number, number': function (re, im) {\n return new Complex(re, im)\n },\n\n // TODO: this signature should be redundant\n 'BigNumber, BigNumber': function (re, im) {\n return new Complex(re.toNumber(), im.toNumber())\n },\n\n Fraction: function (x) {\n return new Complex(x.valueOf(), 0)\n },\n\n Complex: function (x) {\n return x.clone()\n },\n\n string: function (x) {\n return Complex(x) // for example '2 + 3i'\n },\n\n null: function (x) {\n return Complex(0)\n },\n\n Object: function (x) {\n if ('re' in x && 'im' in x) {\n return new Complex(x.re, x.im)\n }\n\n if (('r' in x && 'phi' in x) || ('abs' in x && 'arg' in x)) {\n return new Complex(x)\n }\n\n throw new Error('Expected object with properties (re and im) or (r and phi) or (abs and arg)')\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'fraction'\nconst dependencies = ['typed', 'Fraction']\n\nexport const createFraction = /* #__PURE__ */ factory(name, dependencies, ({ typed, Fraction }) => {\n /**\n * Create a fraction convert a value to a fraction.\n *\n * Syntax:\n * math.fraction(numerator, denominator)\n * math.fraction({n: numerator, d: denominator})\n * math.fraction(matrix: Array | Matrix) Turn all matrix entries\n * into fractions\n *\n * Examples:\n *\n * math.fraction(1, 3)\n * math.fraction('2/3')\n * math.fraction({n: 2, d: 3})\n * math.fraction([0.2, 0.25, 1.25])\n *\n * See also:\n *\n * bignumber, number, string, unit\n *\n * @param {number | string | Fraction | BigNumber | Array | Matrix} [args]\n * Arguments specifying the numerator and denominator of\n * the fraction\n * @return {Fraction | Array | Matrix} Returns a fraction\n */\n return typed('fraction', {\n number: function (x) {\n if (!isFinite(x) || isNaN(x)) {\n throw new Error(x + ' cannot be represented as a fraction')\n }\n\n return new Fraction(x)\n },\n\n string: function (x) {\n return new Fraction(x)\n },\n\n 'number, number': function (numerator, denominator) {\n return new Fraction(numerator, denominator)\n },\n\n null: function (x) {\n return new Fraction(0)\n },\n\n BigNumber: function (x) {\n return new Fraction(x.toString())\n },\n\n Fraction: function (x) {\n return x // fractions are immutable\n },\n\n Object: function (x) {\n return new Fraction(x)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'matrix'\nconst dependencies = ['typed', 'Matrix', 'DenseMatrix', 'SparseMatrix']\n\nexport const createMatrix = /* #__PURE__ */ factory(name, dependencies, ({ typed, Matrix, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a Matrix. The function creates a new `math.Matrix` object from\n * an `Array`. A Matrix has utility functions to manipulate the data in the\n * matrix, like getting the size and getting or setting values in the matrix.\n * Supported storage formats are 'dense' and 'sparse'.\n *\n * Syntax:\n *\n * math.matrix() // creates an empty matrix using default storage format (dense).\n * math.matrix(data) // creates a matrix with initial data using default storage format (dense).\n * math.matrix('dense') // creates an empty matrix using the given storage format.\n * math.matrix(data, 'dense') // creates a matrix with initial data using the given storage format.\n * math.matrix(data, 'sparse') // creates a sparse matrix with initial data.\n * math.matrix(data, 'sparse', 'number') // creates a sparse matrix with initial data, number data type.\n *\n * Examples:\n *\n * let m = math.matrix([[1, 2], [3, 4]])\n * m.size() // Array [2, 2]\n * m.resize([3, 2], 5)\n * m.valueOf() // Array [[1, 2], [3, 4], [5, 5]]\n * m.get([1, 0]) // number 3\n *\n * See also:\n *\n * bignumber, boolean, complex, index, number, string, unit, sparse\n *\n * @param {Array | Matrix} [data] A multi dimensional array\n * @param {string} [format] The Matrix storage format\n *\n * @return {Matrix} The created matrix\n */\n return typed(name, {\n '': function () {\n return _create([])\n },\n\n string: function (format) {\n return _create([], format)\n },\n\n 'string, string': function (format, datatype) {\n return _create([], format, datatype)\n },\n\n Array: function (data) {\n return _create(data)\n },\n\n Matrix: function (data) {\n return _create(data, data.storage())\n },\n\n 'Array | Matrix, string': _create,\n\n 'Array | Matrix, string, string': _create\n })\n\n /**\n * Create a new Matrix with given storage format\n * @param {Array} data\n * @param {string} [format]\n * @param {string} [datatype]\n * @returns {Matrix} Returns a new Matrix\n * @private\n */\n function _create (data, format, datatype) {\n // get storage format constructor\n if (format === 'dense' || format === 'default' || format === undefined) {\n return new DenseMatrix(data, datatype)\n }\n\n if (format === 'sparse') {\n return new SparseMatrix(data, datatype)\n }\n\n throw new TypeError('Unknown matrix type ' + JSON.stringify(format) + '.')\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'splitUnit'\nconst dependencies = ['typed']\n\nexport const createSplitUnit = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Split a unit in an array of units whose sum is equal to the original unit.\n *\n * Syntax:\n *\n * splitUnit(unit: Unit, parts: Array.)\n *\n * Example:\n *\n * math.splitUnit(new Unit(1, 'm'), ['feet', 'inch'])\n * // [ 3 feet, 3.3700787401575 inch ]\n *\n * See also:\n *\n * unit\n *\n * @param {Array} [parts] An array of strings or valueless units.\n * @return {Array} An array of units.\n */\n return typed(name, {\n 'Unit, Array': function (unit, parts) {\n return unit.splitUnit(parts)\n }\n })\n})\n","import { isInteger, log2, log10, cbrt, expm1, sign, toFixed, log1p } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function absNumber (a) {\n return Math.abs(a)\n}\nabsNumber.signature = n1\n\nexport function addNumber (a, b) {\n return a + b\n}\naddNumber.signature = n2\n\nexport function subtractNumber (a, b) {\n return a - b\n}\nsubtractNumber.signature = n2\n\nexport function multiplyNumber (a, b) {\n return a * b\n}\nmultiplyNumber.signature = n2\n\nexport function divideNumber (a, b) {\n return a / b\n}\ndivideNumber.signature = n2\n\nexport function unaryMinusNumber (x) {\n return -x\n}\nunaryMinusNumber.signature = n1\n\nexport function unaryPlusNumber (x) {\n return x\n}\nunaryPlusNumber.signature = n1\n\nexport function cbrtNumber (x) {\n return cbrt(x)\n}\ncbrtNumber.signature = n1\n\nexport function ceilNumber (x) {\n return Math.ceil(x)\n}\nceilNumber.signature = n1\n\nexport function cubeNumber (x) {\n return x * x * x\n}\ncubeNumber.signature = n1\n\nexport function expNumber (x) {\n return Math.exp(x)\n}\nexpNumber.signature = n1\n\nexport function expm1Number (x) {\n return expm1(x)\n}\nexpm1Number.signature = n1\n\nexport function fixNumber (x) {\n return (x > 0) ? Math.floor(x) : Math.ceil(x)\n}\nfixNumber.signature = n1\n\nexport function floorNumber (x) {\n return Math.floor(x)\n}\nfloorNumber.signature = n1\n\n/**\n * Calculate gcd for numbers\n * @param {number} a\n * @param {number} b\n * @returns {number} Returns the greatest common denominator of a and b\n */\nexport function gcdNumber (a, b) {\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function gcd must be integer numbers')\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n let r\n while (b !== 0) {\n r = a % b\n a = b\n b = r\n }\n return (a < 0) ? -a : a\n}\ngcdNumber.signature = n2\n\n/**\n * Calculate lcm for two numbers\n * @param {number} a\n * @param {number} b\n * @returns {number} Returns the least common multiple of a and b\n */\nexport function lcmNumber (a, b) {\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function lcm must be integer numbers')\n }\n\n if (a === 0 || b === 0) {\n return 0\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n // evaluate lcm here inline to reduce overhead\n let t\n const prod = a * b\n while (b !== 0) {\n t = b\n b = a % t\n a = t\n }\n return Math.abs(prod / a)\n}\nlcmNumber.signature = n2\n\n/**\n * Calculate the logarithm of a value.\n * @param {number} x\n * @return {number}\n */\nexport function logNumber (x) {\n return Math.log(x)\n}\nlogNumber.signature = n1\n\n/**\n * Calculate the 10-base logarithm of a number\n * @param {number} x\n * @return {number}\n */\nexport function log10Number (x) {\n return log10(x)\n}\nlog10Number.signature = n1\n\n/**\n * Calculate the 2-base logarithm of a number\n * @param {number} x\n * @return {number}\n */\nexport function log2Number (x) {\n return log2(x)\n}\nlog2Number.signature = n1\n\n/**\n * Calculate the natural logarithm of a `number+1`\n * @param {number} x\n * @returns {number}\n */\nexport function log1pNumber (x) {\n return log1p(x)\n}\nlog1pNumber.signature = n1\n\n/**\n * Calculate the modulus of two numbers\n * @param {number} x\n * @param {number} y\n * @returns {number} res\n * @private\n */\nexport function modNumber (x, y) {\n if (y > 0) {\n // We don't use JavaScript's % operator here as this doesn't work\n // correctly for x < 0 and x === 0\n // see https://en.wikipedia.org/wiki/Modulo_operation\n return x - y * Math.floor(x / y)\n } else if (y === 0) {\n return x\n } else { // y < 0\n // TODO: implement mod for a negative divisor\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n}\nmodNumber.signature = n2\n\n/**\n * Calculate the nth root of a, solve x^root == a\n * http://rosettacode.org/wiki/Nth_root#JavaScript\n * @param {number} a\n * @param {number} root\n * @private\n */\nexport function nthRootNumber (a, root) {\n const inv = root < 0\n if (inv) {\n root = -root\n }\n\n if (root === 0) {\n throw new Error('Root must be non-zero')\n }\n if (a < 0 && (Math.abs(root) % 2 !== 1)) {\n throw new Error('Root must be odd when a is negative.')\n }\n\n // edge cases zero and infinity\n if (a === 0) {\n return inv ? Infinity : 0\n }\n if (!isFinite(a)) {\n return inv ? 0 : a\n }\n\n let x = Math.pow(Math.abs(a), 1 / root)\n // If a < 0, we require that root is an odd integer,\n // so (-1) ^ (1/root) = -1\n x = a < 0 ? -x : x\n return inv ? 1 / x : x\n\n // Very nice algorithm, but fails with nthRoot(-2, 3).\n // Newton's method has some well-known problems at times:\n // https://en.wikipedia.org/wiki/Newton%27s_method#Failure_analysis\n /*\n let x = 1 // Initial guess\n let xPrev = 1\n let i = 0\n const iMax = 10000\n do {\n const delta = (a / Math.pow(x, root - 1) - x) / root\n xPrev = x\n x = x + delta\n i++\n }\n while (xPrev !== x && i < iMax)\n\n if (xPrev !== x) {\n throw new Error('Function nthRoot failed to converge')\n }\n\n return inv ? 1 / x : x\n */\n}\nnthRootNumber.signature = n2\n\nexport function signNumber (x) {\n return sign(x)\n}\nsignNumber.signature = n1\n\nexport function sqrtNumber (x) {\n return Math.sqrt(x)\n}\nsqrtNumber.signature = n1\n\nexport function squareNumber (x) {\n return x * x\n}\nsquareNumber.signature = n1\n\n/**\n * Calculate xgcd for two numbers\n * @param {number} a\n * @param {number} b\n * @return {number} result\n * @private\n */\nexport function xgcdNumber (a, b) {\n // source: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm\n let t // used to swap two variables\n let q // quotient\n let r // remainder\n let x = 0\n let lastx = 1\n let y = 1\n let lasty = 0\n\n if (!isInteger(a) || !isInteger(b)) {\n throw new Error('Parameters in function xgcd must be integer numbers')\n }\n\n while (b) {\n q = Math.floor(a / b)\n r = a - q * b\n\n t = x\n x = lastx - q * x\n lastx = t\n\n t = y\n y = lasty - q * y\n lasty = t\n\n a = b\n b = r\n }\n\n let res\n if (a < 0) {\n res = [-a, -lastx, -lasty]\n } else {\n res = [a, a ? lastx : 0, lasty]\n }\n return res\n}\nxgcdNumber.signature = n2\n\n/**\n * Calculates the power of x to y, x^y, for two numbers.\n * @param {number} x\n * @param {number} y\n * @return {number} res\n */\nexport function powNumber (x, y) {\n // x^Infinity === 0 if -1 < x < 1\n // A real number 0 is returned instead of complex(0)\n if ((x * x < 1 && y === Infinity) ||\n (x * x > 1 && y === -Infinity)) {\n return 0\n }\n\n return Math.pow(x, y)\n}\npowNumber.signature = n2\n\n/**\n * round a number to the given number of decimals, or to zero if decimals is\n * not provided\n * @param {number} value\n * @param {number} decimals number of decimals, between 0 and 15 (0 by default)\n * @return {number} roundedValue\n */\nexport function roundNumber (value, decimals = 0) {\n return parseFloat(toFixed(value, decimals))\n}\nroundNumber.signature = n2\n\n/**\n * Calculate the norm of a number, the absolute value.\n * @param {number} x\n * @return {number}\n */\nexport function normNumber (x) {\n return Math.abs(x)\n}\nnormNumber.signature = n1\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { unaryMinusNumber } from '../../plain/number/index.js'\n\nconst name = 'unaryMinus'\nconst dependencies = ['typed']\n\nexport const createUnaryMinus = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Inverse the sign of a value, apply a unary minus operation.\n *\n * For matrices, the function is evaluated element wise. Boolean values and\n * strings will be converted to a number. For complex numbers, both real and\n * complex value are inverted.\n *\n * Syntax:\n *\n * math.unaryMinus(x)\n *\n * Examples:\n *\n * math.unaryMinus(3.5) // returns -3.5\n * math.unaryMinus(-4.2) // returns 4.2\n *\n * See also:\n *\n * add, subtract, unaryPlus\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Number to be inverted.\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Returns the value with inverted sign.\n */\n return typed(name, {\n number: unaryMinusNumber,\n\n Complex: function (x) {\n return x.neg()\n },\n\n BigNumber: function (x) {\n return x.neg()\n },\n\n Fraction: function (x) {\n return x.neg()\n },\n\n Unit: function (x) {\n const res = x.clone()\n res.value = this(x.value)\n return res\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since unaryMinus(0) = 0\n return deepMap(x, this, true)\n }\n\n // TODO: add support for string\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { unaryPlusNumber } from '../../plain/number/index.js'\n\nconst name = 'unaryPlus'\nconst dependencies = ['typed', 'config', 'BigNumber']\n\nexport const createUnaryPlus = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, BigNumber }) => {\n /**\n * Unary plus operation.\n * Boolean values and strings will be converted to a number, numeric values will be returned as is.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.unaryPlus(x)\n *\n * Examples:\n *\n * math.unaryPlus(3.5) // returns 3.5\n * math.unaryPlus(1) // returns 1\n *\n * See also:\n *\n * unaryMinus, add, subtract\n *\n * @param {number | BigNumber | Fraction | string | Complex | Unit | Array | Matrix} x\n * Input value\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Returns the input value when numeric, converts to a number when input is non-numeric.\n */\n return typed(name, {\n number: unaryPlusNumber,\n\n Complex: function (x) {\n return x // complex numbers are immutable\n },\n\n BigNumber: function (x) {\n return x // bignumbers are immutable\n },\n\n Fraction: function (x) {\n return x // fractions are immutable\n },\n\n Unit: function (x) {\n return x.clone()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since unaryPlus(0) = 0\n return deepMap(x, this, true)\n },\n\n 'boolean | string': function (x) {\n // convert to a number or bignumber\n return (config.number === 'BigNumber') ? new BigNumber(+x) : +x\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { absNumber } from '../../plain/number/index.js'\n\nconst name = 'abs'\nconst dependencies = ['typed']\n\nexport const createAbs = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the absolute value of a number. For matrices, the function is\n * evaluated element wise.\n *\n * Syntax:\n *\n * math.abs(x)\n *\n * Examples:\n *\n * math.abs(3.5) // returns number 3.5\n * math.abs(-4.2) // returns number 4.2\n *\n * math.abs([3, -5, -1, 0, 2]) // returns Array [3, 5, 1, 0, 2]\n *\n * See also:\n *\n * sign\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * A number or matrix for which to get the absolute value\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}\n * Absolute value of `x`\n */\n return typed(name, {\n number: absNumber,\n\n Complex: function (x) {\n return x.abs()\n },\n\n BigNumber: function (x) {\n return x.abs()\n },\n\n Fraction: function (x) {\n return x.abs()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since abs(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.abs()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { arraySize } from '../../utils/array.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { IndexError } from '../../error/IndexError.js'\n\nconst name = 'apply'\nconst dependencies = ['typed', 'isInteger']\n\nexport const createApply = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger }) => {\n /**\n * Apply a function that maps an array to a scalar\n * along a given axis of a matrix or array.\n * Returns a new matrix or array with one less dimension than the input.\n *\n * Syntax:\n *\n * math.apply(A, dim, callback)\n *\n * Where:\n *\n * - `dim: number` is a zero-based dimension over which to concatenate the matrices.\n *\n * Examples:\n *\n * const A = [[1, 2], [3, 4]]\n * const sum = math.sum\n *\n * math.apply(A, 0, sum) // returns [4, 6]\n * math.apply(A, 1, sum) // returns [3, 7]\n *\n * See also:\n *\n * map, filter, forEach\n *\n * @param {Array | Matrix} array The input Matrix\n * @param {number} dim The dimension along which the callback is applied\n * @param {Function} callback The callback function that is applied. This Function\n * should take an array or 1-d matrix as an input and\n * return a number.\n * @return {Array | Matrix} res The residual matrix with the function applied over some dimension.\n */\n return typed(name, {\n 'Array | Matrix, number | BigNumber, function': function (mat, dim, callback) {\n if (!isInteger(dim)) {\n throw new TypeError('Integer number expected for dimension')\n }\n\n const size = Array.isArray(mat) ? arraySize(mat) : mat.size()\n if (dim < 0 || (dim >= size.length)) {\n throw new IndexError(dim, size.length)\n }\n\n if (isMatrix(mat)) {\n return mat.create(_apply(mat.valueOf(), dim, callback))\n } else {\n return _apply(mat, dim, callback)\n }\n }\n })\n})\n\n/**\n * Recursively reduce a matrix\n * @param {Array} mat\n * @param {number} dim\n * @param {Function} callback\n * @returns {Array} ret\n * @private\n */\nfunction _apply (mat, dim, callback) {\n let i, ret, tran\n\n if (dim <= 0) {\n if (!Array.isArray(mat[0])) {\n return callback(mat)\n } else {\n tran = _switch(mat)\n ret = []\n for (i = 0; i < tran.length; i++) {\n ret[i] = _apply(tran[i], dim - 1, callback)\n }\n return ret\n }\n } else {\n ret = []\n for (i = 0; i < mat.length; i++) {\n ret[i] = _apply(mat[i], dim - 1, callback)\n }\n return ret\n }\n}\n\n/**\n * Transpose a matrix\n * @param {Array} mat\n * @returns {Array} ret\n * @private\n */\nfunction _switch (mat) {\n const I = mat.length\n const J = mat[0].length\n let i, j\n const ret = []\n for (j = 0; j < J; j++) {\n const tmp = []\n for (i = 0; i < I; i++) {\n tmp.push(mat[i][j])\n }\n ret.push(tmp)\n }\n return ret\n}\n","import { factory } from '../../utils/factory.js'\nimport { addNumber } from '../../plain/number/index.js'\n\nconst name = 'addScalar'\nconst dependencies = ['typed']\n\nexport const createAddScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Add two scalar values, `x + y`.\n * This function is meant for internal use: it is used by the public function\n * `add`\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x First value to add\n * @param {number | BigNumber | Fraction | Complex} y Second value to add\n * @return {number | BigNumber | Fraction | Complex | Unit} Sum of `x` and `y`\n * @private\n */\n return typed(name, {\n\n 'number, number': addNumber,\n\n 'Complex, Complex': function (x, y) {\n return x.add(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.plus(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.add(y)\n },\n\n 'Unit, Unit': function (x, y) {\n if (x.value === null || x.value === undefined) throw new Error('Parameter x contains a unit with undefined value')\n if (y.value === null || y.value === undefined) throw new Error('Parameter y contains a unit with undefined value')\n if (!x.equalBase(y)) throw new Error('Units do not match')\n\n const res = x.clone()\n res.value = this(res.value, y.value)\n res.fixPrefix = false\n return res\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isBigNumber, isComplex, isFraction } from '../../utils/is.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cbrtNumber } from '../../plain/number/index.js'\n\nconst name = 'cbrt'\nconst dependencies = [\n 'config',\n 'typed',\n 'isNegative',\n 'unaryMinus',\n 'matrix',\n 'Complex',\n 'BigNumber',\n 'Fraction'\n]\n\nexport const createCbrt = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, isNegative, unaryMinus, matrix, Complex, BigNumber, Fraction }) => {\n /**\n * Calculate the cubic root of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cbrt(x)\n * math.cbrt(x, allRoots)\n *\n * Examples:\n *\n * math.cbrt(27) // returns 3\n * math.cube(3) // returns 27\n * math.cbrt(-64) // returns -4\n * math.cbrt(math.unit('27 m^3')) // returns Unit 3 m\n * math.cbrt([27, 64, 125]) // returns [3, 4, 5]\n *\n * const x = math.complex('8i')\n * math.cbrt(x) // returns Complex 1.7320508075689 + i\n * math.cbrt(x, true) // returns Matrix [\n * // 1.7320508075689 + i\n * // -1.7320508075689 + i\n * // -2i\n * // ]\n *\n * See also:\n *\n * square, sqrt, cube\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x\n * Value for which to calculate the cubic root.\n * @param {boolean} [allRoots] Optional, false by default. Only applicable\n * when `x` is a number or complex number. If true, all complex\n * roots are returned, if false (default) the principal root is\n * returned.\n * @return {number | BigNumber | Complex | Unit | Array | Matrix}\n * Returns the cubic root of `x`\n */\n return typed(name, {\n number: cbrtNumber,\n // note: signature 'number, boolean' is also supported,\n // created by typed as it knows how to convert number to Complex\n\n Complex: _cbrtComplex,\n\n 'Complex, boolean': _cbrtComplex,\n\n BigNumber: function (x) {\n return x.cbrt()\n },\n\n Unit: _cbrtUnit,\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since cbrt(0) = 0\n return deepMap(x, this, true)\n }\n })\n\n /**\n * Calculate the cubic root for a complex number\n * @param {Complex} x\n * @param {boolean} [allRoots] If true, the function will return an array\n * with all three roots. If false or undefined,\n * the principal root is returned.\n * @returns {Complex | Array. | Matrix.} Returns the cubic root(s) of x\n * @private\n */\n function _cbrtComplex (x, allRoots) {\n // https://www.wikiwand.com/en/Cube_root#/Complex_numbers\n\n const arg3 = x.arg() / 3\n const abs = x.abs()\n\n // principal root:\n const principal = new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3).exp())\n\n if (allRoots) {\n const all = [\n principal,\n new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 + Math.PI * 2 / 3).exp()),\n new Complex(cbrtNumber(abs), 0).mul(new Complex(0, arg3 - Math.PI * 2 / 3).exp())\n ]\n\n return (config.matrix === 'Array') ? all : matrix(all)\n } else {\n return principal\n }\n }\n\n /**\n * Calculate the cubic root for a Unit\n * @param {Unit} x\n * @return {Unit} Returns the cubic root of x\n * @private\n */\n function _cbrtUnit (x) {\n if (x.value && isComplex(x.value)) {\n let result = x.clone()\n result.value = 1.0\n result = result.pow(1.0 / 3) // Compute the units\n result.value = _cbrtComplex(x.value) // Compute the value\n return result\n } else {\n const negate = isNegative(x.value)\n if (negate) {\n x.value = unaryMinus(x.value)\n }\n\n // TODO: create a helper function for this\n let third\n if (isBigNumber(x.value)) {\n third = new BigNumber(1).div(3)\n } else if (isFraction(x.value)) {\n third = new Fraction(1, 3)\n } else {\n third = 1 / 3\n }\n\n const result = x.pow(third)\n\n if (negate) {\n result.value = unaryMinus(result.value)\n }\n\n return result\n }\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm11'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm11 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked NZ times (number of nonzero items in S).\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm11 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // initialize ptr\n cptr[j] = cindex.length\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = aindex[k]\n // invoke callback\n const v = inverse ? cf(b, avalues[k]) : cf(avalues[k], b)\n // check value is zero\n if (!eq(v, zero)) {\n // push index & value\n cindex.push(i)\n cvalues.push(v)\n }\n }\n }\n // update ptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return s.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { clone } from '../../../utils/object.js'\n\nconst name = 'algorithm14'\nconst dependencies = ['typed']\n\nexport const createAlgorithm14 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over DenseMatrix items and invokes the callback function f(Aij..z, b).\n * Callback function invoked MxN times.\n *\n * C(i,j,...z) = f(Aij..z, b)\n *\n * @param {Matrix} a The DenseMatrix instance (A)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij..z,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Aij..z)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97659042\n */\n return function algorithm14 (a, b, callback, inverse) {\n // a arrays\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // populate cdata, iterate through dimensions\n const cdata = asize.length > 0 ? _iterate(cf, 0, asize, asize[0], adata, b, inverse) : []\n\n // c matrix\n return a.createDenseMatrix({\n data: cdata,\n size: clone(asize),\n datatype: dt\n })\n }\n\n // recursive function\n function _iterate (f, level, s, n, av, bv, inverse) {\n // initialize array for this level\n const cv = []\n // check we reach the last level\n if (level === s.length - 1) {\n // loop arrays in last level\n for (let i = 0; i < n; i++) {\n // invoke callback and store value\n cv[i] = inverse ? f(bv, av[i]) : f(av[i], bv)\n }\n } else {\n // iterate current level\n for (let j = 0; j < n; j++) {\n // iterate next level\n cv[j] = _iterate(f, level + 1, s, s[level + 1], av[j], bv, inverse)\n }\n }\n return cv\n }\n})\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { ceilNumber } from '../../plain/number/index.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'ceil'\nconst dependencies = ['typed', 'config', 'round', 'matrix', 'equalScalar']\n\nexport const createCeil = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, round, matrix, equalScalar }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards plus infinity\n * If `x` is complex, both real and imaginary part are rounded towards plus infinity.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.ceil(x)\n * math.ceil(x, n)\n *\n * Examples:\n *\n * math.ceil(3.2) // returns number 4\n * math.ceil(3.8) // returns number 4\n * math.ceil(-4.2) // returns number -4\n * math.ceil(-4.7) // returns number -4\n *\n * math.ceil(3.212, 2) // returns number 3.22\n * math.ceil(3.288, 2) // returns number 3.29\n * math.ceil(-4.212, 2) // returns number -4.21\n * math.ceil(-4.782, 2) // returns number -4.78\n *\n * const c = math.complex(3.24, -2.71)\n * math.ceil(c) // returns Complex 4 - 2i\n * math.ceil(c, 1) // returns Complex 3.3 - 2.7i\n *\n * math.ceil([3.2, 3.8, -4.7]) // returns Array [4, 4, -4]\n * math.ceil([3.21, 3.82, -4.71], 1) // returns Array [3.3, 3.9, -4.7]\n *\n * See also:\n *\n * floor, fix, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('ceil', {\n number: function (x) {\n if (nearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return ceilNumber(x)\n }\n },\n\n 'number, number': function (x, n) {\n if (nearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n let [number, exponent] = `${x}e`.split('e')\n const result = Math.ceil(Number(`${number}e${Number(exponent) + n}`));\n [number, exponent] = `${result}e`.split('e')\n return Number(`${number}e${Number(exponent) - n}`)\n }\n },\n\n Complex: function (x) {\n return x.ceil()\n },\n\n 'Complex, number': function (x, n) {\n return x.ceil(n)\n },\n\n BigNumber: function (x) {\n if (bigNearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return x.ceil()\n }\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (bigNearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n return x.toDecimalPlaces(n.toNumber(), Decimal.ROUND_CEIL)\n }\n },\n\n Fraction: function (x) {\n return x.ceil()\n },\n\n 'Fraction, number': function (x, n) {\n return x.ceil(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number': function (x, n) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cubeNumber } from '../../plain/number/index.js'\n\nconst name = 'cube'\nconst dependencies = ['typed']\n\nexport const createCube = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the cube of a value, `x * x * x`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cube(x)\n *\n * Examples:\n *\n * math.cube(2) // returns number 8\n * math.pow(2, 3) // returns number 8\n * math.cube(4) // returns number 64\n * 4 * 4 * 4 // returns number 64\n *\n * math.cube([1, 2, 3, 4]) // returns Array [1, 8, 27, 64]\n *\n * See also:\n *\n * multiply, square, pow, cbrt\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x Number for which to calculate the cube\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} Cube of x\n */\n return typed(name, {\n number: cubeNumber,\n\n Complex: function (x) {\n return x.mul(x).mul(x) // Is faster than pow(x, 3)\n },\n\n BigNumber: function (x) {\n return x.times(x).times(x)\n },\n\n Fraction: function (x) {\n return x.pow(3) // Is faster than mul()mul()mul()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since cube(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.pow(3)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { expNumber } from '../../plain/number/index.js'\n\nconst name = 'exp'\nconst dependencies = ['typed']\n\nexport const createExp = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the exponent of a value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.exp(x)\n *\n * Examples:\n *\n * math.exp(2) // returns number 7.3890560989306495\n * math.pow(math.e, 2) // returns number 7.3890560989306495\n * math.log(math.exp(2)) // returns number 2\n *\n * math.exp([1, 2, 3])\n * // returns Array [\n * // 2.718281828459045,\n * // 7.3890560989306495,\n * // 20.085536923187668\n * // ]\n *\n * See also:\n *\n * expm1, log, pow\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x A number or matrix to exponentiate\n * @return {number | BigNumber | Complex | Array | Matrix} Exponent of `x`\n */\n return typed(name, {\n number: expNumber,\n\n Complex: function (x) {\n return x.exp()\n },\n\n BigNumber: function (x) {\n return x.exp()\n },\n\n 'Array | Matrix': function (x) {\n // TODO: exp(sparse) should return a dense matrix since exp(0)==1\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { expm1Number } from '../../plain/number/index.js'\n\nconst name = 'expm1'\nconst dependencies = ['typed', 'Complex']\n\nexport const createExpm1 = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex }) => {\n /**\n * Calculate the value of subtracting 1 from the exponential value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.expm1(x)\n *\n * Examples:\n *\n * math.expm1(2) // returns number 6.38905609893065\n * math.pow(math.e, 2) - 1 // returns number 6.3890560989306495\n * math.log(math.expm1(2) + 1) // returns number 2\n *\n * math.expm1([1, 2, 3])\n * // returns Array [\n * // 1.718281828459045,\n * // 6.3890560989306495,\n * // 19.085536923187668\n * // ]\n *\n * See also:\n *\n * exp, log, pow\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x A number or matrix to apply expm1\n * @return {number | BigNumber | Complex | Array | Matrix} Exponent of `x`\n */\n return typed(name, {\n number: expm1Number,\n\n Complex: function (x) {\n const r = Math.exp(x.re)\n return new Complex(\n r * Math.cos(x.im) - 1,\n r * Math.sin(x.im)\n )\n },\n\n BigNumber: function (x) {\n return x.exp().minus(1)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'fix'\nconst dependencies = ['typed', 'Complex', 'matrix', 'ceil', 'floor']\n\nexport const createFix = /* #__PURE__ */ factory(name, dependencies, ({ typed, Complex, matrix, ceil, floor }) => {\n const algorithm14 = createAlgorithm14({ typed })\n /**\n * Round a value towards zero.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.fix(x)\n *\n * Examples:\n *\n * math.fix(3.2) // returns number 3\n * math.fix(3.8) // returns number 3\n * math.fix(-4.2) // returns number -4\n * math.fix(-4.7) // returns number -4\n *\n * math.fix(3.12, 1) // returns number 3.1\n * math.fix(3.18, 1) // returns number 3.1\n * math.fix(-4.12, 1) // returns number -4.1\n * math.fix(-4.17, 1) // returns number -4.1\n *\n * const c = math.complex(3.22, -2.78)\n * math.fix(c) // returns Complex 3 - 2i\n * math.fix(c, 1) // returns Complex 3.2 - 2.7i\n *\n * math.fix([3.2, 3.8, -4.7]) // returns Array [3, 3, -4]\n * math.fix([3.2, 3.8, -4.7], 1) // returns Array [3.2, 3.8, -4.7]\n *\n * See also:\n *\n * ceil, floor, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('fix', {\n number: function (x) {\n return (x > 0) ? floor(x) : ceil(x)\n },\n\n 'number, number | BigNumber': function (x, n) {\n return (x > 0) ? floor(x, n) : ceil(x, n)\n },\n\n Complex: function (x) {\n return new Complex(\n (x.re > 0) ? Math.floor(x.re) : Math.ceil(x.re),\n (x.im > 0) ? Math.floor(x.im) : Math.ceil(x.im)\n )\n },\n\n 'Complex, number | BigNumber': function (x, n) {\n return new Complex(\n (x.re > 0) ? floor(x.re, n) : ceil(x.re, n),\n (x.im > 0) ? floor(x.im, n) : ceil(x.im, n)\n )\n },\n\n BigNumber: function (x) {\n return x.isNegative() ? ceil(x) : floor(x)\n },\n\n 'BigNumber, number | BigNumber': function (x, n) {\n return x.isNegative() ? ceil(x, n) : floor(x, n)\n },\n\n Fraction: function (x) {\n return x.s < 0 ? x.ceil() : x.floor()\n },\n\n 'Fraction, number | BigNumber': function (x, n) {\n return x.s < 0 ? x.ceil(n) : x.floor(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since fix(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number | BigNumber': function (x, n) {\n // deep map collection, skip zeros since fix(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import Decimal from 'decimal.js'\nimport { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'floor'\nconst dependencies = ['typed', 'config', 'round', 'matrix', 'equalScalar']\n\nexport const createFloor = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, round, matrix, equalScalar }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards minus infinity.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.floor(x)\n * math.floor(x, n)\n *\n * Examples:\n *\n * math.floor(3.2) // returns number 3\n * math.floor(3.8) // returns number 3\n * math.floor(-4.2) // returns number -5\n * math.floor(-4.7) // returns number -5\n *\n * math.floor(3.212, 2) // returns number 3.21\n * math.floor(3.288, 2) // returns number 3.28\n * math.floor(-4.212, 2) // returns number -4.22\n * math.floor(-4.782, 2) // returns number -4.79\n *\n * const c = math.complex(3.24, -2.71)\n * math.floor(c) // returns Complex 3 - 3i\n * math.floor(c, 1) // returns Complex 3.2 - 2.8i\n *\n * math.floor([3.2, 3.8, -4.7]) // returns Array [3, 3, -5]\n * math.floor([3.21, 3.82, -4.71], 1) // returns Array [3.2, 3.8, -4.8]\n *\n * See also:\n *\n * ceil, fix, round\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed('floor', {\n number: function (x) {\n if (nearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return Math.floor(x)\n }\n },\n\n 'number, number': function (x, n) {\n if (nearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n let [number, exponent] = `${x}e`.split('e')\n const result = Math.floor(Number(`${number}e${Number(exponent) + n}`));\n [number, exponent] = `${result}e`.split('e')\n return Number(`${number}e${Number(exponent) - n}`)\n }\n },\n\n Complex: function (x) {\n return x.floor()\n },\n\n 'Complex, number': function (x, n) {\n return x.floor(n)\n },\n\n BigNumber: function (x) {\n if (bigNearlyEqual(x, round(x), config.epsilon)) {\n return round(x)\n } else {\n return x.floor()\n }\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (bigNearlyEqual(x, round(x, n), config.epsilon)) {\n return round(x, n)\n } else {\n return x.toDecimalPlaces(n.toNumber(), Decimal.ROUND_FLOOR)\n }\n },\n\n Fraction: function (x) {\n return x.floor()\n },\n\n 'Fraction, number': function (x, n) {\n return x.floor(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since floor(0) = 0\n return deepMap(x, this, true)\n },\n\n 'Array | Matrix, number': function (x, n) {\n // deep map collection, skip zeros since ceil(0) = 0\n return deepMap(x, i => this(i, n), true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm01'\nconst dependencies = ['typed']\n\nexport const createAlgorithm01 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over SparseMatrix nonzero items and invokes the callback function f(Dij, Sij).\n * Callback function invoked NNZ times (number of nonzero items in SparseMatrix).\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ Dij ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (S)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm1 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // process data types\n const dt = typeof adt === 'string' && adt === bdt ? adt : undefined\n // callback function\n const cf = dt ? typed.find(callback, [dt, dt]) : callback\n\n // vars\n let i, j\n\n // result (DenseMatrix)\n const cdata = []\n // initialize c\n for (i = 0; i < rows; i++) { cdata[i] = [] }\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns in b\n for (j = 0; j < columns; j++) {\n // column mark\n const mark = j + 1\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // update workspace\n x[i] = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n // mark i as updated\n w[i] = mark\n }\n // loop rows\n for (i = 0; i < rows; i++) {\n // check row is in workspace\n if (w[i] === mark) {\n // c[i][j] was already calculated\n cdata[i][j] = x[i]\n } else {\n // item does not exist in S\n cdata[i][j] = adata[i][j]\n }\n }\n }\n\n // return dense matrix\n return denseMatrix.createDenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm04'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm04 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤ A(i,j) ; A(i,j) !== 0\n * └ B(i,j) ; B(i,j) !== 0\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm04 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspace\n const xa = avalues && bvalues ? [] : undefined\n const xb = avalues && bvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // vars\n let i, j, k, k0, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop A(:,j)\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // update c\n cindex.push(i)\n // update workspace\n wa[i] = mark\n // check we need to process values\n if (xa) { xa[i] = avalues[k] }\n }\n // loop B(:,j)\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // check row exists in A\n if (wa[i] === mark) {\n // update record in xa @ i\n if (xa) {\n // invoke callback\n const v = cf(xa[i], bvalues[k])\n // check for zero\n if (!eq(v, zero)) {\n // update workspace\n xa[i] = v\n } else {\n // remove mark (index will be removed later)\n wa[i] = null\n }\n }\n } else {\n // update c\n cindex.push(i)\n // update workspace\n wb[i] = mark\n // check we need to process values\n if (xb) { xb[i] = bvalues[k] }\n }\n }\n // check we need to process values (non pattern matrix)\n if (xa && xb) {\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // check workspace has value @ i\n if (wa[i] === mark) {\n // push value (Aij != 0 || (Aij != 0 && Bij != 0))\n cvalues[k] = xa[i]\n // increment pointer\n k++\n } else if (wb[i] === mark) {\n // push value (bij != 0)\n cvalues[k] = xb[i]\n // increment pointer\n k++\n } else {\n // remove index @ k\n cindex.splice(k, 1)\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm10'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm10 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked NZ times (number of nonzero items in S).\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ b ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm10 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cdata = []\n\n // workspaces\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const r = aindex[k]\n // update workspace\n x[r] = avalues[k]\n w[r] = mark\n }\n // loop rows\n for (let i = 0; i < rows; i++) {\n // initialize C on first column\n if (j === 0) {\n // create row array\n cdata[i] = []\n }\n // check sparse matrix has a value @ i,j\n if (w[i] === mark) {\n // invoke callback, update C\n cdata[i][j] = inverse ? cf(b, x[i]) : cf(x[i], b)\n } else {\n // dense matrix value @ i, j\n cdata[i][j] = b\n }\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm13'\nconst dependencies = ['typed']\n\nexport const createAlgorithm13 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over DenseMatrix items and invokes the callback function f(Aij..z, Bij..z).\n * Callback function invoked MxN times.\n *\n * C(i,j,...z) = f(Aij..z, Bij..z)\n *\n * @param {Matrix} a The DenseMatrix instance (A)\n * @param {Matrix} b The DenseMatrix instance (B)\n * @param {Function} callback The f(Aij..z,Bij..z) operation to invoke\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97658658\n */\n return function algorithm13 (a, b, callback) {\n // a arrays\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b arrays\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // c arrays\n const csize = []\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // validate each one of the dimension sizes\n for (let s = 0; s < asize.length; s++) {\n // must match\n if (asize[s] !== bsize[s]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n // update dimension in c\n csize[s] = asize[s]\n }\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // populate cdata, iterate through dimensions\n const cdata = csize.length > 0 ? _iterate(cf, 0, csize, csize[0], adata, bdata) : []\n\n // c matrix\n return a.createDenseMatrix({\n data: cdata,\n size: csize,\n datatype: dt\n })\n }\n\n // recursive function\n function _iterate (f, level, s, n, av, bv) {\n // initialize array for this level\n const cv = []\n // check we reach the last level\n if (level === s.length - 1) {\n // loop arrays in last level\n for (let i = 0; i < n; i++) {\n // invoke callback and store value\n cv[i] = f(av[i], bv[i])\n }\n } else {\n // iterate current level\n for (let j = 0; j < n; j++) {\n // iterate next level\n cv[j] = _iterate(f, level + 1, s, s[level + 1], av[j], bv[j])\n }\n }\n return cv\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { gcdNumber } from '../../plain/number/index.js'\n\nconst name = 'gcd'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createGcd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the greatest common divisor for two or more values or arrays.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.gcd(a, b)\n * math.gcd(a, b, c, ...)\n *\n * Examples:\n *\n * math.gcd(8, 12) // returns 4\n * math.gcd(-4, 6) // returns 2\n * math.gcd(25, 15, -10) // returns 5\n *\n * math.gcd([8, -4], [12, 6]) // returns [4, 2]\n *\n * See also:\n *\n * lcm, xgcd\n *\n * @param {... number | BigNumber | Fraction | Array | Matrix} args Two or more integer numbers\n * @return {number | BigNumber | Fraction | Array | Matrix} The greatest common divisor\n */\n return typed(name, {\n\n 'number, number': gcdNumber,\n\n 'BigNumber, BigNumber': _gcdBigNumber,\n\n 'Fraction, Fraction': function (x, y) {\n return x.gcd(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm10(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n },\n\n // TODO: need a smarter notation here\n 'Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber': function (a, b, args) {\n let res = this(a, b)\n for (let i = 0; i < args.length; i++) {\n res = this(res, args[i])\n }\n return res\n }\n })\n\n /**\n * Calculate gcd for BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @returns {BigNumber} Returns greatest common denominator of a and b\n * @private\n */\n function _gcdBigNumber (a, b) {\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function gcd must be integer numbers')\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n const zero = new BigNumber(0)\n while (!b.isZero()) {\n const r = a.mod(b)\n a = b\n b = r\n }\n return a.lt(zero) ? a.neg() : a\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm02'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm02 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix nonzero items and invokes the callback function f(Dij, Sij).\n * Callback function invoked NNZ times (number of nonzero items in SparseMatrix).\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (S)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm02 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result (SparseMatrix)\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // loop columns in b\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = bindex[k]\n // update C(i,j)\n const cij = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n // check for nonzero\n if (!eq(cij, zero)) {\n // push i & v\n cindex.push(i)\n cvalues.push(cij)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return sparseMatrix.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\nimport { scatter } from '../../../utils/collection.js'\n\nconst name = 'algorithm06'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm06 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked (Anz U Bnz) times, where Anz and Bnz are the nonzero elements in both matrices.\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm06 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const x = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const w = []\n // marks indicating value in a given row has been updated\n const u = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // scatter the values of A(:,j) into workspace\n scatter(a, j, w, x, u, mark, cindex, cf)\n // scatter the values of B(:,j) into workspace\n scatter(b, j, w, x, u, mark, cindex, cf)\n // check we need to process values (non pattern matrix)\n if (x) {\n // initialize first index in j\n let k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n const i = cindex[k]\n // check function was invoked on current row (Aij !=0 && Bij != 0)\n if (u[i] === mark) {\n // value @ i\n const v = x[i]\n // check for zero value\n if (!eq(v, zero)) {\n // push value\n cvalues.push(v)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n } else {\n // initialize first index in j\n let p = cptr[j]\n // loop index in j\n while (p < cindex.length) {\n // row\n const r = cindex[p]\n // check function was invoked on current row (Aij !=0 && Bij != 0)\n if (u[r] !== mark) {\n // remove value @ i, do not increment pointer\n cindex.splice(p, 1)\n } else {\n // increment pointer\n p++\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { lcmNumber } from '../../plain/number/index.js'\n\nconst name = 'lcm'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar'\n]\n\nexport const createLcm = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the least common multiple for two or more values or arrays.\n *\n * lcm is defined as:\n *\n * lcm(a, b) = abs(a * b) / gcd(a, b)\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.lcm(a, b)\n * math.lcm(a, b, c, ...)\n *\n * Examples:\n *\n * math.lcm(4, 6) // returns 12\n * math.lcm(6, 21) // returns 42\n * math.lcm(6, 21, 5) // returns 210\n *\n * math.lcm([4, 6], [6, 21]) // returns [12, 42]\n *\n * See also:\n *\n * gcd, xgcd\n *\n * @param {... number | BigNumber | Array | Matrix} args Two or more integer numbers\n * @return {number | BigNumber | Array | Matrix} The least common multiple\n */\n return typed(name, {\n 'number, number': lcmNumber,\n\n 'BigNumber, BigNumber': _lcmBigNumber,\n\n 'Fraction, Fraction': function (x, y) {\n return x.lcm(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n return algorithm11(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n },\n\n // TODO: need a smarter notation here\n 'Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber': function (a, b, args) {\n let res = this(a, b)\n for (let i = 0; i < args.length; i++) {\n res = this(res, args[i])\n }\n return res\n }\n })\n\n /**\n * Calculate lcm for two BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @returns {BigNumber} Returns the least common multiple of a and b\n * @private\n */\n function _lcmBigNumber (a, b) {\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function lcm must be integer numbers')\n }\n\n if (a.isZero()) {\n return a\n }\n if (b.isZero()) {\n return b\n }\n\n // https://en.wikipedia.org/wiki/Euclidean_algorithm\n // evaluate lcm here inline to reduce overhead\n const prod = a.times(b)\n while (!b.isZero()) {\n const t = b\n b = a.mod(t)\n a = t\n }\n return prod.div(a).abs()\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log10Number } from '../../plain/number/index.js'\n\nconst name = 'log10'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createLog10 = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the 10-base logarithm of a value. This is the same as calculating `log(x, 10)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log10(x)\n *\n * Examples:\n *\n * math.log10(0.00001) // returns -5\n * math.log10(10000) // returns 4\n * math.log(10000) / math.log(10) // returns 4\n * math.pow(10, 4) // returns 10000\n *\n * See also:\n *\n * exp, log, log1p, log2\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the 10-base logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return log10Number(x)\n } else {\n // negative value -> complex value computation\n return new Complex(x, 0).log().div(Math.LN10)\n }\n },\n\n Complex: function (x) {\n return new Complex(x).log().div(Math.LN10)\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.log()\n } else {\n // downgrade to number, return Complex valued result\n return new Complex(x.toNumber(), 0).log().div(Math.LN10)\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log2Number } from '../../plain/number/index.js'\n\nconst name = 'log2'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createLog2 = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log2(x)\n *\n * Examples:\n *\n * math.log2(0.03125) // returns -5\n * math.log2(16) // returns 4\n * math.log2(16) / math.log2(2) // returns 4\n * math.pow(2, 4) // returns 16\n *\n * See also:\n *\n * exp, log, log1p, log10\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the 2-base logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return log2Number(x)\n } else {\n // negative value -> complex value computation\n return _log2Complex(new Complex(x, 0))\n }\n },\n\n Complex: _log2Complex,\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.log(2)\n } else {\n // downgrade to number, return Complex valued result\n return _log2Complex(new Complex(x.toNumber(), 0))\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n\n /**\n * Calculate log2 for a complex value\n * @param {Complex} x\n * @returns {Complex}\n * @private\n */\n function _log2Complex (x) {\n const newX = Math.sqrt(x.re * x.re + x.im * x.im)\n return new Complex(\n (Math.log2) ? Math.log2(newX) : Math.log(newX) / Math.LN2,\n Math.atan2(x.im, x.re) / Math.LN2\n )\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm03'\nconst dependencies = ['typed']\n\nexport const createAlgorithm03 = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterates over SparseMatrix items and invokes the callback function f(Dij, Sij).\n * Callback function invoked M*N times.\n *\n *\n * ┌ f(Dij, Sij) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ f(Dij, 0) ; otherwise\n *\n *\n * @param {Matrix} denseMatrix The DenseMatrix instance (D)\n * @param {Matrix} sparseMatrix The SparseMatrix instance (C)\n * @param {Function} callback The f(Dij,Sij) operation to invoke, where Dij = DenseMatrix(i,j) and Sij = SparseMatrix(i,j)\n * @param {boolean} inverse A true value indicates callback should be invoked f(Sij,Dij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97477571\n */\n return function algorithm03 (denseMatrix, sparseMatrix, callback, inverse) {\n // dense matrix arrays\n const adata = denseMatrix._data\n const asize = denseMatrix._size\n const adt = denseMatrix._datatype\n // sparse matrix arrays\n const bvalues = sparseMatrix._values\n const bindex = sparseMatrix._index\n const bptr = sparseMatrix._ptr\n const bsize = sparseMatrix._size\n const bdt = sparseMatrix._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!bvalues) { throw new Error('Cannot perform operation on Dense Matrix and Pattern Sparse Matrix') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result (DenseMatrix)\n const cdata = []\n\n // initialize dense matrix\n for (let z = 0; z < rows; z++) {\n // initialize row\n cdata[z] = []\n }\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns in b\n for (let j = 0; j < columns; j++) {\n // column mark\n const mark = j + 1\n // values in column j\n for (let k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n const i = bindex[k]\n // update workspace\n x[i] = inverse ? cf(bvalues[k], adata[i][j]) : cf(adata[i][j], bvalues[k])\n w[i] = mark\n }\n // process workspace\n for (let y = 0; y < rows; y++) {\n // check we have a calculated value for current row\n if (w[y] === mark) {\n // use calculated value\n cdata[y][j] = x[y]\n } else {\n // calculate value\n cdata[y][j] = inverse ? cf(zero, adata[y][j]) : cf(adata[y][j], zero)\n }\n }\n }\n\n // return dense matrix\n return denseMatrix.createDenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm05'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm05 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 || B(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm05 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const xa = cvalues ? [] : undefined\n const xb = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // vars\n let i, j, k, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop values A(:,j)\n for (k = aptr[j], k1 = aptr[j + 1]; k < k1; k++) {\n // row\n i = aindex[k]\n // push index\n cindex.push(i)\n // update workspace\n wa[i] = mark\n // check we need to process values\n if (xa) { xa[i] = avalues[k] }\n }\n // loop values B(:,j)\n for (k = bptr[j], k1 = bptr[j + 1]; k < k1; k++) {\n // row\n i = bindex[k]\n // check row existed in A\n if (wa[i] !== mark) {\n // push index\n cindex.push(i)\n }\n // update workspace\n wb[i] = mark\n // check we need to process values\n if (xb) { xb[i] = bvalues[k] }\n }\n // check we need to process values (non pattern matrix)\n if (cvalues) {\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // marks\n const wai = wa[i]\n const wbi = wb[i]\n // check Aij or Bij are nonzero\n if (wai === mark || wbi === mark) {\n // matrix values @ i,j\n const va = wai === mark ? xa[i] : zero\n const vb = wbi === mark ? xb[i] : zero\n // Cij\n const vc = cf(va, vb)\n // check for zero\n if (!eq(vc, zero)) {\n // push value\n cvalues.push(vc)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'algorithm12'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm12 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix S nonzero items and invokes the callback function f(Sij, b).\n * Callback function invoked MxN times.\n *\n *\n * ┌ f(Sij, b) ; S(i,j) !== 0\n * C(i,j) = ┤\n * └ f(0, b) ; otherwise\n *\n *\n * @param {Matrix} s The SparseMatrix instance (S)\n * @param {Scalar} b The Scalar value\n * @param {Function} callback The f(Aij,b) operation to invoke\n * @param {boolean} inverse A true value indicates callback should be invoked f(b,Sij)\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * https://github.com/josdejong/mathjs/pull/346#issuecomment-97626813\n */\n return function algorithm12 (s, b, callback, inverse) {\n // sparse matrix arrays\n const avalues = s._values\n const aindex = s._index\n const aptr = s._ptr\n const asize = s._size\n const adt = s._datatype\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrix and Scalar value') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string') {\n // datatype\n dt = adt\n // convert b to the same datatype\n b = typed.convert(b, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cdata = []\n\n // workspaces\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // values in j\n for (let k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n const r = aindex[k]\n // update workspace\n x[r] = avalues[k]\n w[r] = mark\n }\n // loop rows\n for (let i = 0; i < rows; i++) {\n // initialize C on first column\n if (j === 0) {\n // create row array\n cdata[i] = []\n }\n // check sparse matrix has a value @ i,j\n if (w[i] === mark) {\n // invoke callback, update C\n cdata[i][j] = inverse ? cf(b, x[i]) : cf(x[i], b)\n } else {\n // dense matrix value @ i, j\n cdata[i][j] = inverse ? cf(b, 0) : cf(0, b)\n }\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { modNumber } from '../../plain/number/index.js'\n\nconst name = 'mod'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createMod = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculates the modulus, the remainder of an integer division.\n *\n * For matrices, the function is evaluated element wise.\n *\n * The modulus is defined as:\n *\n * x - y * floor(x / y)\n *\n * See https://en.wikipedia.org/wiki/Modulo_operation.\n *\n * Syntax:\n *\n * math.mod(x, y)\n *\n * Examples:\n *\n * math.mod(8, 3) // returns 2\n * math.mod(11, 2) // returns 1\n *\n * function isOdd(x) {\n * return math.mod(x, 2) != 0\n * }\n *\n * isOdd(2) // returns false\n * isOdd(3) // returns true\n *\n * See also:\n *\n * divide\n *\n * @param {number | BigNumber | Fraction | Array | Matrix} x Dividend\n * @param {number | BigNumber | Fraction | Array | Matrix} y Divisor\n * @return {number | BigNumber | Fraction | Array | Matrix} Returns the remainder of `x` divided by `y`.\n */\n return typed(name, {\n\n 'number, number': modNumber,\n\n 'BigNumber, BigNumber': function (x, y) {\n if (y.isNeg()) {\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n return y.isZero() ? x : x.mod(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n if (y.compare(0) < 0) {\n throw new Error('Cannot calculate mod for a negative divisor')\n }\n // Workaround suggested in Fraction.js library to calculate correct modulo for negative dividend\n return x.compare(0) >= 0 ? x.mod(y) : x.mod(y).add(y).mod(y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { multiplyNumber } from '../../plain/number/index.js'\n\nconst name = 'multiplyScalar'\nconst dependencies = ['typed']\n\nexport const createMultiplyScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Multiply two scalar values, `x * y`.\n * This function is meant for internal use: it is used by the public function\n * `multiply`\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x First value to multiply\n * @param {number | BigNumber | Fraction | Complex} y Second value to multiply\n * @return {number | BigNumber | Fraction | Complex | Unit} Multiplication of `x` and `y`\n * @private\n */\n return typed('multiplyScalar', {\n\n 'number, number': multiplyNumber,\n\n 'Complex, Complex': function (x, y) {\n return x.mul(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.times(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.mul(y)\n },\n\n 'number | Fraction | BigNumber | Complex, Unit': function (x, y) {\n const res = y.clone()\n res.value = (res.value === null) ? res._normalize(x) : this(res.value, x)\n return res\n },\n\n 'Unit, number | Fraction | BigNumber | Complex': function (x, y) {\n const res = x.clone()\n res.value = (res.value === null) ? res._normalize(y) : this(res.value, y)\n return res\n },\n\n 'Unit, Unit': function (x, y) {\n return x.multiply(y)\n }\n\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { extend } from '../../utils/object.js'\nimport { arraySize } from '../../utils/array.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'multiply'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'addScalar',\n 'multiplyScalar',\n 'equalScalar',\n 'dot'\n]\n\nexport const createMultiply = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, addScalar, multiplyScalar, equalScalar, dot }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n function _validateMatrixDimensions (size1, size2) {\n // check left operand dimensions\n switch (size1.length) {\n case 1:\n // check size2\n switch (size2.length) {\n case 1:\n // Vector x Vector\n if (size1[0] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Vectors must have the same length')\n }\n break\n case 2:\n // Vector x Matrix\n if (size1[0] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Vector length (' + size1[0] + ') must match Matrix rows (' + size2[0] + ')')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)')\n }\n break\n case 2:\n // check size2\n switch (size2.length) {\n case 1:\n // Matrix x Vector\n if (size1[1] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Matrix columns (' + size1[1] + ') must match Vector length (' + size2[0] + ')')\n }\n break\n case 2:\n // Matrix x Matrix\n if (size1[1] !== size2[0]) {\n // throw error\n throw new RangeError('Dimension mismatch in multiplication. Matrix A columns (' + size1[1] + ') must match Matrix B rows (' + size2[0] + ')')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)')\n }\n break\n default:\n throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix A has ' + size1.length + ' dimensions)')\n }\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (N)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {number} Scalar value\n */\n function _multiplyVectorVector (a, b, n) {\n // check empty vector\n if (n === 0) { throw new Error('Cannot multiply two empty vectors') }\n return dot(a, b)\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (M)\n * @param {Matrix} b Matrix (MxN)\n *\n * @return {Matrix} Dense Vector (N)\n */\n function _multiplyVectorMatrix (a, b) {\n // process storage\n if (b.storage() !== 'dense') {\n throw new Error('Support for SparseMatrix not implemented')\n }\n return _multiplyVectorDenseMatrix(a, b)\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Dense Vector (M)\n * @param {Matrix} b Dense Matrix (MxN)\n *\n * @return {Matrix} Dense Vector (N)\n */\n function _multiplyVectorDenseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // rows & columns\n const alength = asize[0]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix columns\n for (let j = 0; j < bcolumns; j++) {\n // sum (do not initialize it with zero)\n let sum = mf(adata[0], bdata[0][j])\n // loop vector\n for (let i = 1; i < alength; i++) {\n // multiply & accumulate\n sum = af(sum, mf(adata[i], bdata[i][j]))\n }\n c[j] = sum\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [bcolumns],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Matrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} Dense Vector (M)\n */\n const _multiplyMatrixVector = typed('_multiplyMatrixVector', {\n 'DenseMatrix, any': _multiplyDenseMatrixVector,\n 'SparseMatrix, any': _multiplySparseMatrixVector\n })\n\n /**\n * C = A * B\n *\n * @param {Matrix} a Matrix (MxN)\n * @param {Matrix} b Matrix (NxC)\n *\n * @return {Matrix} Matrix (MxC)\n */\n const _multiplyMatrixMatrix = typed('_multiplyMatrixMatrix', {\n 'DenseMatrix, DenseMatrix': _multiplyDenseMatrixDenseMatrix,\n 'DenseMatrix, SparseMatrix': _multiplyDenseMatrixSparseMatrix,\n 'SparseMatrix, DenseMatrix': _multiplySparseMatrixDenseMatrix,\n 'SparseMatrix, SparseMatrix': _multiplySparseMatrixSparseMatrix\n })\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} Dense Vector (M)\n */\n function _multiplyDenseMatrixVector (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = asize[0]\n const acolumns = asize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix a rows\n for (let i = 0; i < arows; i++) {\n // current row\n const row = adata[i]\n // sum (do not initialize it with zero)\n let sum = mf(row[0], bdata[0])\n // loop matrix a columns\n for (let j = 1; j < acolumns; j++) {\n // multiply & accumulate\n sum = af(sum, mf(row[j], bdata[j]))\n }\n c[i] = sum\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [arows],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b DenseMatrix (NxC)\n *\n * @return {Matrix} DenseMatrix (MxC)\n */\n function _multiplyDenseMatrixDenseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b dense\n const bdata = b._data\n const bsize = b._size\n const bdt = b._datatype\n // rows & columns\n const arows = asize[0]\n const acolumns = asize[1]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const c = []\n\n // loop matrix a rows\n for (let i = 0; i < arows; i++) {\n // current row\n const row = adata[i]\n // initialize row array\n c[i] = []\n // loop matrix b columns\n for (let j = 0; j < bcolumns; j++) {\n // sum (avoid initializing sum to zero)\n let sum = mf(row[0], bdata[0][j])\n // loop matrix a columns\n for (let x = 1; x < acolumns; x++) {\n // multiply & accumulate\n sum = af(sum, mf(row[x], bdata[x][j]))\n }\n c[i][j] = sum\n }\n }\n\n // return matrix\n return a.createDenseMatrix({\n data: c,\n size: [arows, bcolumns],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a DenseMatrix (MxN)\n * @param {Matrix} b SparseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplyDenseMatrixSparseMatrix (a, b) {\n // a dense\n const adata = a._data\n const asize = a._size\n const adt = a._datatype\n // b sparse\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n // validate b matrix\n if (!bvalues) { throw new Error('Cannot multiply Dense Matrix times Pattern only Matrix') }\n // rows & columns\n const arows = asize[0]\n const bcolumns = bsize[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n // c matrix\n const c = b.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // indeces in column jb\n const kb0 = bptr[jb]\n const kb1 = bptr[jb + 1]\n // do not process column jb if no data exists\n if (kb1 > kb0) {\n // last row mark processed\n let last = 0\n // loop a rows\n for (let i = 0; i < arows; i++) {\n // column mark\n const mark = i + 1\n // C[i, jb]\n let cij\n // values in b column j\n for (let kb = kb0; kb < kb1; kb++) {\n // row\n const ib = bindex[kb]\n // check value has been initialized\n if (last !== mark) {\n // first value in column jb\n cij = mf(adata[i][ib], bvalues[kb])\n // update mark\n last = mark\n } else {\n // accumulate value\n cij = af(cij, mf(adata[i][ib], bvalues[kb]))\n }\n }\n // check column has been processed and value != 0\n if (last === mark && !eq(cij, zero)) {\n // push row & value\n cindex.push(i)\n cvalues.push(cij)\n }\n }\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b Dense Vector (N)\n *\n * @return {Matrix} SparseMatrix (M, 1)\n */\n function _multiplySparseMatrixVector (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // validate a matrix\n if (!avalues) { throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix') }\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = a._size[0]\n const brows = b._size[0]\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // workspace\n const x = []\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n\n // update ptr\n cptr[0] = 0\n // rows in b\n for (let ib = 0; ib < brows; ib++) {\n // b[ib]\n const vbi = bdata[ib]\n // check b[ib] != 0, avoid loops\n if (!eq(vbi, zero)) {\n // A values & index in ib column\n for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // a row\n const ia = aindex[ka]\n // check value exists in current j\n if (!w[ia]) {\n // ia is new entry in j\n w[ia] = true\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(vbi, avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(vbi, avalues[ka]))\n }\n }\n }\n }\n // copy values from x to column jb of c\n for (let p1 = cindex.length, p = 0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n // update ptr\n cptr[1] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, 1],\n datatype: dt\n })\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b DenseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplySparseMatrixDenseMatrix (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // validate a matrix\n if (!avalues) { throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix') }\n // b dense\n const bdata = b._data\n const bdt = b._datatype\n // rows & columns\n const arows = a._size[0]\n const brows = b._size[0]\n const bcolumns = b._size[1]\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n // equalScalar signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n }\n\n // result\n const cvalues = []\n const cindex = []\n const cptr = []\n // c matrix\n const c = a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // workspace\n const x = []\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // mark in workspace for current column\n const mark = jb + 1\n // rows in jb\n for (let ib = 0; ib < brows; ib++) {\n // b[ib, jb]\n const vbij = bdata[ib][jb]\n // check b[ib, jb] != 0, avoid loops\n if (!eq(vbij, zero)) {\n // A values & index in ib column\n for (let ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // a row\n const ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(vbij, avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(vbij, avalues[ka]))\n }\n }\n }\n }\n // copy values from x to column jb of c\n for (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * C = A * B\n *\n * @param {Matrix} a SparseMatrix (MxN)\n * @param {Matrix} b SparseMatrix (NxC)\n *\n * @return {Matrix} SparseMatrix (MxC)\n */\n function _multiplySparseMatrixSparseMatrix (a, b) {\n // a sparse\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const adt = a._datatype\n // b sparse\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bdt = b._datatype\n\n // rows & columns\n const arows = a._size[0]\n const bcolumns = b._size[1]\n // flag indicating both matrices (a & b) contain data\n const values = avalues && bvalues\n\n // datatype\n let dt\n // addScalar signature to use\n let af = addScalar\n // multiplyScalar signature to use\n let mf = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n // datatype\n dt = adt\n // find signatures that matches (dt, dt)\n af = typed.find(addScalar, [dt, dt])\n mf = typed.find(multiplyScalar, [dt, dt])\n }\n\n // result\n const cvalues = values ? [] : undefined\n const cindex = []\n const cptr = []\n // c matrix\n const c = a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [arows, bcolumns],\n datatype: dt\n })\n\n // workspace\n const x = values ? [] : undefined\n // vector with marks indicating a value x[i] exists in a given column\n const w = []\n // variables\n let ka, ka0, ka1, kb, kb0, kb1, ia, ib\n // loop b columns\n for (let jb = 0; jb < bcolumns; jb++) {\n // update ptr\n cptr[jb] = cindex.length\n // mark in workspace for current column\n const mark = jb + 1\n // B values & index in j\n for (kb0 = bptr[jb], kb1 = bptr[jb + 1], kb = kb0; kb < kb1; kb++) {\n // b row\n ib = bindex[kb]\n // check we need to process values\n if (values) {\n // loop values in a[:,ib]\n for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // row\n ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n // x(ia) = A\n x[ia] = mf(bvalues[kb], avalues[ka])\n } else {\n // i exists in C already\n x[ia] = af(x[ia], mf(bvalues[kb], avalues[ka]))\n }\n }\n } else {\n // loop values in a[:,ib]\n for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {\n // row\n ia = aindex[ka]\n // check value exists in current j\n if (w[ia] !== mark) {\n // ia is new entry in j\n w[ia] = mark\n // add i to pattern of C\n cindex.push(ia)\n }\n }\n }\n }\n // check we need to process matrix values (pattern matrix)\n if (values) {\n // copy values from x to column jb of c\n for (let p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {\n // row\n const ic = cindex[p]\n // copy value\n cvalues[p] = x[ic]\n }\n }\n }\n // update ptr\n cptr[bcolumns] = cindex.length\n\n // return sparse matrix\n return c\n }\n\n /**\n * Multiply two or more values, `x * y`.\n * For matrices, the matrix product is calculated.\n *\n * Syntax:\n *\n * math.multiply(x, y)\n * math.multiply(x, y, z, ...)\n *\n * Examples:\n *\n * math.multiply(4, 5.2) // returns number 20.8\n * math.multiply(2, 3, 4) // returns number 24\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(4, 1)\n * math.multiply(a, b) // returns Complex 5 + 14i\n *\n * const c = [[1, 2], [4, 3]]\n * const d = [[1, 2, 3], [3, -4, 7]]\n * math.multiply(c, d) // returns Array [[7, -6, 17], [13, -4, 33]]\n *\n * const e = math.unit('2.1 km')\n * math.multiply(3, e) // returns Unit 6.3 km\n *\n * See also:\n *\n * divide, prod, cross, dot\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to multiply\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to multiply\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`\n */\n return typed(name, extend({\n // we extend the signatures of multiplyScalar with signatures dealing with matrices\n\n 'Array, Array': function (x, y) {\n // check dimensions\n _validateMatrixDimensions(arraySize(x), arraySize(y))\n\n // use dense matrix implementation\n const m = this(matrix(x), matrix(y))\n // return array or scalar\n return isMatrix(m) ? m.valueOf() : m\n },\n\n 'Matrix, Matrix': function (x, y) {\n // dimensions\n const xsize = x.size()\n const ysize = y.size()\n\n // check dimensions\n _validateMatrixDimensions(xsize, ysize)\n\n // process dimensions\n if (xsize.length === 1) {\n // process y dimensions\n if (ysize.length === 1) {\n // Vector * Vector\n return _multiplyVectorVector(x, y, xsize[0])\n }\n // Vector * Matrix\n return _multiplyVectorMatrix(x, y)\n }\n // process y dimensions\n if (ysize.length === 1) {\n // Matrix * Vector\n return _multiplyMatrixVector(x, y)\n }\n // Matrix * Matrix\n return _multiplyMatrixMatrix(x, y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use Matrix * Matrix implementation\n return this(x, matrix(y))\n },\n\n 'Array, Matrix': function (x, y) {\n // use Matrix * Matrix implementation\n return this(matrix(x, y.storage()), y)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, multiplyScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, multiplyScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, multiplyScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, multiplyScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, multiplyScalar, true).valueOf()\n },\n\n 'any, any': multiplyScalar,\n\n 'any, any, ...any': function (x, y, rest) {\n let result = this(x, y)\n\n for (let i = 0; i < rest.length; i++) {\n result = this(result, rest[i])\n }\n\n return result\n }\n }, multiplyScalar.signatures))\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { nthRootNumber } from '../../plain/number/index.js'\n\nconst name = 'nthRoot'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber'\n]\n\nexport const createNthRoot = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the nth root of a value.\n * The principal nth root of a positive real number A, is the positive real\n * solution of the equation\n *\n * x^root = A\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.nthRoot(a)\n * math.nthRoot(a, root)\n *\n * Examples:\n *\n * math.nthRoot(9, 2) // returns 3, as 3^2 == 9\n * math.sqrt(9) // returns 3, as 3^2 == 9\n * math.nthRoot(64, 3) // returns 4, as 4^3 == 64\n *\n * See also:\n *\n * sqrt, pow\n *\n * @param {number | BigNumber | Array | Matrix | Complex} a\n * Value for which to calculate the nth root\n * @param {number | BigNumber} [root=2] The root.\n * @return {number | Complex | Array | Matrix} Returns the nth root of `a`\n */\n const complexErr = ('' +\n 'Complex number not supported in function nthRoot. ' +\n 'Use nthRoots instead.'\n )\n return typed(name, {\n\n number: function (x) {\n return nthRootNumber(x, 2)\n },\n\n 'number, number': nthRootNumber,\n\n BigNumber: function (x) {\n return _bigNthRoot(x, new BigNumber(2))\n },\n Complex: function (x) {\n throw new Error(complexErr)\n },\n 'Complex, number': function (x, y) {\n throw new Error(complexErr)\n },\n 'BigNumber, BigNumber': _bigNthRoot,\n\n 'Array | Matrix': function (x) {\n return this(x, 2)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // sparse + sparse\n return algorithm06(x, y, this)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // dense + sparse\n return algorithm01(x, y, this, false)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // density must be one (no zeros in matrix)\n if (y.density() === 1) {\n // sparse - scalar\n return algorithm11(y, x, this, true)\n } else {\n // throw exception\n throw new Error('Root must be non-zero')\n }\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n\n /**\n * Calculate the nth root of a for BigNumbers, solve x^root == a\n * https://rosettacode.org/wiki/Nth_root#JavaScript\n * @param {BigNumber} a\n * @param {BigNumber} root\n * @private\n */\n function _bigNthRoot (a, root) {\n const precision = BigNumber.precision\n const Big = BigNumber.clone({ precision: precision + 2 })\n const zero = new BigNumber(0)\n\n const one = new Big(1)\n const inv = root.isNegative()\n if (inv) {\n root = root.neg()\n }\n\n if (root.isZero()) {\n throw new Error('Root must be non-zero')\n }\n if (a.isNegative() && !root.abs().mod(2).equals(1)) {\n throw new Error('Root must be odd when a is negative.')\n }\n\n // edge cases zero and infinity\n if (a.isZero()) {\n return inv ? new Big(Infinity) : 0\n }\n if (!a.isFinite()) {\n return inv ? zero : a\n }\n\n let x = a.abs().pow(one.div(root))\n // If a < 0, we require that root is an odd integer,\n // so (-1) ^ (1/root) = -1\n x = a.isNeg() ? x.neg() : x\n return new BigNumber((inv ? one.div(x) : x).toPrecision(precision))\n }\n})\n\nexport const createNthRootNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, {\n number: nthRootNumber,\n 'number, number': nthRootNumber\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { signNumber } from '../../plain/number/index.js'\n\nconst name = 'sign'\nconst dependencies = ['typed', 'BigNumber', 'Fraction', 'complex']\n\nexport const createSign = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber, complex, Fraction }) => {\n /**\n * Compute the sign of a value. The sign of a value x is:\n *\n * - 1 when x > 0\n * - -1 when x < 0\n * - 0 when x == 0\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sign(x)\n *\n * Examples:\n *\n * math.sign(3.5) // returns 1\n * math.sign(-4.2) // returns -1\n * math.sign(0) // returns 0\n *\n * math.sign([3, 5, -2, 0, 2]) // returns [1, 1, -1, 0, 1]\n *\n * See also:\n *\n * abs\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * The number for which to determine the sign\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}e\n * The sign of `x`\n */\n return typed(name, {\n number: signNumber,\n\n Complex: function (x) {\n return x.im === 0 ? complex(signNumber(x.re)) : x.sign()\n },\n\n BigNumber: function (x) {\n return new BigNumber(x.cmp(0))\n },\n\n Fraction: function (x) {\n return new Fraction(x.s, 1)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sign(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return this(x.value)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'sqrt'\nconst dependencies = ['config', 'typed', 'Complex']\n\nexport const createSqrt = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, Complex }) => {\n /**\n * Calculate the square root of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sqrt(x)\n *\n * Examples:\n *\n * math.sqrt(25) // returns 5\n * math.square(5) // returns 25\n * math.sqrt(-4) // returns Complex 2i\n *\n * See also:\n *\n * square, multiply, cube, cbrt, sqrtm\n *\n * @param {number | BigNumber | Complex | Array | Matrix | Unit} x\n * Value for which to calculate the square root.\n * @return {number | BigNumber | Complex | Array | Matrix | Unit}\n * Returns the square root of `x`\n */\n return typed('sqrt', {\n number: _sqrtNumber,\n\n Complex: function (x) {\n return x.sqrt()\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.sqrt()\n } else {\n // negative value -> downgrade to number to do complex value computation\n return _sqrtNumber(x.toNumber())\n }\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sqrt(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n // Someday will work for complex units when they are implemented\n return x.pow(0.5)\n }\n\n })\n\n /**\n * Calculate sqrt for a number\n * @param {number} x\n * @returns {number | Complex} Returns the square root of x\n * @private\n */\n function _sqrtNumber (x) {\n if (isNaN(x)) {\n return NaN\n } else if (x >= 0 || config.predictable) {\n return Math.sqrt(x)\n } else {\n return new Complex(x, 0).sqrt()\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { squareNumber } from '../../plain/number/index.js'\n\nconst name = 'square'\nconst dependencies = ['typed']\n\nexport const createSquare = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the square of a value, `x * x`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.square(x)\n *\n * Examples:\n *\n * math.square(2) // returns number 4\n * math.square(3) // returns number 9\n * math.pow(3, 2) // returns number 9\n * math.multiply(3, 3) // returns number 9\n *\n * math.square([1, 2, 3, 4]) // returns Array [1, 4, 9, 16]\n *\n * See also:\n *\n * multiply, cube, sqrt, pow\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x\n * Number for which to calculate the square\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}\n * Squared value\n */\n return typed(name, {\n number: squareNumber,\n\n Complex: function (x) {\n return x.mul(x)\n },\n\n BigNumber: function (x) {\n return x.times(x)\n },\n\n Fraction: function (x) {\n return x.mul(x)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since square(0) = 0\n return deepMap(x, this, true)\n },\n\n Unit: function (x) {\n return x.pow(2)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'subtract'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'addScalar',\n 'unaryMinus',\n 'DenseMatrix'\n]\n\nexport const createSubtract = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, addScalar, unaryMinus, DenseMatrix }) => {\n // TODO: split function subtract in two: subtract and subtractScalar\n\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Subtract two values, `x - y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.subtract(x, y)\n *\n * Examples:\n *\n * math.subtract(5.3, 2) // returns number 3.3\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(4, 1)\n * math.subtract(a, b) // returns Complex -2 + 2i\n *\n * math.subtract([5, 7, 4], 4) // returns Array [1, 3, 0]\n *\n * const c = math.unit('2.1 km')\n * const d = math.unit('500m')\n * math.subtract(c, d) // returns Unit 1.6 km\n *\n * See also:\n *\n * add\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x\n * Initial value\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y\n * Value to subtract from `x`\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Subtraction of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': function (x, y) {\n return x - y\n },\n\n 'Complex, Complex': function (x, y) {\n return x.sub(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.minus(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.sub(y)\n },\n\n 'Unit, Unit': function (x, y) {\n if (x.value === null) {\n throw new Error('Parameter x contains a unit with undefined value')\n }\n\n if (y.value === null) {\n throw new Error('Parameter y contains a unit with undefined value')\n }\n\n if (!x.equalBase(y)) {\n throw new Error('Units do not match')\n }\n\n const res = x.clone()\n res.value = this(res.value, y.value)\n res.fixPrefix = false\n\n return res\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n checkEqualDimensions(x, y)\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, unaryMinus(y), addScalar)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\n/**\n * Check whether matrix x and y have the same number of dimensions.\n * Throws a DimensionError when dimensions are not equal\n * @param {Matrix} x\n * @param {Matrix} y\n */\nfunction checkEqualDimensions (x, y) {\n const xsize = x.size()\n const ysize = y.size()\n\n if (xsize.length !== ysize.length) {\n throw new DimensionError(xsize.length, ysize.length)\n }\n}\n","import { factory } from '../../utils/factory.js'\nimport { xgcdNumber } from '../../plain/number/index.js'\n\nconst name = 'xgcd'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createXgcd = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Calculate the extended greatest common divisor for two values.\n * See https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.\n *\n * Syntax:\n *\n * math.xgcd(a, b)\n *\n * Examples:\n *\n * math.xgcd(8, 12) // returns [4, -1, 1]\n * math.gcd(8, 12) // returns 4\n * math.xgcd(36163, 21199) // returns [1247, -7, 12]\n *\n * See also:\n *\n * gcd, lcm\n *\n * @param {number | BigNumber} a An integer number\n * @param {number | BigNumber} b An integer number\n * @return {Array} Returns an array containing 3 integers `[div, m, n]`\n * where `div = gcd(a, b)` and `a*m + b*n = div`\n */\n return typed(name, {\n 'number, number': function (a, b) {\n const res = xgcdNumber(a, b)\n\n return (config.matrix === 'Array')\n ? res\n : matrix(res)\n },\n 'BigNumber, BigNumber': _xgcdBigNumber\n // TODO: implement support for Fraction\n })\n\n /**\n * Calculate xgcd for two BigNumbers\n * @param {BigNumber} a\n * @param {BigNumber} b\n * @return {BigNumber[]} result\n * @private\n */\n function _xgcdBigNumber (a, b) {\n // source: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm\n let // used to swap two variables\n t\n\n let // quotient\n q\n\n let // remainder\n r\n\n const zero = new BigNumber(0)\n const one = new BigNumber(1)\n let x = zero\n let lastx = one\n let y = one\n let lasty = zero\n\n if (!a.isInt() || !b.isInt()) {\n throw new Error('Parameters in function xgcd must be integer numbers')\n }\n\n while (!b.isZero()) {\n q = a.div(b).floor()\n r = a.mod(b)\n\n t = x\n x = lastx.minus(q.times(x))\n lastx = t\n\n t = y\n y = lasty.minus(q.times(y))\n lasty = t\n\n a = b\n b = r\n }\n\n let res\n if (a.lt(zero)) {\n res = [a.neg(), lastx.neg(), lasty.neg()]\n } else {\n res = [a, !a.isZero() ? lastx : 0, lasty]\n }\n return (config.matrix === 'Array') ? res : matrix(res)\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm09'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm09 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and invokes the callback function f(Aij, Bij).\n * Callback function invoked NZA times, number of nonzero elements in A.\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0\n * C(i,j) = ┤\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm09 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = avalues && bvalues ? [] : undefined\n const cindex = []\n const cptr = []\n\n // workspaces\n const x = cvalues ? [] : undefined\n // marks indicating we have a value in x for a given column\n const w = []\n\n // vars\n let i, j, k, k0, k1\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // column mark\n const mark = j + 1\n // check we need to process values\n if (x) {\n // loop B(:,j)\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // update workspace\n w[i] = mark\n x[i] = bvalues[k]\n }\n }\n // loop A(:,j)\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // check we need to process values\n if (x) {\n // b value @ i,j\n const vb = w[i] === mark ? x[i] : zero\n // invoke f\n const vc = cf(avalues[k], vb)\n // check zero value\n if (!eq(vc, zero)) {\n // push index\n cindex.push(i)\n // push value\n cvalues.push(vc)\n }\n } else {\n // push index\n cindex.push(i)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm09 } from '../../type/matrix/utils/algorithm09.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotMultiply'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'multiplyScalar'\n]\n\nexport const createDotMultiply = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, multiplyScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm09 = createAlgorithm09({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Multiply two matrices element wise. The function accepts both matrices and\n * scalar values.\n *\n * Syntax:\n *\n * math.dotMultiply(x, y)\n *\n * Examples:\n *\n * math.dotMultiply(2, 4) // returns 8\n *\n * a = [[9, 5], [6, 1]]\n * b = [[3, 2], [5, 2]]\n *\n * math.dotMultiply(a, b) // returns [[27, 10], [30, 2]]\n * math.multiply(a, b) // returns [[52, 28], [23, 14]]\n *\n * See also:\n *\n * multiply, divide, dotDivide\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Left hand value\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Right hand value\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`\n */\n return typed(name, {\n\n 'any, any': multiplyScalar,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm09(x, y, multiplyScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, multiplyScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, multiplyScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, multiplyScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, multiplyScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, multiplyScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, multiplyScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, multiplyScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, multiplyScalar, true).valueOf()\n }\n })\n})\n","/**\n * Bitwise and for Bignumbers\n *\n * Special Cases:\n * N & n = N\n * n & 0 = 0\n * n & -1 = n\n * n & n = n\n * I & I = I\n * -I & -I = -I\n * I & -I = 0\n * I & n = n\n * I & -n = I\n * -I & n = 0\n * -I & -n = -I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` & `y`, is fully precise\n * @private\n */\nexport function bitAndBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitAnd')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n\n if (x.isZero() || y.eq(-1) || x.eq(y)) {\n return x\n }\n if (y.isZero() || x.eq(-1)) {\n return y\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if (!x.isFinite() && !y.isFinite()) {\n if (x.isNegative() === y.isNegative()) {\n return x\n }\n return new BigNumber(0)\n }\n if (!x.isFinite()) {\n if (y.isNegative()) {\n return x\n }\n if (x.isNegative()) {\n return new BigNumber(0)\n }\n return y\n }\n if (!y.isFinite()) {\n if (x.isNegative()) {\n return y\n }\n if (y.isNegative()) {\n return new BigNumber(0)\n }\n return x\n }\n }\n return bitwise(x, y, function (a, b) { return a & b })\n}\n\n/**\n * Bitwise not\n * @param {BigNumber} x\n * @return {BigNumber} Result of ~`x`, fully precise\n *\n */\nexport function bitNotBigNumber (x) {\n if (x.isFinite() && !x.isInteger()) {\n throw new Error('Integer expected in function bitNot')\n }\n\n const BigNumber = x.constructor\n const prevPrec = BigNumber.precision\n BigNumber.config({ precision: 1E9 })\n\n const result = x.plus(new BigNumber(1))\n result.s = -result.s || null\n\n BigNumber.config({ precision: prevPrec })\n return result\n}\n\n/**\n * Bitwise OR for BigNumbers\n *\n * Special Cases:\n * N | n = N\n * n | 0 = n\n * n | -1 = -1\n * n | n = n\n * I | I = I\n * -I | -I = -I\n * I | -n = -1\n * I | -I = -1\n * I | n = I\n * -I | n = -I\n * -I | -n = -n\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` | `y`, fully precise\n */\nexport function bitOrBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitOr')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n\n const negOne = new BigNumber(-1)\n if (x.isZero() || y.eq(negOne) || x.eq(y)) {\n return y\n }\n if (y.isZero() || x.eq(negOne)) {\n return x\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if ((!x.isFinite() && !x.isNegative() && y.isNegative()) ||\n (x.isNegative() && !y.isNegative() && !y.isFinite())) {\n return negOne\n }\n if (x.isNegative() && y.isNegative()) {\n return x.isFinite() ? x : y\n }\n return x.isFinite() ? y : x\n }\n\n return bitwise(x, y, function (a, b) { return a | b })\n}\n\n/**\n * Applies bitwise function to numbers\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @param {function (a, b)} func\n * @return {BigNumber}\n */\nexport function bitwise (x, y, func) {\n const BigNumber = x.constructor\n\n let xBits, yBits\n const xSign = +(x.s < 0)\n const ySign = +(y.s < 0)\n if (xSign) {\n xBits = decCoefficientToBinaryString(bitNotBigNumber(x))\n for (let i = 0; i < xBits.length; ++i) {\n xBits[i] ^= 1\n }\n } else {\n xBits = decCoefficientToBinaryString(x)\n }\n if (ySign) {\n yBits = decCoefficientToBinaryString(bitNotBigNumber(y))\n for (let i = 0; i < yBits.length; ++i) {\n yBits[i] ^= 1\n }\n } else {\n yBits = decCoefficientToBinaryString(y)\n }\n\n let minBits, maxBits, minSign\n if (xBits.length <= yBits.length) {\n minBits = xBits\n maxBits = yBits\n minSign = xSign\n } else {\n minBits = yBits\n maxBits = xBits\n minSign = ySign\n }\n\n let shortLen = minBits.length\n let longLen = maxBits.length\n const expFuncVal = func(xSign, ySign) ^ 1\n let outVal = new BigNumber(expFuncVal ^ 1)\n let twoPower = new BigNumber(1)\n const two = new BigNumber(2)\n\n const prevPrec = BigNumber.precision\n BigNumber.config({ precision: 1E9 })\n\n while (shortLen > 0) {\n if (func(minBits[--shortLen], maxBits[--longLen]) === expFuncVal) {\n outVal = outVal.plus(twoPower)\n }\n twoPower = twoPower.times(two)\n }\n while (longLen > 0) {\n if (func(minSign, maxBits[--longLen]) === expFuncVal) {\n outVal = outVal.plus(twoPower)\n }\n twoPower = twoPower.times(two)\n }\n\n BigNumber.config({ precision: prevPrec })\n\n if (expFuncVal === 0) {\n outVal.s = -outVal.s\n }\n return outVal\n}\n\n/* Extracted from decimal.js, and edited to specialize. */\nfunction decCoefficientToBinaryString (x) {\n // Convert to string\n const a = x.d // array with digits\n let r = a[0] + ''\n\n for (let i = 1; i < a.length; ++i) {\n let s = a[i] + ''\n for (let z = 7 - s.length; z--;) {\n s = '0' + s\n }\n\n r += s\n }\n\n let j = r.length\n while (r.charAt(j) === '0') {\n j--\n }\n\n let xe = x.e\n let str = r.slice(0, j + 1 || 1)\n const strL = str.length\n if (xe > 0) {\n if (++xe > strL) {\n // Append zeros.\n xe -= strL\n while (xe--) {\n str += '0'\n }\n } else if (xe < strL) {\n str = str.slice(0, xe) + '.' + str.slice(xe)\n }\n }\n\n // Convert from base 10 (decimal) to base 2\n const arr = [0]\n for (let i = 0; i < str.length;) {\n let arrL = arr.length\n while (arrL--) {\n arr[arrL] *= 10\n }\n\n arr[0] += parseInt(str.charAt(i++)) // convert to int\n for (let j = 0; j < arr.length; ++j) {\n if (arr[j] > 1) {\n if (arr[j + 1] === null || arr[j + 1] === undefined) {\n arr[j + 1] = 0\n }\n\n arr[j + 1] += arr[j] >> 1\n arr[j] &= 1\n }\n }\n }\n\n return arr.reverse()\n}\n\n/**\n * Bitwise XOR for BigNumbers\n *\n * Special Cases:\n * N ^ n = N\n * n ^ 0 = n\n * n ^ n = 0\n * n ^ -1 = ~n\n * I ^ n = I\n * I ^ -n = -I\n * I ^ -I = -1\n * -I ^ n = -I\n * -I ^ -n = I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` ^ `y`, fully precise\n *\n */\nexport function bitXor (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function bitXor')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN()) {\n return new BigNumber(NaN)\n }\n if (x.isZero()) {\n return y\n }\n if (y.isZero()) {\n return x\n }\n\n if (x.eq(y)) {\n return new BigNumber(0)\n }\n\n const negOne = new BigNumber(-1)\n if (x.eq(negOne)) {\n return bitNotBigNumber(y)\n }\n if (y.eq(negOne)) {\n return bitNotBigNumber(x)\n }\n\n if (!x.isFinite() || !y.isFinite()) {\n if (!x.isFinite() && !y.isFinite()) {\n return negOne\n }\n return new BigNumber(x.isNegative() === y.isNegative()\n ? Infinity\n : -Infinity)\n }\n return bitwise(x, y, function (a, b) { return a ^ b })\n}\n\n/**\n * Bitwise left shift\n *\n * Special Cases:\n * n << -n = N\n * n << N = N\n * N << n = N\n * n << 0 = n\n * 0 << n = 0\n * I << I = N\n * I << n = I\n * n << I = I\n *\n * @param {BigNumber} x\n * @param {BigNumber} y\n * @return {BigNumber} Result of `x` << `y`\n *\n */\nexport function leftShiftBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function leftShift')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN() || (y.isNegative() && !y.isZero())) {\n return new BigNumber(NaN)\n }\n if (x.isZero() || y.isZero()) {\n return x\n }\n if (!x.isFinite() && !y.isFinite()) {\n return new BigNumber(NaN)\n }\n\n // Math.pow(2, y) is fully precise for y < 55, and fast\n if (y.lt(55)) {\n return x.times(Math.pow(2, y.toNumber()) + '')\n }\n return x.times(new BigNumber(2).pow(y))\n}\n\n/*\n * Special Cases:\n * n >> -n = N\n * n >> N = N\n * N >> n = N\n * I >> I = N\n * n >> 0 = n\n * I >> n = I\n * -I >> n = -I\n * -I >> I = -I\n * n >> I = I\n * -n >> I = -1\n * 0 >> n = 0\n *\n * @param {BigNumber} value\n * @param {BigNumber} value\n * @return {BigNumber} Result of `x` >> `y`\n *\n */\nexport function rightArithShiftBigNumber (x, y) {\n if ((x.isFinite() && !x.isInteger()) || (y.isFinite() && !y.isInteger())) {\n throw new Error('Integers expected in function rightArithShift')\n }\n\n const BigNumber = x.constructor\n if (x.isNaN() || y.isNaN() || (y.isNegative() && !y.isZero())) {\n return new BigNumber(NaN)\n }\n if (x.isZero() || y.isZero()) {\n return x\n }\n if (!y.isFinite()) {\n if (x.isNegative()) {\n return new BigNumber(-1)\n }\n if (!x.isFinite()) {\n return new BigNumber(NaN)\n }\n return new BigNumber(0)\n }\n\n // Math.pow(2, y) is fully precise for y < 55, and fast\n if (y.lt(55)) {\n return x.div(Math.pow(2, y.toNumber()) + '').floor()\n }\n return x.div(new BigNumber(2).pow(y)).floor()\n}\n","import { isInteger } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function bitAndNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitAnd')\n }\n\n return x & y\n}\nbitAndNumber.signature = n2\n\nexport function bitNotNumber (x) {\n if (!isInteger(x)) {\n throw new Error('Integer expected in function bitNot')\n }\n\n return ~x\n}\nbitNotNumber.signature = n1\n\nexport function bitOrNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitOr')\n }\n\n return x | y\n}\nbitOrNumber.signature = n2\n\nexport function bitXorNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function bitXor')\n }\n\n return x ^ y\n}\nbitXorNumber.signature = n2\n\nexport function leftShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function leftShift')\n }\n\n return x << y\n}\nleftShiftNumber.signature = n2\n\nexport function rightArithShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function rightArithShift')\n }\n\n return x >> y\n}\nrightArithShiftNumber.signature = n2\n\nexport function rightLogShiftNumber (x, y) {\n if (!isInteger(x) || !isInteger(y)) {\n throw new Error('Integers expected in function rightLogShift')\n }\n\n return x >>> y\n}\nrightLogShiftNumber.signature = n2\n","import { bitAndBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitAndNumber } from '../../plain/number/index.js'\n\nconst name = 'bitAnd'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar'\n]\n\nexport const createBitAnd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise AND two values, `x & y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.bitAnd(x, y)\n *\n * Examples:\n *\n * math.bitAnd(53, 131) // returns number 1\n *\n * math.bitAnd([1, 12, 31], 42) // returns Array [0, 8, 10]\n *\n * See also:\n *\n * bitNot, bitOr, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to and\n * @param {number | BigNumber | Array | Matrix} y Second value to and\n * @return {number | BigNumber | Array | Matrix} AND of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitAndNumber,\n\n 'BigNumber, BigNumber': bitAndBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm11(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { bitNotBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitNotNumber } from '../../plain/number/index.js'\n\nconst name = 'bitNot'\nconst dependencies = ['typed']\n\nexport const createBitNot = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Bitwise NOT value, `~x`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.bitNot(x)\n *\n * Examples:\n *\n * math.bitNot(1) // returns number -2\n *\n * math.bitNot([2, -3, 4]) // returns Array [-3, 2, 5]\n *\n * See also:\n *\n * bitAnd, bitOr, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to not\n * @return {number | BigNumber | Array | Matrix} NOT of `x`\n */\n return typed(name, {\n number: bitNotNumber,\n\n BigNumber: bitNotBigNumber,\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { bitOrBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { bitOrNumber } from '../../plain/number/index.js'\n\nconst name = 'bitOr'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createBitOr = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise OR two values, `x | y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the lowest print base.\n *\n * Syntax:\n *\n * math.bitOr(x, y)\n *\n * Examples:\n *\n * math.bitOr(1, 2) // returns number 3\n *\n * math.bitOr([1, 2, 3], 4) // returns Array [5, 6, 7]\n *\n * See also:\n *\n * bitAnd, bitNot, bitXor, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to or\n * @param {number | BigNumber | Array | Matrix} y Second value to or\n * @return {number | BigNumber | Array | Matrix} OR of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitOrNumber,\n\n 'BigNumber, BigNumber': bitOrBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm07'\nconst dependencies = ['typed', 'DenseMatrix']\n\nexport const createAlgorithm07 = /* #__PURE__ */ factory(name, dependencies, ({ typed, DenseMatrix }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B items (zero and nonzero) and invokes the callback function f(Aij, Bij).\n * Callback function invoked MxN times.\n *\n * C(i,j) = f(Aij, Bij)\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} DenseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm07 (a, b, callback) {\n // sparse matrix arrays\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // vars\n let i, j\n\n // result arrays\n const cdata = []\n // initialize c\n for (i = 0; i < rows; i++) { cdata[i] = [] }\n\n // workspaces\n const xa = []\n const xb = []\n // marks indicating we have a value in x for a given column\n const wa = []\n const wb = []\n\n // loop columns\n for (j = 0; j < columns; j++) {\n // columns mark\n const mark = j + 1\n // scatter the values of A(:,j) into workspace\n _scatter(a, j, wa, xa, mark)\n // scatter the values of B(:,j) into workspace\n _scatter(b, j, wb, xb, mark)\n // loop rows\n for (i = 0; i < rows; i++) {\n // matrix values @ i,j\n const va = wa[i] === mark ? xa[i] : zero\n const vb = wb[i] === mark ? xb[i] : zero\n // invoke callback\n cdata[i][j] = cf(va, vb)\n }\n }\n\n // return dense matrix\n return new DenseMatrix({\n data: cdata,\n size: [rows, columns],\n datatype: dt\n })\n }\n\n function _scatter (m, j, w, x, mark) {\n // a arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // loop values in column j\n for (let k = ptr[j], k1 = ptr[j + 1]; k < k1; k++) {\n // row\n const i = index[k]\n // update workspace\n w[i] = mark\n x[i] = values[k]\n }\n }\n})\n","import { bitXor as bigBitXor } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { factory } from '../../utils/factory.js'\nimport { bitXorNumber } from '../../plain/number/index.js'\n\nconst name = 'bitXor'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createBitXor = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise XOR two values, `x ^ y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.bitXor(x, y)\n *\n * Examples:\n *\n * math.bitXor(1, 2) // returns number 3\n *\n * math.bitXor([2, 3, 4], 4) // returns Array [6, 7, 0]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, leftShift, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x First value to xor\n * @param {number | BigNumber | Array | Matrix} y Second value to xor\n * @return {number | BigNumber | Array | Matrix} XOR of `x` and `y`\n */\n return typed(name, {\n\n 'number, number': bitXorNumber,\n\n 'BigNumber, BigNumber': bigBitXor,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'arg'\nconst dependencies = ['typed']\n\nexport const createArg = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the argument of a complex value.\n * For a complex number `a + bi`, the argument is computed as `atan2(b, a)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.arg(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 2)\n * math.arg(a) / math.pi // returns number 0.25\n *\n * const b = math.complex('2 + 3i')\n * math.arg(b) // returns number 0.982793723247329\n * math.atan2(3, 2) // returns number 0.982793723247329\n *\n * See also:\n *\n * re, im, conj, abs\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The argument of x\n */\n return typed(name, {\n number: function (x) {\n return Math.atan2(0, x)\n },\n\n BigNumber: function (x) {\n return x.constructor.atan2(0, x)\n },\n\n Complex: function (x) {\n return x.arg()\n },\n\n // TODO: implement BigNumber support for function arg\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'conj'\nconst dependencies = ['typed']\n\nexport const createConj = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the complex conjugate of a complex value.\n * If `x = a+bi`, the complex conjugate of `x` is `a - bi`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.conj(x)\n *\n * Examples:\n *\n * math.conj(math.complex('2 + 3i')) // returns Complex 2 - 3i\n * math.conj(math.complex('2 - 3i')) // returns Complex 2 + 3i\n * math.conj(math.complex('-5.2i')) // returns Complex 5.2i\n *\n * See also:\n *\n * re, im, arg, abs\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Complex | Array | Matrix}\n * The complex conjugate of x\n */\n return typed(name, {\n number: function (x) {\n return x\n },\n\n BigNumber: function (x) {\n return x\n },\n\n Complex: function (x) {\n return x.conjugate()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'im'\nconst dependencies = ['typed']\n\nexport const createIm = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Get the imaginary part of a complex number.\n * For a complex number `a + bi`, the function returns `b`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.im(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 3)\n * math.re(a) // returns number 2\n * math.im(a) // returns number 3\n *\n * math.re(math.complex('-5.2i')) // returns number -5.2\n * math.re(math.complex(2.4)) // returns number 0\n *\n * See also:\n *\n * re, conj, abs, arg\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The imaginary part of x\n */\n return typed(name, {\n number: function (x) {\n return 0\n },\n\n BigNumber: function (x) {\n return x.mul(0)\n },\n\n Complex: function (x) {\n return x.im\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 're'\nconst dependencies = ['typed']\n\nexport const createRe = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Get the real part of a complex number.\n * For a complex number `a + bi`, the function returns `a`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.re(x)\n *\n * Examples:\n *\n * const a = math.complex(2, 3)\n * math.re(a) // returns number 2\n * math.im(a) // returns number 3\n *\n * math.re(math.complex('-5.2i')) // returns number 0\n * math.re(math.complex(2.4)) // returns number 2.4\n *\n * See also:\n *\n * im, conj, abs, arg\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * A complex number or array with complex numbers\n * @return {number | BigNumber | Array | Matrix} The real part of x\n */\n return typed(name, {\n number: function (x) {\n return x\n },\n\n BigNumber: function (x) {\n return x\n },\n\n Complex: function (x) {\n return x.re\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","const n1 = 'number'\nconst n2 = 'number, number'\n\nexport function notNumber (x) {\n return !x\n}\nnotNumber.signature = n1\n\nexport function orNumber (x, y) {\n return !!(x || y)\n}\norNumber.signature = n2\n\nexport function xorNumber (x, y) {\n return !!x !== !!y\n}\nxorNumber.signature = n2\n\nexport function andNumber (x, y) {\n return !!(x && y)\n}\nandNumber.signature = n2\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { notNumber } from '../../plain/number/index.js'\n\nconst name = 'not'\nconst dependencies = ['typed']\n\nexport const createNot = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Logical `not`. Flips boolean value of a given parameter.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.not(x)\n *\n * Examples:\n *\n * math.not(2) // returns false\n * math.not(0) // returns true\n * math.not(true) // returns false\n *\n * a = [2, -7, 0]\n * math.not(a) // returns [false, false, true]\n *\n * See also:\n *\n * and, or, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @return {boolean | Array | Matrix}\n * Returns true when input is a zero or empty value.\n */\n return typed(name, {\n number: notNumber,\n\n Complex: function (x) {\n return x.re === 0 && x.im === 0\n },\n\n BigNumber: function (x) {\n return x.isZero() || x.isNaN()\n },\n\n Unit: function (x) {\n return x.value !== null ? this(x.value) : true\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\nimport { factory } from '../../utils/factory.js'\nimport { orNumber } from '../../plain/number/index.js'\n\nconst name = 'or'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createOr = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `or`. Test if at least one value is defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.or(x, y)\n *\n * Examples:\n *\n * math.or(2, 4) // returns true\n *\n * a = [2, 5, 0]\n * b = [0, 22, 0]\n * c = 0\n *\n * math.or(a, b) // returns [true, true, false]\n * math.or(b, c) // returns [false, true, false]\n *\n * See also:\n *\n * and, not, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when one of the inputs is defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': orNumber,\n\n 'Complex, Complex': function (x, y) {\n return (x.re !== 0 || x.im !== 0) || (y.re !== 0 || y.im !== 0)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return (!x.isZero() && !x.isNaN()) || (!y.isZero() && !y.isNaN())\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { factory } from '../../utils/factory.js'\nimport { xorNumber } from '../../plain/number/index.js'\n\nconst name = 'xor'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createXor = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `xor`. Test whether one and only one value is defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.xor(x, y)\n *\n * Examples:\n *\n * math.xor(2, 4) // returns false\n *\n * a = [2, 0, 0]\n * b = [2, 7, 0]\n * c = 0\n *\n * math.xor(a, b) // returns [false, true, false]\n * math.xor(a, c) // returns [true, false, false]\n *\n * See also:\n *\n * and, not, or\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when one and only one input is defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': xorNumber,\n\n 'Complex, Complex': function (x, y) {\n return ((x.re !== 0 || x.im !== 0) !== (y.re !== 0 || y.im !== 0))\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return ((!x.isZero() && !x.isNaN()) !== (!y.isZero() && !y.isNaN()))\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { isBigNumber, isMatrix, isNumber } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { arraySize } from '../../utils/array.js'\nimport { IndexError } from '../../error/IndexError.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'concat'\nconst dependencies = ['typed', 'matrix', 'isInteger']\n\nexport const createConcat = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, isInteger }) => {\n /**\n * Concatenate two or more matrices.\n *\n * Syntax:\n *\n * math.concat(A, B, C, ...)\n * math.concat(A, B, C, ..., dim)\n *\n * Where:\n *\n * - `dim: number` is a zero-based dimension over which to concatenate the matrices.\n * By default the last dimension of the matrices.\n *\n * Examples:\n *\n * const A = [[1, 2], [5, 6]]\n * const B = [[3, 4], [7, 8]]\n *\n * math.concat(A, B) // returns [[1, 2, 3, 4], [5, 6, 7, 8]]\n * math.concat(A, B, 0) // returns [[1, 2], [5, 6], [3, 4], [7, 8]]\n * math.concat('hello', ' ', 'world') // returns 'hello world'\n *\n * See also:\n *\n * size, squeeze, subset, transpose\n *\n * @param {... Array | Matrix} args Two or more matrices\n * @return {Array | Matrix} Concatenated matrix\n */\n return typed(name, {\n // TODO: change signature to '...Array | Matrix, dim?' when supported\n '...Array | Matrix | number | BigNumber': function (args) {\n let i\n const len = args.length\n let dim = -1 // zero-based dimension\n let prevDim\n let asMatrix = false\n const matrices = [] // contains multi dimensional arrays\n\n for (i = 0; i < len; i++) {\n const arg = args[i]\n\n // test whether we need to return a Matrix (if not we return an Array)\n if (isMatrix(arg)) {\n asMatrix = true\n }\n\n if (isNumber(arg) || isBigNumber(arg)) {\n if (i !== len - 1) {\n throw new Error('Dimension must be specified as last argument')\n }\n\n // last argument contains the dimension on which to concatenate\n prevDim = dim\n dim = arg.valueOf() // change BigNumber to number\n\n if (!isInteger(dim)) {\n throw new TypeError('Integer number expected for dimension')\n }\n\n if (dim < 0 || (i > 0 && dim > prevDim)) {\n // TODO: would be more clear when throwing a DimensionError here\n throw new IndexError(dim, prevDim + 1)\n }\n } else {\n // this is a matrix or array\n const m = clone(arg).valueOf()\n const size = arraySize(m)\n matrices[i] = m\n prevDim = dim\n dim = size.length - 1\n\n // verify whether each of the matrices has the same number of dimensions\n if (i > 0 && dim !== prevDim) {\n throw new DimensionError(prevDim + 1, dim + 1)\n }\n }\n }\n\n if (matrices.length === 0) {\n throw new SyntaxError('At least one matrix expected')\n }\n\n let res = matrices.shift()\n while (matrices.length) {\n res = _concat(res, matrices.shift(), dim, 0)\n }\n\n return asMatrix ? matrix(res) : res\n },\n\n '...string': function (args) {\n return args.join('')\n }\n })\n})\n\n/**\n * Recursively concatenate two matrices.\n * The contents of the matrices is not cloned.\n * @param {Array} a Multi dimensional array\n * @param {Array} b Multi dimensional array\n * @param {number} concatDim The dimension on which to concatenate (zero-based)\n * @param {number} dim The current dim (zero-based)\n * @return {Array} c The concatenated matrix\n * @private\n */\nfunction _concat (a, b, concatDim, dim) {\n if (dim < concatDim) {\n // recurse into next dimension\n if (a.length !== b.length) {\n throw new DimensionError(a.length, b.length)\n }\n\n const c = []\n for (let i = 0; i < a.length; i++) {\n c[i] = _concat(a[i], b[i], concatDim, dim + 1)\n }\n return c\n } else {\n // concatenate this dimension\n return a.concat(b)\n }\n}\n","import { factory } from '../../utils/factory.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\n\nconst name = 'column'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\nexport const createColumn = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n /**\n * Return a column from a Matrix.\n *\n * Syntax:\n *\n * math.column(value, index)\n *\n * Example:\n *\n * // get a column\n * const d = [[1, 2], [3, 4]]\n * math.column(d, 1) // returns [[2], [4]]\n *\n * See also:\n *\n * row\n *\n * @param {Array | Matrix } value An array or matrix\n * @param {number} column The index of the column\n * @return {Array | Matrix} The retrieved column\n */\n return typed(name, {\n 'Matrix, number': _column,\n\n 'Array, number': function (value, column) {\n return _column(matrix(clone(value)), column).valueOf()\n }\n })\n\n /**\n * Retrieve a column of a matrix\n * @param {Matrix } value A matrix\n * @param {number} column The index of the column\n * @return {Matrix} The retrieved column\n */\n function _column (value, column) {\n // check dimensions\n if (value.size().length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n\n validateIndex(column, value.size()[1])\n\n const rowRange = range(0, value.size()[0])\n const index = new Index(rowRange, column)\n return value.subset(index)\n }\n})\n","import { arraySize, squeeze } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'cross'\nconst dependencies = ['typed', 'matrix', 'subtract', 'multiply']\n\nexport const createCross = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, multiply }) => {\n /**\n * Calculate the cross product for two vectors in three dimensional space.\n * The cross product of `A = [a1, a2, a3]` and `B = [b1, b2, b3]` is defined\n * as:\n *\n * cross(A, B) = [\n * a2 * b3 - a3 * b2,\n * a3 * b1 - a1 * b3,\n * a1 * b2 - a2 * b1\n * ]\n *\n * If one of the input vectors has a dimension greater than 1, the output\n * vector will be a 1x3 (2-dimensional) matrix.\n *\n * Syntax:\n *\n * math.cross(x, y)\n *\n * Examples:\n *\n * math.cross([1, 1, 0], [0, 1, 1]) // Returns [1, -1, 1]\n * math.cross([3, -3, 1], [4, 9, 2]) // Returns [-15, -2, 39]\n * math.cross([2, 3, 4], [5, 6, 7]) // Returns [-3, 6, -3]\n * math.cross([[1, 2, 3]], [[4], [5], [6]]) // Returns [[-3, 6, -3]]\n *\n * See also:\n *\n * dot, multiply\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {Array | Matrix} Returns the cross product of `x` and `y`\n */\n return typed(name, {\n 'Matrix, Matrix': function (x, y) {\n return matrix(_cross(x.toArray(), y.toArray()))\n },\n\n 'Matrix, Array': function (x, y) {\n return matrix(_cross(x.toArray(), y))\n },\n\n 'Array, Matrix': function (x, y) {\n return matrix(_cross(x, y.toArray()))\n },\n\n 'Array, Array': _cross\n })\n\n /**\n * Calculate the cross product for two arrays\n * @param {Array} x First vector\n * @param {Array} y Second vector\n * @returns {Array} Returns the cross product of x and y\n * @private\n */\n function _cross (x, y) {\n const highestDimension = Math.max(arraySize(x).length, arraySize(y).length)\n\n x = squeeze(x)\n y = squeeze(y)\n\n const xSize = arraySize(x)\n const ySize = arraySize(y)\n\n if (xSize.length !== 1 || ySize.length !== 1 || xSize[0] !== 3 || ySize[0] !== 3) {\n throw new RangeError('Vectors with length 3 expected ' +\n '(Size A = [' + xSize.join(', ') + '], B = [' + ySize.join(', ') + '])')\n }\n\n const product = [\n subtract(multiply(x[1], y[2]), multiply(x[2], y[1])),\n subtract(multiply(x[2], y[0]), multiply(x[0], y[2])),\n subtract(multiply(x[0], y[1]), multiply(x[1], y[0]))\n ]\n\n if (highestDimension > 1) {\n return [product]\n } else {\n return product\n }\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { arraySize } from '../../utils/array.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'diag'\nconst dependencies = ['typed', 'matrix', 'DenseMatrix', 'SparseMatrix']\n\nexport const createDiag = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a diagonal matrix or retrieve the diagonal of a matrix\n *\n * When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.\n * When `x` is a two dimensional matrix, the matrixes `k`th diagonal will be returned as vector.\n * When k is positive, the values are placed on the super diagonal.\n * When k is negative, the values are placed on the sub diagonal.\n *\n * Syntax:\n *\n * math.diag(X)\n * math.diag(X, format)\n * math.diag(X, k)\n * math.diag(X, k, format)\n *\n * Examples:\n *\n * // create a diagonal matrix\n * math.diag([1, 2, 3]) // returns [[1, 0, 0], [0, 2, 0], [0, 0, 3]]\n * math.diag([1, 2, 3], 1) // returns [[0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]\n * math.diag([1, 2, 3], -1) // returns [[0, 0, 0], [1, 0, 0], [0, 2, 0], [0, 0, 3]]\n *\n * // retrieve the diagonal from a matrix\n * const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]\n * math.diag(a) // returns [1, 5, 9]\n *\n * See also:\n *\n * ones, zeros, identity\n *\n * @param {Matrix | Array} x A two dimensional matrix or a vector\n * @param {number | BigNumber} [k=0] The diagonal where the vector will be filled\n * in or retrieved.\n * @param {string} [format='dense'] The matrix storage format.\n *\n * @returns {Matrix | Array} Diagonal matrix from input vector, or diagonal from input matrix.\n */\n return typed(name, {\n // FIXME: simplify this huge amount of signatures as soon as typed-function supports optional arguments\n\n Array: function (x) {\n return _diag(x, 0, arraySize(x), null)\n },\n\n 'Array, number': function (x, k) {\n return _diag(x, k, arraySize(x), null)\n },\n\n 'Array, BigNumber': function (x, k) {\n return _diag(x, k.toNumber(), arraySize(x), null)\n },\n\n 'Array, string': function (x, format) {\n return _diag(x, 0, arraySize(x), format)\n },\n\n 'Array, number, string': function (x, k, format) {\n return _diag(x, k, arraySize(x), format)\n },\n\n 'Array, BigNumber, string': function (x, k, format) {\n return _diag(x, k.toNumber(), arraySize(x), format)\n },\n\n Matrix: function (x) {\n return _diag(x, 0, x.size(), x.storage())\n },\n\n 'Matrix, number': function (x, k) {\n return _diag(x, k, x.size(), x.storage())\n },\n\n 'Matrix, BigNumber': function (x, k) {\n return _diag(x, k.toNumber(), x.size(), x.storage())\n },\n\n 'Matrix, string': function (x, format) {\n return _diag(x, 0, x.size(), format)\n },\n\n 'Matrix, number, string': function (x, k, format) {\n return _diag(x, k, x.size(), format)\n },\n\n 'Matrix, BigNumber, string': function (x, k, format) {\n return _diag(x, k.toNumber(), x.size(), format)\n }\n })\n\n /**\n * Creeate diagonal matrix from a vector or vice versa\n * @param {Array | Matrix} x\n * @param {number} k\n * @param {string} format Storage format for matrix. If null,\n * an Array is returned\n * @returns {Array | Matrix}\n * @private\n */\n function _diag (x, k, size, format) {\n if (!isInteger(k)) {\n throw new TypeError('Second parameter in function diag must be an integer')\n }\n\n const kSuper = k > 0 ? k : 0\n const kSub = k < 0 ? -k : 0\n\n // check dimensions\n switch (size.length) {\n case 1:\n return _createDiagonalMatrix(x, k, format, size[0], kSub, kSuper)\n case 2:\n return _getDiagonal(x, k, format, size, kSub, kSuper)\n }\n throw new RangeError('Matrix for function diag must be 2 dimensional')\n }\n\n function _createDiagonalMatrix (x, k, format, l, kSub, kSuper) {\n // matrix size\n const ms = [l + kSub, l + kSuper]\n\n if (format && format !== 'sparse' && format !== 'dense') {\n throw new TypeError(`Unknown matrix type ${format}\"`)\n }\n\n // create diagonal matrix\n const m = format === 'sparse'\n ? SparseMatrix.diagonal(ms, x, k)\n : DenseMatrix.diagonal(ms, x, k)\n // check we need to return a matrix\n return format !== null ? m : m.valueOf()\n }\n\n function _getDiagonal (x, k, format, s, kSub, kSuper) {\n // check x is a Matrix\n if (isMatrix(x)) {\n // get diagonal matrix\n const dm = x.diagonal(k)\n // check we need to return a matrix\n if (format !== null) {\n // check we need to change matrix format\n if (format !== dm.storage()) { return matrix(dm, format) }\n return dm\n }\n return dm.valueOf()\n }\n // vector size\n const n = Math.min(s[0] - kSub, s[1] - kSuper)\n // diagonal values\n const vector = []\n // loop diagonal\n for (let i = 0; i < n; i++) {\n vector[i] = x[i + kSub][i + kSuper]\n }\n // check we need to return a matrix\n return format !== null ? matrix(vector) : vector\n }\n})\n","// (c) 2018, Mariusz Nowak\n// SPDX-License-Identifier: ISC\n// Derived from https://github.com/medikoo/lru-queue\nexport function lruQueue (limit) {\n let size = 0\n let base = 1\n let queue = Object.create(null)\n let map = Object.create(null)\n let index = 0\n const del = function (id) {\n const oldIndex = map[id]\n if (!oldIndex) return\n delete queue[oldIndex]\n delete map[id]\n --size\n if (base !== oldIndex) return\n if (!size) {\n index = 0\n base = 1\n return\n }\n while (!hasOwnProperty.call(queue, ++base)) continue\n }\n limit = Math.abs(limit)\n return {\n hit: function (id) {\n const oldIndex = map[id]; const nuIndex = ++index\n queue[nuIndex] = id\n map[id] = nuIndex\n if (!oldIndex) {\n ++size\n if (size <= limit) return undefined\n id = queue[base]\n del(id)\n return id\n }\n delete queue[oldIndex]\n if (base !== oldIndex) return undefined\n while (!hasOwnProperty.call(queue, ++base)) continue\n return undefined\n },\n delete: del,\n clear: function () {\n size = index = 0\n base = 1\n queue = Object.create(null)\n map = Object.create(null)\n }\n }\n};\n","// function utils\n\nimport { lruQueue } from './lruQueue.js'\n\n/**\n * Memoize a given function by caching the computed result.\n * The cache of a memoized function can be cleared by deleting the `cache`\n * property of the function.\n *\n * @param {function} fn The function to be memoized.\n * Must be a pure function.\n * @param {Object} [options]\n * @param {function(args: Array): string} [options.hasher]\n * A custom hash builder. Is JSON.stringify by default.\n * @param {number | undefined} [options.limit]\n * Maximum number of values that may be cached. Undefined indicates\n * unlimited (default)\n * @return {function} Returns the memoized function\n */\nexport function memoize (fn, { hasher, limit } = {}) {\n limit = limit == null ? Number.POSITIVE_INFINITY : limit\n hasher = hasher == null ? JSON.stringify : hasher\n\n return function memoize () {\n if (typeof memoize.cache !== 'object') {\n memoize.cache = {\n values: new Map(),\n lru: lruQueue(limit || Number.POSITIVE_INFINITY)\n }\n }\n const args = []\n for (let i = 0; i < arguments.length; i++) {\n args[i] = arguments[i]\n }\n const hash = hasher(args)\n\n if (memoize.cache.values.has(hash)) {\n memoize.cache.lru.hit(hash)\n return memoize.cache.values.get(hash)\n }\n\n const newVal = fn.apply(fn, args)\n memoize.cache.values.set(hash, newVal)\n memoize.cache.values.delete(memoize.cache.lru.hit(hash))\n\n return newVal\n }\n}\n\n/**\n * Memoize a given function by caching all results and the arguments,\n * and comparing against the arguments of previous results before\n * executing again.\n * This is less performant than `memoize` which calculates a hash,\n * which is very fast to compare. Use `memoizeCompare` only when it is\n * not possible to create a unique serializable hash from the function\n * arguments.\n * The isEqual function must compare two sets of arguments\n * and return true when equal (can be a deep equality check for example).\n * @param {function} fn\n * @param {function(a: *, b: *) : boolean} isEqual\n * @returns {function}\n */\nexport function memoizeCompare (fn, isEqual) {\n const memoize = function memoize () {\n const args = []\n for (let i = 0; i < arguments.length; i++) {\n args[i] = arguments[i]\n }\n\n for (let c = 0; c < memoize.cache.length; c++) {\n const cached = memoize.cache[c]\n\n if (isEqual(args, cached.args)) {\n // TODO: move this cache entry to the top so recently used entries move up?\n return cached.res\n }\n }\n\n const res = fn.apply(fn, args)\n memoize.cache.unshift({ args, res })\n\n return res\n }\n\n memoize.cache = []\n\n return memoize\n}\n\n/**\n * Find the maximum number of arguments expected by a typed function.\n * @param {function} fn A typed function\n * @return {number} Returns the maximum number of expected arguments.\n * Returns -1 when no signatures where found on the function.\n */\nexport function maxArgumentCount (fn) {\n return Object.keys(fn.signatures || {})\n .reduce(function (args, signature) {\n const count = (signature.match(/,/g) || []).length + 1\n return Math.max(args, count)\n }, -1)\n}\n","import { filter, filterRegExp } from '../../utils/array.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'filter'\nconst dependencies = ['typed']\n\nexport const createFilter = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Filter the items in an array or one dimensional matrix.\n *\n * Syntax:\n *\n * math.filter(x, test)\n *\n * Examples:\n *\n * function isPositive (x) {\n * return x > 0\n * }\n * math.filter([6, -2, -1, 4, 3], isPositive) // returns [6, 4, 3]\n *\n * math.filter([\"23\", \"foo\", \"100\", \"55\", \"bar\"], /[0-9]+/) // returns [\"23\", \"100\", \"55\"]\n *\n * See also:\n *\n * forEach, map, sort\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to filter\n * @param {Function | RegExp} test\n * A function or regular expression to test items.\n * All entries for which `test` returns true are returned.\n * When `test` is a function, it is invoked with three parameters:\n * the value of the element, the index of the element, and the\n * matrix/array being traversed. The function must return a boolean.\n * @return {Matrix | Array} Returns the filtered matrix.\n */\n return typed('filter', {\n 'Array, function': _filterCallback,\n\n 'Matrix, function': function (x, test) {\n return x.create(_filterCallback(x.toArray(), test))\n },\n\n 'Array, RegExp': filterRegExp,\n\n 'Matrix, RegExp': function (x, test) {\n return x.create(filterRegExp(x.toArray(), test))\n }\n })\n})\n\n/**\n * Filter values in a callback given a callback function\n * @param {Array} x\n * @param {Function} callback\n * @return {Array} Returns the filtered array\n * @private\n */\nfunction _filterCallback (x, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n return filter(x, function (value, index, array) {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, [index])\n } else { // 3 or -1\n return callback(value, [index], array)\n }\n })\n}\n","import { clone } from '../../utils/object.js'\nimport { flatten as flattenArray } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'flatten'\nconst dependencies = ['typed', 'matrix']\n\nexport const createFlatten = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Flatten a multi dimensional matrix into a single dimensional matrix.\n *\n * Syntax:\n *\n * math.flatten(x)\n *\n * Examples:\n *\n * math.flatten([[1,2], [3,4]]) // returns [1, 2, 3, 4]\n *\n * See also:\n *\n * concat, resize, size, squeeze\n *\n * @param {Matrix | Array} x Matrix to be flattened\n * @return {Matrix | Array} Returns the flattened matrix\n */\n return typed(name, {\n Array: function (x) {\n return flattenArray(clone(x))\n },\n\n Matrix: function (x) {\n const flat = flattenArray(clone(x.toArray()))\n // TODO: return the same matrix type as x\n return matrix(flat)\n }\n })\n})\n","import { maxArgumentCount } from '../../utils/function.js'\nimport { forEach as forEachArray } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'forEach'\nconst dependencies = ['typed']\n\nexport const createForEach = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Iterate over all elements of a matrix/array, and executes the given callback function.\n *\n * Syntax:\n *\n * math.forEach(x, callback)\n *\n * Examples:\n *\n * math.forEach([1, 2, 3], function(value) {\n * console.log(value)\n * })\n * // outputs 1, 2, 3\n *\n * See also:\n *\n * filter, map, sort\n *\n * @param {Matrix | Array} x The matrix to iterate on.\n * @param {Function} callback The callback function is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the Matrix/array being traversed.\n */\n return typed(name, {\n 'Array, function': _forEach,\n\n 'Matrix, function': function (x, callback) {\n return x.forEach(callback)\n }\n })\n})\n\n/**\n * forEach for a multi dimensional array\n * @param {Array} array\n * @param {Function} callback\n * @private\n */\nfunction _forEach (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n forEachArray(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n recurse(child, index.concat(i))\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n callback(value)\n } else if (args === 2) {\n callback(value, index)\n } else { // 3 or -1\n callback(value, index, array)\n }\n }\n }\n recurse(array, [])\n}\n","import { factory } from '../../utils/factory.js'\nimport { getArrayDataType } from '../../utils/array.js'\nimport { typeOf } from '../../utils/is.js'\n\nconst name = 'getMatrixDataType'\nconst dependencies = ['typed']\n\nexport const createGetMatrixDataType = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Find the data type of all elements in a matrix or array,\n * for example 'number' if all items are a number and 'Complex' if all values\n * are complex numbers.\n * If a matrix contains more than one data type, it will return 'mixed'.\n *\n * Syntax:\n *\n * math.getMatrixDataType(x)\n *\n * Examples:\n *\n * const x = [ [1, 2, 3], [4, 5, 6] ]\n * const mixedX = [ [1, true], [2, 3] ]\n * const fractionX = [ [math.fraction(1, 3)], [math.fraction(1, 3] ]\n * const unitX = [ [math.unit('5cm')], [math.unit('5cm')] ]\n * const bigNumberX = [ [math.bignumber(1)], [math.bignumber(0)] ]\n * const sparse = math.sparse(x)\n * const dense = math.matrix(x)\n * math.getMatrixDataType(x) // returns 'number'\n * math.getMatrixDataType(sparse) // returns 'number'\n * math.getMatrixDataType(dense) // returns 'number'\n * math.getMatrixDataType(mixedX) // returns 'mixed'\n * math.getMatrixDataType(fractionX) // returns 'Fraction'\n * math.getMatrixDataType(unitX) // returns 'Unit'\n * math.getMatrixDataType(bigNumberX) // return 'BigNumber'\n *\n * See also:\n * SparseMatrix, DenseMatrix\n *\n * @param {...Matrix | Array} x The Matrix with values.\n *\n * @return {string} A string representation of the matrix type\n */\n return typed(name, {\n Array: function (x) {\n return getArrayDataType(x, typeOf)\n },\n Matrix: function (x) {\n return x.getDataType()\n }\n })\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { resize } from '../../utils/array.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'identity'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'BigNumber',\n 'DenseMatrix',\n 'SparseMatrix'\n]\n\nexport const createIdentity = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber, DenseMatrix, SparseMatrix }) => {\n /**\n * Create a 2-dimensional identity matrix with size m x n or n x n.\n * The matrix has ones on the diagonal and zeros elsewhere.\n *\n * Syntax:\n *\n * math.identity(n)\n * math.identity(n, format)\n * math.identity(m, n)\n * math.identity(m, n, format)\n * math.identity([m, n])\n * math.identity([m, n], format)\n *\n * Examples:\n *\n * math.identity(3) // returns [[1, 0, 0], [0, 1, 0], [0, 0, 1]]\n * math.identity(3, 2) // returns [[1, 0], [0, 1], [0, 0]]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.identity(math.size(A)) // returns [[1, 0, 0], [0, 1, 0]]\n *\n * See also:\n *\n * diag, ones, zeros, size, range\n *\n * @param {...number | Matrix | Array} size The size for the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Matrix | Array | number} A matrix with ones on the diagonal.\n */\n return typed(name, {\n '': function () {\n return (config.matrix === 'Matrix') ? matrix([]) : []\n },\n\n string: function (format) {\n return matrix(format)\n },\n\n 'number | BigNumber': function (rows) {\n return _identity(rows, rows, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber, string': function (rows, format) {\n return _identity(rows, rows, format)\n },\n\n 'number | BigNumber, number | BigNumber': function (rows, cols) {\n return _identity(rows, cols, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber, number | BigNumber, string': function (rows, cols, format) {\n return _identity(rows, cols, format)\n },\n\n Array: function (size) {\n return _identityVector(size)\n },\n\n 'Array, string': function (size, format) {\n return _identityVector(size, format)\n },\n\n Matrix: function (size) {\n return _identityVector(size.valueOf(), size.storage())\n },\n\n 'Matrix, string': function (size, format) {\n return _identityVector(size.valueOf(), format)\n }\n })\n\n function _identityVector (size, format) {\n switch (size.length) {\n case 0: return format ? matrix(format) : []\n case 1: return _identity(size[0], size[0], format)\n case 2: return _identity(size[0], size[1], format)\n default: throw new Error('Vector containing two values expected')\n }\n }\n\n /**\n * Create an identity matrix\n * @param {number | BigNumber} rows\n * @param {number | BigNumber} cols\n * @param {string} [format]\n * @returns {Matrix}\n * @private\n */\n function _identity (rows, cols, format) {\n // BigNumber constructor with the right precision\n const Big = (isBigNumber(rows) || isBigNumber(cols))\n ? BigNumber\n : null\n\n if (isBigNumber(rows)) rows = rows.toNumber()\n if (isBigNumber(cols)) cols = cols.toNumber()\n\n if (!isInteger(rows) || rows < 1) {\n throw new Error('Parameters in function identity must be positive integers')\n }\n if (!isInteger(cols) || cols < 1) {\n throw new Error('Parameters in function identity must be positive integers')\n }\n\n const one = Big ? new BigNumber(1) : 1\n const defaultValue = Big ? new Big(0) : 0\n const size = [rows, cols]\n\n // check we need to return a matrix\n if (format) {\n // create diagonal matrix (use optimized implementation for storage format)\n if (format === 'sparse') {\n return SparseMatrix.diagonal(size, one, 0, defaultValue)\n }\n if (format === 'dense') {\n return DenseMatrix.diagonal(size, one, 0, defaultValue)\n }\n throw new TypeError(`Unknown matrix type \"${format}\"`)\n }\n\n // create and resize array\n const res = resize([], size, defaultValue)\n // fill in ones on the diagonal\n const minimum = rows < cols ? rows : cols\n // fill diagonal\n for (let d = 0; d < minimum; d++) {\n res[d][d] = one\n }\n return res\n }\n})\n","import { arraySize as size } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'kron'\nconst dependencies = ['typed', 'matrix', 'multiplyScalar']\n\nexport const createKron = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, multiplyScalar }) => {\n /**\n * Calculates the kronecker product of 2 matrices or vectors.\n *\n * NOTE: If a one dimensional vector / matrix is given, it will be\n * wrapped so its two dimensions.\n * See the examples.\n *\n * Syntax:\n *\n * math.kron(x, y)\n *\n * Examples:\n *\n * math.kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])\n * // returns [ [ 1, 2, 0, 0 ], [ 3, 4, 0, 0 ], [ 0, 0, 1, 2 ], [ 0, 0, 3, 4 ] ]\n *\n * math.kron([1,1], [2,3,4])\n * // returns [ [ 2, 3, 4, 2, 3, 4 ] ]\n *\n * See also:\n *\n * multiply, dot, cross\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {Array | Matrix} Returns the kronecker product of `x` and `y`\n */\n return typed(name, {\n 'Matrix, Matrix': function (x, y) {\n return matrix(_kron(x.toArray(), y.toArray()))\n },\n\n 'Matrix, Array': function (x, y) {\n return matrix(_kron(x.toArray(), y))\n },\n\n 'Array, Matrix': function (x, y) {\n return matrix(_kron(x, y.toArray()))\n },\n\n 'Array, Array': _kron\n })\n\n /**\n * Calculate the kronecker product of two matrices / vectors\n * @param {Array} a First vector\n * @param {Array} b Second vector\n * @returns {Array} Returns the kronecker product of x and y\n * @private\n */\n function _kron (a, b) {\n // Deal with the dimensions of the matricies.\n if (size(a).length === 1) {\n // Wrap it in a 2D Matrix\n a = [a]\n }\n if (size(b).length === 1) {\n // Wrap it in a 2D Matrix\n b = [b]\n }\n if (size(a).length > 2 || size(b).length > 2) {\n throw new RangeError('Vectors with dimensions greater then 2 are not supported expected ' +\n '(Size x = ' + JSON.stringify(a.length) + ', y = ' + JSON.stringify(b.length) + ')')\n }\n const t = []\n let r = []\n\n return a.map(function (a) {\n return b.map(function (b) {\n r = []\n t.push(r)\n return a.map(function (y) {\n return b.map(function (x) {\n return r.push(multiplyScalar(y, x))\n })\n })\n })\n }) && t\n }\n})\n","import { maxArgumentCount } from '../../utils/function.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'map'\nconst dependencies = ['typed']\n\nexport const createMap = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Create a new matrix or array with the results of the callback function executed on\n * each entry of the matrix/array.\n *\n * Syntax:\n *\n * math.map(x, callback)\n *\n * Examples:\n *\n * math.map([1, 2, 3], function(value) {\n * return value * value\n * }) // returns [1, 4, 9]\n *\n * See also:\n *\n * filter, forEach, sort\n *\n * @param {Matrix | Array} x The matrix to iterate on.\n * @param {Function} callback The callback method is invoked with three\n * parameters: the value of the element, the index\n * of the element, and the matrix being traversed.\n * @return {Matrix | array} Transformed map of x\n */\n return typed(name, {\n 'Array, function': _map,\n\n 'Matrix, function': function (x, callback) {\n return x.map(callback)\n }\n })\n})\n\n/**\n * Map for a multi dimensional array\n * @param {Array} array\n * @param {Function} callback\n * @return {Array}\n * @private\n */\nfunction _map (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n return value.map(function (child, i) {\n // we create a copy of the index array and append the new index value\n return recurse(child, index.concat(i))\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, index)\n } else { // 3 or -1\n return callback(value, index, array)\n }\n }\n }\n\n return recurse(array, [])\n}\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'diff'\nconst dependencies = ['typed', 'matrix', 'subtract', 'number']\n\nexport const createDiff = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, number }) => {\n /**\n * Create a new matrix or array of the difference between elements of the given array\n * The optional dim parameter lets you specify the dimension to evaluate the difference of\n * If no dimension parameter is passed it is assumed as dimension 0\n *\n * Dimension is zero-based in javascript and one-based in the parser and can be a number or bignumber\n * Arrays must be 'rectangular' meaning arrays like [1, 2]\n * If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays\n *\n * Syntax:\n *\n * math.diff(arr)\n * math.diff(arr, dim)\n *\n * Examples:\n *\n * const arr = [1, 2, 4, 7, 0]\n * math.diff(arr) // returns [1, 2, 3, -7] (no dimension passed so 0 is assumed)\n * math.diff(math.matrix(arr)) // returns math.matrix([1, 2, 3, -7])\n *\n * const arr = [[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [9, 8, 7, 6, 4]]\n * math.diff(arr) // returns [[0, 0, 0, 0, 0], [8, 6, 4, 2, -1]]\n * math.diff(arr, 0) // returns [[0, 0, 0, 0, 0], [8, 6, 4, 2, -1]]\n * math.diff(arr, 1) // returns [[1, 1, 1, 1], [1, 1, 1, 1], [-1, -1, -1, -2]]\n * math.diff(arr, math.bignumber(1)) // returns [[1, 1, 1, 1], [1, 1, 1, 1], [-1, -1, -1, -2]]\n *\n * math.diff(arr, 2) // throws RangeError as arr is 2 dimensional not 3\n * math.diff(arr, -1) // throws RangeError as negative dimensions are not allowed\n *\n * // These will all produce the same result\n * math.diff([[1, 2], [3, 4]])\n * math.diff([math.matrix([1, 2]), math.matrix([3, 4])])\n * math.diff([[1, 2], math.matrix([3, 4])])\n * math.diff([math.matrix([1, 2]), [3, 4]])\n * // They do not produce the same result as math.diff(math.matrix([[1, 2], [3, 4]])) as this returns a matrix\n *\n * See Also:\n *\n * sum\n * subtract\n * partitionSelect\n *\n * @param {Array | Matrix} arr An array or matrix\n * @param {number} dim Dimension\n * @return {Array | Matrix} Difference between array elements in given dimension\n */\n return typed(name, {\n 'Array | Matrix': function (arr) { // No dimension specified => assume dimension 0\n if (isMatrix(arr)) {\n return matrix(_diff(arr.toArray()))\n } else {\n return _diff(arr)\n }\n },\n 'Array | Matrix, number': function (arr, dim) {\n if (!isInteger(dim)) throw new RangeError('Dimension must be a whole number')\n if (isMatrix(arr)) {\n return matrix(_recursive(arr.toArray(), dim))\n } else {\n return _recursive(arr, dim)\n }\n },\n 'Array | Matrix, BigNumber': function (arr, dim) {\n return this(arr, number(dim))\n }\n })\n\n /**\n * Recursively find the correct dimension in the array/matrix\n * Then Apply _diff to that dimension\n *\n * @param {Array} arr The array\n * @param {number} dim Dimension\n * @return {Array} resulting array\n */\n function _recursive (arr, dim) {\n if (isMatrix(arr)) {\n arr = arr.toArray() // Makes sure arrays like [ matrix([0, 1]), matrix([1, 0]) ] are processed properly\n }\n if (!Array.isArray(arr)) {\n throw RangeError('Array/Matrix does not have that many dimensions')\n }\n if (dim > 0) {\n const result = []\n arr.forEach(element => {\n result.push(_recursive(element, dim - 1))\n })\n return result\n } else if (dim === 0) {\n return _diff(arr)\n } else {\n throw RangeError('Cannot have negative dimension')\n }\n }\n\n /**\n * Difference between elements in the array\n *\n * @param {Array} arr An array\n * @return {Array} resulting array\n */\n function _diff (arr) {\n const result = []\n const size = arr.length\n if (size < 2) {\n return arr\n }\n for (let i = 1; i < size; i++) {\n result.push(_ElementDiff(arr[i - 1], arr[i]))\n }\n return result\n }\n\n /**\n * Difference between 2 objects\n *\n * @param {Object} obj1 First object\n * @param {Object} obj2 Second object\n * @return {Array} resulting array\n */\n function _ElementDiff (obj1, obj2) {\n // Convert matrices to arrays\n if (isMatrix(obj1)) obj1 = obj1.toArray()\n if (isMatrix(obj2)) obj2 = obj2.toArray()\n\n const obj1IsArray = Array.isArray(obj1)\n const obj2IsArray = Array.isArray(obj2)\n if (obj1IsArray && obj2IsArray) {\n return _ArrayDiff(obj1, obj2)\n }\n if (!obj1IsArray && !obj2IsArray) {\n return subtract(obj2, obj1) // Difference is (second - first) NOT (first - second)\n }\n throw TypeError('Cannot calculate difference between 1 array and 1 non-array')\n }\n\n /**\n * Difference of elements in 2 arrays\n *\n * @param {Array} arr1 Array 1\n * @param {Array} arr2 Array 2\n * @return {Array} resulting array\n */\n function _ArrayDiff (arr1, arr2) {\n if (arr1.length !== arr2.length) {\n throw RangeError('Not all sub-arrays have the same length')\n }\n const result = []\n const size = arr1.length\n for (let i = 0; i < size; i++) {\n result.push(_ElementDiff(arr1[i], arr2[i]))\n }\n return result\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { resize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ones'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createOnes = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Create a matrix filled with ones. The created matrix can have one or\n * multiple dimensions.\n *\n * Syntax:\n *\n * math.ones(m)\n * math.ones(m, format)\n * math.ones(m, n)\n * math.ones(m, n, format)\n * math.ones([m, n])\n * math.ones([m, n], format)\n * math.ones([m, n, p, ...])\n * math.ones([m, n, p, ...], format)\n *\n * Examples:\n *\n * math.ones(3) // returns [1, 1, 1]\n * math.ones(3, 2) // returns [[1, 1], [1, 1], [1, 1]]\n * math.ones(3, 2, 'dense') // returns Dense Matrix [[1, 1], [1, 1], [1, 1]]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.ones(math.size(A)) // returns [[1, 1, 1], [1, 1, 1]]\n *\n * See also:\n *\n * zeros, identity, size, range\n *\n * @param {...number | Array} size The size of each dimension of the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Array | Matrix | number} A matrix filled with ones\n */\n return typed('ones', {\n '': function () {\n return (config.matrix === 'Array')\n ? _ones([])\n : _ones([], 'default')\n },\n\n // math.ones(m, n, p, ..., format)\n // TODO: more accurate signature '...number | BigNumber, string' as soon as typed-function supports this\n '...number | BigNumber | string': function (size) {\n const last = size[size.length - 1]\n if (typeof last === 'string') {\n const format = size.pop()\n return _ones(size, format)\n } else if (config.matrix === 'Array') {\n return _ones(size)\n } else {\n return _ones(size, 'default')\n }\n },\n\n Array: _ones,\n\n Matrix: function (size) {\n const format = size.storage()\n return _ones(size.valueOf(), format)\n },\n\n 'Array | Matrix, string': function (size, format) {\n return _ones(size.valueOf(), format)\n }\n })\n\n /**\n * Create an Array or Matrix with ones\n * @param {Array} size\n * @param {string} [format='default']\n * @return {Array | Matrix}\n * @private\n */\n function _ones (size, format) {\n const hasBigNumbers = _normalize(size)\n const defaultValue = hasBigNumbers ? new BigNumber(1) : 1\n _validate(size)\n\n if (format) {\n // return a matrix\n const m = matrix(format)\n if (size.length > 0) {\n return m.resize(size, defaultValue)\n }\n return m\n } else {\n // return an Array\n const arr = []\n if (size.length > 0) {\n return resize(arr, size, defaultValue)\n }\n return arr\n }\n }\n\n // replace BigNumbers with numbers, returns true if size contained BigNumbers\n function _normalize (size) {\n let hasBigNumbers = false\n size.forEach(function (value, index, arr) {\n if (isBigNumber(value)) {\n hasBigNumbers = true\n arr[index] = value.toNumber()\n }\n })\n return hasBigNumbers\n }\n\n // validate arguments\n function _validate (size) {\n size.forEach(function (value) {\n if (typeof value !== 'number' || !isInteger(value) || value < 0) {\n throw new Error('Parameters in function ones must be positive integers')\n }\n })\n }\n})\n","\nexport function noBignumber () {\n throw new Error('No \"bignumber\" implementation available')\n}\n\nexport function noFraction () {\n throw new Error('No \"fraction\" implementation available')\n}\n\nexport function noMatrix () {\n throw new Error('No \"matrix\" implementation available')\n}\n\nexport function noIndex () {\n throw new Error('No \"index\" implementation available')\n}\n\nexport function noSubset () {\n throw new Error('No \"matrix\" implementation available')\n}\n","import { factory } from '../../utils/factory.js'\nimport { noBignumber, noMatrix } from '../../utils/noop.js'\n\nconst name = 'range'\nconst dependencies = ['typed', 'config', '?matrix', '?bignumber', 'smaller', 'smallerEq', 'larger', 'largerEq']\n\nexport const createRange = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq }) => {\n /**\n * Create an array from a range.\n * By default, the range end is excluded. This can be customized by providing\n * an extra parameter `includeEnd`.\n *\n * Syntax:\n *\n * math.range(str [, includeEnd]) // Create a range from a string,\n * // where the string contains the\n * // start, optional step, and end,\n * // separated by a colon.\n * math.range(start, end [, includeEnd]) // Create a range with start and\n * // end and a step size of 1.\n * math.range(start, end, step [, includeEnd]) // Create a range with start, step,\n * // and end.\n *\n * Where:\n *\n * - `str: string`\n * A string 'start:end' or 'start:step:end'\n * - `start: {number | BigNumber}`\n * Start of the range\n * - `end: number | BigNumber`\n * End of the range, excluded by default, included when parameter includeEnd=true\n * - `step: number | BigNumber`\n * Step size. Default value is 1.\n * - `includeEnd: boolean`\n * Option to specify whether to include the end or not. False by default.\n *\n * Examples:\n *\n * math.range(2, 6) // [2, 3, 4, 5]\n * math.range(2, -3, -1) // [2, 1, 0, -1, -2]\n * math.range('2:1:6') // [2, 3, 4, 5]\n * math.range(2, 6, true) // [2, 3, 4, 5, 6]\n *\n * See also:\n *\n * ones, zeros, size, subset\n *\n * @param {*} args Parameters describing the ranges `start`, `end`, and optional `step`.\n * @return {Array | Matrix} range\n */\n return typed(name, {\n // TODO: simplify signatures when typed-function supports default values and optional arguments\n\n // TODO: a number or boolean should not be converted to string here\n string: _strRange,\n 'string, boolean': _strRange,\n\n 'number, number': function (start, end) {\n return _out(_rangeEx(start, end, 1))\n },\n 'number, number, number': function (start, end, step) {\n return _out(_rangeEx(start, end, step))\n },\n 'number, number, boolean': function (start, end, includeEnd) {\n return includeEnd\n ? _out(_rangeInc(start, end, 1))\n : _out(_rangeEx(start, end, 1))\n },\n 'number, number, number, boolean': function (start, end, step, includeEnd) {\n return includeEnd\n ? _out(_rangeInc(start, end, step))\n : _out(_rangeEx(start, end, step))\n },\n\n 'BigNumber, BigNumber': function (start, end) {\n const BigNumber = start.constructor\n\n return _out(_bigRangeEx(start, end, new BigNumber(1)))\n },\n 'BigNumber, BigNumber, BigNumber': function (start, end, step) {\n return _out(_bigRangeEx(start, end, step))\n },\n 'BigNumber, BigNumber, boolean': function (start, end, includeEnd) {\n const BigNumber = start.constructor\n\n return includeEnd\n ? _out(_bigRangeInc(start, end, new BigNumber(1)))\n : _out(_bigRangeEx(start, end, new BigNumber(1)))\n },\n 'BigNumber, BigNumber, BigNumber, boolean': function (start, end, step, includeEnd) {\n return includeEnd\n ? _out(_bigRangeInc(start, end, step))\n : _out(_bigRangeEx(start, end, step))\n }\n\n })\n\n function _out (arr) {\n if (config.matrix === 'Matrix') {\n return matrix ? matrix(arr) : noMatrix()\n }\n\n return arr\n }\n\n function _strRange (str, includeEnd) {\n const r = _parse(str)\n if (!r) {\n throw new SyntaxError('String \"' + str + '\" is no valid range')\n }\n\n let fn\n if (config.number === 'BigNumber') {\n if (bignumber === undefined) {\n noBignumber()\n }\n\n fn = includeEnd ? _bigRangeInc : _bigRangeEx\n return _out(fn(\n bignumber(r.start),\n bignumber(r.end),\n bignumber(r.step)))\n } else {\n fn = includeEnd ? _rangeInc : _rangeEx\n return _out(fn(r.start, r.end, r.step))\n }\n }\n\n /**\n * Create a range with numbers. End is excluded\n * @param {number} start\n * @param {number} end\n * @param {number} step\n * @returns {Array} range\n * @private\n */\n function _rangeEx (start, end, step) {\n const array = []\n let x = start\n if (step > 0) {\n while (smaller(x, end)) {\n array.push(x)\n x += step\n }\n } else if (step < 0) {\n while (larger(x, end)) {\n array.push(x)\n x += step\n }\n }\n\n return array\n }\n\n /**\n * Create a range with numbers. End is included\n * @param {number} start\n * @param {number} end\n * @param {number} step\n * @returns {Array} range\n * @private\n */\n function _rangeInc (start, end, step) {\n const array = []\n let x = start\n if (step > 0) {\n while (smallerEq(x, end)) {\n array.push(x)\n x += step\n }\n } else if (step < 0) {\n while (largerEq(x, end)) {\n array.push(x)\n x += step\n }\n }\n\n return array\n }\n\n /**\n * Create a range with big numbers. End is excluded\n * @param {BigNumber} start\n * @param {BigNumber} end\n * @param {BigNumber} step\n * @returns {Array} range\n * @private\n */\n function _bigRangeEx (start, end, step) {\n const zero = bignumber(0)\n const array = []\n let x = start\n if (step.gt(zero)) {\n while (smaller(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n } else if (step.lt(zero)) {\n while (larger(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n }\n\n return array\n }\n\n /**\n * Create a range with big numbers. End is included\n * @param {BigNumber} start\n * @param {BigNumber} end\n * @param {BigNumber} step\n * @returns {Array} range\n * @private\n */\n function _bigRangeInc (start, end, step) {\n const zero = bignumber(0)\n const array = []\n let x = start\n if (step.gt(zero)) {\n while (smallerEq(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n } else if (step.lt(zero)) {\n while (largerEq(x, end)) {\n array.push(x)\n x = x.plus(step)\n }\n }\n\n return array\n }\n\n /**\n * Parse a string into a range,\n * The string contains the start, optional step, and end, separated by a colon.\n * If the string does not contain a valid range, null is returned.\n * For example str='0:2:11'.\n * @param {string} str\n * @return {{start: number, end: number, step: number} | null} range Object containing properties start, end, step\n * @private\n */\n function _parse (str) {\n const args = str.split(':')\n\n // number\n const nums = args.map(function (arg) {\n // use Number and not parseFloat as Number returns NaN on invalid garbage in the string\n return Number(arg)\n })\n\n const invalid = nums.some(function (num) {\n return isNaN(num)\n })\n if (invalid) {\n return null\n }\n\n switch (nums.length) {\n case 2:\n return {\n start: nums[0],\n end: nums[1],\n step: 1\n }\n\n case 3:\n return {\n start: nums[0],\n end: nums[2],\n step: nums[1]\n }\n\n default:\n return null\n }\n }\n})\n","import { reshape as arrayReshape } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'reshape'\nconst dependencies = ['typed', 'isInteger', 'matrix']\n\nexport const createReshape = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger, matrix }) => {\n /**\n * Reshape a multi dimensional array to fit the specified dimensions\n *\n * Syntax:\n *\n * math.reshape(x, sizes)\n *\n * Examples:\n *\n * math.reshape([1, 2, 3, 4, 5, 6], [2, 3])\n * // returns Array [[1, 2, 3], [4, 5, 6]]\n *\n * math.reshape([[1, 2], [3, 4]], [1, 4])\n * // returns Array [[1, 2, 3, 4]]\n *\n * math.reshape([[1, 2], [3, 4]], [4])\n * // returns Array [1, 2, 3, 4]\n *\n * const x = math.matrix([1, 2, 3, 4, 5, 6, 7, 8])\n * math.reshape(x, [2, 2, 2])\n * // returns Matrix [[[1, 2], [3, 4]], [[5, 6], [7, 8]]]\n *\n * See also:\n *\n * size, squeeze, resize\n *\n * @param {Array | Matrix | *} x Matrix to be reshaped\n * @param {number[]} sizes One dimensional array with integral sizes for\n * each dimension\n *\n * @return {* | Array | Matrix} A reshaped clone of matrix `x`\n *\n * @throws {TypeError} If `sizes` does not contain solely integers\n * @throws {DimensionError} If the product of the new dimension sizes does\n * not equal that of the old ones\n */\n return typed(name, {\n\n 'Matrix, Array': function (x, sizes) {\n if (x.reshape) {\n return x.reshape(sizes)\n } else {\n return matrix(arrayReshape(x.valueOf(), sizes))\n }\n },\n\n 'Array, Array': function (x, sizes) {\n sizes.forEach(function (size) {\n if (!isInteger(size)) {\n throw new TypeError('Invalid size for dimension: ' + size)\n }\n })\n return arrayReshape(x, sizes)\n }\n\n })\n})\n","/**\n * Create a syntax error with the message:\n * 'Wrong number of arguments in function ( provided, - expected)'\n * @param {string} fn Function name\n * @param {number} count Actual argument count\n * @param {number} min Minimum required argument count\n * @param {number} [max] Maximum required argument count\n * @extends Error\n */\nexport function ArgumentsError (fn, count, min, max) {\n if (!(this instanceof ArgumentsError)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.fn = fn\n this.count = count\n this.min = min\n this.max = max\n\n this.message = 'Wrong number of arguments in function ' + fn +\n ' (' + count + ' provided, ' +\n min + ((max !== undefined && max !== null) ? ('-' + max) : '') + ' expected)'\n\n this.stack = (new Error()).stack\n}\n\nArgumentsError.prototype = new Error()\nArgumentsError.prototype.constructor = Error\nArgumentsError.prototype.name = 'ArgumentsError'\nArgumentsError.prototype.isArgumentsError = true\n","import { isBigNumber, isMatrix } from '../../utils/is.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { ArgumentsError } from '../../error/ArgumentsError.js'\nimport { isInteger } from '../../utils/number.js'\nimport { format } from '../../utils/string.js'\nimport { clone } from '../../utils/object.js'\nimport { resize as arrayResize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'resize'\nconst dependencies = ['config', 'matrix']\n\nexport const createResize = /* #__PURE__ */ factory(name, dependencies, ({ config, matrix }) => {\n /**\n * Resize a matrix\n *\n * Syntax:\n *\n * math.resize(x, size)\n * math.resize(x, size, defaultValue)\n *\n * Examples:\n *\n * math.resize([1, 2, 3, 4, 5], [3]) // returns Array [1, 2, 3]\n * math.resize([1, 2, 3], [5], 0) // returns Array [1, 2, 3, 0, 0]\n * math.resize(2, [2, 3], 0) // returns Matrix [[2, 0, 0], [0, 0, 0]]\n * math.resize(\"hello\", [8], \"!\") // returns string 'hello!!!'\n *\n * See also:\n *\n * size, squeeze, subset, reshape\n *\n * @param {Array | Matrix | *} x Matrix to be resized\n * @param {Array | Matrix} size One dimensional array with numbers\n * @param {number | string} [defaultValue=0] Zero by default, except in\n * case of a string, in that case\n * defaultValue = ' '\n * @return {* | Array | Matrix} A resized clone of matrix `x`\n */\n // TODO: rework resize to a typed-function\n return function resize (x, size, defaultValue) {\n if (arguments.length !== 2 && arguments.length !== 3) {\n throw new ArgumentsError('resize', arguments.length, 2, 3)\n }\n\n if (isMatrix(size)) {\n size = size.valueOf() // get Array\n }\n\n if (isBigNumber(size[0])) {\n // convert bignumbers to numbers\n size = size.map(function (value) {\n return !isBigNumber(value) ? value : value.toNumber()\n })\n }\n\n // check x is a Matrix\n if (isMatrix(x)) {\n // use optimized matrix implementation, return copy\n return x.resize(size, defaultValue, true)\n }\n\n if (typeof x === 'string') {\n // resize string\n return _resizeString(x, size, defaultValue)\n }\n\n // check result should be a matrix\n const asMatrix = Array.isArray(x) ? false : (config.matrix !== 'Array')\n\n if (size.length === 0) {\n // output a scalar\n while (Array.isArray(x)) {\n x = x[0]\n }\n\n return clone(x)\n } else {\n // output an array/matrix\n if (!Array.isArray(x)) {\n x = [x]\n }\n x = clone(x)\n\n const res = arrayResize(x, size, defaultValue)\n return asMatrix ? matrix(res) : res\n }\n }\n\n /**\n * Resize a string\n * @param {string} str\n * @param {number[]} size\n * @param {string} [defaultChar=' ']\n * @private\n */\n function _resizeString (str, size, defaultChar) {\n if (defaultChar !== undefined) {\n if (typeof defaultChar !== 'string' || defaultChar.length !== 1) {\n throw new TypeError('Single character expected as defaultValue')\n }\n } else {\n defaultChar = ' '\n }\n\n if (size.length !== 1) {\n throw new DimensionError(size.length, 1)\n }\n const len = size[0]\n if (typeof len !== 'number' || !isInteger(len)) {\n throw new TypeError('Invalid size, must contain positive integers ' +\n '(size: ' + format(size) + ')')\n }\n\n if (str.length > len) {\n return str.substring(0, len)\n } else if (str.length < len) {\n let res = str\n for (let i = 0, ii = len - str.length; i < ii; i++) {\n res += defaultChar\n }\n return res\n } else {\n return str\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { arraySize } from '../../utils/array.js'\n\nconst name = 'rotate'\nconst dependencies = [\n 'typed',\n 'multiply',\n 'rotationMatrix'\n]\n\nexport const createRotate = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed, multiply, rotationMatrix\n }) => {\n /**\n * Rotate a vector of size 1x2 counter-clockwise by a given angle\n * Rotate a vector of size 1x3 counter-clockwise by a given angle around the given axis\n *\n * Syntax:\n *\n * math.rotate(w, theta)\n * math.rotate(w, theta, v)\n *\n * Examples:\n *\n * math.rotate([11, 12], math.pi / 2) // returns matrix([-12, 11])\n * math.rotate(matrix([11, 12]), math.pi / 2) // returns matrix([-12, 11])\n *\n * math.rotate([1, 0, 0], unit('90deg'), [0, 0, 1]) // returns matrix([0, 1, 0])\n * math.rotate(matrix([1, 0, 0]), unit('90deg'), [0, 0, 1]) // returns matrix([0, 1, 0])\n *\n * math.rotate([1, 0], math.complex(1 + i)) // returns matrix([cos(1 + i) - sin(1 + i), sin(1 + i) + cos(1 + i)])\n *\n * See also:\n *\n * matrix, rotationMatrix\n *\n * @param {Array | Matrix} w Vector to rotate\n * @param {number | BigNumber | Complex | Unit} theta Rotation angle\n * @param {Array | Matrix} [v] Rotation axis\n * @return {Array | Matrix} Multiplication of the rotation matrix and w\n */\n return typed(name, {\n 'Array , number | BigNumber | Complex | Unit': function (w, theta) {\n _validateSize(w, 2)\n const matrixRes = multiply(rotationMatrix(theta), w)\n return matrixRes.toArray()\n },\n\n 'Matrix , number | BigNumber | Complex | Unit': function (w, theta) {\n _validateSize(w, 2)\n return multiply(rotationMatrix(theta), w)\n },\n\n 'Array, number | BigNumber | Complex | Unit, Array | Matrix': function (w, theta, v) {\n _validateSize(w, 3)\n const matrixRes = multiply(rotationMatrix(theta, v), w)\n return matrixRes\n },\n\n 'Matrix, number | BigNumber | Complex | Unit, Array | Matrix': function (w, theta, v) {\n _validateSize(w, 3)\n return multiply(rotationMatrix(theta, v), w)\n }\n })\n\n function _validateSize (v, expectedSize) {\n const actualSize = Array.isArray(v) ? arraySize(v) : v.size()\n if (actualSize.length > 2) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n if (actualSize.length === 2 && actualSize[1] !== 1) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n if (actualSize[0] !== expectedSize) {\n throw new RangeError(`Vector must be of dimensions 1x${expectedSize}`)\n }\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'rotationMatrix'\nconst dependencies = [\n 'typed',\n 'config',\n 'multiplyScalar',\n 'addScalar',\n 'unaryMinus',\n 'norm',\n 'matrix',\n 'BigNumber',\n 'DenseMatrix',\n 'SparseMatrix',\n 'cos',\n 'sin'\n]\n\nexport const createRotationMatrix = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed, config, multiplyScalar,\n addScalar, unaryMinus, norm, BigNumber,\n matrix, DenseMatrix, SparseMatrix, cos, sin\n }) => {\n /**\n * Create a 2-dimensional counter-clockwise rotation matrix (2x2) for a given angle (expressed in radians).\n * Create a 2-dimensional counter-clockwise rotation matrix (3x3) by a given angle (expressed in radians) around a given axis (1x3).\n *\n * Syntax:\n *\n * math.rotationMatrix(theta)\n * math.rotationMatrix(theta, format)\n * math.rotationMatrix(theta, [v])\n * math.rotationMatrix(theta, [v], format)\n *\n * Examples:\n *\n * math.rotationMatrix(math.pi / 2) // returns [[0, -1], [1, 0]]\n * math.rotationMatrix(math.bignumber(1)) // returns [[bignumber(cos(1)), bignumber(-sin(1))], [bignumber(sin(1)), bignumber(cos(1))]]\n * math.rotationMatrix(math.complex(1 + i)) // returns [[cos(1 + i), -sin(1 + i)], [sin(1 + i), cos(1 + i)]]\n * math.rotationMatrix(math.unit('1rad')) // returns [[cos(1), -sin(1)], [sin(1), cos(1)]]\n *\n * math.rotationMatrix(math.pi / 2, [0, 1, 0]) // returns [[0, 0, 1], [0, 1, 0], [-1, 0, 0]]\n * math.rotationMatrix(math.pi / 2, matrix([0, 1, 0])) // returns matrix([[0, 0, 1], [0, 1, 0], [-1, 0, 0]])\n *\n *\n * See also:\n *\n * matrix, cos, sin\n *\n *\n * @param {number | BigNumber | Complex | Unit} theta Rotation angle\n * @param {Array | Matrix} [v] Rotation axis\n * @param {string} [format] Result Matrix storage format\n * @return {Array | Matrix} Rotation matrix\n */\n\n return typed(name, {\n '': function () {\n return (config.matrix === 'Matrix') ? matrix([]) : []\n },\n\n string: function (format) {\n return matrix(format)\n },\n\n 'number | BigNumber | Complex | Unit': function (theta) {\n return _rotationMatrix2x2(theta, config.matrix === 'Matrix' ? 'dense' : undefined)\n },\n\n 'number | BigNumber | Complex | Unit, string': function (theta, format) {\n return _rotationMatrix2x2(theta, format)\n },\n\n 'number | BigNumber | Complex | Unit, Array': function (theta, v) {\n const matrixV = matrix(v)\n _validateVector(matrixV)\n return _rotationMatrix3x3(theta, matrixV, undefined)\n },\n\n 'number | BigNumber | Complex | Unit, Matrix': function (theta, v) {\n _validateVector(v)\n const storageType = v.storage() || (config.matrix === 'Matrix' ? 'dense' : undefined)\n return _rotationMatrix3x3(theta, v, storageType)\n },\n\n 'number | BigNumber | Complex | Unit, Array, string': function (theta, v, format) {\n const matrixV = matrix(v)\n _validateVector(matrixV)\n return _rotationMatrix3x3(theta, matrixV, format)\n },\n\n 'number | BigNumber | Complex | Unit, Matrix, string': function (theta, v, format) {\n _validateVector(v)\n return _rotationMatrix3x3(theta, v, format)\n }\n\n })\n\n /**\n * Returns 2x2 matrix of 2D rotation of angle theta\n *\n * @param {number | BigNumber | Complex | Unit} theta The rotation angle\n * @param {string} format The result Matrix storage format\n * @returns {Matrix}\n * @private\n */\n function _rotationMatrix2x2 (theta, format) {\n const Big = isBigNumber(theta)\n\n const minusOne = Big ? new BigNumber(-1) : -1\n const cosTheta = cos(theta)\n const sinTheta = sin(theta)\n const data = [[cosTheta, multiplyScalar(minusOne, sinTheta)], [sinTheta, cosTheta]]\n\n return _convertToFormat(data, format)\n }\n\n function _validateVector (v) {\n const size = v.size()\n if (size.length < 1 || size[0] !== 3) {\n throw new RangeError('Vector must be of dimensions 1x3')\n }\n }\n\n function _mul (array) {\n return array.reduce((p, curr) => multiplyScalar(p, curr))\n }\n\n function _convertToFormat (data, format) {\n if (format) {\n if (format === 'sparse') {\n return new SparseMatrix(data)\n }\n if (format === 'dense') {\n return new DenseMatrix(data)\n }\n throw new TypeError(`Unknown matrix type \"${format}\"`)\n }\n return data\n }\n\n /**\n * Returns a 3x3 matrix of rotation of angle theta around vector v\n *\n * @param {number | BigNumber | Complex | Unit} theta The rotation angle\n * @param {Matrix} v The rotation axis vector\n * @param {string} format The storage format of the resulting matrix\n * @returns {Matrix}\n * @private\n */\n function _rotationMatrix3x3 (theta, v, format) {\n const normV = norm(v)\n if (normV === 0) {\n throw new RangeError('Rotation around zero vector')\n }\n\n const Big = isBigNumber(theta) ? BigNumber : null\n\n const one = Big ? new Big(1) : 1\n const minusOne = Big ? new Big(-1) : -1\n const vx = Big ? new Big(v.get([0]) / normV) : v.get([0]) / normV\n const vy = Big ? new Big(v.get([1]) / normV) : v.get([1]) / normV\n const vz = Big ? new Big(v.get([2]) / normV) : v.get([2]) / normV\n const c = cos(theta)\n const oneMinusC = addScalar(one, unaryMinus(c))\n const s = sin(theta)\n\n const r11 = addScalar(c, _mul([vx, vx, oneMinusC]))\n const r12 = addScalar(_mul([vx, vy, oneMinusC]), _mul([minusOne, vz, s]))\n const r13 = addScalar(_mul([vx, vz, oneMinusC]), _mul([vy, s]))\n\n const r21 = addScalar(_mul([vx, vy, oneMinusC]), _mul([vz, s]))\n const r22 = addScalar(c, _mul([vy, vy, oneMinusC]))\n const r23 = addScalar(_mul([vy, vz, oneMinusC]), _mul([minusOne, vx, s]))\n\n const r31 = addScalar(_mul([vx, vz, oneMinusC]), _mul([minusOne, vy, s]))\n const r32 = addScalar(_mul([vy, vz, oneMinusC]), _mul([vx, s]))\n const r33 = addScalar(c, _mul([vz, vz, oneMinusC]))\n\n const data = [[r11, r12, r13], [r21, r22, r23], [r31, r32, r33]]\n\n return _convertToFormat(data, format)\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\n\nconst name = 'row'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\nexport const createRow = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n /**\n * Return a row from a Matrix.\n *\n * Syntax:\n *\n * math.row(value, index)\n *\n * Example:\n *\n * // get a row\n * const d = [[1, 2], [3, 4]]\n * math.row(d, 1) // returns [[3, 4]]\n *\n * See also:\n *\n * column\n *\n * @param {Array | Matrix } value An array or matrix\n * @param {number} row The index of the row\n * @return {Array | Matrix} The retrieved row\n */\n return typed(name, {\n 'Matrix, number': _row,\n\n 'Array, number': function (value, row) {\n return _row(matrix(clone(value)), row).valueOf()\n }\n })\n\n /**\n * Retrieve a row of a matrix\n * @param {Matrix } value A matrix\n * @param {number} row The index of the row\n * @return {Matrix} The retrieved row\n */\n function _row (value, row) {\n // check dimensions\n if (value.size().length !== 2) {\n throw new Error('Only two dimensional matrix is supported')\n }\n\n validateIndex(row, value.size()[0])\n\n const columnRange = range(0, value.size()[1])\n const index = new Index(row, columnRange)\n return value.subset(index)\n }\n})\n","import { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { noMatrix } from '../../utils/noop.js'\n\nconst name = 'size'\nconst dependencies = ['typed', 'config', '?matrix']\n\nexport const createSize = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix }) => {\n /**\n * Calculate the size of a matrix or scalar.\n *\n * Syntax:\n *\n * math.size(x)\n *\n * Examples:\n *\n * math.size(2.3) // returns []\n * math.size('hello world') // returns [11]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.size(A) // returns [2, 3]\n * math.size(math.range(1,6)) // returns [5]\n *\n * See also:\n *\n * resize, squeeze, subset\n *\n * @param {boolean | number | Complex | Unit | string | Array | Matrix} x A matrix\n * @return {Array | Matrix} A vector with size of `x`.\n */\n return typed(name, {\n Matrix: function (x) {\n return x.create(x.size())\n },\n\n Array: arraySize,\n\n string: function (x) {\n return (config.matrix === 'Array') ? [x.length] : matrix([x.length])\n },\n\n 'number | Complex | BigNumber | Unit | boolean | null': function (x) {\n // scalar\n return (config.matrix === 'Array')\n ? []\n : matrix ? matrix([]) : noMatrix()\n }\n })\n})\n","import { clone } from '../../utils/object.js'\nimport { squeeze as arraySqueeze } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'squeeze'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSqueeze = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.\n *\n * Syntax:\n *\n * math.squeeze(x)\n *\n * Examples:\n *\n * math.squeeze([3]) // returns 3\n * math.squeeze([[3]]) // returns 3\n *\n * const A = math.zeros(3, 1) // returns [[0], [0], [0]] (size 3x1)\n * math.squeeze(A) // returns [0, 0, 0] (size 3)\n *\n * const B = math.zeros(1, 3) // returns [[0, 0, 0]] (size 1x3)\n * math.squeeze(B) // returns [0, 0, 0] (size 3)\n *\n * // only inner and outer dimensions are removed\n * const C = math.zeros(2, 1, 3) // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)\n * math.squeeze(C) // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)\n *\n * See also:\n *\n * subset\n *\n * @param {Matrix | Array} x Matrix to be squeezed\n * @return {Matrix | Array} Squeezed matrix\n */\n return typed(name, {\n Array: function (x) {\n return arraySqueeze(clone(x))\n },\n\n Matrix: function (x) {\n const res = arraySqueeze(x.toArray())\n // FIXME: return the same type of matrix as the input\n return Array.isArray(res) ? matrix(res) : res\n },\n\n any: function (x) {\n // scalar\n return clone(x)\n }\n })\n})\n","import { hasOwnProperty } from './object.js'\n\n/**\n * Get a property of a plain object\n * Throws an error in case the object is not a plain object or the\n * property is not defined on the object itself\n * @param {Object} object\n * @param {string} prop\n * @return {*} Returns the property value when safe\n */\nfunction getSafeProperty (object, prop) {\n // only allow getting safe properties of a plain object\n if (isPlainObject(object) && isSafeProperty(object, prop)) {\n return object[prop]\n }\n\n if (typeof object[prop] === 'function' && isSafeMethod(object, prop)) {\n throw new Error('Cannot access method \"' + prop + '\" as a property')\n }\n\n throw new Error('No access to property \"' + prop + '\"')\n}\n\n/**\n * Set a property on a plain object.\n * Throws an error in case the object is not a plain object or the\n * property would override an inherited property like .constructor or .toString\n * @param {Object} object\n * @param {string} prop\n * @param {*} value\n * @return {*} Returns the value\n */\n// TODO: merge this function into access.js?\nfunction setSafeProperty (object, prop, value) {\n // only allow setting safe properties of a plain object\n if (isPlainObject(object) && isSafeProperty(object, prop)) {\n object[prop] = value\n return value\n }\n\n throw new Error('No access to property \"' + prop + '\"')\n}\n\n/**\n * Test whether a property is safe to use for an object.\n * For example .toString and .constructor are not safe\n * @param {string} prop\n * @return {boolean} Returns true when safe\n */\nfunction isSafeProperty (object, prop) {\n if (!object || typeof object !== 'object') {\n return false\n }\n // SAFE: whitelisted\n // e.g length\n if (hasOwnProperty(safeNativeProperties, prop)) {\n return true\n }\n // UNSAFE: inherited from Object prototype\n // e.g constructor\n if (prop in Object.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Object.prototype is a root object\n return false\n }\n // UNSAFE: inherited from Function prototype\n // e.g call, apply\n if (prop in Function.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Function.prototype is a root object\n return false\n }\n return true\n}\n\n/**\n * Validate whether a method is safe.\n * Throws an error when that's not the case.\n * @param {Object} object\n * @param {string} method\n */\n// TODO: merge this function into assign.js?\nfunction validateSafeMethod (object, method) {\n if (!isSafeMethod(object, method)) {\n throw new Error('No access to method \"' + method + '\"')\n }\n}\n\n/**\n * Check whether a method is safe.\n * Throws an error when that's not the case (for example for `constructor`).\n * @param {Object} object\n * @param {string} method\n * @return {boolean} Returns true when safe, false otherwise\n */\nfunction isSafeMethod (object, method) {\n if (object === null || object === undefined || typeof object[method] !== 'function') {\n return false\n }\n // UNSAFE: ghosted\n // e.g overridden toString\n // Note that IE10 doesn't support __proto__ and we can't do this check there.\n if (hasOwnProperty(object, method) &&\n (Object.getPrototypeOf && (method in Object.getPrototypeOf(object)))) {\n return false\n }\n // SAFE: whitelisted\n // e.g toString\n if (hasOwnProperty(safeNativeMethods, method)) {\n return true\n }\n // UNSAFE: inherited from Object prototype\n // e.g constructor\n if (method in Object.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Object.prototype is a root object\n return false\n }\n // UNSAFE: inherited from Function prototype\n // e.g call, apply\n if (method in Function.prototype) {\n // 'in' is used instead of hasOwnProperty for nodejs v0.10\n // which is inconsistent on root prototypes. It is safe\n // here because Function.prototype is a root object\n return false\n }\n return true\n}\n\nfunction isPlainObject (object) {\n return typeof object === 'object' && object && object.constructor === Object\n}\n\nconst safeNativeProperties = {\n length: true,\n name: true\n}\n\nconst safeNativeMethods = {\n toString: true,\n valueOf: true,\n toLocaleString: true\n}\n\nexport { getSafeProperty }\nexport { setSafeProperty }\nexport { isSafeProperty }\nexport { validateSafeMethod }\nexport { isSafeMethod }\nexport { isPlainObject }\n","import { isIndex } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { validateIndex } from '../../utils/array.js'\nimport { getSafeProperty, setSafeProperty } from '../../utils/customs.js'\nimport { DimensionError } from '../../error/DimensionError.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'subset'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSubset = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Get or set a subset of a matrix or string.\n *\n * Syntax:\n * math.subset(value, index) // retrieve a subset\n * math.subset(value, index, replacement [, defaultValue]) // replace a subset\n *\n * Examples:\n *\n * // get a subset\n * const d = [[1, 2], [3, 4]]\n * math.subset(d, math.index(1, 0)) // returns 3\n * math.subset(d, math.index([0, 1], 1)) // returns [[2], [4]]\n *\n * // replace a subset\n * const e = []\n * const f = math.subset(e, math.index(0, [0, 2]), [5, 6]) // f = [[5, 6]]\n * const g = math.subset(f, math.index(1, 1), 7, 0) // g = [[5, 6], [0, 7]]\n *\n * See also:\n *\n * size, resize, squeeze, index\n *\n * @param {Array | Matrix | string} matrix An array, matrix, or string\n * @param {Index} index An index containing ranges for each\n * dimension\n * @param {*} [replacement] An array, matrix, or scalar.\n * If provided, the subset is replaced with replacement.\n * If not provided, the subset is returned\n * @param {*} [defaultValue=undefined] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * math.matrix elements will be left undefined.\n * @return {Array | Matrix | string} Either the retrieved subset or the updated matrix.\n */\n return typed(name, {\n // get subset\n 'Array, Index': function (value, index) {\n const m = matrix(value)\n const subset = m.subset(index) // returns a Matrix\n return index.isScalar()\n ? subset\n : subset.valueOf() // return an Array (like the input)\n },\n\n 'Matrix, Index': function (value, index) {\n return value.subset(index)\n },\n\n 'Object, Index': _getObjectProperty,\n\n 'string, Index': _getSubstring,\n\n // set subset\n 'Array, Index, any': function (value, index, replacement) {\n return matrix(clone(value))\n .subset(index, replacement, undefined)\n .valueOf()\n },\n\n 'Array, Index, any, any': function (value, index, replacement, defaultValue) {\n return matrix(clone(value))\n .subset(index, replacement, defaultValue)\n .valueOf()\n },\n\n 'Matrix, Index, any': function (value, index, replacement) {\n return value.clone().subset(index, replacement)\n },\n\n 'Matrix, Index, any, any': function (value, index, replacement, defaultValue) {\n return value.clone().subset(index, replacement, defaultValue)\n },\n\n 'string, Index, string': _setSubstring,\n 'string, Index, string, string': _setSubstring,\n 'Object, Index, any': _setObjectProperty\n })\n})\n\n/**\n * Retrieve a subset of a string\n * @param {string} str string from which to get a substring\n * @param {Index} index An index containing ranges for each dimension\n * @returns {string} substring\n * @private\n */\nfunction _getSubstring (str, index) {\n if (!isIndex(index)) {\n // TODO: better error message\n throw new TypeError('Index expected')\n }\n if (index.size().length !== 1) {\n throw new DimensionError(index.size().length, 1)\n }\n\n // validate whether the range is out of range\n const strLen = str.length\n validateIndex(index.min()[0], strLen)\n validateIndex(index.max()[0], strLen)\n\n const range = index.dimension(0)\n\n let substr = ''\n range.forEach(function (v) {\n substr += str.charAt(v)\n })\n\n return substr\n}\n\n/**\n * Replace a substring in a string\n * @param {string} str string to be replaced\n * @param {Index} index An index containing ranges for each dimension\n * @param {string} replacement Replacement string\n * @param {string} [defaultValue] Default value to be uses when resizing\n * the string. is ' ' by default\n * @returns {string} result\n * @private\n */\nfunction _setSubstring (str, index, replacement, defaultValue) {\n if (!index || index.isIndex !== true) {\n // TODO: better error message\n throw new TypeError('Index expected')\n }\n if (index.size().length !== 1) {\n throw new DimensionError(index.size().length, 1)\n }\n if (defaultValue !== undefined) {\n if (typeof defaultValue !== 'string' || defaultValue.length !== 1) {\n throw new TypeError('Single character expected as defaultValue')\n }\n } else {\n defaultValue = ' '\n }\n\n const range = index.dimension(0)\n const len = range.size()[0]\n\n if (len !== replacement.length) {\n throw new DimensionError(range.size()[0], replacement.length)\n }\n\n // validate whether the range is out of range\n const strLen = str.length\n validateIndex(index.min()[0])\n validateIndex(index.max()[0])\n\n // copy the string into an array with characters\n const chars = []\n for (let i = 0; i < strLen; i++) {\n chars[i] = str.charAt(i)\n }\n\n range.forEach(function (v, i) {\n chars[v] = replacement.charAt(i[0])\n })\n\n // initialize undefined characters with a space\n if (chars.length > strLen) {\n for (let i = strLen - 1, len = chars.length; i < len; i++) {\n if (!chars[i]) {\n chars[i] = defaultValue\n }\n }\n }\n\n return chars.join('')\n}\n\n/**\n * Retrieve a property from an object\n * @param {Object} object\n * @param {Index} index\n * @return {*} Returns the value of the property\n * @private\n */\nfunction _getObjectProperty (object, index) {\n if (index.size().length !== 1) {\n throw new DimensionError(index.size(), 1)\n }\n\n const key = index.dimension(0)\n if (typeof key !== 'string') {\n throw new TypeError('String expected as index to retrieve an object property')\n }\n\n return getSafeProperty(object, key)\n}\n\n/**\n * Set a property on an object\n * @param {Object} object\n * @param {Index} index\n * @param {*} replacement\n * @return {*} Returns the updated object\n * @private\n */\nfunction _setObjectProperty (object, index, replacement) {\n if (index.size().length !== 1) {\n throw new DimensionError(index.size(), 1)\n }\n\n const key = index.dimension(0)\n if (typeof key !== 'string') {\n throw new TypeError('String expected as index to retrieve an object property')\n }\n\n // clone the object, and apply the property to the clone\n const updated = clone(object)\n setSafeProperty(updated, key, replacement)\n\n return updated\n}\n","import { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'transpose'\nconst dependencies = ['typed', 'matrix']\n\nexport const createTranspose = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n /**\n * Transpose a matrix. All values of the matrix are reflected over its\n * main diagonal. Only applicable to two dimensional matrices containing\n * a vector (i.e. having size `[1,n]` or `[n,1]`). One dimensional\n * vectors and scalars return the input unchanged.\n *\n * Syntax:\n *\n * math.transpose(x)\n *\n * Examples:\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.transpose(A) // returns [[1, 4], [2, 5], [3, 6]]\n *\n * See also:\n *\n * diag, inv, subset, squeeze\n *\n * @param {Array | Matrix} x Matrix to be transposed\n * @return {Array | Matrix} The transposed matrix\n */\n return typed('transpose', {\n\n Array: function (x) {\n // use dense matrix implementation\n return this(matrix(x)).valueOf()\n },\n\n Matrix: function (x) {\n // matrix size\n const size = x.size()\n\n // result\n let c\n\n // process dimensions\n switch (size.length) {\n case 1:\n // vector\n c = x.clone()\n break\n\n case 2:\n {\n // rows and columns\n const rows = size[0]\n const columns = size[1]\n\n // check columns\n if (columns === 0) {\n // throw exception\n throw new RangeError('Cannot transpose a 2D matrix with no columns (size: ' + format(size) + ')')\n }\n\n // process storage format\n switch (x.storage()) {\n case 'dense':\n c = _denseTranspose(x, rows, columns)\n break\n case 'sparse':\n c = _sparseTranspose(x, rows, columns)\n break\n }\n }\n break\n\n default:\n // multi dimensional\n throw new RangeError('Matrix must be a vector or two dimensional (size: ' + format(this._size) + ')')\n }\n return c\n },\n\n // scalars\n any: function (x) {\n return clone(x)\n }\n })\n\n function _denseTranspose (m, rows, columns) {\n // matrix array\n const data = m._data\n // transposed matrix data\n const transposed = []\n let transposedRow\n // loop columns\n for (let j = 0; j < columns; j++) {\n // initialize row\n transposedRow = transposed[j] = []\n // loop rows\n for (let i = 0; i < rows; i++) {\n // set data\n transposedRow[i] = clone(data[i][j])\n }\n }\n // return matrix\n return m.createDenseMatrix({\n data: transposed,\n size: [columns, rows],\n datatype: m._datatype\n })\n }\n\n function _sparseTranspose (m, rows, columns) {\n // matrix arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // result matrices\n const cvalues = values ? [] : undefined\n const cindex = []\n const cptr = []\n // row counts\n const w = []\n for (let x = 0; x < rows; x++) { w[x] = 0 }\n // vars\n let p, l, j\n // loop values in matrix\n for (p = 0, l = index.length; p < l; p++) {\n // number of values in row\n w[index[p]]++\n }\n // cumulative sum\n let sum = 0\n // initialize cptr with the cummulative sum of row counts\n for (let i = 0; i < rows; i++) {\n // update cptr\n cptr.push(sum)\n // update sum\n sum += w[i]\n // update w\n w[i] = cptr[i]\n }\n // update cptr\n cptr.push(sum)\n // loop columns\n for (j = 0; j < columns; j++) {\n // values & index in column\n for (let k0 = ptr[j], k1 = ptr[j + 1], k = k0; k < k1; k++) {\n // C values & index\n const q = w[index[k]]++\n // C[j, i] = A[i, j]\n cindex[q] = j\n // check we need to process values (pattern matrix)\n if (values) { cvalues[q] = clone(values[k]) }\n }\n }\n // return matrix\n return m.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [columns, rows],\n datatype: m._datatype\n })\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'ctranspose'\nconst dependencies = ['typed', 'transpose', 'conj']\n\nexport const createCtranspose = /* #__PURE__ */ factory(name, dependencies, ({ typed, transpose, conj }) => {\n /**\n * Transpose and complex conjugate a matrix. All values of the matrix are\n * reflected over its main diagonal and then the complex conjugate is\n * taken. This is equivalent to complex conjugation for scalars and\n * vectors.\n *\n * Syntax:\n *\n * math.ctranspose(x)\n *\n * Examples:\n *\n * const A = [[1, 2, 3], [4, 5, math.complex(6,7)]]\n * math.ctranspose(A) // returns [[1, 4], [2, 5], [3, {re:6,im:7}]]\n *\n * See also:\n *\n * transpose, diag, inv, subset, squeeze\n *\n * @param {Array | Matrix} x Matrix to be ctransposed\n * @return {Array | Matrix} The ctransposed matrix\n */\n return typed(name, {\n any: function (x) {\n return conj(transpose(x))\n }\n })\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { resize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'zeros'\nconst dependencies = ['typed', 'config', 'matrix', 'BigNumber']\n\nexport const createZeros = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, BigNumber }) => {\n /**\n * Create a matrix filled with zeros. The created matrix can have one or\n * multiple dimensions.\n *\n * Syntax:\n *\n * math.zeros(m)\n * math.zeros(m, format)\n * math.zeros(m, n)\n * math.zeros(m, n, format)\n * math.zeros([m, n])\n * math.zeros([m, n], format)\n *\n * Examples:\n *\n * math.zeros(3) // returns [0, 0, 0]\n * math.zeros(3, 2) // returns [[0, 0], [0, 0], [0, 0]]\n * math.zeros(3, 'dense') // returns [0, 0, 0]\n *\n * const A = [[1, 2, 3], [4, 5, 6]]\n * math.zeros(math.size(A)) // returns [[0, 0, 0], [0, 0, 0]]\n *\n * See also:\n *\n * ones, identity, size, range\n *\n * @param {...number | Array} size The size of each dimension of the matrix\n * @param {string} [format] The Matrix storage format\n *\n * @return {Array | Matrix} A matrix filled with zeros\n */\n return typed(name, {\n '': function () {\n return (config.matrix === 'Array')\n ? _zeros([])\n : _zeros([], 'default')\n },\n\n // math.zeros(m, n, p, ..., format)\n // TODO: more accurate signature '...number | BigNumber, string' as soon as typed-function supports this\n '...number | BigNumber | string': function (size) {\n const last = size[size.length - 1]\n if (typeof last === 'string') {\n const format = size.pop()\n return _zeros(size, format)\n } else if (config.matrix === 'Array') {\n return _zeros(size)\n } else {\n return _zeros(size, 'default')\n }\n },\n\n Array: _zeros,\n\n Matrix: function (size) {\n const format = size.storage()\n return _zeros(size.valueOf(), format)\n },\n\n 'Array | Matrix, string': function (size, format) {\n return _zeros(size.valueOf(), format)\n }\n })\n\n /**\n * Create an Array or Matrix with zeros\n * @param {Array} size\n * @param {string} [format='default']\n * @return {Array | Matrix}\n * @private\n */\n function _zeros (size, format) {\n const hasBigNumbers = _normalize(size)\n const defaultValue = hasBigNumbers ? new BigNumber(0) : 0\n _validate(size)\n\n if (format) {\n // return a matrix\n const m = matrix(format)\n if (size.length > 0) {\n return m.resize(size, defaultValue)\n }\n return m\n } else {\n // return an Array\n const arr = []\n if (size.length > 0) {\n return resize(arr, size, defaultValue)\n }\n return arr\n }\n }\n\n // replace BigNumbers with numbers, returns true if size contained BigNumbers\n function _normalize (size) {\n let hasBigNumbers = false\n size.forEach(function (value, index, arr) {\n if (isBigNumber(value)) {\n hasBigNumbers = true\n arr[index] = value.toNumber()\n }\n })\n return hasBigNumbers\n }\n\n // validate arguments\n function _validate (size) {\n size.forEach(function (value) {\n if (typeof value !== 'number' || !isInteger(value) || value < 0) {\n throw new Error('Parameters in function zeros must be positive integers')\n }\n })\n }\n})\n\n// TODO: zeros contains almost the same code as ones. Reuse this?\n","/* eslint-disable no-loss-of-precision */\n\nimport { deepMap } from '../../utils/collection.js'\nimport { sign } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'erf'\nconst dependencies = [\n 'typed'\n]\n\nexport const createErf = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the erf function of a value using a rational Chebyshev\n * approximations for different intervals of x.\n *\n * This is a translation of W. J. Cody's Fortran implementation from 1987\n * ( https://www.netlib.org/specfun/erf ). See the AMS publication\n * \"Rational Chebyshev Approximations for the Error Function\" by W. J. Cody\n * for an explanation of this process.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.erf(x)\n *\n * Examples:\n *\n * math.erf(0.2) // returns 0.22270258921047847\n * math.erf(-0.5) // returns -0.5204998778130465\n * math.erf(4) // returns 0.9999999845827421\n *\n * @param {number | Array | Matrix} x A real number\n * @return {number | Array | Matrix} The erf of `x`\n */\n return typed('name', {\n number: function (x) {\n const y = Math.abs(x)\n\n if (y >= MAX_NUM) {\n return sign(x)\n }\n if (y <= THRESH) {\n return sign(x) * erf1(y)\n }\n if (y <= 4.0) {\n return sign(x) * (1 - erfc2(y))\n }\n return sign(x) * (1 - erfc3(y))\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n\n // TODO: For complex numbers, use the approximation for the Faddeeva function\n // from \"More Efficient Computation of the Complex Error Function\" (AMS)\n\n })\n\n /**\n * Approximates the error function erf() for x <= 0.46875 using this function:\n * n\n * erf(x) = x * sum (p_j * x^(2j)) / (q_j * x^(2j))\n * j=0\n */\n function erf1 (y) {\n const ysq = y * y\n let xnum = P[0][4] * ysq\n let xden = ysq\n let i\n\n for (i = 0; i < 3; i += 1) {\n xnum = (xnum + P[0][i]) * ysq\n xden = (xden + Q[0][i]) * ysq\n }\n return y * (xnum + P[0][3]) / (xden + Q[0][3])\n }\n\n /**\n * Approximates the complement of the error function erfc() for\n * 0.46875 <= x <= 4.0 using this function:\n * n\n * erfc(x) = e^(-x^2) * sum (p_j * x^j) / (q_j * x^j)\n * j=0\n */\n function erfc2 (y) {\n let xnum = P[1][8] * y\n let xden = y\n let i\n\n for (i = 0; i < 7; i += 1) {\n xnum = (xnum + P[1][i]) * y\n xden = (xden + Q[1][i]) * y\n }\n const result = (xnum + P[1][7]) / (xden + Q[1][7])\n const ysq = parseInt(y * 16) / 16\n const del = (y - ysq) * (y + ysq)\n return Math.exp(-ysq * ysq) * Math.exp(-del) * result\n }\n\n /**\n * Approximates the complement of the error function erfc() for x > 4.0 using\n * this function:\n *\n * erfc(x) = (e^(-x^2) / x) * [ 1/sqrt(pi) +\n * n\n * 1/(x^2) * sum (p_j * x^(-2j)) / (q_j * x^(-2j)) ]\n * j=0\n */\n function erfc3 (y) {\n let ysq = 1 / (y * y)\n let xnum = P[2][5] * ysq\n let xden = ysq\n let i\n\n for (i = 0; i < 4; i += 1) {\n xnum = (xnum + P[2][i]) * ysq\n xden = (xden + Q[2][i]) * ysq\n }\n let result = ysq * (xnum + P[2][4]) / (xden + Q[2][4])\n result = (SQRPI - result) / y\n ysq = parseInt(y * 16) / 16\n const del = (y - ysq) * (y + ysq)\n return Math.exp(-ysq * ysq) * Math.exp(-del) * result\n }\n})\n\n/**\n * Upper bound for the first approximation interval, 0 <= x <= THRESH\n * @constant\n */\nconst THRESH = 0.46875\n\n/**\n * Constant used by W. J. Cody's Fortran77 implementation to denote sqrt(pi)\n * @constant\n */\nconst SQRPI = 5.6418958354775628695e-1\n\n/**\n * Coefficients for each term of the numerator sum (p_j) for each approximation\n * interval (see W. J. Cody's paper for more details)\n * @constant\n */\nconst P = [[\n 3.16112374387056560e00, 1.13864154151050156e02,\n 3.77485237685302021e02, 3.20937758913846947e03,\n 1.85777706184603153e-1\n], [\n 5.64188496988670089e-1, 8.88314979438837594e00,\n 6.61191906371416295e01, 2.98635138197400131e02,\n 8.81952221241769090e02, 1.71204761263407058e03,\n 2.05107837782607147e03, 1.23033935479799725e03,\n 2.15311535474403846e-8\n], [\n 3.05326634961232344e-1, 3.60344899949804439e-1,\n 1.25781726111229246e-1, 1.60837851487422766e-2,\n 6.58749161529837803e-4, 1.63153871373020978e-2\n]]\n\n/**\n * Coefficients for each term of the denominator sum (q_j) for each approximation\n * interval (see W. J. Cody's paper for more details)\n * @constant\n */\nconst Q = [[\n 2.36012909523441209e01, 2.44024637934444173e02,\n 1.28261652607737228e03, 2.84423683343917062e03\n], [\n 1.57449261107098347e01, 1.17693950891312499e02,\n 5.37181101862009858e02, 1.62138957456669019e03,\n 3.29079923573345963e03, 4.36261909014324716e03,\n 3.43936767414372164e03, 1.23033935480374942e03\n], [\n 2.56852019228982242e00, 1.87295284992346047e00,\n 5.27905102951428412e-1, 6.05183413124413191e-2,\n 2.33520497626869185e-3\n]]\n\n/**\n * Maximum/minimum safe numbers to input to erf() (in ES6+, this number is\n * Number.[MAX|MIN]_SAFE_INTEGER). erf() for all numbers beyond this limit will\n * return 1\n */\nconst MAX_NUM = Math.pow(2, 53)\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'mode'\nconst dependencies = ['typed', 'isNaN', 'isNumeric']\n\nexport const createMode = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNaN, isNumeric }) => {\n /**\n * Computes the mode of a set of numbers or a list with values(numbers or characters).\n * If there are more than one modes, it returns a list of those values.\n *\n * Syntax:\n *\n * math.mode(a, b, c, ...)\n * math.mode(A)\n *\n * Examples:\n *\n * math.mode(2, 1, 4, 3, 1) // returns [1]\n * math.mode([1, 2.7, 3.2, 4, 2.7]) // returns [2.7]\n * math.mode(1, 4, 6, 1, 6) // returns [1, 6]\n * math.mode('a','a','b','c') // returns [\"a\"]\n * math.mode(1, 1.5, 'abc') // returns [1, 1.5, \"abc\"]\n *\n * See also:\n *\n * median,\n * mean\n *\n * @param {... *} args A single matrix\n * @return {*} The mode of all values\n */\n return typed(name, {\n 'Array | Matrix': _mode,\n\n '...': function (args) {\n return _mode(args)\n }\n })\n\n /**\n * Calculates the mode in an 1-dimensional array\n * @param {Array} values\n * @return {Array} mode\n * @private\n */\n function _mode (values) {\n values = flatten(values.valueOf())\n const num = values.length\n if (num === 0) {\n throw new Error('Cannot calculate mode of an empty array')\n }\n\n const count = {}\n let mode = []\n let max = 0\n for (let i = 0; i < values.length; i++) {\n const value = values[i]\n\n if (isNumeric(value) && isNaN(value)) {\n throw new Error('Cannot calculate mode of an array containing NaN values')\n }\n\n if (!(value in count)) {\n count[value] = 0\n }\n\n count[value]++\n\n if (count[value] === max) {\n mode.push(value)\n } else if (count[value] > max) {\n max = count[value]\n mode = [value]\n }\n }\n return mode\n }\n})\n","import { typeOf } from '../../../utils/is.js'\n\n/**\n * Improve error messages for statistics functions. Errors are typically\n * thrown in an internally used function like larger, causing the error\n * not to mention the function (like max) which is actually used by the user.\n *\n * @param {Error} err\n * @param {String} fnName\n * @param {*} [value]\n * @return {Error}\n */\nexport function improveErrorMessage (err, fnName, value) {\n // TODO: add information with the index (also needs transform in expression parser)\n let details\n\n if (String(err).indexOf('Unexpected type') !== -1) {\n details = arguments.length > 2\n ? ' (type: ' + typeOf(value) + ', value: ' + JSON.stringify(value) + ')'\n : ' (type: ' + err.data.actual + ')'\n\n return new TypeError('Cannot calculate ' + fnName + ', unexpected type of argument' + details)\n }\n\n if (String(err).indexOf('complex numbers') !== -1) {\n details = arguments.length > 2\n ? ' (type: ' + typeOf(value) + ', value: ' + JSON.stringify(value) + ')'\n : ''\n\n return new TypeError('Cannot calculate ' + fnName + ', no ordering relation is defined for complex numbers' + details)\n }\n\n return err\n}\n","import { deepForEach } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'prod'\nconst dependencies = ['typed', 'config', 'multiplyScalar', 'numeric']\n\nexport const createProd = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, multiplyScalar, numeric }) => {\n /**\n * Compute the product of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the sum of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.prod(a, b, c, ...)\n * math.prod(A)\n *\n * Examples:\n *\n * math.multiply(2, 3) // returns 6\n * math.prod(2, 3) // returns 6\n * math.prod(2, 3, 4) // returns 24\n * math.prod([2, 3, 4]) // returns 24\n * math.prod([[2, 5], [4, 3]]) // returns 120\n *\n * See also:\n *\n * mean, median, min, max, sum, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The product of all values\n */\n return typed(name, {\n // prod([a, b, c, d, ...])\n 'Array | Matrix': _prod,\n\n // prod([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n // TODO: implement prod(A, dim)\n throw new Error('prod(A, dim) is not yet supported')\n // return reduce(arguments[0], arguments[1], math.prod)\n },\n\n // prod(a, b, c, d, ...)\n '...': function (args) {\n return _prod(args)\n }\n })\n\n /**\n * Recursively calculate the product of an n-dimensional array\n * @param {Array} array\n * @return {number} prod\n * @private\n */\n function _prod (array) {\n let prod\n\n deepForEach(array, function (value) {\n try {\n prod = (prod === undefined) ? value : multiplyScalar(prod, value)\n } catch (err) {\n throw improveErrorMessage(err, 'prod', value)\n }\n })\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof prod === 'string') {\n prod = numeric(prod, config.number)\n }\n\n if (prod === undefined) {\n throw new Error('Cannot calculate prod of an empty array')\n }\n\n return prod\n }\n})\n","import { format as formatString } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'format'\nconst dependencies = ['typed']\n\nexport const createFormat = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Format a value of any type into a string.\n *\n * Syntax:\n *\n * math.format(value)\n * math.format(value, options)\n * math.format(value, precision)\n * math.format(value, callback)\n *\n * Where:\n *\n * - `value: *`\n * The value to be formatted\n * - `options: Object`\n * An object with formatting options. Available options:\n * - `notation: string`\n * Number notation. Choose from:\n * - 'fixed'\n * Always use regular number notation.\n * For example '123.40' and '14000000'\n * - 'exponential'\n * Always use exponential notation.\n * For example '1.234e+2' and '1.4e+7'\n * - 'engineering'\n * Always use engineering notation: always have exponential notation,\n * and select the exponent to be a multiple of 3.\n * For example '123.4e+0' and '14.0e+6'\n * - 'auto' (default)\n * Regular number notation for numbers having an absolute value between\n * `lower` and `upper` bounds, and uses exponential notation elsewhere.\n * Lower bound is included, upper bound is excluded.\n * For example '123.4' and '1.4e7'.\n * - 'bin', 'oct, or 'hex'\n * Format the number using binary, octal, or hexadecimal notation.\n * For example '0b1101' and '0x10fe'.\n * - `wordSize: number`\n * The word size in bits to use for formatting in binary, octal, or\n * hexadecimal notation. To be used only with 'bin', 'oct', or 'hex'\n * values for 'notation' option. When this option is defined the value\n * is formatted as a signed twos complement integer of the given word\n * size and the size suffix is appended to the output.\n * For example format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'.\n * Default value is undefined.\n * - `precision: number`\n * A number between 0 and 16 to round the digits of the number. In case\n * of notations 'exponential', 'engineering', and 'auto', `precision`\n * defines the total number of significant digits returned.\n * In case of notation 'fixed', `precision` defines the number of\n * significant digits after the decimal point.\n * `precision` is undefined by default.\n * - `lowerExp: number`\n * Exponent determining the lower boundary for formatting a value with\n * an exponent when `notation='auto`. Default value is `-3`.\n * - `upperExp: number`\n * Exponent determining the upper boundary for formatting a value with\n * an exponent when `notation='auto`. Default value is `5`.\n * - `fraction: string`. Available values: 'ratio' (default) or 'decimal'.\n * For example `format(fraction(1, 3))` will output '1/3' when 'ratio' is\n * configured, and will output `0.(3)` when 'decimal' is configured.\n * - `callback: function`\n * A custom formatting function, invoked for all numeric elements in `value`,\n * for example all elements of a matrix, or the real and imaginary\n * parts of a complex number. This callback can be used to override the\n * built-in numeric notation with any type of formatting. Function `callback`\n * is called with `value` as parameter and must return a string.\n *\n * When `value` is an Object:\n *\n * - When the object contains a property `format` being a function, this function\n * is invoked as `value.format(options)` and the result is returned.\n * - When the object has its own `toString` method, this method is invoked\n * and the result is returned.\n * - In other cases the function will loop over all object properties and\n * return JSON object notation like '{\"a\": 2, \"b\": 3}'.\n *\n * When value is a function:\n *\n * - When the function has a property `syntax`, it returns this\n * syntax description.\n * - In other cases, a string `'function'` is returned.\n *\n * Examples:\n *\n * math.format(6.4) // returns '6.4'\n * math.format(1240000) // returns '1.24e6'\n * math.format(1/3) // returns '0.3333333333333333'\n * math.format(1/3, 3) // returns '0.333'\n * math.format(21385, 2) // returns '21000'\n * math.format(12e8, {notation: 'fixed'}) // returns '1200000000'\n * math.format(2.3, {notation: 'fixed', precision: 4}) // returns '2.3000'\n * math.format(52.8, {notation: 'exponential'}) // returns '5.28e+1'\n * math.format(12400,{notation: 'engineering'}) // returns '12.400e+3'\n * math.format(2000, {lowerExp: -2, upperExp: 2}) // returns '2e+3'\n *\n * function formatCurrency(value) {\n * // return currency notation with two digits:\n * return '$' + value.toFixed(2)\n *\n * // you could also use math.format inside the callback:\n * // return '$' + math.format(value, {notation: 'fixed', precision: 2})\n * }\n * math.format([2.1, 3, 0.016], formatCurrency} // returns '[$2.10, $3.00, $0.02]'\n *\n * See also:\n *\n * print\n *\n * @param {*} value Value to be stringified\n * @param {Object | Function | number} [options] Formatting options\n * @return {string} The formatted value\n */\n return typed(name, {\n any: formatString,\n 'any, Object | function | number': formatString\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'bin'\nconst dependencies = ['typed', 'format']\n\n/**\n * Format a number as binary.\n *\n * Syntax:\n *\n * math.bin(value)\n *\n * Examples:\n *\n * //the following outputs \"0b10\"\n * math.bin(2)\n *\n * See also:\n *\n * oct\n * hex\n *\n * @param {number} value Value to be stringified\n * @param {number} wordSize Optional word size (see `format`)\n * @return {string} The formatted value\n */\nexport const createBin = factory(name, dependencies, ({ typed, format }) => {\n return typed(name, {\n 'number | BigNumber': function (n) {\n return format(n, { notation: 'bin' })\n },\n 'number | BigNumber, number': function (n, wordSize) {\n return format(n, { notation: 'bin', wordSize: wordSize })\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'oct'\nconst dependencies = ['typed', 'format']\n\n/**\n * Format a number as octal.\n *\n * Syntax:\n *\n * math.oct(value)\n *\n * Examples:\n *\n * //the following outputs \"0o70\"\n * math.oct(56)\n *\n * See also:\n *\n * bin\n * hex\n *\n * @param {number} value Value to be stringified\n * @param {number} wordSize Optional word size (see `format`)\n * @return {string} The formatted value\n */\n\nexport const createOct = factory(name, dependencies, ({ typed, format }) => {\n return typed(name, {\n 'number | BigNumber': function (n) {\n return format(n, { notation: 'oct' })\n },\n 'number | BigNumber, number': function (n, wordSize) {\n return format(n, { notation: 'oct', wordSize: wordSize })\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'hex'\nconst dependencies = ['typed', 'format']\n\n/**\n * Format a number as hexadecimal.\n *\n * Syntax:\n *\n * math.hex(value)\n *\n * Examples:\n *\n * //the following outputs \"0xF0\"\n * math.hex(240)\n *\n * See also:\n *\n * oct\n * bin\n *\n * @param {number} value Value to be stringified\n * @param {number} wordSize Optional word size (see `format`)\n * @return {string} The formatted value\n */\nexport const createHex = factory(name, dependencies, ({ typed, format }) => {\n return typed(name, {\n 'number | BigNumber': function (n) {\n return format(n, { notation: 'hex' })\n },\n 'number | BigNumber, number': function (n, wordSize) {\n return format(n, { notation: 'hex', wordSize: wordSize })\n }\n })\n})\n","import { format } from '../../utils/string.js'\nimport { isString } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'print'\nconst dependencies = ['typed']\n\nexport const createPrint = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Interpolate values into a string template.\n *\n * Syntax:\n *\n * math.print(template, values)\n * math.print(template, values, precision)\n * math.print(template, values, options)\n *\n * Example usage:\n *\n * // the following outputs: 'Lucy is 5 years old'\n * math.print('Lucy is $age years old', {age: 5})\n *\n * // the following outputs: 'The value of pi is 3.141592654'\n * math.print('The value of pi is $pi', {pi: math.pi}, 10)\n *\n * // the following outputs: 'hello Mary! The date is 2013-03-23'\n * math.print('Hello $user.name! The date is $date', {\n * user: {\n * name: 'Mary',\n * },\n * date: new Date(2013, 2, 23).toISOString().substring(0, 10)\n * })\n *\n * // the following outputs: 'My favorite fruits are apples and bananas !'\n * math.print('My favorite fruits are $0 and $1 !', [\n * 'apples',\n * 'bananas'\n * ])\n *\n * See also:\n *\n * format\n *\n * @param {string} template A string containing variable placeholders.\n * @param {Object | Array | Matrix} values An object or array containing variables\n * which will be filled in in the template.\n * @param {number | Object} [options] Formatting options,\n * or the number of digits to format numbers.\n * See function math.format for a description\n * of all options.\n * @return {string} Interpolated string\n */\n return typed(name, {\n // note: Matrix will be converted automatically to an Array\n 'string, Object | Array': _print,\n 'string, Object | Array, number | Object': _print\n })\n})\n\n/**\n * Interpolate values into a string template.\n * @param {string} template\n * @param {Object} values\n * @param {number | Object} [options]\n * @returns {string} Interpolated string\n * @private\n */\nfunction _print (template, values, options) {\n return template.replace(/\\$([\\w.]+)/g, function (original, key) {\n const keys = key.split('.')\n let value = values[keys.shift()]\n while (keys.length && value !== undefined) {\n const k = keys.shift()\n value = k ? value[k] : value + '.'\n }\n\n if (value !== undefined) {\n if (!isString(value)) {\n return format(value, options)\n } else {\n return value\n }\n }\n\n return original\n }\n )\n}\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'to'\nconst dependencies = [\n 'typed',\n 'matrix'\n]\n\nexport const createTo = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Change the unit of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.to(x, unit)\n *\n * Examples:\n *\n * math.to(math.unit('2 inch'), 'cm') // returns Unit 5.08 cm\n * math.to(math.unit('2 inch'), math.unit(null, 'cm')) // returns Unit 5.08 cm\n * math.to(math.unit(16, 'bytes'), 'bits') // returns Unit 128 bits\n *\n * See also:\n *\n * unit\n *\n * @param {Unit | Array | Matrix} x The unit to be converted.\n * @param {Unit | Array | Matrix} unit New unit. Can be a string like \"cm\"\n * or a unit without value.\n * @return {Unit | Array | Matrix} value with changed, fixed unit.\n */\n return typed(name, {\n 'Unit, Unit | string': function (x, unit) {\n return x.to(unit)\n },\n\n 'Matrix, Matrix': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'Matrix, any': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm14(x, y, this, false)\n },\n\n 'any, Matrix': function (x, y) {\n // SparseMatrix does not support Units\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'isPrime'\nconst dependencies = ['typed']\n\nexport const createIsPrime = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Test whether a value is prime: has no divisors other than itself and one.\n * The function supports type `number`, `bignumber`.\n *\n * The function is evaluated element-wise in case of Array or Matrix input.\n *\n * Syntax:\n *\n * math.isPrime(x)\n *\n * Examples:\n *\n * math.isPrime(3) // returns true\n * math.isPrime(-2) // returns false\n * math.isPrime(0) // returns false\n * math.isPrime(-0) // returns false\n * math.isPrime(0.5) // returns false\n * math.isPrime('2') // returns true\n * math.isPrime([2, 17, 100]) // returns [true, true, false]\n *\n * See also:\n *\n * isNumeric, isZero, isNegative, isInteger\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be tested\n * @return {boolean} Returns true when `x` is larger than zero.\n * Throws an error in case of an unknown data type.\n */\n return typed(name, {\n number: function (x) {\n if (x * 0 !== 0) {\n return false\n }\n if (x <= 3) {\n return x > 1\n }\n if (x % 2 === 0 || x % 3 === 0) {\n return false\n }\n for (let i = 5; i * i <= x; i += 6) {\n if (x % i === 0 || x % (i + 2) === 0) {\n return false\n }\n }\n return true\n },\n\n BigNumber: function (n) {\n if (n.toNumber() * 0 !== 0) {\n return false\n }\n if (n.lte(3)) return n.gt(1)\n if (n.mod(2).eq(0) || n.mod(3).eq(0)) return false\n\n for (let i = 5; n.gte(i * i); i += 6) {\n if (n.mod(i).eq(0) || n.mod(i + 2).eq(0)) {\n return false\n }\n }\n\n return true\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { noBignumber, noFraction } from '../../utils/noop.js'\n\nconst name = 'numeric'\nconst dependencies = ['number', '?bignumber', '?fraction']\n\nexport const createNumeric = /* #__PURE__ */ factory(name, dependencies, ({ number, bignumber, fraction }) => {\n const validInputTypes = {\n string: true,\n number: true,\n BigNumber: true,\n Fraction: true\n }\n\n // Load the conversion functions for each output type\n const validOutputTypes = {\n number: (x) => number(x),\n BigNumber: bignumber\n ? (x) => bignumber(x)\n : noBignumber,\n Fraction: fraction\n ? (x) => fraction(x)\n : noFraction\n }\n\n /**\n * Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.\n *\n * Syntax:\n *\n * math.numeric(x)\n *\n * Examples:\n *\n * math.numeric('4') // returns number 4\n * math.numeric('4', 'number') // returns number 4\n * math.numeric('4', 'BigNumber') // returns BigNumber 4\n * math.numeric('4', 'Fraction') // returns Fraction 4\n * math.numeric(4, 'Fraction') // returns Fraction 4\n * math.numeric(math.fraction(2, 5), 'number') // returns number 0.4\n *\n * See also:\n *\n * number, fraction, bignumber, string, format\n *\n * @param {string | number | BigNumber | Fraction } value\n * A numeric value or a string containing a numeric value\n * @param {string} outputType\n * Desired numeric output type.\n * Available values: 'number', 'BigNumber', or 'Fraction'\n * @return {number | BigNumber | Fraction}\n * Returns an instance of the numeric in the requested type\n */\n return function numeric (value, outputType) {\n const inputType = typeOf(value)\n\n if (!(inputType in validInputTypes)) {\n throw new TypeError('Cannot convert ' + value + ' of type \"' + inputType + '\"; valid input types are ' + Object.keys(validInputTypes).join(', '))\n }\n if (!(outputType in validOutputTypes)) {\n throw new TypeError('Cannot convert ' + value + ' to type \"' + outputType + '\"; valid output types are ' + Object.keys(validOutputTypes).join(', '))\n }\n\n if (outputType === inputType) {\n return value\n } else {\n return validOutputTypes[outputType](value)\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { typeOf } from '../../utils/is.js'\n\nconst name = 'divideScalar'\nconst dependencies = ['typed', 'numeric']\n\nexport const createDivideScalar = /* #__PURE__ */ factory(name, dependencies, ({ typed, numeric }) => {\n /**\n * Divide two scalar values, `x / y`.\n * This function is meant for internal use: it is used by the public functions\n * `divide` and `inv`.\n *\n * This function does not support collections (Array or Matrix).\n *\n * @param {number | BigNumber | Fraction | Complex | Unit} x Numerator\n * @param {number | BigNumber | Fraction | Complex} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit} Quotient, `x / y`\n * @private\n */\n return typed(name, {\n 'number, number': function (x, y) {\n return x / y\n },\n\n 'Complex, Complex': function (x, y) {\n return x.div(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.div(y)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.div(y)\n },\n\n 'Unit, number | Fraction | BigNumber': function (x, y) {\n const res = x.clone()\n // TODO: move the divide function to Unit.js, it uses internals of Unit\n const one = numeric(1, typeOf(y))\n res.value = this(((res.value === null) ? res._normalize(one) : res.value), y)\n return res\n },\n\n 'number | Fraction | BigNumber, Unit': function (x, y) {\n let res = y.clone()\n res = res.pow(-1)\n // TODO: move the divide function to Unit.js, it uses internals of Unit\n const one = numeric(1, typeOf(x))\n res.value = this(x, ((y.value === null) ? y._normalize(one) : y.value))\n return res\n },\n\n 'Unit, Unit': function (x, y) {\n return x.divide(y)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { arraySize as size } from '../../utils/array.js'\nimport { powNumber } from '../../plain/number/index.js'\n\nconst name = 'pow'\nconst dependencies = [\n 'typed',\n 'config',\n 'identity',\n 'multiply',\n 'matrix',\n 'fraction',\n 'number',\n 'Complex'\n]\n\nexport const createPow = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, identity, multiply, matrix, number, fraction, Complex }) => {\n /**\n * Calculates the power of x to y, `x ^ y`.\n * Matrix exponentiation is supported for square matrices `x`, and positive\n * integer exponents `y`.\n *\n * For cubic roots of negative numbers, the function returns the principal\n * root by default. In order to let the function return the real root,\n * math.js can be configured with `math.config({predictable: true})`.\n * To retrieve all cubic roots of a value, use `math.cbrt(x, true)`.\n *\n * Syntax:\n *\n * math.pow(x, y)\n *\n * Examples:\n *\n * math.pow(2, 3) // returns number 8\n *\n * const a = math.complex(2, 3)\n * math.pow(a, 2) // returns Complex -5 + 12i\n *\n * const b = [[1, 2], [4, 3]]\n * math.pow(b, 2) // returns Array [[9, 8], [16, 17]]\n *\n * See also:\n *\n * multiply, sqrt, cbrt, nthRoot\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x The base\n * @param {number | BigNumber | Complex} y The exponent\n * @return {number | BigNumber | Complex | Array | Matrix} The value of `x` to the power `y`\n */\n return typed(name, {\n 'number, number': _pow,\n\n 'Complex, Complex': function (x, y) {\n return x.pow(y)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n if (y.isInteger() || x >= 0 || config.predictable) {\n return x.pow(y)\n } else {\n return new Complex(x.toNumber(), 0).pow(y.toNumber(), 0)\n }\n },\n\n 'Fraction, Fraction': function (x, y) {\n if (y.d !== 1) {\n if (config.predictable) {\n throw new Error('Function pow does not support non-integer exponents for fractions.')\n } else {\n return _pow(x.valueOf(), y.valueOf())\n }\n } else {\n return x.pow(y)\n }\n },\n\n 'Array, number': _powArray,\n\n 'Array, BigNumber': function (x, y) {\n return _powArray(x, y.toNumber())\n },\n\n 'Matrix, number': _powMatrix,\n\n 'Matrix, BigNumber': function (x, y) {\n return _powMatrix(x, y.toNumber())\n },\n\n 'Unit, number | BigNumber': function (x, y) {\n return x.pow(y)\n }\n\n })\n\n /**\n * Calculates the power of x to y, x^y, for two numbers.\n * @param {number} x\n * @param {number} y\n * @return {number | Complex} res\n * @private\n */\n function _pow (x, y) {\n // Alternatively could define a 'realmode' config option or something, but\n // 'predictable' will work for now\n if (config.predictable && !isInteger(y) && x < 0) {\n // Check to see if y can be represented as a fraction\n try {\n const yFrac = fraction(y)\n const yNum = number(yFrac)\n if (y === yNum || Math.abs((y - yNum) / y) < 1e-14) {\n if (yFrac.d % 2 === 1) {\n return (yFrac.n % 2 === 0 ? 1 : -1) * Math.pow(-x, y)\n }\n }\n } catch (ex) {\n // fraction() throws an error if y is Infinity, etc.\n }\n\n // Unable to express y as a fraction, so continue on\n }\n\n // **for predictable mode** x^Infinity === NaN if x < -1\n // N.B. this behavour is different from `Math.pow` which gives\n // (-2)^Infinity === Infinity\n if (config.predictable &&\n ((x < -1 && y === Infinity) ||\n (x > -1 && x < 0 && y === -Infinity))) {\n return NaN\n }\n\n if (isInteger(y) || x >= 0 || config.predictable) {\n return powNumber(x, y)\n } else {\n // TODO: the following infinity checks are duplicated from powNumber. Deduplicate this somehow\n\n // x^Infinity === 0 if -1 < x < 1\n // A real number 0 is returned instead of complex(0)\n if ((x * x < 1 && y === Infinity) ||\n (x * x > 1 && y === -Infinity)) {\n return 0\n }\n\n return new Complex(x, 0).pow(y, 0)\n }\n }\n\n /**\n * Calculate the power of a 2d array\n * @param {Array} x must be a 2 dimensional, square matrix\n * @param {number} y a positive, integer value\n * @returns {Array}\n * @private\n */\n function _powArray (x, y) {\n if (!isInteger(y) || y < 0) {\n throw new TypeError('For A^b, b must be a positive integer (value is ' + y + ')')\n }\n // verify that A is a 2 dimensional square matrix\n const s = size(x)\n if (s.length !== 2) {\n throw new Error('For A^b, A must be 2 dimensional (A has ' + s.length + ' dimensions)')\n }\n if (s[0] !== s[1]) {\n throw new Error('For A^b, A must be square (size is ' + s[0] + 'x' + s[1] + ')')\n }\n\n let res = identity(s[0]).valueOf()\n let px = x\n while (y >= 1) {\n if ((y & 1) === 1) {\n res = multiply(px, res)\n }\n y >>= 1\n px = multiply(px, px)\n }\n return res\n }\n\n /**\n * Calculate the power of a 2d matrix\n * @param {Matrix} x must be a 2 dimensional, square matrix\n * @param {number} y a positive, integer value\n * @returns {Matrix}\n * @private\n */\n function _powMatrix (x, y) {\n return matrix(_powArray(x.valueOf(), y))\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { isInteger } from '../../utils/number.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { roundNumber } from '../../plain/number/index.js'\n\nconst NO_INT = 'Number of decimals in function round must be an integer'\n\nconst name = 'round'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createRound = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, BigNumber, DenseMatrix }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Round a value towards the nearest integer.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.round(x)\n * math.round(x, n)\n *\n * Examples:\n *\n * math.round(3.22) // returns number 3\n * math.round(3.82) // returns number 4\n * math.round(-4.2) // returns number -4\n * math.round(-4.7) // returns number -5\n * math.round(3.22, 1) // returns number 3.2\n * math.round(3.88, 1) // returns number 3.9\n * math.round(-4.21, 1) // returns number -4.2\n * math.round(-4.71, 1) // returns number -4.7\n * math.round(math.pi, 3) // returns number 3.142\n * math.round(123.45678, 2) // returns number 123.46\n *\n * const c = math.complex(3.2, -2.7)\n * math.round(c) // returns Complex 3 - 3i\n *\n * math.round([3.2, 3.8, -4.7]) // returns Array [3, 4, -5]\n *\n * See also:\n *\n * ceil, fix, floor\n *\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} x Number to be rounded\n * @param {number | BigNumber | Array} [n=0] Number of decimals\n * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Rounded value\n */\n return typed(name, {\n ...roundNumberSignatures,\n\n Complex: function (x) {\n return x.round()\n },\n\n 'Complex, number': function (x, n) {\n if (n % 1) { throw new TypeError(NO_INT) }\n\n return x.round(n)\n },\n\n 'Complex, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n const _n = n.toNumber()\n return x.round(_n)\n },\n\n 'number, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n return new BigNumber(x).toDecimalPlaces(n.toNumber())\n },\n\n BigNumber: function (x) {\n return x.toDecimalPlaces(0)\n },\n\n 'BigNumber, BigNumber': function (x, n) {\n if (!n.isInteger()) { throw new TypeError(NO_INT) }\n\n return x.toDecimalPlaces(n.toNumber())\n },\n\n Fraction: function (x) {\n return x.round()\n },\n\n 'Fraction, number': function (x, n) {\n if (n % 1) { throw new TypeError(NO_INT) }\n return x.round(n)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since round(0) = 0\n return deepMap(x, this, true)\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | Complex | BigNumber, SparseMatrix': function (x, y) {\n // check scalar is zero\n if (equalScalar(x, 0)) {\n // do not execute algorithm, result will be a zero matrix\n return zeros(y.size(), y.storage())\n }\n return algorithm12(y, x, this, true)\n },\n\n 'number | Complex | BigNumber, DenseMatrix': function (x, y) {\n // check scalar is zero\n if (equalScalar(x, 0)) {\n // do not execute algorithm, result will be a zero matrix\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | Complex | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nconst roundNumberSignatures = {\n number: roundNumber,\n\n 'number, number': function (x, n) {\n if (!isInteger(n)) { throw new TypeError(NO_INT) }\n if (n < 0 || n > 15) { throw new Error('Number of decimals in function round must be in te range of 0-15') }\n\n return roundNumber(x, n)\n }\n}\n\nexport const createRoundNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, roundNumberSignatures)\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { logNumber } from '../../plain/number/index.js'\n\nconst name = 'log'\nconst dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n\nexport const createLog = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n /**\n * Calculate the logarithm of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log(x)\n * math.log(x, base)\n *\n * Examples:\n *\n * math.log(3.5) // returns 1.252762968495368\n * math.exp(math.log(2.4)) // returns 2.4\n *\n * math.pow(10, 4) // returns 10000\n * math.log(10000, 10) // returns 4\n * math.log(10000) / math.log(10) // returns 4\n *\n * math.log(1024, 2) // returns 10\n * math.pow(2, 10) // returns 1024\n *\n * See also:\n *\n * exp, log2, log10, log1p\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm.\n * @param {number | BigNumber | Complex} [base=e]\n * Optional base for the logarithm. If not provided, the natural\n * logarithm of `x` is calculated.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the logarithm of `x`\n */\n return typed(name, {\n number: function (x) {\n if (x >= 0 || config.predictable) {\n return logNumber(x)\n } else {\n // negative value -> complex value computation\n return new Complex(x, 0).log()\n }\n },\n\n Complex: function (x) {\n return x.log()\n },\n\n BigNumber: function (x) {\n if (!x.isNegative() || config.predictable) {\n return x.ln()\n } else {\n // downgrade to number, return Complex valued result\n return new Complex(x.toNumber(), 0).log()\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n 'any, any': function (x, base) {\n // calculate logarithm for a specified base, log(x, base)\n return divideScalar(this(x), this(base))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { log1p as _log1p } from '../../utils/number.js'\n\nconst name = 'log1p'\nconst dependencies = ['typed', 'config', 'divideScalar', 'log', 'Complex']\n\nexport const createLog1p = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, log, Complex }) => {\n /**\n * Calculate the logarithm of a `value+1`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.log1p(x)\n * math.log1p(x, base)\n *\n * Examples:\n *\n * math.log1p(2.5) // returns 1.252762968495368\n * math.exp(math.log1p(1.4)) // returns 2.4\n *\n * math.pow(10, 4) // returns 10000\n * math.log1p(9999, 10) // returns 4\n * math.log1p(9999) / math.log(10) // returns 4\n *\n * See also:\n *\n * exp, log, log2, log10\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the logarithm of `x+1`.\n * @param {number | BigNumber | Complex} [base=e]\n * Optional base for the logarithm. If not provided, the natural\n * logarithm of `x+1` is calculated.\n * @return {number | BigNumber | Complex | Array | Matrix}\n * Returns the logarithm of `x+1`\n */\n return typed(name, {\n number: function (x) {\n if (x >= -1 || config.predictable) {\n return _log1p(x)\n } else {\n // negative value -> complex value computation\n return _log1pComplex(new Complex(x, 0))\n }\n },\n\n Complex: _log1pComplex,\n\n BigNumber: function (x) {\n const y = x.plus(1)\n if (!y.isNegative() || config.predictable) {\n return y.ln()\n } else {\n // downgrade to number, return Complex valued result\n return _log1pComplex(new Complex(x.toNumber(), 0))\n }\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n },\n\n 'any, any': function (x, base) {\n // calculate logarithm for a specified base, log1p(x, base)\n return divideScalar(this(x), log(base))\n }\n })\n\n /**\n * Calculate the natural logarithm of a complex number + 1\n * @param {Complex} x\n * @returns {Complex}\n * @private\n */\n function _log1pComplex (x) {\n const xRe1p = x.re + 1\n return new Complex(\n Math.log(Math.sqrt(xRe1p * xRe1p + x.im * x.im)),\n Math.atan2(x.im, xRe1p)\n )\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'nthRoots'\nconst dependencies = ['config', 'typed', 'divideScalar', 'Complex']\n\nexport const createNthRoots = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, Complex }) => {\n /**\n * Each function here returns a real multiple of i as a Complex value.\n * @param {number} val\n * @return {Complex} val, i*val, -val or -i*val for index 0, 1, 2, 3\n */\n // This is used to fix float artifacts for zero-valued components.\n const _calculateExactResult = [\n function realPos (val) { return new Complex(val, 0) },\n function imagPos (val) { return new Complex(0, val) },\n function realNeg (val) { return new Complex(-val, 0) },\n function imagNeg (val) { return new Complex(0, -val) }\n ]\n\n /**\n * Calculate the nth root of a Complex Number a using De Movire's Theorem.\n * @param {Complex} a\n * @param {number} root\n * @return {Array} array of n Complex Roots\n */\n function _nthComplexRoots (a, root) {\n if (root < 0) throw new Error('Root must be greater than zero')\n if (root === 0) throw new Error('Root must be non-zero')\n if (root % 1 !== 0) throw new Error('Root must be an integer')\n if (a === 0 || a.abs() === 0) return [new Complex(0, 0)]\n const aIsNumeric = typeof (a) === 'number'\n let offset\n // determine the offset (argument of a)/(pi/2)\n if (aIsNumeric || a.re === 0 || a.im === 0) {\n if (aIsNumeric) {\n offset = 2 * (+(a < 0)) // numeric value on the real axis\n } else if (a.im === 0) {\n offset = 2 * (+(a.re < 0)) // complex value on the real axis\n } else {\n offset = 2 * (+(a.im < 0)) + 1 // complex value on the imaginary axis\n }\n }\n const arg = a.arg()\n const abs = a.abs()\n const roots = []\n const r = Math.pow(abs, 1 / root)\n for (let k = 0; k < root; k++) {\n const halfPiFactor = (offset + 4 * k) / root\n /**\n * If (offset + 4*k)/root is an integral multiple of pi/2\n * then we can produce a more exact result.\n */\n if (halfPiFactor === Math.round(halfPiFactor)) {\n roots.push(_calculateExactResult[halfPiFactor % 4](r))\n continue\n }\n roots.push(new Complex({ r: r, phi: (arg + 2 * Math.PI * k) / root }))\n }\n return roots\n }\n\n /**\n * Calculate the nth roots of a value.\n * An nth root of a positive real number A,\n * is a positive real solution of the equation \"x^root = A\".\n * This function returns an array of complex values.\n *\n * Syntax:\n *\n * math.nthRoots(x)\n * math.nthRoots(x, root)\n *\n * Examples:\n *\n * math.nthRoots(1)\n * // returns [\n * // {re: 1, im: 0},\n * // {re: -1, im: 0}\n * // ]\n * nthRoots(1, 3)\n * // returns [\n * // { re: 1, im: 0 },\n * // { re: -0.4999999999999998, im: 0.8660254037844387 },\n * // { re: -0.5000000000000004, im: -0.8660254037844385 }\n * ]\n *\n * See also:\n *\n * nthRoot, pow, sqrt\n *\n * @param {number | BigNumber | Fraction | Complex} x Number to be rounded\n * @return {number | BigNumber | Fraction | Complex} Rounded value\n */\n return typed(name, {\n Complex: function (x) {\n return _nthComplexRoots(x, 2)\n },\n 'Complex, number': _nthComplexRoots\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotPow'\nconst dependencies = [\n 'typed',\n 'equalScalar',\n 'matrix',\n 'pow',\n 'DenseMatrix'\n]\n\nexport const createDotPow = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar, matrix, pow, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculates the power of x to y element wise.\n *\n * Syntax:\n *\n * math.dotPow(x, y)\n *\n * Examples:\n *\n * math.dotPow(2, 3) // returns number 8\n *\n * const a = [[1, 2], [4, 3]]\n * math.dotPow(a, 2) // returns Array [[1, 4], [16, 9]]\n * math.pow(a, 2) // returns Array [[9, 8], [16, 17]]\n *\n * See also:\n *\n * pow, sqrt, multiply\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x The base\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y The exponent\n * @return {number | BigNumber | Complex | Unit | Array | Matrix} The value of `x` to the power `y`\n */\n return typed(name, {\n\n 'any, any': pow,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, pow, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, pow, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, pow, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, pow)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'dotDivide'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'divideScalar',\n 'DenseMatrix'\n]\n\nexport const createDotDivide = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, divideScalar, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Divide two matrices element wise. The function accepts both matrices and\n * scalar values.\n *\n * Syntax:\n *\n * math.dotDivide(x, y)\n *\n * Examples:\n *\n * math.dotDivide(2, 4) // returns 0.5\n *\n * a = [[9, 5], [6, 1]]\n * b = [[3, 2], [5, 2]]\n *\n * math.dotDivide(a, b) // returns [[3, 2.5], [1.2, 0.5]]\n * math.divide(a, b) // returns [[1.75, 0.75], [-1.75, 2.25]]\n *\n * See also:\n *\n * divide, multiply, dotMultiply\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Numerator\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Quotient, `x ./ y`\n */\n return typed(name, {\n\n 'any, any': divideScalar,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, divideScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, divideScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, divideScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, divideScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, divideScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, divideScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, divideScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, divideScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, divideScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, divideScalar, true).valueOf()\n }\n })\n})\n","import { isArray, isMatrix, isDenseMatrix, isSparseMatrix } from '../../../../utils/is.js'\nimport { arraySize } from '../../../../utils/array.js'\nimport { format } from '../../../../utils/string.js'\n\nexport function createSolveValidation ({ DenseMatrix }) {\n /**\n * Validates matrix and column vector b for backward/forward substitution algorithms.\n *\n * @param {Matrix} m An N x N matrix\n * @param {Array | Matrix} b A column vector\n * @param {Boolean} copy Return a copy of vector b\n *\n * @return {DenseMatrix} Dense column vector b\n */\n return function solveValidation (m, b, copy) {\n const mSize = m.size()\n\n if (mSize.length !== 2) {\n throw new RangeError('Matrix must be two dimensional (size: ' + format(mSize) + ')')\n }\n\n const rows = mSize[0]\n const columns = mSize[1]\n\n if (rows !== columns) {\n throw new RangeError('Matrix must be square (size: ' + format(mSize) + ')')\n }\n\n let data = []\n\n if (isMatrix(b)) {\n const bSize = b.size()\n const bdata = b._data\n\n // 1-dim vector\n if (bSize.length === 1) {\n if (bSize[0] !== rows) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [bdata[i]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n\n // 2-dim column\n if (bSize.length === 2) {\n if (bSize[0] !== rows || bSize[1] !== 1) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n if (isDenseMatrix(b)) {\n if (copy) {\n data = []\n\n for (let i = 0; i < rows; i++) {\n data[i] = [bdata[i][0]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n\n return b\n }\n\n if (isSparseMatrix(b)) {\n for (let i = 0; i < rows; i++) { data[i] = [0] }\n\n const values = b._values\n const index = b._index\n const ptr = b._ptr\n\n for (let k1 = ptr[1], k = ptr[0]; k < k1; k++) {\n const i = index[k]\n data[i][0] = values[k]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1],\n datatype: b._datatype\n })\n }\n }\n\n throw new RangeError('Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.')\n }\n\n if (isArray(b)) {\n const bsize = arraySize(b)\n\n if (bsize.length === 1) {\n if (bsize[0] !== rows) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [b[i]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1]\n })\n }\n\n if (bsize.length === 2) {\n if (bsize[0] !== rows || bsize[1] !== 1) {\n throw new RangeError('Dimension mismatch. Matrix columns must match vector length.')\n }\n\n for (let i = 0; i < rows; i++) {\n data[i] = [b[i][0]]\n }\n\n return new DenseMatrix({\n data: data,\n size: [rows, 1]\n })\n }\n\n throw new RangeError('Dimension mismatch. The right side has to be either 1- or 2-dimensional vector.')\n }\n }\n}\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'lsolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createLsolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds one solution of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix. Throws an error if there's no solution.\n *\n * `L * x = b`\n *\n * Syntax:\n *\n * math.lsolve(L, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = lsolve(a, b) // [[-5.5], [20]]\n *\n * See also:\n *\n * lsolveAll, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} L A N x N matrix or array (L)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix | Array} A column vector with the linear system solution (x)\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseForwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseForwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const r = _denseForwardSubstitution(m, b)\n return r.valueOf()\n }\n })\n\n function _denseForwardSubstitution (m, b) {\n // validate matrix and vector, return copy of column vector b\n b = solveValidation(m, b, true)\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n // result\n const x = []\n\n const mdata = m._data\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n const bj = bdata[j][0] || 0\n let xj\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n const vjj = mdata[j][j]\n\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n xj = divideScalar(bj, vjj)\n\n // loop rows\n for (let i = j + 1; i < rows; i++) {\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))]\n }\n } else {\n // degenerate row, we can choose any value\n xj = 0\n }\n\n x[j] = [xj]\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n\n function _sparseForwardSubstitution (m, b) {\n // validate matrix and vector, return copy of column vector b\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // result\n const x = []\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n const bj = bdata[j][0] || 0\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n let vjj = 0\n // matrix values & indices (column j)\n const jValues = []\n const jIndices = []\n\n // first and last index in the column\n const firstIndex = ptr[j]\n const lastIndex = ptr[j + 1]\n\n // values in column, find value at [j, j]\n for (let k = firstIndex; k < lastIndex; k++) {\n const i = index[k]\n\n // check row (rows are not sorted!)\n if (i === j) {\n vjj = values[k]\n } else if (i > j) {\n // store lower triangular\n jValues.push(values[k])\n jIndices.push(i)\n }\n }\n\n // at this point we must have a value in vjj\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n const xj = divideScalar(bj, vjj)\n\n for (let k = 0, l = jIndices.length; k < l; k++) {\n const i = jIndices[k]\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, jValues[k]))]\n }\n\n x[j] = [xj]\n } else {\n // degenerate row, we can choose any value\n x[j] = [0]\n }\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'usolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createUsolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds one solution of a linear equation system by backward substitution. Matrix must be an upper triangular matrix. Throws an error if there's no solution.\n *\n * `U * x = b`\n *\n * Syntax:\n *\n * math.usolve(U, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = usolve(a, b) // [[8], [9]]\n *\n * See also:\n *\n * usolveAll, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} U A N x N matrix or array (U)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix | Array} A column vector with the linear system solution (x)\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseBackwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseBackwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const r = _denseBackwardSubstitution(m, b)\n return r.valueOf()\n }\n })\n\n function _denseBackwardSubstitution (m, b) {\n // make b into a column vector\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n // result\n const x = []\n\n const mdata = m._data\n // loop columns backwards\n for (let j = columns - 1; j >= 0; j--) {\n // b[j]\n const bj = bdata[j][0] || 0\n // x[j]\n let xj\n\n if (!equalScalar(bj, 0)) {\n // value at [j, j]\n const vjj = mdata[j][j]\n\n if (equalScalar(vjj, 0)) {\n // system cannot be solved\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n xj = divideScalar(bj, vjj)\n\n // loop rows\n for (let i = j - 1; i >= 0; i--) {\n // update copy of b\n bdata[i] = [subtract(bdata[i][0] || 0, multiplyScalar(xj, mdata[i][j]))]\n }\n } else {\n // zero value at j\n xj = 0\n }\n // update x\n x[j] = [xj]\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n\n function _sparseBackwardSubstitution (m, b) {\n // make b into a column vector\n b = solveValidation(m, b, true)\n\n const bdata = b._data\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // result\n const x = []\n\n // loop columns backwards\n for (let j = columns - 1; j >= 0; j--) {\n const bj = bdata[j][0] || 0\n\n if (!equalScalar(bj, 0)) {\n // non-degenerate row, find solution\n\n let vjj = 0\n\n // upper triangular matrix values & index (column j)\n const jValues = []\n const jIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[j]\n const lastIndex = ptr[j + 1]\n\n // values in column, find value at [j, j], loop backwards\n for (let k = lastIndex - 1; k >= firstIndex; k--) {\n const i = index[k]\n\n // check row (rows are not sorted!)\n if (i === j) {\n vjj = values[k]\n } else if (i < j) {\n // store upper triangular\n jValues.push(values[k])\n jIndices.push(i)\n }\n }\n\n // at this point we must have a value in vjj\n if (equalScalar(vjj, 0)) {\n throw new Error('Linear system cannot be solved since matrix is singular')\n }\n\n const xj = divideScalar(bj, vjj)\n\n for (let k = 0, lastIndex = jIndices.length; k < lastIndex; k++) {\n const i = jIndices[k]\n bdata[i] = [subtract(bdata[i][0], multiplyScalar(xj, jValues[k]))]\n }\n\n x[j] = [xj]\n } else {\n // degenerate row, we can choose any value\n x[j] = [0]\n }\n }\n\n return new DenseMatrix({\n data: x,\n size: [rows, 1]\n })\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'lsolveAll'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createLsolveAll = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds all solutions of a linear equation system by forwards substitution. Matrix must be a lower triangular matrix.\n *\n * `L * x = b`\n *\n * Syntax:\n *\n * math.lsolve(L, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = lsolve(a, b) // [ [[-5.5], [20]] ]\n *\n * See also:\n *\n * lsolve, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} L A N x N matrix or array (L)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix[] | Array[]} An array of affine-independent column vectors (x) that solve the linear system\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseForwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseForwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const R = _denseForwardSubstitution(m, b)\n return R.map(r => r.valueOf())\n }\n })\n\n function _denseForwardSubstitution (m, b_) {\n // the algorithm is derived from\n // https://www.overleaf.com/project/5e6c87c554a3190001a3fc93\n\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const M = m._data\n const rows = m._size[0]\n const columns = m._size[1]\n\n // loop columns\n for (let i = 0; i < columns; i++) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n if (!equalScalar(M[i][i], 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], M[i][i])\n\n for (let j = i + 1; j < columns; j++) {\n // b[j] -= b[i] * M[j,i]\n b[j] = subtract(b[j], multiplyScalar(b[i], M[j][i]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = i + 1; j < columns; j++) {\n bNew[j] = subtract(bNew[j], M[j][i])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n\n function _sparseForwardSubstitution (m, b_) {\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // loop columns\n for (let i = 0; i < columns; i++) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n // values & indices (column i)\n const iValues = []\n const iIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[i]\n const lastIndex = ptr[i + 1]\n\n // find the value at [i, i]\n let Mii = 0\n for (let j = firstIndex; j < lastIndex; j++) {\n const J = index[j]\n // check row\n if (J === i) {\n Mii = values[j]\n } else if (J > i) {\n // store lower triangular\n iValues.push(values[j])\n iIndices.push(J)\n }\n }\n\n if (!equalScalar(Mii, 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], Mii)\n\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n b[J] = subtract(b[J], multiplyScalar(b[i], iValues[j]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n bNew[J] = subtract(bNew[J], iValues[j])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\n\nconst name = 'usolveAll'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createUsolveAll = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, multiplyScalar, subtract, equalScalar, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Finds all solutions of a linear equation system by backward substitution. Matrix must be an upper triangular matrix.\n *\n * `U * x = b`\n *\n * Syntax:\n *\n * math.usolve(U, b)\n *\n * Examples:\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = usolve(a, b) // [ [[8], [9]] ]\n *\n * See also:\n *\n * usolve, lup, slu, usolve, lusolve\n *\n * @param {Matrix, Array} U A N x N matrix or array (U)\n * @param {Matrix, Array} b A column vector with the b values\n *\n * @return {DenseMatrix[] | Array[]} An array of affine-independent column vectors (x) that solve the linear system\n */\n return typed(name, {\n\n 'SparseMatrix, Array | Matrix': function (m, b) {\n return _sparseBackwardSubstitution(m, b)\n },\n\n 'DenseMatrix, Array | Matrix': function (m, b) {\n return _denseBackwardSubstitution(m, b)\n },\n\n 'Array, Array | Matrix': function (a, b) {\n const m = matrix(a)\n const R = _denseBackwardSubstitution(m, b)\n return R.map(r => r.valueOf())\n }\n })\n\n function _denseBackwardSubstitution (m, b_) {\n // the algorithm is derived from\n // https://www.overleaf.com/project/5e6c87c554a3190001a3fc93\n\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const M = m._data\n const rows = m._size[0]\n const columns = m._size[1]\n\n // loop columns backwards\n for (let i = columns - 1; i >= 0; i--) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n if (!equalScalar(M[i][i], 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], M[i][i])\n\n for (let j = i - 1; j >= 0; j--) {\n // b[j] -= b[i] * M[j,i]\n b[j] = subtract(b[j], multiplyScalar(b[i], M[j][i]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n for (let j = i - 1; j >= 0; j--) {\n bNew[j] = subtract(bNew[j], M[j][i])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n\n function _sparseBackwardSubstitution (m, b_) {\n // array of right-hand sides\n const B = [solveValidation(m, b_, true)._data.map(e => e[0])]\n\n const rows = m._size[0]\n const columns = m._size[1]\n\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n\n // loop columns backwards\n for (let i = columns - 1; i >= 0; i--) {\n let L = B.length\n\n // loop right-hand sides\n for (let k = 0; k < L; k++) {\n const b = B[k]\n\n // values & indices (column i)\n const iValues = []\n const iIndices = []\n\n // first & last indeces in column\n const firstIndex = ptr[i]\n const lastIndex = ptr[i + 1]\n\n // find the value at [i, i]\n let Mii = 0\n for (let j = lastIndex - 1; j >= firstIndex; j--) {\n const J = index[j]\n // check row\n if (J === i) {\n Mii = values[j]\n } else if (J < i) {\n // store upper triangular\n iValues.push(values[j])\n iIndices.push(J)\n }\n }\n\n if (!equalScalar(Mii, 0)) {\n // non-singular row\n\n b[i] = divideScalar(b[i], Mii)\n\n // loop upper triangular\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n b[J] = subtract(b[J], multiplyScalar(b[i], iValues[j]))\n }\n } else if (!equalScalar(b[i], 0)) {\n // singular row, nonzero RHS\n\n if (k === 0) {\n // There is no valid solution\n return []\n } else {\n // This RHS is invalid but other solutions may still exist\n B.splice(k, 1)\n k -= 1\n L -= 1\n }\n } else if (k === 0) {\n // singular row, RHS is zero\n\n const bNew = [...b]\n bNew[i] = 1\n\n // loop upper triangular\n for (let j = 0, lastIndex = iIndices.length; j < lastIndex; j++) {\n const J = iIndices[j]\n bNew[J] = subtract(bNew[J], iValues[j])\n }\n\n B.push(bNew)\n }\n }\n }\n\n return B.map(x => new DenseMatrix({ data: x.map(e => [e]), size: [rows, 1] }))\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { DimensionError } from '../../../error/DimensionError.js'\n\nconst name = 'algorithm08'\nconst dependencies = ['typed', 'equalScalar']\n\nexport const createAlgorithm08 = /* #__PURE__ */ factory(name, dependencies, ({ typed, equalScalar }) => {\n /**\n * Iterates over SparseMatrix A and SparseMatrix B nonzero items and invokes the callback function f(Aij, Bij).\n * Callback function invoked MAX(NNZA, NNZB) times\n *\n *\n * ┌ f(Aij, Bij) ; A(i,j) !== 0 && B(i,j) !== 0\n * C(i,j) = ┤ A(i,j) ; A(i,j) !== 0\n * └ 0 ; otherwise\n *\n *\n * @param {Matrix} a The SparseMatrix instance (A)\n * @param {Matrix} b The SparseMatrix instance (B)\n * @param {Function} callback The f(Aij,Bij) operation to invoke\n *\n * @return {Matrix} SparseMatrix (C)\n *\n * see https://github.com/josdejong/mathjs/pull/346#issuecomment-97620294\n */\n return function algorithm08 (a, b, callback) {\n // sparse matrix arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // sparse matrix arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n const bsize = b._size\n const bdt = b._datatype\n\n // validate dimensions\n if (asize.length !== bsize.length) { throw new DimensionError(asize.length, bsize.length) }\n\n // check rows & columns\n if (asize[0] !== bsize[0] || asize[1] !== bsize[1]) { throw new RangeError('Dimension mismatch. Matrix A (' + asize + ') must match Matrix B (' + bsize + ')') }\n\n // sparse matrix cannot be a Pattern matrix\n if (!avalues || !bvalues) { throw new Error('Cannot perform operation on Pattern Sparse Matrices') }\n\n // rows & columns\n const rows = asize[0]\n const columns = asize[1]\n\n // datatype\n let dt\n // equal signature to use\n let eq = equalScalar\n // zero value\n let zero = 0\n // callback signature to use\n let cf = callback\n\n // process data types\n if (typeof adt === 'string' && adt === bdt) {\n // datatype\n dt = adt\n // find signature that matches (dt, dt)\n eq = typed.find(equalScalar, [dt, dt])\n // convert 0 to the same datatype\n zero = typed.convert(0, dt)\n // callback\n cf = typed.find(callback, [dt, dt])\n }\n\n // result arrays\n const cvalues = []\n const cindex = []\n const cptr = []\n\n // workspace\n const x = []\n // marks indicating we have a value in x for a given column\n const w = []\n\n // vars\n let k, k0, k1, i\n\n // loop columns\n for (let j = 0; j < columns; j++) {\n // update cptr\n cptr[j] = cindex.length\n // columns mark\n const mark = j + 1\n // loop values in a\n for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = aindex[k]\n // mark workspace\n w[i] = mark\n // set value\n x[i] = avalues[k]\n // add index\n cindex.push(i)\n }\n // loop values in b\n for (k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {\n // row\n i = bindex[k]\n // check value exists in workspace\n if (w[i] === mark) {\n // evaluate callback\n x[i] = cf(x[i], bvalues[k])\n }\n }\n // initialize first index in j\n k = cptr[j]\n // loop index in j\n while (k < cindex.length) {\n // row\n i = cindex[k]\n // value @ i\n const v = x[i]\n // check for zero value\n if (!eq(v, zero)) {\n // push value\n cvalues.push(v)\n // increment pointer\n k++\n } else {\n // remove value @ i, do not increment pointer\n cindex.splice(k, 1)\n }\n }\n }\n // update cptr\n cptr[columns] = cindex.length\n\n // return sparse matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [rows, columns],\n datatype: dt\n })\n }\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { leftShiftNumber } from '../../plain/number/index.js'\nimport { leftShiftBigNumber } from '../../utils/bignumber/bitwise.js'\n\nconst name = 'leftShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createLeftShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise left logical shift of a value x by y number of bits, `x << y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.leftShift(x, y)\n *\n * Examples:\n *\n * math.leftShift(1, 2) // returns number 4\n *\n * math.leftShift([1, 2, 3], 4) // returns Array [16, 32, 64]\n *\n * See also:\n *\n * leftShift, bitNot, bitOr, bitXor, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be shifted\n * @param {number | BigNumber} y Amount of shifts\n * @return {number | BigNumber | Array | Matrix} `x` shifted left `y` times\n */\n return typed(name, {\n\n 'number, number': leftShiftNumber,\n\n 'BigNumber, BigNumber': leftShiftBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { rightArithShiftBigNumber } from '../../utils/bignumber/bitwise.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { rightArithShiftNumber } from '../../plain/number/index.js'\n\nconst name = 'rightArithShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createRightArithShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise right arithmetic shift of a value x by y number of bits, `x >> y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.rightArithShift(x, y)\n *\n * Examples:\n *\n * math.rightArithShift(4, 2) // returns number 1\n *\n * math.rightArithShift([16, -32, 64], 4) // returns Array [1, -2, 3]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, bitXor, rightArithShift, rightLogShift\n *\n * @param {number | BigNumber | Array | Matrix} x Value to be shifted\n * @param {number | BigNumber} y Amount of shifts\n * @return {number | BigNumber | Array | Matrix} `x` sign-filled shifted right `y` times\n */\n return typed(name, {\n\n 'number, number': rightArithShiftNumber,\n\n 'BigNumber, BigNumber': rightArithShiftBigNumber,\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm08 } from '../../type/matrix/utils/algorithm08.js'\nimport { factory } from '../../utils/factory.js'\nimport { rightLogShiftNumber } from '../../plain/number/index.js'\n\nconst name = 'rightLogShift'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'DenseMatrix'\n]\n\nexport const createRightLogShift = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, DenseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm08 = createAlgorithm08({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Bitwise right logical shift of value x by y number of bits, `x >>> y`.\n * For matrices, the function is evaluated element wise.\n * For units, the function is evaluated on the best prefix base.\n *\n * Syntax:\n *\n * math.rightLogShift(x, y)\n *\n * Examples:\n *\n * math.rightLogShift(4, 2) // returns number 1\n *\n * math.rightLogShift([16, -32, 64], 4) // returns Array [1, 2, 3]\n *\n * See also:\n *\n * bitAnd, bitNot, bitOr, bitXor, leftShift, rightLogShift\n *\n * @param {number | Array | Matrix} x Value to be shifted\n * @param {number} y Amount of shifts\n * @return {number | Array | Matrix} `x` zero-filled shifted right `y` times\n */\n\n return typed(name, {\n\n 'number, number': rightLogShiftNumber,\n\n // 'BigNumber, BigNumber': ..., // TODO: implement BigNumber support for rightLogShift\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm08(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n // check scalar\n if (equalScalar(y, 0)) {\n return x.clone()\n }\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm10(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // check scalar\n if (equalScalar(x, 0)) {\n return zeros(y.size(), y.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js'\nimport { factory } from '../../utils/factory.js'\nimport { andNumber } from '../../plain/number/index.js'\n\nconst name = 'and'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'zeros',\n 'not'\n]\n\nexport const createAnd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, zeros, not }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm06 = createAlgorithm06({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Logical `and`. Test whether two values are both defined with a nonzero/nonempty value.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.and(x, y)\n *\n * Examples:\n *\n * math.and(2, 4) // returns true\n *\n * a = [2, 0, 0]\n * b = [3, 7, 0]\n * c = 0\n *\n * math.and(a, b) // returns [true, false, false]\n * math.and(a, c) // returns [false, false, false]\n *\n * See also:\n *\n * not, or, xor\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x First value to check\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} y Second value to check\n * @return {boolean | Array | Matrix}\n * Returns true when both inputs are defined with a nonzero/nonempty value.\n */\n return typed(name, {\n\n 'number, number': andNumber,\n\n 'Complex, Complex': function (x, y) {\n return (x.re !== 0 || x.im !== 0) && (y.re !== 0 || y.im !== 0)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return !x.isZero() && !y.isZero() && !x.isNaN() && !y.isNaN()\n },\n\n 'Unit, Unit': function (x, y) {\n return this(x.value || 0, y.value || 0)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm06(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm02(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n // check scalar\n if (not(y)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n // check scalar\n if (not(y)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n // check scalar\n if (not(x)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm11(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n // check scalar\n if (not(x)) {\n // return zero matrix\n return zeros(x.size(), x.storage())\n }\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y)).valueOf()\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm05 } from '../../type/matrix/utils/algorithm05.js'\n\nconst name = 'compare'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'Fraction',\n 'DenseMatrix'\n]\n\nexport const createCompare = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, equalScalar, matrix, BigNumber, Fraction, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm05 = createAlgorithm05({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.\n *\n * x and y are considered equal when the relative difference between x and y\n * is smaller than the configured epsilon. The function cannot be used to\n * compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.compare(x, y)\n *\n * Examples:\n *\n * math.compare(6, 1) // returns 1\n * math.compare(2, 3) // returns -1\n * math.compare(7, 7) // returns 0\n * math.compare('10', '2') // returns 1\n * math.compare('1000', '1e3') // returns 0\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('40 mm')\n * math.compare(a, b) // returns 1\n *\n * math.compare(2, [1, 2, 3]) // returns [1, 0, -1]\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, larger, largerEq, compareNatural, compareText\n *\n * @param {number | BigNumber | Fraction | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | Unit | string | Array | Matrix} y Second value to compare\n * @return {number | BigNumber | Fraction | Array | Matrix} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x === y ? 0 : (x > y ? 1 : -1)\n },\n\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n ? 0\n : (x > y ? 1 : -1)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return bigNearlyEqual(x, y, config.epsilon)\n ? new BigNumber(0)\n : new BigNumber(x.cmp(y))\n },\n\n 'Fraction, Fraction': function (x, y) {\n return new Fraction(x.compare(y))\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm05(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createCompareNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return nearlyEqual(x, y, config.epsilon)\n ? 0\n : (x > y ? 1 : -1)\n }\n })\n})\n","import naturalSort from 'javascript-natural-sort'\nimport { isDenseMatrix, isSparseMatrix, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'compareNatural'\nconst dependencies = [\n 'typed',\n 'compare'\n]\n\nexport const createCompareNatural = /* #__PURE__ */ factory(name, dependencies, ({ typed, compare }) => {\n const compareBooleans = compare.signatures['boolean,boolean']\n\n /**\n * Compare two values of any type in a deterministic, natural way.\n *\n * For numeric values, the function works the same as `math.compare`.\n * For types of values that can't be compared mathematically,\n * the function compares in a natural way.\n *\n * For numeric values, x and y are considered equal when the relative\n * difference between x and y is smaller than the configured epsilon.\n * The function cannot be used to compare values smaller than\n * approximately 2.22e-16.\n *\n * For Complex numbers, first the real parts are compared. If equal,\n * the imaginary parts are compared.\n *\n * Strings are compared with a natural sorting algorithm, which\n * orders strings in a \"logic\" way following some heuristics.\n * This differs from the function `compare`, which converts the string\n * into a numeric value and compares that. The function `compareText`\n * on the other hand compares text lexically.\n *\n * Arrays and Matrices are compared value by value until there is an\n * unequal pair of values encountered. Objects are compared by sorted\n * keys until the keys or their values are unequal.\n *\n * Syntax:\n *\n * math.compareNatural(x, y)\n *\n * Examples:\n *\n * math.compareNatural(6, 1) // returns 1\n * math.compareNatural(2, 3) // returns -1\n * math.compareNatural(7, 7) // returns 0\n *\n * math.compareNatural('10', '2') // returns 1\n * math.compareText('10', '2') // returns -1\n * math.compare('10', '2') // returns 1\n *\n * math.compareNatural('Answer: 10', 'Answer: 2') // returns 1\n * math.compareText('Answer: 10', 'Answer: 2') // returns -1\n * math.compare('Answer: 10', 'Answer: 2')\n * // Error: Cannot convert \"Answer: 10\" to a number\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('40 mm')\n * math.compareNatural(a, b) // returns 1\n *\n * const c = math.complex('2 + 3i')\n * const d = math.complex('2 + 4i')\n * math.compareNatural(c, d) // returns -1\n *\n * math.compareNatural([1, 2, 4], [1, 2, 3]) // returns 1\n * math.compareNatural([1, 2, 3], [1, 2]) // returns 1\n * math.compareNatural([1, 5], [1, 2, 3]) // returns 1\n * math.compareNatural([1, 2], [1, 2]) // returns 0\n *\n * math.compareNatural({a: 2}, {a: 4}) // returns -1\n *\n * See also:\n *\n * compare, compareText\n *\n * @param {*} x First value to compare\n * @param {*} y Second value to compare\n * @return {number} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n const typeX = typeOf(x)\n const typeY = typeOf(y)\n let c\n\n // numeric types\n if ((typeX === 'number' || typeX === 'BigNumber' || typeX === 'Fraction') &&\n (typeY === 'number' || typeY === 'BigNumber' || typeY === 'Fraction')) {\n c = compare(x, y)\n if (c.toString() !== '0') {\n // c can be number, BigNumber, or Fraction\n return c > 0 ? 1 : -1 // return a number\n } else {\n return naturalSort(typeX, typeY)\n }\n }\n\n // matrix types\n if (typeX === 'Array' || typeX === 'Matrix' ||\n typeY === 'Array' || typeY === 'Matrix') {\n c = compareMatricesAndArrays(this, x, y)\n if (c !== 0) {\n return c\n } else {\n return naturalSort(typeX, typeY)\n }\n }\n\n // in case of different types, order by name of type, i.e. 'BigNumber' < 'Complex'\n if (typeX !== typeY) {\n return naturalSort(typeX, typeY)\n }\n\n if (typeX === 'Complex') {\n return compareComplexNumbers(x, y)\n }\n\n if (typeX === 'Unit') {\n if (x.equalBase(y)) {\n return this(x.value, y.value)\n }\n\n // compare by units\n return compareArrays(this, x.formatUnits(), y.formatUnits())\n }\n\n if (typeX === 'boolean') {\n return compareBooleans(x, y)\n }\n\n if (typeX === 'string') {\n return naturalSort(x, y)\n }\n\n if (typeX === 'Object') {\n return compareObjects(this, x, y)\n }\n\n if (typeX === 'null') {\n return 0\n }\n\n if (typeX === 'undefined') {\n return 0\n }\n\n // this should not occur...\n throw new TypeError('Unsupported type of value \"' + typeX + '\"')\n }\n })\n\n /**\n * Compare mixed matrix/array types, by converting to same-shaped array.\n * This comparator is non-deterministic regarding input types.\n * @param {Array | SparseMatrix | DenseMatrix | *} x\n * @param {Array | SparseMatrix | DenseMatrix | *} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareMatricesAndArrays (compareNatural, x, y) {\n if (isSparseMatrix(x) && isSparseMatrix(y)) {\n return compareArrays(compareNatural, x.toJSON().values, y.toJSON().values)\n }\n if (isSparseMatrix(x)) {\n // note: convert to array is expensive\n return compareMatricesAndArrays(compareNatural, x.toArray(), y)\n }\n if (isSparseMatrix(y)) {\n // note: convert to array is expensive\n return compareMatricesAndArrays(compareNatural, x, y.toArray())\n }\n\n // convert DenseArray into Array\n if (isDenseMatrix(x)) {\n return compareMatricesAndArrays(compareNatural, x.toJSON().data, y)\n }\n if (isDenseMatrix(y)) {\n return compareMatricesAndArrays(compareNatural, x, y.toJSON().data)\n }\n\n // convert scalars to array\n if (!Array.isArray(x)) {\n return compareMatricesAndArrays(compareNatural, [x], y)\n }\n if (!Array.isArray(y)) {\n return compareMatricesAndArrays(compareNatural, x, [y])\n }\n\n return compareArrays(compareNatural, x, y)\n }\n\n /**\n * Compare two Arrays\n *\n * - First, compares value by value\n * - Next, if all corresponding values are equal,\n * look at the length: longest array will be considered largest\n *\n * @param {Array} x\n * @param {Array} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareArrays (compareNatural, x, y) {\n // compare each value\n for (let i = 0, ii = Math.min(x.length, y.length); i < ii; i++) {\n const v = compareNatural(x[i], y[i])\n if (v !== 0) {\n return v\n }\n }\n\n // compare the size of the arrays\n if (x.length > y.length) { return 1 }\n if (x.length < y.length) { return -1 }\n\n // both Arrays have equal size and content\n return 0\n }\n\n /**\n * Compare two objects\n *\n * - First, compare sorted property names\n * - Next, compare the property values\n *\n * @param {Object} x\n * @param {Object} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\n function compareObjects (compareNatural, x, y) {\n const keysX = Object.keys(x)\n const keysY = Object.keys(y)\n\n // compare keys\n keysX.sort(naturalSort)\n keysY.sort(naturalSort)\n const c = compareArrays(compareNatural, keysX, keysY)\n if (c !== 0) {\n return c\n }\n\n // compare values\n for (let i = 0; i < keysX.length; i++) {\n const v = compareNatural(x[keysX[i]], y[keysY[i]])\n if (v !== 0) {\n return v\n }\n }\n\n return 0\n }\n})\n\n/**\n * Compare two complex numbers, `x` and `y`:\n *\n * - First, compare the real values of `x` and `y`\n * - If equal, compare the imaginary values of `x` and `y`\n *\n * @params {Complex} x\n * @params {Complex} y\n * @returns {number} Returns the comparison result: -1, 0, or 1\n */\nfunction compareComplexNumbers (x, y) {\n if (x.re > y.re) { return 1 }\n if (x.re < y.re) { return -1 }\n\n if (x.im > y.im) { return 1 }\n if (x.im < y.im) { return -1 }\n\n return 0\n}\n","import { compareText as _compareText } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'compareText'\nconst dependencies = [\n 'typed',\n 'matrix'\n]\n\nexport const createCompareText = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Compare two strings lexically. Comparison is case sensitive.\n * Returns 1 when x > y, -1 when x < y, and 0 when x == y.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.compareText(x, y)\n *\n * Examples:\n *\n * math.compareText('B', 'A') // returns 1\n * math.compareText('2', '10') // returns 1\n * math.compare('2', '10') // returns -1\n * math.compareNatural('2', '10') // returns -1\n *\n * math.compareText('B', ['A', 'B', 'C']) // returns [1, 0, -1]\n *\n * See also:\n *\n * equal, equalText, compare, compareNatural\n *\n * @param {string | Array | DenseMatrix} x First string to compare\n * @param {string | Array | DenseMatrix} y Second string to compare\n * @return {number | Array | DenseMatrix} Returns the result of the comparison:\n * 1 when x > y, -1 when x < y, and 0 when x == y.\n */\n return typed(name, {\n\n 'any, any': _compareText,\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, _compareText)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, _compareText, false)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, _compareText, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, _compareText, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, _compareText, true).valueOf()\n }\n })\n})\n\nexport const createCompareTextNumber = /* #__PURE__ */ factory(name, ['typed'], ({ typed }) => {\n return typed(name, {\n 'any, any': _compareText\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'equal'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'DenseMatrix'\n]\n\nexport const createEqual = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether two values are equal.\n *\n * The function tests whether the relative difference between x and y is\n * smaller than the configured epsilon. The function cannot be used to\n * compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * In case of complex numbers, x.re must equal y.re, and x.im must equal y.im.\n *\n * Values `null` and `undefined` are compared strictly, thus `null` is only\n * equal to `null` and nothing else, and `undefined` is only equal to\n * `undefined` and nothing else. Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.equal(x, y)\n *\n * Examples:\n *\n * math.equal(2 + 2, 3) // returns false\n * math.equal(2 + 2, 4) // returns true\n *\n * const a = math.unit('50 cm')\n * const b = math.unit('5 m')\n * math.equal(a, b) // returns true\n *\n * const c = [2, 5, 1]\n * const d = [2, 7, 1]\n *\n * math.equal(c, d) // returns [true, false, true]\n * math.deepEqual(c, d) // returns false\n *\n * math.equal(\"1000\", \"1e3\") // returns true\n * math.equal(0, null) // returns false\n *\n * See also:\n *\n * unequal, smaller, smallerEq, larger, largerEq, compare, deepEqual, equalText\n *\n * @param {number | BigNumber | boolean | Complex | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | boolean | Complex | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the compared values are equal, else returns false\n */\n return typed(name, {\n\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y === null }\n if (y === null) { return x === null }\n if (x === undefined) { return y === undefined }\n if (y === undefined) { return x === undefined }\n\n return equalScalar(x, y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, equalScalar)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, equalScalar, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, equalScalar, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, equalScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, equalScalar, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, equalScalar, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, equalScalar, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, equalScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, equalScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, equalScalar, true).valueOf()\n }\n })\n})\n\nexport const createEqualNumber = factory(name, ['typed', 'equalScalar'], ({ typed, equalScalar }) => {\n return typed(name, {\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y === null }\n if (y === null) { return x === null }\n if (x === undefined) { return y === undefined }\n if (y === undefined) { return x === undefined }\n\n return equalScalar(x, y)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'equalText'\nconst dependencies = [\n 'typed',\n 'compareText',\n 'isZero'\n]\n\nexport const createEqualText = /* #__PURE__ */ factory(name, dependencies, ({ typed, compareText, isZero }) => {\n /**\n * Check equality of two strings. Comparison is case sensitive.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.equalText(x, y)\n *\n * Examples:\n *\n * math.equalText('Hello', 'Hello') // returns true\n * math.equalText('a', 'A') // returns false\n * math.equal('2e3', '2000') // returns true\n * math.equalText('2e3', '2000') // returns false\n *\n * math.equalText('B', ['A', 'B', 'C']) // returns [false, true, false]\n *\n * See also:\n *\n * equal, compareText, compare, compareNatural\n *\n * @param {string | Array | DenseMatrix} x First string to compare\n * @param {string | Array | DenseMatrix} y Second string to compare\n * @return {number | Array | DenseMatrix} Returns true if the values are equal, and false if not.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n return isZero(compareText(x, y))\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'smaller'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createSmaller = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is smaller than y.\n *\n * The function returns true when x is smaller than y and the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.smaller(x, y)\n *\n * Examples:\n *\n * math.smaller(2, 3) // returns true\n * math.smaller(5, 2 * 2) // returns false\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('2 inch')\n * math.smaller(a, b) // returns true\n *\n * See also:\n *\n * equal, unequal, smallerEq, smaller, smallerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x < y\n },\n\n 'number, number': function (x, y) {\n return x < y && !nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.lt(y) && !bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) === -1\n },\n\n 'Complex, Complex': function (x, y) {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createSmallerNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x < y && !nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'smallerEq'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createSmallerEq = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is smaller or equal to y.\n *\n * The function returns true when x is smaller than y or the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.smallerEq(x, y)\n *\n * Examples:\n *\n * math.smaller(1 + 2, 3) // returns false\n * math.smallerEq(1 + 2, 3) // returns true\n *\n * See also:\n *\n * equal, unequal, smaller, larger, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x <= y\n },\n\n 'number, number': function (x, y) {\n return x <= y || nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.lte(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) !== 1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createSmallerEqNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x <= y || nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'larger'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createLarger = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is larger than y.\n *\n * The function returns true when x is larger than y and the relative\n * difference between x and y is larger than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.larger(x, y)\n *\n * Examples:\n *\n * math.larger(2, 3) // returns false\n * math.larger(5, 2 + 2) // returns true\n *\n * const a = math.unit('5 cm')\n * const b = math.unit('2 inch')\n * math.larger(a, b) // returns false\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is larger than y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x > y\n },\n\n 'number, number': function (x, y) {\n return x > y && !nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.gt(y) && !bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) === 1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createLargerNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x > y && !nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual.js'\nimport { nearlyEqual } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'largerEq'\nconst dependencies = [\n 'typed',\n 'config',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createLargerEq = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether value x is larger or equal to y.\n *\n * The function returns true when x is larger than y or the relative\n * difference between x and y is smaller than the configured epsilon. The\n * function cannot be used to compare values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.largerEq(x, y)\n *\n * Examples:\n *\n * math.larger(2, 1 + 1) // returns false\n * math.largerEq(2, 1 + 1) // returns true\n *\n * See also:\n *\n * equal, unequal, smaller, smallerEq, larger, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the x is larger or equal to y, else returns false\n */\n return typed(name, {\n\n 'boolean, boolean': function (x, y) {\n return x >= y\n },\n\n 'number, number': function (x, y) {\n return x >= y || nearlyEqual(x, y, config.epsilon)\n },\n\n 'BigNumber, BigNumber': function (x, y) {\n return x.gte(y) || bigNearlyEqual(x, y, config.epsilon)\n },\n\n 'Fraction, Fraction': function (x, y) {\n return x.compare(y) !== -1\n },\n\n 'Complex, Complex': function () {\n throw new TypeError('No ordering relation is defined for complex numbers')\n },\n\n 'Unit, Unit': function (x, y) {\n if (!x.equalBase(y)) {\n throw new Error('Cannot compare units with different base')\n }\n return this(x.value, y.value)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, this)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, this, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, this, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, this, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n\nexport const createLargerEqNumber = /* #__PURE__ */ factory(name, ['typed', 'config'], ({ typed, config }) => {\n return typed(name, {\n 'number, number': function (x, y) {\n return x >= y || nearlyEqual(x, y, config.epsilon)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'deepEqual'\nconst dependencies = [\n 'typed',\n 'equal'\n]\n\nexport const createDeepEqual = /* #__PURE__ */ factory(name, dependencies, ({ typed, equal }) => {\n /**\n * Test element wise whether two matrices are equal.\n * The function accepts both matrices and scalar values.\n *\n * Strings are compared by their numerical value.\n *\n * Syntax:\n *\n * math.deepEqual(x, y)\n *\n * Examples:\n *\n * math.deepEqual(2, 4) // returns false\n *\n * a = [2, 5, 1]\n * b = [2, 7, 1]\n *\n * math.deepEqual(a, b) // returns false\n * math.equal(a, b) // returns [true, false, true]\n *\n * See also:\n *\n * equal, unequal\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First matrix to compare\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second matrix to compare\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix}\n * Returns true when the input matrices have the same size and each of their elements is equal.\n */\n return typed(name, {\n 'any, any': function (x, y) {\n return _deepEqual(x.valueOf(), y.valueOf())\n }\n })\n\n /**\n * Test whether two arrays have the same size and all elements are equal\n * @param {Array | *} x\n * @param {Array | *} y\n * @return {boolean} Returns true if both arrays are deep equal\n */\n function _deepEqual (x, y) {\n if (Array.isArray(x)) {\n if (Array.isArray(y)) {\n const len = x.length\n if (len !== y.length) {\n return false\n }\n\n for (let i = 0; i < len; i++) {\n if (!_deepEqual(x[i], y[i])) {\n return false\n }\n }\n\n return true\n } else {\n return false\n }\n } else {\n if (Array.isArray(y)) {\n return false\n } else {\n return equal(x, y)\n }\n }\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm07 } from '../../type/matrix/utils/algorithm07.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\n\nconst name = 'unequal'\nconst dependencies = [\n 'typed',\n 'config',\n 'equalScalar',\n 'matrix',\n 'DenseMatrix'\n]\n\nexport const createUnequal = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, equalScalar, matrix, DenseMatrix }) => {\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm07 = createAlgorithm07({ typed, DenseMatrix })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Test whether two values are unequal.\n *\n * The function tests whether the relative difference between x and y is\n * larger than the configured epsilon. The function cannot be used to compare\n * values smaller than approximately 2.22e-16.\n *\n * For matrices, the function is evaluated element wise.\n * In case of complex numbers, x.re must unequal y.re, or x.im must unequal y.im.\n * Strings are compared by their numerical value.\n *\n * Values `null` and `undefined` are compared strictly, thus `null` is unequal\n * with everything except `null`, and `undefined` is unequal with everything\n * except `undefined`.\n *\n * Syntax:\n *\n * math.unequal(x, y)\n *\n * Examples:\n *\n * math.unequal(2 + 2, 3) // returns true\n * math.unequal(2 + 2, 4) // returns false\n *\n * const a = math.unit('50 cm')\n * const b = math.unit('5 m')\n * math.unequal(a, b) // returns false\n *\n * const c = [2, 5, 1]\n * const d = [2, 7, 1]\n *\n * math.unequal(c, d) // returns [false, true, false]\n * math.deepEqual(c, d) // returns false\n *\n * math.unequal(0, null) // returns true\n * See also:\n *\n * equal, deepEqual, smaller, smallerEq, larger, largerEq, compare\n *\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit | string | Array | Matrix | undefined} x First value to compare\n * @param {number | BigNumber | Fraction | boolean | Complex | Unit | string | Array | Matrix | undefined} y Second value to compare\n * @return {boolean | Array | Matrix} Returns true when the compared values are unequal, else returns false\n */\n return typed('unequal', {\n\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y !== null }\n if (y === null) { return x !== null }\n if (x === undefined) { return y !== undefined }\n if (y === undefined) { return x !== undefined }\n\n return _unequal(x, y)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm07(x, y, _unequal)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm03(y, x, _unequal, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, _unequal, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, _unequal)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm12(x, y, _unequal, false)\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, _unequal, false)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm12(y, x, _unequal, true)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, _unequal, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, _unequal, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, _unequal, true).valueOf()\n }\n })\n\n function _unequal (x, y) {\n return !equalScalar(x, y)\n }\n})\n\nexport const createUnequalNumber = factory(name, ['typed', 'equalScalar'], ({ typed, equalScalar }) => {\n return typed(name, {\n 'any, any': function (x, y) {\n // strict equality for null and undefined?\n if (x === null) { return y !== null }\n if (y === null) { return x !== null }\n if (x === undefined) { return y !== undefined }\n if (y === undefined) { return x !== undefined }\n\n return !equalScalar(x, y)\n }\n })\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'partitionSelect'\nconst dependencies = ['typed', 'isNumeric', 'isNaN', 'compare']\n\nexport const createPartitionSelect = /* #__PURE__ */ factory(name, dependencies, ({ typed, isNumeric, isNaN, compare }) => {\n const asc = compare\n const desc = (a, b) => -compare(a, b)\n\n /**\n * Partition-based selection of an array or 1D matrix.\n * Will find the kth smallest value, and mutates the input array.\n * Uses Quickselect.\n *\n * Syntax:\n *\n * math.partitionSelect(x, k)\n * math.partitionSelect(x, k, compare)\n *\n * Examples:\n *\n * math.partitionSelect([5, 10, 1], 2) // returns 10\n * math.partitionSelect(['C', 'B', 'A', 'D'], 1) // returns 'B'\n *\n * function sortByLength (a, b) {\n * return a.length - b.length\n * }\n * math.partitionSelect(['Langdon', 'Tom', 'Sara'], 2, sortByLength) // returns 'Langdon'\n *\n * See also:\n *\n * sort\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to sort\n * @param {Number} k The kth smallest value to be retrieved zero-based index\n * @param {Function | 'asc' | 'desc'} [compare='asc']\n * An optional comparator function. The function is called as\n * `compare(a, b)`, and must return 1 when a > b, -1 when a < b,\n * and 0 when a == b.\n * @return {*} Returns the kth lowest value.\n */\n return typed(name, {\n 'Array | Matrix, number': function (x, k) {\n return _partitionSelect(x, k, asc)\n },\n\n 'Array | Matrix, number, string': function (x, k, compare) {\n if (compare === 'asc') {\n return _partitionSelect(x, k, asc)\n } else if (compare === 'desc') {\n return _partitionSelect(x, k, desc)\n } else {\n throw new Error('Compare string must be \"asc\" or \"desc\"')\n }\n },\n\n 'Array | Matrix, number, function': _partitionSelect\n })\n\n function _partitionSelect (x, k, compare) {\n if (!isInteger(k) || k < 0) {\n throw new Error('k must be a non-negative integer')\n }\n\n if (isMatrix(x)) {\n const size = x.size()\n if (size.length > 1) {\n throw new Error('Only one dimensional matrices supported')\n }\n return quickSelect(x.valueOf(), k, compare)\n }\n\n if (Array.isArray(x)) {\n return quickSelect(x, k, compare)\n }\n }\n\n /**\n * Quickselect algorithm.\n * Code adapted from:\n * https://blog.teamleadnet.com/2012/07/quick-select-algorithm-find-kth-element.html\n *\n * @param {Array} arr\n * @param {Number} k\n * @param {Function} compare\n * @private\n */\n function quickSelect (arr, k, compare) {\n if (k >= arr.length) {\n throw new Error('k out of bounds')\n }\n\n // check for NaN values since these can cause an infinite while loop\n for (let i = 0; i < arr.length; i++) {\n if (isNumeric(arr[i]) && isNaN(arr[i])) {\n return arr[i] // return NaN\n }\n }\n\n let from = 0\n let to = arr.length - 1\n\n // if from == to we reached the kth element\n while (from < to) {\n let r = from\n let w = to\n const pivot = arr[Math.floor(Math.random() * (to - from + 1)) + from]\n\n // stop if the reader and writer meets\n while (r < w) {\n // arr[r] >= pivot\n if (compare(arr[r], pivot) >= 0) { // put the large values at the end\n const tmp = arr[w]\n arr[w] = arr[r]\n arr[r] = tmp\n --w\n } else { // the value is smaller than the pivot, skip\n ++r\n }\n }\n\n // if we stepped up (r++) we need to step one down (arr[r] > pivot)\n if (compare(arr[r], pivot) > 0) {\n --r\n }\n\n // the r pointer is on the end of the first k elements\n if (k <= r) {\n to = r\n } else {\n from = r + 1\n }\n }\n\n return arr[k]\n }\n})\n","import { arraySize as size } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'sort'\nconst dependencies = ['typed', 'matrix', 'compare', 'compareNatural']\n\nexport const createSort = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, compare, compareNatural }) => {\n const compareAsc = compare\n const compareDesc = (a, b) => -compare(a, b)\n\n /**\n * Sort the items in a matrix.\n *\n * Syntax:\n *\n * math.sort(x)\n * math.sort(x, compare)\n *\n * Examples:\n *\n * math.sort([5, 10, 1]) // returns [1, 5, 10]\n * math.sort(['C', 'B', 'A', 'D'], math.compareNatural)\n * // returns ['A', 'B', 'C', 'D']\n *\n * function sortByLength (a, b) {\n * return a.length - b.length\n * }\n * math.sort(['Langdon', 'Tom', 'Sara'], sortByLength)\n * // returns ['Tom', 'Sara', 'Langdon']\n *\n * See also:\n *\n * filter, forEach, map, compare, compareNatural\n *\n * @param {Matrix | Array} x A one dimensional matrix or array to sort\n * @param {Function | 'asc' | 'desc' | 'natural'} [compare='asc']\n * An optional _comparator function or name. The function is called as\n * `compare(a, b)`, and must return 1 when a > b, -1 when a < b,\n * and 0 when a == b.\n * @return {Matrix | Array} Returns the sorted matrix.\n */\n return typed(name, {\n Array: function (x) {\n _arrayIsVector(x)\n return x.sort(compareAsc)\n },\n\n Matrix: function (x) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(compareAsc), x.storage())\n },\n\n 'Array, function': function (x, _comparator) {\n _arrayIsVector(x)\n return x.sort(_comparator)\n },\n\n 'Matrix, function': function (x, _comparator) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(_comparator), x.storage())\n },\n\n 'Array, string': function (x, order) {\n _arrayIsVector(x)\n return x.sort(_comparator(order))\n },\n\n 'Matrix, string': function (x, order) {\n _matrixIsVector(x)\n return matrix(x.toArray().sort(_comparator(order)), x.storage())\n }\n })\n\n /**\n * Get the comparator for given order ('asc', 'desc', 'natural')\n * @param {'asc' | 'desc' | 'natural'} order\n * @return {Function} Returns a _comparator function\n */\n function _comparator (order) {\n if (order === 'asc') {\n return compareAsc\n } else if (order === 'desc') {\n return compareDesc\n } else if (order === 'natural') {\n return compareNatural\n } else {\n throw new Error('String \"asc\", \"desc\", or \"natural\" expected')\n }\n }\n\n /**\n * Validate whether an array is one dimensional\n * Throws an error when this is not the case\n * @param {Array} array\n * @private\n */\n function _arrayIsVector (array) {\n if (size(array).length !== 1) {\n throw new Error('One dimensional array expected')\n }\n }\n\n /**\n * Validate whether a matrix is one dimensional\n * Throws an error when this is not the case\n * @param {Matrix} matrix\n * @private\n */\n function _matrixIsVector (matrix) {\n if (matrix.size().length !== 1) {\n throw new Error('One dimensional matrix expected')\n }\n }\n})\n","import { deepForEach, reduce, containsCollections } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'max'\nconst dependencies = ['typed', 'config', 'numeric', 'larger']\n\nexport const createMax = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, larger }) => {\n /**\n * Compute the maximum value of a matrix or a list with values.\n * In case of a multi dimensional array, the maximum of the flattened array\n * will be calculated. When `dim` is provided, the maximum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.max(a, b, c, ...)\n * math.max(A)\n * math.max(A, dim)\n *\n * Examples:\n *\n * math.max(2, 1, 4, 3) // returns 4\n * math.max([2, 1, 4, 3]) // returns 4\n *\n * // maximum over a specified dimension (zero-based)\n * math.max([[2, 5], [4, 3], [1, 7]], 0) // returns [4, 7]\n * math.max([[2, 5], [4, 3]], [1, 7], 1) // returns [5, 4, 7]\n *\n * math.max(2.7, 7.1, -4.5, 2.0, 4.1) // returns 7.1\n * math.min(2.7, 7.1, -4.5, 2.0, 4.1) // returns -4.5\n *\n * See also:\n *\n * mean, median, min, prod, std, sum, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The maximum value\n */\n return typed(name, {\n // max([a, b, c, d, ...])\n 'Array | Matrix': _max,\n\n // max([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return reduce(array, dim.valueOf(), _largest)\n },\n\n // max(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function max')\n }\n\n return _max(args)\n }\n })\n\n /**\n * Return the largest of two values\n * @param {*} x\n * @param {*} y\n * @returns {*} Returns x when x is largest, or y when y is largest\n * @private\n */\n function _largest (x, y) {\n try {\n return larger(x, y) ? x : y\n } catch (err) {\n throw improveErrorMessage(err, 'max', y)\n }\n }\n\n /**\n * Recursively calculate the maximum value in an n-dimensional array\n * @param {Array} array\n * @return {number} max\n * @private\n */\n function _max (array) {\n let res\n\n deepForEach(array, function (value) {\n try {\n if (isNaN(value) && typeof value === 'number') {\n res = NaN\n } else if (res === undefined || larger(value, res)) {\n res = value\n }\n } catch (err) {\n throw improveErrorMessage(err, 'max', value)\n }\n })\n\n if (res === undefined) {\n throw new Error('Cannot calculate max of an empty array')\n }\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof res === 'string') {\n res = numeric(res, config.number)\n }\n\n return res\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'min'\nconst dependencies = ['typed', 'config', 'numeric', 'smaller']\n\nexport const createMin = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, smaller }) => {\n /**\n * Compute the minimum value of a matrix or a list of values.\n * In case of a multi dimensional array, the minimum of the flattened array\n * will be calculated. When `dim` is provided, the minimum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.min(a, b, c, ...)\n * math.min(A)\n * math.min(A, dim)\n *\n * Examples:\n *\n * math.min(2, 1, 4, 3) // returns 1\n * math.min([2, 1, 4, 3]) // returns 1\n *\n * // minimum over a specified dimension (zero-based)\n * math.min([[2, 5], [4, 3], [1, 7]], 0) // returns [1, 3]\n * math.min([[2, 5], [4, 3], [1, 7]], 1) // returns [2, 3, 1]\n *\n * math.max(2.7, 7.1, -4.5, 2.0, 4.1) // returns 7.1\n * math.min(2.7, 7.1, -4.5, 2.0, 4.1) // returns -4.5\n *\n * See also:\n *\n * mean, median, max, prod, std, sum, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The minimum value\n */\n return typed(name, {\n // min([a, b, c, d, ...])\n 'Array | Matrix': _min,\n\n // min([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return reduce(array, dim.valueOf(), _smallest)\n },\n\n // min(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function min')\n }\n\n return _min(args)\n }\n })\n\n /**\n * Return the smallest of two values\n * @param {*} x\n * @param {*} y\n * @returns {*} Returns x when x is smallest, or y when y is smallest\n * @private\n */\n function _smallest (x, y) {\n try {\n return smaller(x, y) ? x : y\n } catch (err) {\n throw improveErrorMessage(err, 'min', y)\n }\n }\n\n /**\n * Recursively calculate the minimum value in an n-dimensional array\n * @param {Array} array\n * @return {number} min\n * @private\n */\n function _min (array) {\n let min\n\n deepForEach(array, function (value) {\n try {\n if (isNaN(value) && typeof value === 'number') {\n min = NaN\n } else if (min === undefined || smaller(value, min)) {\n min = value\n }\n } catch (err) {\n throw improveErrorMessage(err, 'min', value)\n }\n })\n\n if (min === undefined) {\n throw new Error('Cannot calculate min of an empty array')\n }\n\n // make sure returning numeric value: parse a string into a numeric value\n if (typeof min === 'string') {\n min = numeric(min, config.number)\n }\n\n return min\n }\n})\n","import { isArray, isMatrix, isString, typeOf } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ImmutableDenseMatrix'\nconst dependencies = [\n 'smaller',\n 'DenseMatrix'\n]\n\nexport const createImmutableDenseMatrixClass = /* #__PURE__ */ factory(name, dependencies, ({ smaller, DenseMatrix }) => {\n function ImmutableDenseMatrix (data, datatype) {\n if (!(this instanceof ImmutableDenseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }\n if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }\n\n if (isMatrix(data) || isArray(data)) {\n // use DenseMatrix implementation\n const matrix = new DenseMatrix(data, datatype)\n // internal structures\n this._data = matrix._data\n this._size = matrix._size\n this._datatype = matrix._datatype\n this._min = null\n this._max = null\n } else if (data && isArray(data.data) && isArray(data.size)) {\n // initialize fields from JSON representation\n this._data = data.data\n this._size = data.size\n this._datatype = data.datatype\n this._min = typeof data.min !== 'undefined' ? data.min : null\n this._max = typeof data.max !== 'undefined' ? data.max : null\n } else if (data) {\n // unsupported type\n throw new TypeError('Unsupported type of data (' + typeOf(data) + ')')\n } else {\n // nothing provided\n this._data = []\n this._size = [0]\n this._datatype = datatype\n this._min = null\n this._max = null\n }\n }\n\n ImmutableDenseMatrix.prototype = new DenseMatrix()\n\n /**\n * Attach type information\n */\n ImmutableDenseMatrix.prototype.type = 'ImmutableDenseMatrix'\n ImmutableDenseMatrix.prototype.isImmutableDenseMatrix = true\n\n /**\n * Get a subset of the matrix, or replace a subset of the matrix.\n *\n * Usage:\n * const subset = matrix.subset(index) // retrieve subset\n * const value = matrix.subset(index, replacement) // replace subset\n *\n * @param {Index} index\n * @param {Array | ImmutableDenseMatrix | *} [replacement]\n * @param {*} [defaultValue=0] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be filled with zeros.\n */\n ImmutableDenseMatrix.prototype.subset = function (index) {\n switch (arguments.length) {\n case 1:\n {\n // use base implementation\n const m = DenseMatrix.prototype.subset.call(this, index)\n // check result is a matrix\n if (isMatrix(m)) {\n // return immutable matrix\n return new ImmutableDenseMatrix({\n data: m._data,\n size: m._size,\n datatype: m._datatype\n })\n }\n return m\n }\n // intentional fall through\n case 2:\n case 3:\n throw new Error('Cannot invoke set subset on an Immutable Matrix instance')\n\n default:\n throw new SyntaxError('Wrong number of arguments')\n }\n }\n\n /**\n * Replace a single element in the matrix.\n * @param {Number[]} index Zero-based index\n * @param {*} value\n * @param {*} [defaultValue] Default value, filled in on new entries when\n * the matrix is resized. If not provided,\n * new matrix elements will be left undefined.\n * @return {ImmutableDenseMatrix} self\n */\n ImmutableDenseMatrix.prototype.set = function () {\n throw new Error('Cannot invoke set on an Immutable Matrix instance')\n }\n\n /**\n * Resize the matrix to the given size. Returns a copy of the matrix when\n * `copy=true`, otherwise return the matrix itself (resize in place).\n *\n * @param {Number[]} size The new size the matrix should have.\n * @param {*} [defaultValue=0] Default value, filled in on new entries.\n * If not provided, the matrix elements will\n * be filled with zeros.\n * @param {boolean} [copy] Return a resized copy of the matrix\n *\n * @return {Matrix} The resized matrix\n */\n ImmutableDenseMatrix.prototype.resize = function () {\n throw new Error('Cannot invoke resize on an Immutable Matrix instance')\n }\n\n /**\n * Disallows reshaping in favor of immutability.\n *\n * @throws {Error} Operation not allowed\n */\n ImmutableDenseMatrix.prototype.reshape = function () {\n throw new Error('Cannot invoke reshape on an Immutable Matrix instance')\n }\n\n /**\n * Create a clone of the matrix\n * @return {ImmutableDenseMatrix} clone\n */\n ImmutableDenseMatrix.prototype.clone = function () {\n return new ImmutableDenseMatrix({\n data: clone(this._data),\n size: clone(this._size),\n datatype: this._datatype\n })\n }\n\n /**\n * Get a JSON representation of the matrix\n * @returns {Object}\n */\n ImmutableDenseMatrix.prototype.toJSON = function () {\n return {\n mathjs: 'ImmutableDenseMatrix',\n data: this._data,\n size: this._size,\n datatype: this._datatype\n }\n }\n\n /**\n * Generate a matrix from a JSON object\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ImmutableDenseMatrix\", data: [], size: []}`,\n * where mathjs is optional\n * @returns {ImmutableDenseMatrix}\n */\n ImmutableDenseMatrix.fromJSON = function (json) {\n return new ImmutableDenseMatrix(json)\n }\n\n /**\n * Swap rows i and j in Matrix.\n *\n * @param {Number} i Matrix row index 1\n * @param {Number} j Matrix row index 2\n *\n * @return {Matrix} The matrix reference\n */\n ImmutableDenseMatrix.prototype.swapRows = function () {\n throw new Error('Cannot invoke swapRows on an Immutable Matrix instance')\n }\n\n /**\n * Calculate the minimum value in the set\n * @return {Number | undefined} min\n */\n ImmutableDenseMatrix.prototype.min = function () {\n // check min has been calculated before\n if (this._min === null) {\n // minimum\n let m = null\n // compute min\n this.forEach(function (v) {\n if (m === null || smaller(v, m)) { m = v }\n })\n this._min = m !== null ? m : undefined\n }\n return this._min\n }\n\n /**\n * Calculate the maximum value in the set\n * @return {Number | undefined} max\n */\n ImmutableDenseMatrix.prototype.max = function () {\n // check max has been calculated before\n if (this._max === null) {\n // maximum\n let m = null\n // compute max\n this.forEach(function (v) {\n if (m === null || smaller(m, v)) { m = v }\n })\n this._max = m !== null ? m : undefined\n }\n return this._max\n }\n\n return ImmutableDenseMatrix\n}, { isClass: true })\n","import { isMatrix, isRange } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Index'\nconst dependencies = ['ImmutableDenseMatrix']\n\nexport const createIndexClass = /* #__PURE__ */ factory(name, dependencies, ({ ImmutableDenseMatrix }) => {\n /**\n * Create an index. An Index can store ranges and sets for multiple dimensions.\n * Matrix.get, Matrix.set, and math.subset accept an Index as input.\n *\n * Usage:\n * const index = new Index(range1, range2, matrix1, array1, ...)\n *\n * Where each parameter can be any of:\n * A number\n * A string (containing a name of an object property)\n * An instance of Range\n * An Array with the Set values\n * A Matrix with the Set values\n *\n * The parameters start, end, and step must be integer numbers.\n *\n * @class Index\n * @Constructor Index\n * @param {...*} ranges\n */\n function Index (ranges) {\n if (!(this instanceof Index)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this._dimensions = []\n this._isScalar = true\n\n for (let i = 0, ii = arguments.length; i < ii; i++) {\n const arg = arguments[i]\n\n if (isRange(arg)) {\n this._dimensions.push(arg)\n this._isScalar = false\n } else if (Array.isArray(arg) || isMatrix(arg)) {\n // create matrix\n const m = _createImmutableMatrix(arg.valueOf())\n this._dimensions.push(m)\n // size\n const size = m.size()\n // scalar\n if (size.length !== 1 || size[0] !== 1) {\n this._isScalar = false\n }\n } else if (typeof arg === 'number') {\n this._dimensions.push(_createImmutableMatrix([arg]))\n } else if (typeof arg === 'string') {\n // object property (arguments.count should be 1)\n this._dimensions.push(arg)\n } else {\n throw new TypeError('Dimension must be an Array, Matrix, number, string, or Range')\n }\n // TODO: implement support for wildcard '*'\n }\n }\n\n /**\n * Attach type information\n */\n Index.prototype.type = 'Index'\n Index.prototype.isIndex = true\n\n function _createImmutableMatrix (arg) {\n // loop array elements\n for (let i = 0, l = arg.length; i < l; i++) {\n if (typeof arg[i] !== 'number' || !isInteger(arg[i])) {\n throw new TypeError('Index parameters must be positive integer numbers')\n }\n }\n // create matrix\n return new ImmutableDenseMatrix(arg)\n }\n\n /**\n * Create a clone of the index\n * @memberof Index\n * @return {Index} clone\n */\n Index.prototype.clone = function () {\n const index = new Index()\n index._dimensions = clone(this._dimensions)\n index._isScalar = this._isScalar\n return index\n }\n\n /**\n * Create an index from an array with ranges/numbers\n * @memberof Index\n * @param {Array.} ranges\n * @return {Index} index\n * @private\n */\n Index.create = function (ranges) {\n const index = new Index()\n Index.apply(index, ranges)\n return index\n }\n\n /**\n * Retrieve the size of the index, the number of elements for each dimension.\n * @memberof Index\n * @returns {number[]} size\n */\n Index.prototype.size = function () {\n const size = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const d = this._dimensions[i]\n size[i] = (typeof d === 'string') ? 1 : d.size()[0]\n }\n\n return size\n }\n\n /**\n * Get the maximum value for each of the indexes ranges.\n * @memberof Index\n * @returns {number[]} max\n */\n Index.prototype.max = function () {\n const values = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const range = this._dimensions[i]\n values[i] = (typeof range === 'string') ? range : range.max()\n }\n\n return values\n }\n\n /**\n * Get the minimum value for each of the indexes ranges.\n * @memberof Index\n * @returns {number[]} min\n */\n Index.prototype.min = function () {\n const values = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const range = this._dimensions[i]\n values[i] = (typeof range === 'string') ? range : range.min()\n }\n\n return values\n }\n\n /**\n * Loop over each of the ranges of the index\n * @memberof Index\n * @param {Function} callback Called for each range with a Range as first\n * argument, the dimension as second, and the\n * index object as third.\n */\n Index.prototype.forEach = function (callback) {\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n callback(this._dimensions[i], i, this)\n }\n }\n\n /**\n * Retrieve the dimension for the given index\n * @memberof Index\n * @param {Number} dim Number of the dimension\n * @returns {Range | null} range\n */\n Index.prototype.dimension = function (dim) {\n return this._dimensions[dim] || null\n }\n\n /**\n * Test whether this index contains an object property\n * @returns {boolean} Returns true if the index is an object property\n */\n Index.prototype.isObjectProperty = function () {\n return this._dimensions.length === 1 && typeof this._dimensions[0] === 'string'\n }\n\n /**\n * Returns the object property name when the Index holds a single object property,\n * else returns null\n * @returns {string | null}\n */\n Index.prototype.getObjectProperty = function () {\n return this.isObjectProperty() ? this._dimensions[0] : null\n }\n\n /**\n * Test whether this index contains only a single value.\n *\n * This is the case when the index is created with only scalar values as ranges,\n * not for ranges resolving into a single value.\n * @memberof Index\n * @return {boolean} isScalar\n */\n Index.prototype.isScalar = function () {\n return this._isScalar\n }\n\n /**\n * Expand the Index into an array.\n * For example new Index([0,3], [2,7]) returns [[0,1,2], [2,3,4,5,6]]\n * @memberof Index\n * @returns {Array} array\n */\n Index.prototype.toArray = function () {\n const array = []\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const dimension = this._dimensions[i]\n array.push((typeof dimension === 'string') ? dimension : dimension.toArray())\n }\n return array\n }\n\n /**\n * Get the primitive value of the Index, a two dimensional array.\n * Equivalent to Index.toArray().\n * @memberof Index\n * @returns {Array} array\n */\n Index.prototype.valueOf = Index.prototype.toArray\n\n /**\n * Get the string representation of the index, for example '[2:6]' or '[0:2:10, 4:7, [1,2,3]]'\n * @memberof Index\n * @returns {String} str\n */\n Index.prototype.toString = function () {\n const strings = []\n\n for (let i = 0, ii = this._dimensions.length; i < ii; i++) {\n const dimension = this._dimensions[i]\n if (typeof dimension === 'string') {\n strings.push(JSON.stringify(dimension))\n } else {\n strings.push(dimension.toString())\n }\n }\n\n return '[' + strings.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the Index\n * @memberof Index\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Index\", \"ranges\": [{\"mathjs\": \"Range\", start: 0, end: 10, step:1}, ...]}`\n */\n Index.prototype.toJSON = function () {\n return {\n mathjs: 'Index',\n dimensions: this._dimensions\n }\n }\n\n /**\n * Instantiate an Index from a JSON object\n * @memberof Index\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Index\", \"dimensions\": [{\"mathjs\": \"Range\", start: 0, end: 10, step:1}, ...]}`\n * @return {Index}\n */\n Index.fromJSON = function (json) {\n return Index.create(json.dimensions)\n }\n\n return Index\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'FibonacciHeap'\nconst dependencies = ['smaller', 'larger']\n\nexport const createFibonacciHeapClass = /* #__PURE__ */ factory(name, dependencies, ({ smaller, larger }) => {\n const oneOverLogPhi = 1.0 / Math.log((1.0 + Math.sqrt(5.0)) / 2.0)\n\n /**\n * Fibonacci Heap implementation, used interally for Matrix math.\n * @class FibonacciHeap\n * @constructor FibonacciHeap\n */\n function FibonacciHeap () {\n if (!(this instanceof FibonacciHeap)) { throw new SyntaxError('Constructor must be called with the new operator') }\n\n // initialize fields\n this._minimum = null\n this._size = 0\n }\n\n /**\n * Attach type information\n */\n FibonacciHeap.prototype.type = 'FibonacciHeap'\n FibonacciHeap.prototype.isFibonacciHeap = true\n\n /**\n * Inserts a new data element into the heap. No heap consolidation is\n * performed at this time, the new node is simply inserted into the root\n * list of this heap. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.insert = function (key, value) {\n // create node\n const node = {\n key: key,\n value: value,\n degree: 0\n }\n // check we have a node in the minimum\n if (this._minimum) {\n // minimum node\n const minimum = this._minimum\n // update left & right of node\n node.left = minimum\n node.right = minimum.right\n minimum.right = node\n node.right.left = node\n // update minimum node in heap if needed\n if (smaller(key, minimum.key)) {\n // node has a smaller key, use it as minimum\n this._minimum = node\n }\n } else {\n // set left & right\n node.left = node\n node.right = node\n // this is the first node\n this._minimum = node\n }\n // increment number of nodes in heap\n this._size++\n // return node\n return node\n }\n\n /**\n * Returns the number of nodes in heap. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.size = function () {\n return this._size\n }\n\n /**\n * Removes all elements from this heap.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.clear = function () {\n this._minimum = null\n this._size = 0\n }\n\n /**\n * Returns true if the heap is empty, otherwise false.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.isEmpty = function () {\n return this._size === 0\n }\n\n /**\n * Extracts the node with minimum key from heap. Amortized running\n * time: O(log n).\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.extractMinimum = function () {\n // node to remove\n const node = this._minimum\n // check we have a minimum\n if (node === null) { return node }\n // current minimum\n let minimum = this._minimum\n // get number of children\n let numberOfChildren = node.degree\n // pointer to the first child\n let x = node.child\n // for each child of node do...\n while (numberOfChildren > 0) {\n // store node in right side\n const tempRight = x.right\n // remove x from child list\n x.left.right = x.right\n x.right.left = x.left\n // add x to root list of heap\n x.left = minimum\n x.right = minimum.right\n minimum.right = x\n x.right.left = x\n // set Parent[x] to null\n x.parent = null\n x = tempRight\n numberOfChildren--\n }\n // remove node from root list of heap\n node.left.right = node.right\n node.right.left = node.left\n // update minimum\n if (node === node.right) {\n // empty\n minimum = null\n } else {\n // update minimum\n minimum = node.right\n // we need to update the pointer to the root with minimum key\n minimum = _findMinimumNode(minimum, this._size)\n }\n // decrement size of heap\n this._size--\n // update minimum\n this._minimum = minimum\n // return node\n return node\n }\n\n /**\n * Removes a node from the heap given the reference to the node. The trees\n * in the heap will be consolidated, if necessary. This operation may fail\n * to remove the correct element if there are nodes with key value -Infinity.\n * Running time: O(log n) amortized.\n * @memberof FibonacciHeap\n */\n FibonacciHeap.prototype.remove = function (node) {\n // decrease key value\n this._minimum = _decreaseKey(this._minimum, node, -1)\n // remove the smallest\n this.extractMinimum()\n }\n\n /**\n * Decreases the key value for a heap node, given the new value to take on.\n * The structure of the heap may be changed and will not be consolidated.\n * Running time: O(1) amortized.\n * @memberof FibonacciHeap\n */\n function _decreaseKey (minimum, node, key) {\n // set node key\n node.key = key\n // get parent node\n const parent = node.parent\n if (parent && smaller(node.key, parent.key)) {\n // remove node from parent\n _cut(minimum, node, parent)\n // remove all nodes from parent to the root parent\n _cascadingCut(minimum, parent)\n }\n // update minimum node if needed\n if (smaller(node.key, minimum.key)) { minimum = node }\n // return minimum\n return minimum\n }\n\n /**\n * The reverse of the link operation: removes node from the child list of parent.\n * This method assumes that min is non-null. Running time: O(1).\n * @memberof FibonacciHeap\n */\n function _cut (minimum, node, parent) {\n // remove node from parent children and decrement Degree[parent]\n node.left.right = node.right\n node.right.left = node.left\n parent.degree--\n // reset y.child if necessary\n if (parent.child === node) { parent.child = node.right }\n // remove child if degree is 0\n if (parent.degree === 0) { parent.child = null }\n // add node to root list of heap\n node.left = minimum\n node.right = minimum.right\n minimum.right = node\n node.right.left = node\n // set parent[node] to null\n node.parent = null\n // set mark[node] to false\n node.mark = false\n }\n\n /**\n * Performs a cascading cut operation. This cuts node from its parent and then\n * does the same for its parent, and so on up the tree.\n * Running time: O(log n); O(1) excluding the recursion.\n * @memberof FibonacciHeap\n */\n function _cascadingCut (minimum, node) {\n // store parent node\n const parent = node.parent\n // if there's a parent...\n if (!parent) { return }\n // if node is unmarked, set it marked\n if (!node.mark) {\n node.mark = true\n } else {\n // it's marked, cut it from parent\n _cut(minimum, node, parent)\n // cut its parent as well\n _cascadingCut(parent)\n }\n }\n\n /**\n * Make the first node a child of the second one. Running time: O(1) actual.\n * @memberof FibonacciHeap\n */\n const _linkNodes = function (node, parent) {\n // remove node from root list of heap\n node.left.right = node.right\n node.right.left = node.left\n // make node a Child of parent\n node.parent = parent\n if (!parent.child) {\n parent.child = node\n node.right = node\n node.left = node\n } else {\n node.left = parent.child\n node.right = parent.child.right\n parent.child.right = node\n node.right.left = node\n }\n // increase degree[parent]\n parent.degree++\n // set mark[node] false\n node.mark = false\n }\n\n function _findMinimumNode (minimum, size) {\n // to find trees of the same degree efficiently we use an array of length O(log n) in which we keep a pointer to one root of each degree\n const arraySize = Math.floor(Math.log(size) * oneOverLogPhi) + 1\n // create list with initial capacity\n const array = new Array(arraySize)\n // find the number of root nodes.\n let numRoots = 0\n let x = minimum\n if (x) {\n numRoots++\n x = x.right\n while (x !== minimum) {\n numRoots++\n x = x.right\n }\n }\n // vars\n let y\n // For each node in root list do...\n while (numRoots > 0) {\n // access this node's degree..\n let d = x.degree\n // get next node\n const next = x.right\n // check if there is a node already in array with the same degree\n while (true) {\n // get node with the same degree is any\n y = array[d]\n if (!y) { break }\n // make one node with the same degree a child of the other, do this based on the key value.\n if (larger(x.key, y.key)) {\n const temp = y\n y = x\n x = temp\n }\n // make y a child of x\n _linkNodes(y, x)\n // we have handled this degree, go to next one.\n array[d] = null\n d++\n }\n // save this node for later when we might encounter another of the same degree.\n array[d] = x\n // move forward through list.\n x = next\n numRoots--\n }\n // Set min to null (effectively losing the root list) and reconstruct the root list from the array entries in array[].\n minimum = null\n // loop nodes in array\n for (let i = 0; i < arraySize; i++) {\n // get current node\n y = array[i]\n if (!y) { continue }\n // check if we have a linked list\n if (minimum) {\n // First remove node from root list.\n y.left.right = y.right\n y.right.left = y.left\n // now add to root list, again.\n y.left = minimum\n y.right = minimum.right\n minimum.right = y\n y.right.left = y\n // check if this is a new min.\n if (smaller(y.key, minimum.key)) { minimum = y }\n } else { minimum = y }\n }\n return minimum\n }\n\n return FibonacciHeap\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'Spa'\nconst dependencies = ['addScalar', 'equalScalar', 'FibonacciHeap']\n\nexport const createSpaClass = /* #__PURE__ */ factory(name, dependencies, ({ addScalar, equalScalar, FibonacciHeap }) => {\n /**\n * An ordered Sparse Accumulator is a representation for a sparse vector that includes a dense array\n * of the vector elements and an ordered list of non-zero elements.\n */\n function Spa () {\n if (!(this instanceof Spa)) { throw new SyntaxError('Constructor must be called with the new operator') }\n\n // allocate vector, TODO use typed arrays\n this._values = []\n this._heap = new FibonacciHeap()\n }\n\n /**\n * Attach type information\n */\n Spa.prototype.type = 'Spa'\n Spa.prototype.isSpa = true\n\n /**\n * Set the value for index i.\n *\n * @param {number} i The index\n * @param {number | BigNumber | Complex} The value at index i\n */\n Spa.prototype.set = function (i, v) {\n // check we have a value @ i\n if (!this._values[i]) {\n // insert in heap\n const node = this._heap.insert(i, v)\n // set the value @ i\n this._values[i] = node\n } else {\n // update the value @ i\n this._values[i].value = v\n }\n }\n\n Spa.prototype.get = function (i) {\n const node = this._values[i]\n if (node) { return node.value }\n return 0\n }\n\n Spa.prototype.accumulate = function (i, v) {\n // node @ i\n let node = this._values[i]\n if (!node) {\n // insert in heap\n node = this._heap.insert(i, v)\n // initialize value\n this._values[i] = node\n } else {\n // accumulate value\n node.value = addScalar(node.value, v)\n }\n }\n\n Spa.prototype.forEach = function (from, to, callback) {\n // references\n const heap = this._heap\n const values = this._values\n // nodes\n const nodes = []\n // node with minimum key, save it\n let node = heap.extractMinimum()\n if (node) { nodes.push(node) }\n // extract nodes from heap (ordered)\n while (node && node.key <= to) {\n // check it is in range\n if (node.key >= from) {\n // check value is not zero\n if (!equalScalar(node.value, 0)) {\n // invoke callback\n callback(node.key, node.value, this)\n }\n }\n // extract next node, save it\n node = heap.extractMinimum()\n if (node) { nodes.push(node) }\n }\n // reinsert all nodes in heap\n for (let i = 0; i < nodes.length; i++) {\n // current node\n const n = nodes[i]\n // insert node in heap\n node = heap.insert(n.key, n.value)\n // update values\n values[node.key] = node\n }\n }\n\n Spa.prototype.swap = function (i, j) {\n // node @ i and j\n let nodei = this._values[i]\n let nodej = this._values[j]\n // check we need to insert indeces\n if (!nodei && nodej) {\n // insert in heap\n nodei = this._heap.insert(i, nodej.value)\n // remove from heap\n this._heap.remove(nodej)\n // set values\n this._values[i] = nodei\n this._values[j] = undefined\n } else if (nodei && !nodej) {\n // insert in heap\n nodej = this._heap.insert(j, nodei.value)\n // remove from heap\n this._heap.remove(nodei)\n // set values\n this._values[j] = nodej\n this._values[i] = undefined\n } else if (nodei && nodej) {\n // swap values\n const v = nodei.value\n nodei.value = nodej.value\n nodej.value = v\n }\n }\n\n return Spa\n}, { isClass: true })\n","import { memoize } from '../function.js'\n\n/**\n * Calculate BigNumber e\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns e\n */\nexport const createBigNumberE = memoize(function (BigNumber) {\n return new BigNumber(1).exp()\n}, { hasher })\n\n/**\n * Calculate BigNumber golden ratio, phi = (1+sqrt(5))/2\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns phi\n */\nexport const createBigNumberPhi = memoize(function (BigNumber) {\n return new BigNumber(1).plus(new BigNumber(5).sqrt()).div(2)\n}, { hasher })\n\n/**\n * Calculate BigNumber pi.\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns pi\n */\nexport const createBigNumberPi = memoize(function (BigNumber) {\n return BigNumber.acos(-1)\n}, { hasher })\n\n/**\n * Calculate BigNumber tau, tau = 2 * pi\n * @param {function} BigNumber BigNumber constructor\n * @returns {BigNumber} Returns tau\n */\nexport const createBigNumberTau = memoize(function (BigNumber) {\n return createBigNumberPi(BigNumber).times(2)\n}, { hasher })\n\n/**\n * Create a hash for a BigNumber constructor function. The created has is\n * the configured precision\n * @param {Array} args Supposed to contain a single entry with\n * a BigNumber constructor\n * @return {number} precision\n * @private\n */\nfunction hasher (args) {\n return args[0].precision\n}\n","import { isComplex, isUnit, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { memoize } from '../../utils/function.js'\nimport { endsWith } from '../../utils/string.js'\nimport { clone, hasOwnProperty } from '../../utils/object.js'\nimport { createBigNumberPi as createPi } from '../../utils/bignumber/constants.js'\n\nconst name = 'Unit'\nconst dependencies = [\n '?on',\n 'config',\n 'addScalar',\n 'subtract',\n 'multiplyScalar',\n 'divideScalar',\n 'pow',\n 'abs',\n 'fix',\n 'round',\n 'equal',\n 'isNumeric',\n 'format',\n 'number',\n 'Complex',\n 'BigNumber',\n 'Fraction'\n]\n\nexport const createUnitClass = /* #__PURE__ */ factory(name, dependencies, ({\n on,\n config,\n addScalar,\n subtract,\n multiplyScalar,\n divideScalar,\n pow,\n abs,\n fix,\n round,\n equal,\n isNumeric,\n format,\n number,\n Complex,\n BigNumber,\n Fraction\n}) => {\n const toNumber = number\n /**\n * A unit can be constructed in the following ways:\n *\n * const a = new Unit(value, name)\n * const b = new Unit(null, name)\n * const c = Unit.parse(str)\n *\n * Example usage:\n *\n * const a = new Unit(5, 'cm') // 50 mm\n * const b = Unit.parse('23 kg') // 23 kg\n * const c = math.in(a, new Unit(null, 'm') // 0.05 m\n * const d = new Unit(9.81, \"m/s^2\") // 9.81 m/s^2\n *\n * @class Unit\n * @constructor Unit\n * @param {number | BigNumber | Fraction | Complex | boolean} [value] A value like 5.2\n * @param {string} [name] A unit name like \"cm\" or \"inch\", or a derived unit of the form: \"u1[^ex1] [u2[^ex2] ...] [/ u3[^ex3] [u4[^ex4]]]\", such as \"kg m^2/s^2\", where each unit appearing after the forward slash is taken to be in the denominator. \"kg m^2 s^-2\" is a synonym and is also acceptable. Any of the units can include a prefix.\n */\n function Unit (value, name) {\n if (!(this instanceof Unit)) {\n throw new Error('Constructor must be called with the new operator')\n }\n\n if (!(value === null || value === undefined || isNumeric(value) || isComplex(value))) {\n throw new TypeError('First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined')\n }\n if (name !== undefined && (typeof name !== 'string' || name === '')) {\n throw new TypeError('Second parameter in Unit constructor must be a string')\n }\n\n if (name !== undefined) {\n const u = Unit.parse(name)\n this.units = u.units\n this.dimensions = u.dimensions\n } else {\n this.units = [\n {\n unit: UNIT_NONE,\n prefix: PREFIXES.NONE, // link to a list with supported prefixes\n power: 0\n }\n ]\n this.dimensions = []\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n this.dimensions[i] = 0\n }\n }\n\n this.value = (value !== undefined && value !== null) ? this._normalize(value) : null\n\n this.fixPrefix = false // if true, function format will not search for the\n // best prefix but leave it as initially provided.\n // fixPrefix is set true by the method Unit.to\n\n // The justification behind this is that if the constructor is explicitly called,\n // the caller wishes the units to be returned exactly as he supplied.\n this.skipAutomaticSimplification = true\n }\n\n /**\n * Attach type information\n */\n Unit.prototype.type = 'Unit'\n Unit.prototype.isUnit = true\n\n // private variables and functions for the Unit parser\n let text, index, c\n\n function skipWhitespace () {\n while (c === ' ' || c === '\\t') {\n next()\n }\n }\n\n function isDigitDot (c) {\n return ((c >= '0' && c <= '9') || c === '.')\n }\n\n function isDigit (c) {\n return ((c >= '0' && c <= '9'))\n }\n\n function next () {\n index++\n c = text.charAt(index)\n }\n\n function revert (oldIndex) {\n index = oldIndex\n c = text.charAt(index)\n }\n\n function parseNumber () {\n let number = ''\n const oldIndex = index\n\n if (c === '+') {\n next()\n } else if (c === '-') {\n number += c\n next()\n }\n\n if (!isDigitDot(c)) {\n // a + or - must be followed by a digit\n revert(oldIndex)\n return null\n }\n\n // get number, can have a single dot\n if (c === '.') {\n number += c\n next()\n if (!isDigit(c)) {\n // this is no legal number, it is just a dot\n revert(oldIndex)\n return null\n }\n } else {\n while (isDigit(c)) {\n number += c\n next()\n }\n if (c === '.') {\n number += c\n next()\n }\n }\n while (isDigit(c)) {\n number += c\n next()\n }\n\n // check for exponential notation like \"2.3e-4\" or \"1.23e50\"\n if (c === 'E' || c === 'e') {\n // The grammar branches here. This could either be part of an exponent or the start of a unit that begins with the letter e, such as \"4exabytes\"\n\n let tentativeNumber = ''\n const tentativeIndex = index\n\n tentativeNumber += c\n next()\n\n if (c === '+' || c === '-') {\n tentativeNumber += c\n next()\n }\n\n // Scientific notation MUST be followed by an exponent (otherwise we assume it is not scientific notation)\n if (!isDigit(c)) {\n // The e or E must belong to something else, so return the number without the e or E.\n revert(tentativeIndex)\n return number\n }\n\n // We can now safely say that this is scientific notation.\n number = number + tentativeNumber\n while (isDigit(c)) {\n number += c\n next()\n }\n }\n\n return number\n }\n\n function parseUnit () {\n let unitName = ''\n\n // Alphanumeric characters only; matches [a-zA-Z0-9]\n while (isDigit(c) || Unit.isValidAlpha(c)) {\n unitName += c\n next()\n }\n\n // Must begin with [a-zA-Z]\n const firstC = unitName.charAt(0)\n if (Unit.isValidAlpha(firstC)) {\n return unitName\n } else {\n return null\n }\n }\n\n function parseCharacter (toFind) {\n if (c === toFind) {\n next()\n return toFind\n } else {\n return null\n }\n }\n\n /**\n * Parse a string into a unit. The value of the unit is parsed as number,\n * BigNumber, or Fraction depending on the math.js config setting `number`.\n *\n * Throws an exception if the provided string does not contain a valid unit or\n * cannot be parsed.\n * @memberof Unit\n * @param {string} str A string like \"5.2 inch\", \"4e2 cm/s^2\"\n * @return {Unit} unit\n */\n Unit.parse = function (str, options) {\n options = options || {}\n text = str\n index = -1\n c = ''\n\n if (typeof text !== 'string') {\n throw new TypeError('Invalid argument in Unit.parse, string expected')\n }\n\n const unit = new Unit()\n unit.units = []\n\n let powerMultiplierCurrent = 1\n let expectingUnit = false\n\n // A unit should follow this pattern:\n // [number] ...[ [*/] unit[^number] ]\n // unit[^number] ... [ [*/] unit[^number] ]\n\n // Rules:\n // number is any floating point number.\n // unit is any alphanumeric string beginning with an alpha. Units with names like e3 should be avoided because they look like the exponent of a floating point number!\n // The string may optionally begin with a number.\n // Each unit may optionally be followed by ^number.\n // Whitespace or a forward slash is recommended between consecutive units, although the following technically is parseable:\n // 2m^2kg/s^2\n // it is not good form. If a unit starts with e, then it could be confused as a floating point number:\n // 4erg\n\n next()\n skipWhitespace()\n\n // Optional number at the start of the string\n const valueStr = parseNumber()\n let value = null\n if (valueStr) {\n if (config.number === 'BigNumber') {\n value = new BigNumber(valueStr)\n } else if (config.number === 'Fraction') {\n try {\n // not all numbers can be turned in Fractions, for example very small numbers not\n value = new Fraction(valueStr)\n } catch (err) {\n value = parseFloat(valueStr)\n }\n } else { // number\n value = parseFloat(valueStr)\n }\n\n skipWhitespace() // Whitespace is not required here\n\n // handle multiplication or division right after the value, like '1/s'\n if (parseCharacter('*')) {\n powerMultiplierCurrent = 1\n expectingUnit = true\n } else if (parseCharacter('/')) {\n powerMultiplierCurrent = -1\n expectingUnit = true\n }\n }\n\n // Stack to keep track of powerMultipliers applied to each parentheses group\n const powerMultiplierStack = []\n\n // Running product of all elements in powerMultiplierStack\n let powerMultiplierStackProduct = 1\n\n while (true) {\n skipWhitespace()\n\n // Check for and consume opening parentheses, pushing powerMultiplierCurrent to the stack\n // A '(' will always appear directly before a unit.\n while (c === '(') {\n powerMultiplierStack.push(powerMultiplierCurrent)\n powerMultiplierStackProduct *= powerMultiplierCurrent\n powerMultiplierCurrent = 1\n next()\n skipWhitespace()\n }\n\n // Is there something here?\n let uStr\n if (c) {\n const oldC = c\n uStr = parseUnit()\n if (uStr === null) {\n throw new SyntaxError('Unexpected \"' + oldC + '\" in \"' + text + '\" at index ' + index.toString())\n }\n } else {\n // End of input.\n break\n }\n\n // Verify the unit exists and get the prefix (if any)\n const res = _findUnit(uStr)\n if (res === null) {\n // Unit not found.\n throw new SyntaxError('Unit \"' + uStr + '\" not found.')\n }\n\n let power = powerMultiplierCurrent * powerMultiplierStackProduct\n // Is there a \"^ number\"?\n skipWhitespace()\n if (parseCharacter('^')) {\n skipWhitespace()\n const p = parseNumber()\n if (p === null) {\n // No valid number found for the power!\n throw new SyntaxError('In \"' + str + '\", \"^\" must be followed by a floating-point number')\n }\n power *= p\n }\n\n // Add the unit to the list\n unit.units.push({\n unit: res.unit,\n prefix: res.prefix,\n power: power\n })\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n unit.dimensions[i] += (res.unit.dimensions[i] || 0) * power\n }\n\n // Check for and consume closing parentheses, popping from the stack.\n // A ')' will always follow a unit.\n skipWhitespace()\n while (c === ')') {\n if (powerMultiplierStack.length === 0) {\n throw new SyntaxError('Unmatched \")\" in \"' + text + '\" at index ' + index.toString())\n }\n powerMultiplierStackProduct /= powerMultiplierStack.pop()\n next()\n skipWhitespace()\n }\n\n // \"*\" and \"/\" should mean we are expecting something to come next.\n // Is there a forward slash? If so, negate powerMultiplierCurrent. The next unit or paren group is in the denominator.\n expectingUnit = false\n\n if (parseCharacter('*')) {\n // explicit multiplication\n powerMultiplierCurrent = 1\n expectingUnit = true\n } else if (parseCharacter('/')) {\n // division\n powerMultiplierCurrent = -1\n expectingUnit = true\n } else {\n // implicit multiplication\n powerMultiplierCurrent = 1\n }\n\n // Replace the unit into the auto unit system\n if (res.unit.base) {\n const baseDim = res.unit.base.key\n UNIT_SYSTEMS.auto[baseDim] = {\n unit: res.unit,\n prefix: res.prefix\n }\n }\n }\n\n // Has the string been entirely consumed?\n skipWhitespace()\n if (c) {\n throw new SyntaxError('Could not parse: \"' + str + '\"')\n }\n\n // Is there a trailing slash?\n if (expectingUnit) {\n throw new SyntaxError('Trailing characters: \"' + str + '\"')\n }\n\n // Is the parentheses stack empty?\n if (powerMultiplierStack.length !== 0) {\n throw new SyntaxError('Unmatched \"(\" in \"' + text + '\"')\n }\n\n // Are there any units at all?\n if (unit.units.length === 0 && !options.allowNoUnits) {\n throw new SyntaxError('\"' + str + '\" contains no units')\n }\n\n unit.value = (value !== undefined) ? unit._normalize(value) : null\n return unit\n }\n\n /**\n * create a copy of this unit\n * @memberof Unit\n * @return {Unit} Returns a cloned version of the unit\n */\n Unit.prototype.clone = function () {\n const unit = new Unit()\n\n unit.fixPrefix = this.fixPrefix\n unit.skipAutomaticSimplification = this.skipAutomaticSimplification\n\n unit.value = clone(this.value)\n unit.dimensions = this.dimensions.slice(0)\n unit.units = []\n for (let i = 0; i < this.units.length; i++) {\n unit.units[i] = { }\n for (const p in this.units[i]) {\n if (hasOwnProperty(this.units[i], p)) {\n unit.units[i][p] = this.units[i][p]\n }\n }\n }\n\n return unit\n }\n\n /**\n * Return whether the unit is derived (such as m/s, or cm^2, but not N)\n * @memberof Unit\n * @return {boolean} True if the unit is derived\n */\n Unit.prototype._isDerived = function () {\n if (this.units.length === 0) {\n return false\n }\n return this.units.length > 1 || Math.abs(this.units[0].power - 1.0) > 1e-15\n }\n\n /**\n * Normalize a value, based on its currently set unit(s)\n * @memberof Unit\n * @param {number | BigNumber | Fraction | boolean} value\n * @return {number | BigNumber | Fraction | boolean} normalized value\n * @private\n */\n Unit.prototype._normalize = function (value) {\n let unitValue, unitOffset, unitPower, unitPrefixValue\n let convert\n\n if (value === null || value === undefined || this.units.length === 0) {\n return value\n } else if (this._isDerived()) {\n // This is a derived unit, so do not apply offsets.\n // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.\n let res = value\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n for (let i = 0; i < this.units.length; i++) {\n unitValue = convert(this.units[i].unit.value)\n unitPrefixValue = convert(this.units[i].prefix.value)\n unitPower = convert(this.units[i].power)\n res = multiplyScalar(res, pow(multiplyScalar(unitValue, unitPrefixValue), unitPower))\n }\n\n return res\n } else {\n // This is a single unit of power 1, like kg or degC\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n unitValue = convert(this.units[0].unit.value)\n unitOffset = convert(this.units[0].unit.offset)\n unitPrefixValue = convert(this.units[0].prefix.value)\n\n return multiplyScalar(addScalar(value, unitOffset), multiplyScalar(unitValue, unitPrefixValue))\n }\n }\n\n /**\n * Denormalize a value, based on its currently set unit(s)\n * @memberof Unit\n * @param {number} value\n * @param {number} [prefixValue] Optional prefix value to be used (ignored if this is a derived unit)\n * @return {number} denormalized value\n * @private\n */\n Unit.prototype._denormalize = function (value, prefixValue) {\n let unitValue, unitOffset, unitPower, unitPrefixValue\n let convert\n\n if (value === null || value === undefined || this.units.length === 0) {\n return value\n } else if (this._isDerived()) {\n // This is a derived unit, so do not apply offsets.\n // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.\n // Also, prefixValue is ignored--but we will still use the prefix value stored in each unit, since kg is usually preferable to g unless the user decides otherwise.\n let res = value\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n for (let i = 0; i < this.units.length; i++) {\n unitValue = convert(this.units[i].unit.value)\n unitPrefixValue = convert(this.units[i].prefix.value)\n unitPower = convert(this.units[i].power)\n res = divideScalar(res, pow(multiplyScalar(unitValue, unitPrefixValue), unitPower))\n }\n\n return res\n } else {\n // This is a single unit of power 1, like kg or degC\n convert = Unit._getNumberConverter(typeOf(value)) // convert to Fraction or BigNumber if needed\n\n unitValue = convert(this.units[0].unit.value)\n unitPrefixValue = convert(this.units[0].prefix.value)\n unitOffset = convert(this.units[0].unit.offset)\n\n if (prefixValue === undefined || prefixValue === null) {\n return subtract(divideScalar(divideScalar(value, unitValue), unitPrefixValue), unitOffset)\n } else {\n return subtract(divideScalar(divideScalar(value, unitValue), prefixValue), unitOffset)\n }\n }\n }\n\n /**\n * Find a unit from a string\n * @memberof Unit\n * @param {string} str A string like 'cm' or 'inch'\n * @returns {Object | null} result When found, an object with fields unit and\n * prefix is returned. Else, null is returned.\n * @private\n */\n const _findUnit = memoize((str) => {\n // First, match units names exactly. For example, a user could define 'mm' as 10^-4 m, which is silly, but then we would want 'mm' to match the user-defined unit.\n if (hasOwnProperty(UNITS, str)) {\n const unit = UNITS[str]\n const prefix = unit.prefixes['']\n return {\n unit,\n prefix\n }\n }\n\n for (const name in UNITS) {\n if (hasOwnProperty(UNITS, name)) {\n if (endsWith(str, name)) {\n const unit = UNITS[name]\n const prefixLen = (str.length - name.length)\n const prefixName = str.substring(0, prefixLen)\n const prefix = hasOwnProperty(unit.prefixes, prefixName)\n ? unit.prefixes[prefixName]\n : undefined\n if (prefix !== undefined) {\n // store unit, prefix, and value\n return {\n unit,\n prefix\n }\n }\n }\n }\n }\n\n return null\n }, { hasher: (args) => args[0], limit: 100 })\n\n /**\n * Test if the given expression is a unit.\n * The unit can have a prefix but cannot have a value.\n * @memberof Unit\n * @param {string} name A string to be tested whether it is a value less unit.\n * The unit can have prefix, like \"cm\"\n * @return {boolean} true if the given string is a unit\n */\n Unit.isValuelessUnit = function (name) {\n return (_findUnit(name) !== null)\n }\n\n /**\n * check if this unit has given base unit\n * If this unit is a derived unit, this will ALWAYS return false, since by definition base units are not derived.\n * @memberof Unit\n * @param {BASE_UNITS | string | undefined} base\n */\n Unit.prototype.hasBase = function (base) {\n if (typeof (base) === 'string') {\n base = BASE_UNITS[base]\n }\n\n if (!base) { return false }\n\n // All dimensions must be the same\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n if (Math.abs((this.dimensions[i] || 0) - (base.dimensions[i] || 0)) > 1e-12) {\n return false\n }\n }\n return true\n }\n\n /**\n * Check if this unit has a base or bases equal to another base or bases\n * For derived units, the exponent on each base also must match\n * @memberof Unit\n * @param {Unit} other\n * @return {boolean} true if equal base\n */\n Unit.prototype.equalBase = function (other) {\n // All dimensions must be the same\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n if (Math.abs((this.dimensions[i] || 0) - (other.dimensions[i] || 0)) > 1e-12) {\n return false\n }\n }\n return true\n }\n\n /**\n * Check if this unit equals another unit\n * @memberof Unit\n * @param {Unit} other\n * @return {boolean} true if both units are equal\n */\n Unit.prototype.equals = function (other) {\n return (this.equalBase(other) && equal(this.value, other.value))\n }\n\n /**\n * Multiply this unit with another one\n * @memberof Unit\n * @param {Unit} other\n * @return {Unit} product of this unit and the other unit\n */\n Unit.prototype.multiply = function (other) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) + (other.dimensions[i] || 0)\n }\n\n // Append other's units list onto res\n for (let i = 0; i < other.units.length; i++) {\n // Make a shallow copy of every unit\n const inverted = {\n ...other.units[i]\n }\n res.units.push(inverted)\n }\n\n // If at least one operand has a value, then the result should also have a value\n if (this.value !== null || other.value !== null) {\n const valThis = this.value === null ? this._normalize(1) : this.value\n const valOther = other.value === null ? other._normalize(1) : other.value\n res.value = multiplyScalar(valThis, valOther)\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Divide this unit by another one\n * @memberof Unit\n * @param {Unit} other\n * @return {Unit} result of dividing this unit by the other unit\n */\n Unit.prototype.divide = function (other) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) - (other.dimensions[i] || 0)\n }\n\n // Invert and append other's units list onto res\n for (let i = 0; i < other.units.length; i++) {\n // Make a shallow copy of every unit\n const inverted = {\n ...other.units[i],\n power: -other.units[i].power\n }\n res.units.push(inverted)\n }\n\n // If at least one operand has a value, the result should have a value\n if (this.value !== null || other.value !== null) {\n const valThis = this.value === null ? this._normalize(1) : this.value\n const valOther = other.value === null ? other._normalize(1) : other.value\n res.value = divideScalar(valThis, valOther)\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Calculate the power of a unit\n * @memberof Unit\n * @param {number | Fraction | BigNumber} p\n * @returns {Unit} The result: this^p\n */\n Unit.prototype.pow = function (p) {\n const res = this.clone()\n\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n // Dimensions arrays may be of different lengths. Default to 0.\n res.dimensions[i] = (this.dimensions[i] || 0) * p\n }\n\n // Adjust the power of each unit in the list\n for (let i = 0; i < res.units.length; i++) {\n res.units[i].power *= p\n }\n\n if (res.value !== null) {\n res.value = pow(res.value, p)\n\n // only allow numeric output, we don't want to return a Complex number\n // if (!isNumeric(res.value)) {\n // res.value = NaN\n // }\n // Update: Complex supported now\n } else {\n res.value = null\n }\n\n res.skipAutomaticSimplification = false\n\n return getNumericIfUnitless(res)\n }\n\n /**\n * Return the numeric value of this unit if it is dimensionless, has a value, and config.predictable == false; or the original unit otherwise\n * @param {Unit} unit\n * @returns {number | Fraction | BigNumber | Unit} The numeric value of the unit if conditions are met, or the original unit otherwise\n */\n function getNumericIfUnitless (unit) {\n if (unit.equalBase(BASE_UNITS.NONE) && unit.value !== null && !config.predictable) {\n return unit.value\n } else {\n return unit\n }\n }\n\n /**\n * Calculate the absolute value of a unit\n * @memberof Unit\n * @param {number | Fraction | BigNumber} x\n * @returns {Unit} The result: |x|, absolute value of x\n */\n Unit.prototype.abs = function () {\n // This gives correct, but unexpected, results for units with an offset.\n // For example, abs(-283.15 degC) = -263.15 degC !!!\n const ret = this.clone()\n ret.value = ret.value !== null ? abs(ret.value) : null\n\n for (const i in ret.units) {\n if (ret.units[i].unit.name === 'VA' || ret.units[i].unit.name === 'VAR') {\n ret.units[i].unit = UNITS.W\n }\n }\n\n return ret\n }\n\n /**\n * Convert the unit to a specific unit name.\n * @memberof Unit\n * @param {string | Unit} valuelessUnit A unit without value. Can have prefix, like \"cm\"\n * @returns {Unit} Returns a clone of the unit with a fixed prefix and unit.\n */\n Unit.prototype.to = function (valuelessUnit) {\n let other\n const value = this.value === null ? this._normalize(1) : this.value\n if (typeof valuelessUnit === 'string') {\n // other = new Unit(null, valuelessUnit)\n other = Unit.parse(valuelessUnit)\n if (!this.equalBase(other)) {\n throw new Error(`Units do not match ('${other.toString()}' != '${this.toString()}')`)\n }\n if (other.value !== null) {\n throw new Error('Cannot convert to a unit with a value')\n }\n\n other.value = clone(value)\n other.fixPrefix = true\n other.skipAutomaticSimplification = true\n return other\n } else if (isUnit(valuelessUnit)) {\n if (!this.equalBase(valuelessUnit)) {\n throw new Error(`Units do not match ('${valuelessUnit.toString()}' != '${this.toString()}')`)\n }\n if (valuelessUnit.value !== null) {\n throw new Error('Cannot convert to a unit with a value')\n }\n other = valuelessUnit.clone()\n other.value = clone(value)\n other.fixPrefix = true\n other.skipAutomaticSimplification = true\n return other\n } else {\n throw new Error('String or Unit expected as parameter')\n }\n }\n\n /**\n * Return the value of the unit when represented with given valueless unit\n * @memberof Unit\n * @param {string | Unit} valuelessUnit For example 'cm' or 'inch'\n * @return {number} Returns the unit value as number.\n */\n // TODO: deprecate Unit.toNumber? It's always better to use toNumeric\n Unit.prototype.toNumber = function (valuelessUnit) {\n return toNumber(this.toNumeric(valuelessUnit))\n }\n\n /**\n * Return the value of the unit in the original numeric type\n * @memberof Unit\n * @param {string | Unit} valuelessUnit For example 'cm' or 'inch'\n * @return {number | BigNumber | Fraction} Returns the unit value\n */\n Unit.prototype.toNumeric = function (valuelessUnit) {\n let other\n if (valuelessUnit) {\n // Allow getting the numeric value without converting to a different unit\n other = this.to(valuelessUnit)\n } else {\n other = this.clone()\n }\n\n if (other._isDerived() || other.units.length === 0) {\n return other._denormalize(other.value)\n } else {\n return other._denormalize(other.value, other.units[0].prefix.value)\n }\n }\n\n /**\n * Get a string representation of the unit.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.toString = function () {\n return this.format()\n }\n\n /**\n * Get a JSON representation of the unit\n * @memberof Unit\n * @returns {Object} Returns a JSON object structured as:\n * `{\"mathjs\": \"Unit\", \"value\": 2, \"unit\": \"cm\", \"fixPrefix\": false}`\n */\n Unit.prototype.toJSON = function () {\n return {\n mathjs: 'Unit',\n value: this._denormalize(this.value),\n unit: this.formatUnits(),\n fixPrefix: this.fixPrefix\n }\n }\n\n /**\n * Instantiate a Unit from a JSON object\n * @memberof Unit\n * @param {Object} json A JSON object structured as:\n * `{\"mathjs\": \"Unit\", \"value\": 2, \"unit\": \"cm\", \"fixPrefix\": false}`\n * @return {Unit}\n */\n Unit.fromJSON = function (json) {\n const unit = new Unit(json.value, json.unit)\n unit.fixPrefix = json.fixPrefix || false\n return unit\n }\n\n /**\n * Returns the string representation of the unit.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.valueOf = Unit.prototype.toString\n\n /**\n * Simplify this Unit's unit list and return a new Unit with the simplified list.\n * The returned Unit will contain a list of the \"best\" units for formatting.\n */\n Unit.prototype.simplify = function () {\n const ret = this.clone()\n\n const proposedUnitList = []\n\n // Search for a matching base\n let matchingBase\n for (const key in currentUnitSystem) {\n if (hasOwnProperty(currentUnitSystem, key)) {\n if (ret.hasBase(BASE_UNITS[key])) {\n matchingBase = key\n break\n }\n }\n }\n\n if (matchingBase === 'NONE') {\n ret.units = []\n } else {\n let matchingUnit\n if (matchingBase) {\n // Does the unit system have a matching unit?\n if (hasOwnProperty(currentUnitSystem, matchingBase)) {\n matchingUnit = currentUnitSystem[matchingBase]\n }\n }\n if (matchingUnit) {\n ret.units = [{\n unit: matchingUnit.unit,\n prefix: matchingUnit.prefix,\n power: 1.0\n }]\n } else {\n // Multiple units or units with powers are formatted like this:\n // 5 (kg m^2) / (s^3 mol)\n // Build an representation from the base units of the current unit system\n let missingBaseDim = false\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n const baseDim = BASE_DIMENSIONS[i]\n if (Math.abs(ret.dimensions[i] || 0) > 1e-12) {\n if (hasOwnProperty(currentUnitSystem, baseDim)) {\n proposedUnitList.push({\n unit: currentUnitSystem[baseDim].unit,\n prefix: currentUnitSystem[baseDim].prefix,\n power: ret.dimensions[i] || 0\n })\n } else {\n missingBaseDim = true\n }\n }\n }\n\n // Is the proposed unit list \"simpler\" than the existing one?\n if (proposedUnitList.length < ret.units.length && !missingBaseDim) {\n // Replace this unit list with the proposed list\n ret.units = proposedUnitList\n }\n }\n }\n\n return ret\n }\n\n /**\n * Returns a new Unit in the SI system with the same value as this one\n */\n Unit.prototype.toSI = function () {\n const ret = this.clone()\n\n const proposedUnitList = []\n\n // Multiple units or units with powers are formatted like this:\n // 5 (kg m^2) / (s^3 mol)\n // Build an representation from the base units of the SI unit system\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n const baseDim = BASE_DIMENSIONS[i]\n if (Math.abs(ret.dimensions[i] || 0) > 1e-12) {\n if (hasOwnProperty(UNIT_SYSTEMS.si, baseDim)) {\n proposedUnitList.push({\n unit: UNIT_SYSTEMS.si[baseDim].unit,\n prefix: UNIT_SYSTEMS.si[baseDim].prefix,\n power: ret.dimensions[i] || 0\n })\n } else {\n throw new Error('Cannot express custom unit ' + baseDim + ' in SI units')\n }\n }\n }\n\n // Replace this unit list with the proposed list\n ret.units = proposedUnitList\n\n ret.fixPrefix = true\n ret.skipAutomaticSimplification = true\n\n return ret\n }\n\n /**\n * Get a string representation of the units of this Unit, without the value. The unit list is formatted as-is without first being simplified.\n * @memberof Unit\n * @return {string}\n */\n Unit.prototype.formatUnits = function () {\n let strNum = ''\n let strDen = ''\n let nNum = 0\n let nDen = 0\n\n for (let i = 0; i < this.units.length; i++) {\n if (this.units[i].power > 0) {\n nNum++\n strNum += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n if (Math.abs(this.units[i].power - 1.0) > 1e-15) {\n strNum += '^' + this.units[i].power\n }\n } else if (this.units[i].power < 0) {\n nDen++\n }\n }\n\n if (nDen > 0) {\n for (let i = 0; i < this.units.length; i++) {\n if (this.units[i].power < 0) {\n if (nNum > 0) {\n strDen += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n if (Math.abs(this.units[i].power + 1.0) > 1e-15) {\n strDen += '^' + (-this.units[i].power)\n }\n } else {\n strDen += ' ' + this.units[i].prefix.name + this.units[i].unit.name\n strDen += '^' + (this.units[i].power)\n }\n }\n }\n }\n // Remove leading \" \"\n strNum = strNum.substr(1)\n strDen = strDen.substr(1)\n\n // Add parans for better copy/paste back into evaluate, for example, or for better pretty print formatting\n if (nNum > 1 && nDen > 0) {\n strNum = '(' + strNum + ')'\n }\n if (nDen > 1 && nNum > 0) {\n strDen = '(' + strDen + ')'\n }\n\n let str = strNum\n if (nNum > 0 && nDen > 0) {\n str += ' / '\n }\n str += strDen\n\n return str\n }\n\n /**\n * Get a string representation of the Unit, with optional formatting options.\n * @memberof Unit\n * @param {Object | number | Function} [options] Formatting options. See\n * lib/utils/number:format for a\n * description of the available\n * options.\n * @return {string}\n */\n Unit.prototype.format = function (options) {\n // Simplfy the unit list, unless it is valueless or was created directly in the\n // constructor or as the result of to or toSI\n const simp = this.skipAutomaticSimplification || this.value === null\n ? this.clone()\n : this.simplify()\n\n // Apply some custom logic for handling VA and VAR. The goal is to express the value of the unit as a real value, if possible. Otherwise, use a real-valued unit instead of a complex-valued one.\n let isImaginary = false\n if (typeof (simp.value) !== 'undefined' && simp.value !== null && isComplex(simp.value)) {\n // TODO: Make this better, for example, use relative magnitude of re and im rather than absolute\n isImaginary = Math.abs(simp.value.re) < 1e-14\n }\n\n for (const i in simp.units) {\n if (hasOwnProperty(simp.units, i)) {\n if (simp.units[i].unit) {\n if (simp.units[i].unit.name === 'VA' && isImaginary) {\n simp.units[i].unit = UNITS.VAR\n } else if (simp.units[i].unit.name === 'VAR' && !isImaginary) {\n simp.units[i].unit = UNITS.VA\n }\n }\n }\n }\n\n // Now apply the best prefix\n // Units must have only one unit and not have the fixPrefix flag set\n if (simp.units.length === 1 && !simp.fixPrefix) {\n // Units must have integer powers, otherwise the prefix will change the\n // outputted value by not-an-integer-power-of-ten\n if (Math.abs(simp.units[0].power - Math.round(simp.units[0].power)) < 1e-14) {\n // Apply the best prefix\n simp.units[0].prefix = simp._bestPrefix()\n }\n }\n\n const value = simp._denormalize(simp.value)\n let str = (simp.value !== null) ? format(value, options || {}) : ''\n const unitStr = simp.formatUnits()\n if (simp.value && isComplex(simp.value)) {\n str = '(' + str + ')' // Surround complex values with ( ) to enable better parsing\n }\n if (unitStr.length > 0 && str.length > 0) {\n str += ' '\n }\n str += unitStr\n\n return str\n }\n\n /**\n * Calculate the best prefix using current value.\n * @memberof Unit\n * @returns {Object} prefix\n * @private\n */\n Unit.prototype._bestPrefix = function () {\n if (this.units.length !== 1) {\n throw new Error('Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!')\n }\n if (Math.abs(this.units[0].power - Math.round(this.units[0].power)) >= 1e-14) {\n throw new Error('Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!')\n }\n\n // find the best prefix value (resulting in the value of which\n // the absolute value of the log10 is closest to zero,\n // though with a little offset of 1.2 for nicer values: you get a\n // sequence 1mm 100mm 500mm 0.6m 1m 10m 100m 500m 0.6km 1km ...\n\n // Note: the units value can be any numeric type, but to find the best\n // prefix it's enough to work with limited precision of a regular number\n // Update: using mathjs abs since we also allow complex numbers\n const absValue = this.value !== null ? abs(this.value) : 0\n const absUnitValue = abs(this.units[0].unit.value)\n let bestPrefix = this.units[0].prefix\n if (absValue === 0) {\n return bestPrefix\n }\n const power = this.units[0].power\n let bestDiff = Math.log(absValue / Math.pow(bestPrefix.value * absUnitValue, power)) / Math.LN10 - 1.2\n if (bestDiff > -2.200001 && bestDiff < 1.800001) return bestPrefix // Allow the original prefix\n bestDiff = Math.abs(bestDiff)\n const prefixes = this.units[0].unit.prefixes\n for (const p in prefixes) {\n if (hasOwnProperty(prefixes, p)) {\n const prefix = prefixes[p]\n if (prefix.scientific) {\n const diff = Math.abs(\n Math.log(absValue / Math.pow(prefix.value * absUnitValue, power)) / Math.LN10 - 1.2)\n\n if (diff < bestDiff ||\n (diff === bestDiff && prefix.name.length < bestPrefix.name.length)) {\n // choose the prefix with the smallest diff, or if equal, choose the one\n // with the shortest name (can happen with SHORTLONG for example)\n bestPrefix = prefix\n bestDiff = diff\n }\n }\n }\n }\n\n return bestPrefix\n }\n\n /**\n * Returns an array of units whose sum is equal to this unit\n * @memberof Unit\n * @param {Array} [parts] An array of strings or valueless units.\n *\n * Example:\n *\n * const u = new Unit(1, 'm')\n * u.splitUnit(['feet', 'inch'])\n * [ 3 feet, 3.3700787401575 inch ]\n *\n * @return {Array} An array of units.\n */\n Unit.prototype.splitUnit = function (parts) {\n let x = this.clone()\n const ret = []\n for (let i = 0; i < parts.length; i++) {\n // Convert x to the requested unit\n x = x.to(parts[i])\n if (i === parts.length - 1) break\n\n // Get the numeric value of this unit\n const xNumeric = x.toNumeric()\n\n // Check to see if xNumeric is nearly equal to an integer,\n // since fix can incorrectly round down if there is round-off error\n const xRounded = round(xNumeric)\n let xFixed\n const isNearlyEqual = equal(xRounded, xNumeric)\n if (isNearlyEqual) {\n xFixed = xRounded\n } else {\n xFixed = fix(x.toNumeric())\n }\n\n const y = new Unit(xFixed, parts[i].toString())\n ret.push(y)\n x = subtract(x, y)\n }\n\n // This little bit fixes a bug where the remainder should be 0 but is a little bit off.\n // But instead of comparing x, the remainder, with zero--we will compare the sum of\n // all the parts so far with the original value. If they are nearly equal,\n // we set the remainder to 0.\n let testSum = 0\n for (let i = 0; i < ret.length; i++) {\n testSum = addScalar(testSum, ret[i].value)\n }\n if (equal(testSum, this.value)) {\n x.value = 0\n }\n\n ret.push(x)\n\n return ret\n }\n\n const PREFIXES = {\n NONE: {\n '': { name: '', value: 1, scientific: true }\n },\n SHORT: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e1, scientific: false },\n h: { name: 'h', value: 1e2, scientific: false },\n k: { name: 'k', value: 1e3, scientific: true },\n M: { name: 'M', value: 1e6, scientific: true },\n G: { name: 'G', value: 1e9, scientific: true },\n T: { name: 'T', value: 1e12, scientific: true },\n P: { name: 'P', value: 1e15, scientific: true },\n E: { name: 'E', value: 1e18, scientific: true },\n Z: { name: 'Z', value: 1e21, scientific: true },\n Y: { name: 'Y', value: 1e24, scientific: true },\n\n d: { name: 'd', value: 1e-1, scientific: false },\n c: { name: 'c', value: 1e-2, scientific: false },\n m: { name: 'm', value: 1e-3, scientific: true },\n u: { name: 'u', value: 1e-6, scientific: true },\n n: { name: 'n', value: 1e-9, scientific: true },\n p: { name: 'p', value: 1e-12, scientific: true },\n f: { name: 'f', value: 1e-15, scientific: true },\n a: { name: 'a', value: 1e-18, scientific: true },\n z: { name: 'z', value: 1e-21, scientific: true },\n y: { name: 'y', value: 1e-24, scientific: true }\n },\n LONG: {\n '': { name: '', value: 1, scientific: true },\n\n deca: { name: 'deca', value: 1e1, scientific: false },\n hecto: { name: 'hecto', value: 1e2, scientific: false },\n kilo: { name: 'kilo', value: 1e3, scientific: true },\n mega: { name: 'mega', value: 1e6, scientific: true },\n giga: { name: 'giga', value: 1e9, scientific: true },\n tera: { name: 'tera', value: 1e12, scientific: true },\n peta: { name: 'peta', value: 1e15, scientific: true },\n exa: { name: 'exa', value: 1e18, scientific: true },\n zetta: { name: 'zetta', value: 1e21, scientific: true },\n yotta: { name: 'yotta', value: 1e24, scientific: true },\n\n deci: { name: 'deci', value: 1e-1, scientific: false },\n centi: { name: 'centi', value: 1e-2, scientific: false },\n milli: { name: 'milli', value: 1e-3, scientific: true },\n micro: { name: 'micro', value: 1e-6, scientific: true },\n nano: { name: 'nano', value: 1e-9, scientific: true },\n pico: { name: 'pico', value: 1e-12, scientific: true },\n femto: { name: 'femto', value: 1e-15, scientific: true },\n atto: { name: 'atto', value: 1e-18, scientific: true },\n zepto: { name: 'zepto', value: 1e-21, scientific: true },\n yocto: { name: 'yocto', value: 1e-24, scientific: true }\n },\n SQUARED: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e2, scientific: false },\n h: { name: 'h', value: 1e4, scientific: false },\n k: { name: 'k', value: 1e6, scientific: true },\n M: { name: 'M', value: 1e12, scientific: true },\n G: { name: 'G', value: 1e18, scientific: true },\n T: { name: 'T', value: 1e24, scientific: true },\n P: { name: 'P', value: 1e30, scientific: true },\n E: { name: 'E', value: 1e36, scientific: true },\n Z: { name: 'Z', value: 1e42, scientific: true },\n Y: { name: 'Y', value: 1e48, scientific: true },\n\n d: { name: 'd', value: 1e-2, scientific: false },\n c: { name: 'c', value: 1e-4, scientific: false },\n m: { name: 'm', value: 1e-6, scientific: true },\n u: { name: 'u', value: 1e-12, scientific: true },\n n: { name: 'n', value: 1e-18, scientific: true },\n p: { name: 'p', value: 1e-24, scientific: true },\n f: { name: 'f', value: 1e-30, scientific: true },\n a: { name: 'a', value: 1e-36, scientific: true },\n z: { name: 'z', value: 1e-42, scientific: true },\n y: { name: 'y', value: 1e-48, scientific: true }\n },\n CUBIC: {\n '': { name: '', value: 1, scientific: true },\n\n da: { name: 'da', value: 1e3, scientific: false },\n h: { name: 'h', value: 1e6, scientific: false },\n k: { name: 'k', value: 1e9, scientific: true },\n M: { name: 'M', value: 1e18, scientific: true },\n G: { name: 'G', value: 1e27, scientific: true },\n T: { name: 'T', value: 1e36, scientific: true },\n P: { name: 'P', value: 1e45, scientific: true },\n E: { name: 'E', value: 1e54, scientific: true },\n Z: { name: 'Z', value: 1e63, scientific: true },\n Y: { name: 'Y', value: 1e72, scientific: true },\n\n d: { name: 'd', value: 1e-3, scientific: false },\n c: { name: 'c', value: 1e-6, scientific: false },\n m: { name: 'm', value: 1e-9, scientific: true },\n u: { name: 'u', value: 1e-18, scientific: true },\n n: { name: 'n', value: 1e-27, scientific: true },\n p: { name: 'p', value: 1e-36, scientific: true },\n f: { name: 'f', value: 1e-45, scientific: true },\n a: { name: 'a', value: 1e-54, scientific: true },\n z: { name: 'z', value: 1e-63, scientific: true },\n y: { name: 'y', value: 1e-72, scientific: true }\n },\n BINARY_SHORT_SI: {\n '': { name: '', value: 1, scientific: true },\n k: { name: 'k', value: 1e3, scientific: true },\n M: { name: 'M', value: 1e6, scientific: true },\n G: { name: 'G', value: 1e9, scientific: true },\n T: { name: 'T', value: 1e12, scientific: true },\n P: { name: 'P', value: 1e15, scientific: true },\n E: { name: 'E', value: 1e18, scientific: true },\n Z: { name: 'Z', value: 1e21, scientific: true },\n Y: { name: 'Y', value: 1e24, scientific: true }\n },\n BINARY_SHORT_IEC: {\n '': { name: '', value: 1, scientific: true },\n Ki: { name: 'Ki', value: 1024, scientific: true },\n Mi: { name: 'Mi', value: Math.pow(1024, 2), scientific: true },\n Gi: { name: 'Gi', value: Math.pow(1024, 3), scientific: true },\n Ti: { name: 'Ti', value: Math.pow(1024, 4), scientific: true },\n Pi: { name: 'Pi', value: Math.pow(1024, 5), scientific: true },\n Ei: { name: 'Ei', value: Math.pow(1024, 6), scientific: true },\n Zi: { name: 'Zi', value: Math.pow(1024, 7), scientific: true },\n Yi: { name: 'Yi', value: Math.pow(1024, 8), scientific: true }\n },\n BINARY_LONG_SI: {\n '': { name: '', value: 1, scientific: true },\n kilo: { name: 'kilo', value: 1e3, scientific: true },\n mega: { name: 'mega', value: 1e6, scientific: true },\n giga: { name: 'giga', value: 1e9, scientific: true },\n tera: { name: 'tera', value: 1e12, scientific: true },\n peta: { name: 'peta', value: 1e15, scientific: true },\n exa: { name: 'exa', value: 1e18, scientific: true },\n zetta: { name: 'zetta', value: 1e21, scientific: true },\n yotta: { name: 'yotta', value: 1e24, scientific: true }\n },\n BINARY_LONG_IEC: {\n '': { name: '', value: 1, scientific: true },\n kibi: { name: 'kibi', value: 1024, scientific: true },\n mebi: { name: 'mebi', value: Math.pow(1024, 2), scientific: true },\n gibi: { name: 'gibi', value: Math.pow(1024, 3), scientific: true },\n tebi: { name: 'tebi', value: Math.pow(1024, 4), scientific: true },\n pebi: { name: 'pebi', value: Math.pow(1024, 5), scientific: true },\n exi: { name: 'exi', value: Math.pow(1024, 6), scientific: true },\n zebi: { name: 'zebi', value: Math.pow(1024, 7), scientific: true },\n yobi: { name: 'yobi', value: Math.pow(1024, 8), scientific: true }\n },\n BTU: {\n '': { name: '', value: 1, scientific: true },\n MM: { name: 'MM', value: 1e6, scientific: true }\n }\n }\n\n PREFIXES.SHORTLONG = Object.assign({}, PREFIXES.SHORT, PREFIXES.LONG)\n PREFIXES.BINARY_SHORT = Object.assign({}, PREFIXES.BINARY_SHORT_SI, PREFIXES.BINARY_SHORT_IEC)\n PREFIXES.BINARY_LONG = Object.assign({}, PREFIXES.BINARY_LONG_SI, PREFIXES.BINARY_LONG_IEC)\n\n /* Internally, each unit is represented by a value and a dimension array. The elements of the dimensions array have the following meaning:\n * Index Dimension\n * ----- ---------\n * 0 Length\n * 1 Mass\n * 2 Time\n * 3 Current\n * 4 Temperature\n * 5 Luminous intensity\n * 6 Amount of substance\n * 7 Angle\n * 8 Bit (digital)\n * For example, the unit \"298.15 K\" is a pure temperature and would have a value of 298.15 and a dimension array of [0, 0, 0, 0, 1, 0, 0, 0, 0]. The unit \"1 cal / (gm °C)\" can be written in terms of the 9 fundamental dimensions as [length^2] / ([time^2] * [temperature]), and would a value of (after conversion to SI) 4184.0 and a dimensions array of [2, 0, -2, 0, -1, 0, 0, 0, 0].\n *\n */\n\n const BASE_DIMENSIONS = ['MASS', 'LENGTH', 'TIME', 'CURRENT', 'TEMPERATURE', 'LUMINOUS_INTENSITY', 'AMOUNT_OF_SUBSTANCE', 'ANGLE', 'BIT']\n\n const BASE_UNITS = {\n NONE: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 0]\n },\n MASS: {\n dimensions: [1, 0, 0, 0, 0, 0, 0, 0, 0]\n },\n LENGTH: {\n dimensions: [0, 1, 0, 0, 0, 0, 0, 0, 0]\n },\n TIME: {\n dimensions: [0, 0, 1, 0, 0, 0, 0, 0, 0]\n },\n CURRENT: {\n dimensions: [0, 0, 0, 1, 0, 0, 0, 0, 0]\n },\n TEMPERATURE: {\n dimensions: [0, 0, 0, 0, 1, 0, 0, 0, 0]\n },\n LUMINOUS_INTENSITY: {\n dimensions: [0, 0, 0, 0, 0, 1, 0, 0, 0]\n },\n AMOUNT_OF_SUBSTANCE: {\n dimensions: [0, 0, 0, 0, 0, 0, 1, 0, 0]\n },\n\n FORCE: {\n dimensions: [1, 1, -2, 0, 0, 0, 0, 0, 0]\n },\n SURFACE: {\n dimensions: [0, 2, 0, 0, 0, 0, 0, 0, 0]\n },\n VOLUME: {\n dimensions: [0, 3, 0, 0, 0, 0, 0, 0, 0]\n },\n ENERGY: {\n dimensions: [1, 2, -2, 0, 0, 0, 0, 0, 0]\n },\n POWER: {\n dimensions: [1, 2, -3, 0, 0, 0, 0, 0, 0]\n },\n PRESSURE: {\n dimensions: [1, -1, -2, 0, 0, 0, 0, 0, 0]\n },\n\n ELECTRIC_CHARGE: {\n dimensions: [0, 0, 1, 1, 0, 0, 0, 0, 0]\n },\n ELECTRIC_CAPACITANCE: {\n dimensions: [-1, -2, 4, 2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_POTENTIAL: {\n dimensions: [1, 2, -3, -1, 0, 0, 0, 0, 0]\n },\n ELECTRIC_RESISTANCE: {\n dimensions: [1, 2, -3, -2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_INDUCTANCE: {\n dimensions: [1, 2, -2, -2, 0, 0, 0, 0, 0]\n },\n ELECTRIC_CONDUCTANCE: {\n dimensions: [-1, -2, 3, 2, 0, 0, 0, 0, 0]\n },\n MAGNETIC_FLUX: {\n dimensions: [1, 2, -2, -1, 0, 0, 0, 0, 0]\n },\n MAGNETIC_FLUX_DENSITY: {\n dimensions: [1, 0, -2, -1, 0, 0, 0, 0, 0]\n },\n\n FREQUENCY: {\n dimensions: [0, 0, -1, 0, 0, 0, 0, 0, 0]\n },\n ANGLE: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 1, 0]\n },\n BIT: {\n dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 1]\n }\n }\n\n for (const key in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, key)) {\n BASE_UNITS[key].key = key\n }\n }\n\n const BASE_UNIT_NONE = {}\n\n const UNIT_NONE = { name: '', base: BASE_UNIT_NONE, value: 1, offset: 0, dimensions: BASE_DIMENSIONS.map(x => 0) }\n\n const UNITS = {\n // length\n meter: {\n name: 'meter',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n inch: {\n name: 'inch',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0254,\n offset: 0\n },\n foot: {\n name: 'foot',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.3048,\n offset: 0\n },\n yard: {\n name: 'yard',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.9144,\n offset: 0\n },\n mile: {\n name: 'mile',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1609.344,\n offset: 0\n },\n link: {\n name: 'link',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.201168,\n offset: 0\n },\n rod: {\n name: 'rod',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 5.0292,\n offset: 0\n },\n chain: {\n name: 'chain',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 20.1168,\n offset: 0\n },\n angstrom: {\n name: 'angstrom',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1e-10,\n offset: 0\n },\n\n m: {\n name: 'm',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n in: {\n name: 'in',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0254,\n offset: 0\n },\n ft: {\n name: 'ft',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.3048,\n offset: 0\n },\n yd: {\n name: 'yd',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.9144,\n offset: 0\n },\n mi: {\n name: 'mi',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 1609.344,\n offset: 0\n },\n li: {\n name: 'li',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.201168,\n offset: 0\n },\n rd: {\n name: 'rd',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 5.029210,\n offset: 0\n },\n ch: {\n name: 'ch',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 20.1168,\n offset: 0\n },\n mil: {\n name: 'mil',\n base: BASE_UNITS.LENGTH,\n prefixes: PREFIXES.NONE,\n value: 0.0000254,\n offset: 0\n }, // 1/1000 inch\n\n // Surface\n m2: {\n name: 'm2',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.SQUARED,\n value: 1,\n offset: 0\n },\n sqin: {\n name: 'sqin',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.00064516,\n offset: 0\n }, // 645.16 mm2\n sqft: {\n name: 'sqft',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.09290304,\n offset: 0\n }, // 0.09290304 m2\n sqyd: {\n name: 'sqyd',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 0.83612736,\n offset: 0\n }, // 0.83612736 m2\n sqmi: {\n name: 'sqmi',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 2589988.110336,\n offset: 0\n }, // 2.589988110336 km2\n sqrd: {\n name: 'sqrd',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 25.29295,\n offset: 0\n }, // 25.29295 m2\n sqch: {\n name: 'sqch',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 404.6873,\n offset: 0\n }, // 404.6873 m2\n sqmil: {\n name: 'sqmil',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 6.4516e-10,\n offset: 0\n }, // 6.4516 * 10^-10 m2\n acre: {\n name: 'acre',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 4046.86,\n offset: 0\n }, // 4046.86 m2\n hectare: {\n name: 'hectare',\n base: BASE_UNITS.SURFACE,\n prefixes: PREFIXES.NONE,\n value: 10000,\n offset: 0\n }, // 10000 m2\n\n // Volume\n m3: {\n name: 'm3',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.CUBIC,\n value: 1,\n offset: 0\n },\n L: {\n name: 'L',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n }, // litre\n l: {\n name: 'l',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n }, // litre\n litre: {\n name: 'litre',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.LONG,\n value: 0.001,\n offset: 0\n },\n cuin: {\n name: 'cuin',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 1.6387064e-5,\n offset: 0\n }, // 1.6387064e-5 m3\n cuft: {\n name: 'cuft',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.028316846592,\n offset: 0\n }, // 28.316 846 592 L\n cuyd: {\n name: 'cuyd',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.764554857984,\n offset: 0\n }, // 764.554 857 984 L\n teaspoon: {\n name: 'teaspoon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.000005,\n offset: 0\n }, // 5 mL\n tablespoon: {\n name: 'tablespoon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.000015,\n offset: 0\n }, // 15 mL\n // {name: 'cup', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000240, offset: 0}, // 240 mL // not possible, we have already another cup\n drop: {\n name: 'drop',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 5e-8,\n offset: 0\n }, // 0.05 mL = 5e-8 m3\n gtt: {\n name: 'gtt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 5e-8,\n offset: 0\n }, // 0.05 mL = 5e-8 m3\n\n // Liquid volume\n minim: {\n name: 'minim',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00000006161152,\n offset: 0\n }, // 0.06161152 mL\n fluiddram: {\n name: 'fluiddram',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0000036966911,\n offset: 0\n }, // 3.696691 mL\n fluidounce: {\n name: 'fluidounce',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00002957353,\n offset: 0\n }, // 29.57353 mL\n gill: {\n name: 'gill',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0001182941,\n offset: 0\n }, // 118.2941 mL\n cc: {\n name: 'cc',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 1e-6,\n offset: 0\n }, // 1e-6 L\n cup: {\n name: 'cup',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0002365882,\n offset: 0\n }, // 236.5882 mL\n pint: {\n name: 'pint',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0004731765,\n offset: 0\n }, // 473.1765 mL\n quart: {\n name: 'quart',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0009463529,\n offset: 0\n }, // 946.3529 mL\n gallon: {\n name: 'gallon',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.003785412,\n offset: 0\n }, // 3.785412 L\n beerbarrel: {\n name: 'beerbarrel',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1173478,\n offset: 0\n }, // 117.3478 L\n oilbarrel: {\n name: 'oilbarrel',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1589873,\n offset: 0\n }, // 158.9873 L\n hogshead: {\n name: 'hogshead',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.2384810,\n offset: 0\n }, // 238.4810 L\n\n // {name: 'min', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00000006161152, offset: 0}, // 0.06161152 mL // min is already in use as minute\n fldr: {\n name: 'fldr',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0000036966911,\n offset: 0\n }, // 3.696691 mL\n floz: {\n name: 'floz',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.00002957353,\n offset: 0\n }, // 29.57353 mL\n gi: {\n name: 'gi',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0001182941,\n offset: 0\n }, // 118.2941 mL\n cp: {\n name: 'cp',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0002365882,\n offset: 0\n }, // 236.5882 mL\n pt: {\n name: 'pt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0004731765,\n offset: 0\n }, // 473.1765 mL\n qt: {\n name: 'qt',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.0009463529,\n offset: 0\n }, // 946.3529 mL\n gal: {\n name: 'gal',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.003785412,\n offset: 0\n }, // 3.785412 L\n bbl: {\n name: 'bbl',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1173478,\n offset: 0\n }, // 117.3478 L\n obl: {\n name: 'obl',\n base: BASE_UNITS.VOLUME,\n prefixes: PREFIXES.NONE,\n value: 0.1589873,\n offset: 0\n }, // 158.9873 L\n // {name: 'hogshead', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.2384810, offset: 0}, // 238.4810 L // TODO: hh?\n\n // Mass\n g: {\n name: 'g',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 0.001,\n offset: 0\n },\n gram: {\n name: 'gram',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.LONG,\n value: 0.001,\n offset: 0\n },\n\n ton: {\n name: 'ton',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 907.18474,\n offset: 0\n },\n t: {\n name: 't',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.SHORT,\n value: 1000,\n offset: 0\n },\n tonne: {\n name: 'tonne',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.LONG,\n value: 1000,\n offset: 0\n },\n\n grain: {\n name: 'grain',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 64.79891e-6,\n offset: 0\n },\n dram: {\n name: 'dram',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 1.7718451953125e-3,\n offset: 0\n },\n ounce: {\n name: 'ounce',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 28.349523125e-3,\n offset: 0\n },\n poundmass: {\n name: 'poundmass',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 453.59237e-3,\n offset: 0\n },\n hundredweight: {\n name: 'hundredweight',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 45.359237,\n offset: 0\n },\n stick: {\n name: 'stick',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 115e-3,\n offset: 0\n },\n stone: {\n name: 'stone',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 6.35029318,\n offset: 0\n },\n\n gr: {\n name: 'gr',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 64.79891e-6,\n offset: 0\n },\n dr: {\n name: 'dr',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 1.7718451953125e-3,\n offset: 0\n },\n oz: {\n name: 'oz',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 28.349523125e-3,\n offset: 0\n },\n lbm: {\n name: 'lbm',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 453.59237e-3,\n offset: 0\n },\n cwt: {\n name: 'cwt',\n base: BASE_UNITS.MASS,\n prefixes: PREFIXES.NONE,\n value: 45.359237,\n offset: 0\n },\n\n // Time\n s: {\n name: 's',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n min: {\n name: 'min',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 60,\n offset: 0\n },\n h: {\n name: 'h',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3600,\n offset: 0\n },\n second: {\n name: 'second',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n sec: {\n name: 'sec',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n minute: {\n name: 'minute',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 60,\n offset: 0\n },\n hour: {\n name: 'hour',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3600,\n offset: 0\n },\n day: {\n name: 'day',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 86400,\n offset: 0\n },\n week: {\n name: 'week',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 7 * 86400,\n offset: 0\n },\n month: {\n name: 'month',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 2629800, // 1/12th of Julian year\n offset: 0\n },\n year: {\n name: 'year',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 31557600, // Julian year\n offset: 0\n },\n decade: {\n name: 'decade',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 315576000, // Julian decade\n offset: 0\n },\n century: {\n name: 'century',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 3155760000, // Julian century\n offset: 0\n },\n millennium: {\n name: 'millennium',\n base: BASE_UNITS.TIME,\n prefixes: PREFIXES.NONE,\n value: 31557600000, // Julian millennium\n offset: 0\n },\n\n // Frequency\n hertz: {\n name: 'Hertz',\n base: BASE_UNITS.FREQUENCY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0,\n reciprocal: true\n },\n Hz: {\n name: 'Hz',\n base: BASE_UNITS.FREQUENCY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0,\n reciprocal: true\n },\n\n // Angle\n rad: {\n name: 'rad',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n radian: {\n name: 'radian',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n // deg = rad / (2*pi) * 360 = rad / 0.017453292519943295769236907684888\n deg: {\n name: 'deg',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n degree: {\n name: 'degree',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // grad = rad / (2*pi) * 400 = rad / 0.015707963267948966192313216916399\n grad: {\n name: 'grad',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.SHORT,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n gradian: {\n name: 'gradian',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.LONG,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // cycle = rad / (2*pi) = rad / 6.2831853071795864769252867665793\n cycle: {\n name: 'cycle',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // arcsec = rad / (3600 * (360 / 2 * pi)) = rad / 0.0000048481368110953599358991410235795\n arcsec: {\n name: 'arcsec',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n // arcmin = rad / (60 * (360 / 2 * pi)) = rad / 0.00029088820866572159615394846141477\n arcmin: {\n name: 'arcmin',\n base: BASE_UNITS.ANGLE,\n prefixes: PREFIXES.NONE,\n value: null, // will be filled in by calculateAngleValues()\n offset: 0\n },\n\n // Electric current\n A: {\n name: 'A',\n base: BASE_UNITS.CURRENT,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n ampere: {\n name: 'ampere',\n base: BASE_UNITS.CURRENT,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n\n // Temperature\n // K(C) = °C + 273.15\n // K(F) = (°F + 459.67) / 1.8\n // K(R) = °R / 1.8\n K: {\n name: 'K',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 0\n },\n degC: {\n name: 'degC',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 273.15\n },\n degF: {\n name: 'degF',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 459.67\n },\n degR: {\n name: 'degR',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 0\n },\n kelvin: {\n name: 'kelvin',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 0\n },\n celsius: {\n name: 'celsius',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1,\n offset: 273.15\n },\n fahrenheit: {\n name: 'fahrenheit',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 459.67\n },\n rankine: {\n name: 'rankine',\n base: BASE_UNITS.TEMPERATURE,\n prefixes: PREFIXES.NONE,\n value: 1 / 1.8,\n offset: 0\n },\n\n // amount of substance\n mol: {\n name: 'mol',\n base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n mole: {\n name: 'mole',\n base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n\n // luminous intensity\n cd: {\n name: 'cd',\n base: BASE_UNITS.LUMINOUS_INTENSITY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n candela: {\n name: 'candela',\n base: BASE_UNITS.LUMINOUS_INTENSITY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n // TODO: units STERADIAN\n // {name: 'sr', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},\n // {name: 'steradian', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},\n\n // Force\n N: {\n name: 'N',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n newton: {\n name: 'newton',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n dyn: {\n name: 'dyn',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.SHORT,\n value: 0.00001,\n offset: 0\n },\n dyne: {\n name: 'dyne',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 0.00001,\n offset: 0\n },\n lbf: {\n name: 'lbf',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 4.4482216152605,\n offset: 0\n },\n poundforce: {\n name: 'poundforce',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 4.4482216152605,\n offset: 0\n },\n kip: {\n name: 'kip',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.LONG,\n value: 4448.2216,\n offset: 0\n },\n kilogramforce: {\n name: 'kilogramforce',\n base: BASE_UNITS.FORCE,\n prefixes: PREFIXES.NONE,\n value: 9.80665,\n offset: 0\n },\n\n // Energy\n J: {\n name: 'J',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n joule: {\n name: 'joule',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n erg: {\n name: 'erg',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.NONE,\n value: 1e-7,\n offset: 0\n },\n Wh: {\n name: 'Wh',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 3600,\n offset: 0\n },\n BTU: {\n name: 'BTU',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.BTU,\n value: 1055.05585262,\n offset: 0\n },\n eV: {\n name: 'eV',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.SHORT,\n value: 1.602176565e-19,\n offset: 0\n },\n electronvolt: {\n name: 'electronvolt',\n base: BASE_UNITS.ENERGY,\n prefixes: PREFIXES.LONG,\n value: 1.602176565e-19,\n offset: 0\n },\n\n // Power\n W: {\n name: 'W',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n watt: {\n name: 'watt',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n hp: {\n name: 'hp',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.NONE,\n value: 745.6998715386,\n offset: 0\n },\n\n // Electrical power units\n VAR: {\n name: 'VAR',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: Complex.I,\n offset: 0\n },\n\n VA: {\n name: 'VA',\n base: BASE_UNITS.POWER,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n\n // Pressure\n Pa: {\n name: 'Pa',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n psi: {\n name: 'psi',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 6894.75729276459,\n offset: 0\n },\n atm: {\n name: 'atm',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 101325,\n offset: 0\n },\n bar: {\n name: 'bar',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.SHORTLONG,\n value: 100000,\n offset: 0\n },\n torr: {\n name: 'torr',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 133.322,\n offset: 0\n },\n mmHg: {\n name: 'mmHg',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 133.322,\n offset: 0\n },\n mmH2O: {\n name: 'mmH2O',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 9.80665,\n offset: 0\n },\n cmH2O: {\n name: 'cmH2O',\n base: BASE_UNITS.PRESSURE,\n prefixes: PREFIXES.NONE,\n value: 98.0665,\n offset: 0\n },\n\n // Electric charge\n coulomb: {\n name: 'coulomb',\n base: BASE_UNITS.ELECTRIC_CHARGE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n C: {\n name: 'C',\n base: BASE_UNITS.ELECTRIC_CHARGE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric capacitance\n farad: {\n name: 'farad',\n base: BASE_UNITS.ELECTRIC_CAPACITANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n F: {\n name: 'F',\n base: BASE_UNITS.ELECTRIC_CAPACITANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric potential\n volt: {\n name: 'volt',\n base: BASE_UNITS.ELECTRIC_POTENTIAL,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n V: {\n name: 'V',\n base: BASE_UNITS.ELECTRIC_POTENTIAL,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric resistance\n ohm: {\n name: 'ohm',\n base: BASE_UNITS.ELECTRIC_RESISTANCE,\n prefixes: PREFIXES.SHORTLONG, // Both Mohm and megaohm are acceptable\n value: 1,\n offset: 0\n },\n /*\n * Unicode breaks in browsers if charset is not specified\n Ω: {\n name: 'Ω',\n base: BASE_UNITS.ELECTRIC_RESISTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n */\n // Electric inductance\n henry: {\n name: 'henry',\n base: BASE_UNITS.ELECTRIC_INDUCTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n H: {\n name: 'H',\n base: BASE_UNITS.ELECTRIC_INDUCTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Electric conductance\n siemens: {\n name: 'siemens',\n base: BASE_UNITS.ELECTRIC_CONDUCTANCE,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n S: {\n name: 'S',\n base: BASE_UNITS.ELECTRIC_CONDUCTANCE,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Magnetic flux\n weber: {\n name: 'weber',\n base: BASE_UNITS.MAGNETIC_FLUX,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n Wb: {\n name: 'Wb',\n base: BASE_UNITS.MAGNETIC_FLUX,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n // Magnetic flux density\n tesla: {\n name: 'tesla',\n base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,\n prefixes: PREFIXES.LONG,\n value: 1,\n offset: 0\n },\n T: {\n name: 'T',\n base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,\n prefixes: PREFIXES.SHORT,\n value: 1,\n offset: 0\n },\n\n // Binary\n b: {\n name: 'b',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_SHORT,\n value: 1,\n offset: 0\n },\n bits: {\n name: 'bits',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_LONG,\n value: 1,\n offset: 0\n },\n B: {\n name: 'B',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_SHORT,\n value: 8,\n offset: 0\n },\n bytes: {\n name: 'bytes',\n base: BASE_UNITS.BIT,\n prefixes: PREFIXES.BINARY_LONG,\n value: 8,\n offset: 0\n }\n }\n\n // aliases (formerly plurals)\n const ALIASES = {\n meters: 'meter',\n inches: 'inch',\n feet: 'foot',\n yards: 'yard',\n miles: 'mile',\n links: 'link',\n rods: 'rod',\n chains: 'chain',\n angstroms: 'angstrom',\n\n lt: 'l',\n litres: 'litre',\n liter: 'litre',\n liters: 'litre',\n teaspoons: 'teaspoon',\n tablespoons: 'tablespoon',\n minims: 'minim',\n fluiddrams: 'fluiddram',\n fluidounces: 'fluidounce',\n gills: 'gill',\n cups: 'cup',\n pints: 'pint',\n quarts: 'quart',\n gallons: 'gallon',\n beerbarrels: 'beerbarrel',\n oilbarrels: 'oilbarrel',\n hogsheads: 'hogshead',\n gtts: 'gtt',\n\n grams: 'gram',\n tons: 'ton',\n tonnes: 'tonne',\n grains: 'grain',\n drams: 'dram',\n ounces: 'ounce',\n poundmasses: 'poundmass',\n hundredweights: 'hundredweight',\n sticks: 'stick',\n lb: 'lbm',\n lbs: 'lbm',\n\n kips: 'kip',\n kgf: 'kilogramforce',\n\n acres: 'acre',\n hectares: 'hectare',\n sqfeet: 'sqft',\n sqyard: 'sqyd',\n sqmile: 'sqmi',\n sqmiles: 'sqmi',\n\n mmhg: 'mmHg',\n mmh2o: 'mmH2O',\n cmh2o: 'cmH2O',\n\n seconds: 'second',\n secs: 'second',\n minutes: 'minute',\n mins: 'minute',\n hours: 'hour',\n hr: 'hour',\n hrs: 'hour',\n days: 'day',\n weeks: 'week',\n months: 'month',\n years: 'year',\n decades: 'decade',\n centuries: 'century',\n millennia: 'millennium',\n\n hertz: 'hertz',\n\n radians: 'radian',\n degrees: 'degree',\n gradians: 'gradian',\n cycles: 'cycle',\n arcsecond: 'arcsec',\n arcseconds: 'arcsec',\n arcminute: 'arcmin',\n arcminutes: 'arcmin',\n\n BTUs: 'BTU',\n watts: 'watt',\n joules: 'joule',\n\n amperes: 'ampere',\n coulombs: 'coulomb',\n volts: 'volt',\n ohms: 'ohm',\n farads: 'farad',\n webers: 'weber',\n teslas: 'tesla',\n electronvolts: 'electronvolt',\n moles: 'mole',\n\n bit: 'bits',\n byte: 'bytes'\n }\n\n /**\n * Calculate the values for the angle units.\n * Value is calculated as number or BigNumber depending on the configuration\n * @param {{number: 'number' | 'BigNumber'}} config\n */\n function calculateAngleValues (config) {\n if (config.number === 'BigNumber') {\n const pi = createPi(BigNumber)\n UNITS.rad.value = new BigNumber(1)\n UNITS.deg.value = pi.div(180) // 2 * pi / 360\n UNITS.grad.value = pi.div(200) // 2 * pi / 400\n UNITS.cycle.value = pi.times(2) // 2 * pi\n UNITS.arcsec.value = pi.div(648000) // 2 * pi / 360 / 3600\n UNITS.arcmin.value = pi.div(10800) // 2 * pi / 360 / 60\n } else { // number\n UNITS.rad.value = 1\n UNITS.deg.value = Math.PI / 180 // 2 * pi / 360\n UNITS.grad.value = Math.PI / 200 // 2 * pi / 400\n UNITS.cycle.value = Math.PI * 2 // 2 * pi\n UNITS.arcsec.value = Math.PI / 648000 // 2 * pi / 360 / 3600\n UNITS.arcmin.value = Math.PI / 10800 // 2 * pi / 360 / 60\n }\n\n // copy to the full names of the angles\n UNITS.radian.value = UNITS.rad.value\n UNITS.degree.value = UNITS.deg.value\n UNITS.gradian.value = UNITS.grad.value\n }\n\n // apply the angle values now\n calculateAngleValues(config)\n\n if (on) {\n // recalculate the values on change of configuration\n on('config', function (curr, prev) {\n if (curr.number !== prev.number) {\n calculateAngleValues(curr)\n }\n })\n }\n\n /**\n * A unit system is a set of dimensionally independent base units plus a set of derived units, formed by multiplication and division of the base units, that are by convention used with the unit system.\n * A user perhaps could issue a command to select a preferred unit system, or use the default (see below).\n * Auto unit system: The default unit system is updated on the fly anytime a unit is parsed. The corresponding unit in the default unit system is updated, so that answers are given in the same units the user supplies.\n */\n const UNIT_SYSTEMS = {\n si: {\n // Base units\n NONE: { unit: UNIT_NONE, prefix: PREFIXES.NONE[''] },\n LENGTH: { unit: UNITS.m, prefix: PREFIXES.SHORT[''] },\n MASS: { unit: UNITS.g, prefix: PREFIXES.SHORT.k },\n TIME: { unit: UNITS.s, prefix: PREFIXES.SHORT[''] },\n CURRENT: { unit: UNITS.A, prefix: PREFIXES.SHORT[''] },\n TEMPERATURE: { unit: UNITS.K, prefix: PREFIXES.SHORT[''] },\n LUMINOUS_INTENSITY: { unit: UNITS.cd, prefix: PREFIXES.SHORT[''] },\n AMOUNT_OF_SUBSTANCE: { unit: UNITS.mol, prefix: PREFIXES.SHORT[''] },\n ANGLE: { unit: UNITS.rad, prefix: PREFIXES.SHORT[''] },\n BIT: { unit: UNITS.bits, prefix: PREFIXES.SHORT[''] },\n\n // Derived units\n FORCE: { unit: UNITS.N, prefix: PREFIXES.SHORT[''] },\n ENERGY: { unit: UNITS.J, prefix: PREFIXES.SHORT[''] },\n POWER: { unit: UNITS.W, prefix: PREFIXES.SHORT[''] },\n PRESSURE: { unit: UNITS.Pa, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CHARGE: { unit: UNITS.C, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CAPACITANCE: { unit: UNITS.F, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_POTENTIAL: { unit: UNITS.V, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_RESISTANCE: { unit: UNITS.ohm, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_INDUCTANCE: { unit: UNITS.H, prefix: PREFIXES.SHORT[''] },\n ELECTRIC_CONDUCTANCE: { unit: UNITS.S, prefix: PREFIXES.SHORT[''] },\n MAGNETIC_FLUX: { unit: UNITS.Wb, prefix: PREFIXES.SHORT[''] },\n MAGNETIC_FLUX_DENSITY: { unit: UNITS.T, prefix: PREFIXES.SHORT[''] },\n FREQUENCY: { unit: UNITS.Hz, prefix: PREFIXES.SHORT[''] }\n }\n }\n\n // Clone to create the other unit systems\n UNIT_SYSTEMS.cgs = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n UNIT_SYSTEMS.cgs.LENGTH = { unit: UNITS.m, prefix: PREFIXES.SHORT.c }\n UNIT_SYSTEMS.cgs.MASS = { unit: UNITS.g, prefix: PREFIXES.SHORT[''] }\n UNIT_SYSTEMS.cgs.FORCE = { unit: UNITS.dyn, prefix: PREFIXES.SHORT[''] }\n UNIT_SYSTEMS.cgs.ENERGY = { unit: UNITS.erg, prefix: PREFIXES.NONE[''] }\n // there are wholly 4 unique cgs systems for electricity and magnetism,\n // so let's not worry about it unless somebody complains\n\n UNIT_SYSTEMS.us = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n UNIT_SYSTEMS.us.LENGTH = { unit: UNITS.ft, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.MASS = { unit: UNITS.lbm, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.TEMPERATURE = { unit: UNITS.degF, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.FORCE = { unit: UNITS.lbf, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.ENERGY = { unit: UNITS.BTU, prefix: PREFIXES.BTU[''] }\n UNIT_SYSTEMS.us.POWER = { unit: UNITS.hp, prefix: PREFIXES.NONE[''] }\n UNIT_SYSTEMS.us.PRESSURE = { unit: UNITS.psi, prefix: PREFIXES.NONE[''] }\n\n // Add additional unit systems here.\n\n // Choose a unit system to seed the auto unit system.\n UNIT_SYSTEMS.auto = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si))\n\n // Set the current unit system\n let currentUnitSystem = UNIT_SYSTEMS.auto\n\n /**\n * Set a unit system for formatting derived units.\n * @param {string} [name] The name of the unit system.\n */\n Unit.setUnitSystem = function (name) {\n if (hasOwnProperty(UNIT_SYSTEMS, name)) {\n currentUnitSystem = UNIT_SYSTEMS[name]\n } else {\n throw new Error('Unit system ' + name + ' does not exist. Choices are: ' + Object.keys(UNIT_SYSTEMS).join(', '))\n }\n }\n\n /**\n * Return the current unit system.\n * @return {string} The current unit system.\n */\n Unit.getUnitSystem = function () {\n for (const key in UNIT_SYSTEMS) {\n if (hasOwnProperty(UNIT_SYSTEMS, key)) {\n if (UNIT_SYSTEMS[key] === currentUnitSystem) {\n return key\n }\n }\n }\n }\n\n /**\n * Converters to convert from number to an other numeric type like BigNumber\n * or Fraction\n */\n Unit.typeConverters = {\n BigNumber: function (x) {\n return new BigNumber(x + '') // stringify to prevent constructor error\n },\n\n Fraction: function (x) {\n return new Fraction(x)\n },\n\n Complex: function (x) {\n return x\n },\n\n number: function (x) {\n return x\n }\n }\n\n /**\n * Retrieve the right convertor function corresponding with the type\n * of provided exampleValue.\n *\n * @param {string} type A string 'number', 'BigNumber', or 'Fraction'\n * In case of an unknown type,\n * @return {Function}\n */\n Unit._getNumberConverter = function (type) {\n if (!Unit.typeConverters[type]) {\n throw new TypeError('Unsupported type \"' + type + '\"')\n }\n\n return Unit.typeConverters[type]\n }\n\n // Add dimensions to each built-in unit\n for (const key in UNITS) {\n if (hasOwnProperty(UNITS, key)) {\n const unit = UNITS[key]\n unit.dimensions = unit.base.dimensions\n }\n }\n\n // Create aliases\n for (const name in ALIASES) {\n if (hasOwnProperty(ALIASES, name)) {\n const unit = UNITS[ALIASES[name]]\n const alias = {}\n for (const key in unit) {\n if (hasOwnProperty(unit, key)) {\n alias[key] = unit[key]\n }\n }\n alias.name = name\n UNITS[name] = alias\n }\n }\n\n /**\n * Checks if a character is a valid latin letter (upper or lower case).\n * Note that this function can be overridden, for example to allow support of other alphabets.\n * @param {string} c Tested character\n */\n Unit.isValidAlpha = function isValidAlpha (c) {\n return /^[a-zA-Z]$/.test(c)\n }\n\n function assertUnitNameIsValid (name) {\n for (let i = 0; i < name.length; i++) {\n c = name.charAt(i)\n\n if (i === 0 && !Unit.isValidAlpha(c)) { throw new Error('Invalid unit name (must begin with alpha character): \"' + name + '\"') }\n\n if (i > 0 && !(Unit.isValidAlpha(c) ||\n isDigit(c))) { throw new Error('Invalid unit name (only alphanumeric characters are allowed): \"' + name + '\"') }\n }\n }\n\n /**\n * Wrapper around createUnitSingle.\n * Example:\n * createUnit({\n * foo: { },\n * bar: {\n * definition: 'kg/foo',\n * aliases: ['ba', 'barr', 'bars'],\n * offset: 200\n * },\n * baz: '4 bar'\n * },\n * {\n * override: true\n * })\n * @param {object} obj Object map. Each key becomes a unit which is defined by its value.\n * @param {object} options\n */\n Unit.createUnit = function (obj, options) {\n if (typeof (obj) !== 'object') {\n throw new TypeError(\"createUnit expects first parameter to be of type 'Object'\")\n }\n\n // Remove all units and aliases we are overriding\n if (options && options.override) {\n for (const key in obj) {\n if (hasOwnProperty(obj, key)) {\n Unit.deleteUnit(key)\n }\n if (obj[key].aliases) {\n for (let i = 0; i < obj[key].aliases.length; i++) {\n Unit.deleteUnit(obj[key].aliases[i])\n }\n }\n }\n }\n\n // TODO: traverse multiple times until all units have been added\n let lastUnit\n for (const key in obj) {\n if (hasOwnProperty(obj, key)) {\n lastUnit = Unit.createUnitSingle(key, obj[key])\n }\n }\n return lastUnit\n }\n\n /**\n * Create a user-defined unit and register it with the Unit type.\n * Example:\n * createUnitSingle('knot', '0.514444444 m/s')\n * createUnitSingle('acre', new Unit(43560, 'ft^2'))\n *\n * @param {string} name The name of the new unit. Must be unique. Example: 'knot'\n * @param {string, Unit, Object} definition Definition of the unit in terms\n * of existing units. For example, '0.514444444 m / s'. Can be a Unit, a string,\n * or an Object. If an Object, may have the following properties:\n * - definition {string|Unit} The definition of this unit.\n * - prefixes {string} \"none\", \"short\", \"long\", \"binary_short\", or \"binary_long\".\n * The default is \"none\".\n * - aliases {Array} Array of strings. Example: ['knots', 'kt', 'kts']\n * - offset {Numeric} An offset to apply when converting from the unit. For\n * example, the offset for celsius is 273.15 and the offset for farhenheit\n * is 459.67. Default is 0.\n * - baseName {string} If the unit's dimension does not match that of any other\n * base unit, the name of the newly create base unit. Otherwise, this property\n * has no effect.\n *\n * @param {Object} options (optional) An object containing any of the following\n * properties:\n * - override {boolean} Whether this unit should be allowed to override existing\n * units.\n *\n * @return {Unit}\n */\n Unit.createUnitSingle = function (name, obj, options) {\n if (typeof (obj) === 'undefined' || obj === null) {\n obj = {}\n }\n\n if (typeof (name) !== 'string') {\n throw new TypeError(\"createUnitSingle expects first parameter to be of type 'string'\")\n }\n\n // Check collisions with existing units\n if (hasOwnProperty(UNITS, name)) {\n throw new Error('Cannot create unit \"' + name + '\": a unit with that name already exists')\n }\n\n // TODO: Validate name for collisions with other built-in functions (like abs or cos, for example), and for acceptable variable names. For example, '42' is probably not a valid unit. Nor is '%', since it is also an operator.\n\n assertUnitNameIsValid(name)\n\n let defUnit = null // The Unit from which the new unit will be created.\n let aliases = []\n let offset = 0\n let definition\n let prefixes\n let baseName\n if (obj && obj.type === 'Unit') {\n defUnit = obj.clone()\n } else if (typeof (obj) === 'string') {\n if (obj !== '') {\n definition = obj\n }\n } else if (typeof (obj) === 'object') {\n definition = obj.definition\n prefixes = obj.prefixes\n offset = obj.offset\n baseName = obj.baseName\n if (obj.aliases) {\n aliases = obj.aliases.valueOf() // aliases could be a Matrix, so convert to Array\n }\n } else {\n throw new TypeError('Cannot create unit \"' + name + '\" from \"' + obj.toString() + '\": expecting \"string\" or \"Unit\" or \"Object\"')\n }\n\n if (aliases) {\n for (let i = 0; i < aliases.length; i++) {\n if (hasOwnProperty(UNITS, aliases[i])) {\n throw new Error('Cannot create alias \"' + aliases[i] + '\": a unit with that name already exists')\n }\n }\n }\n\n if (definition && typeof (definition) === 'string' && !defUnit) {\n try {\n defUnit = Unit.parse(definition, { allowNoUnits: true })\n } catch (ex) {\n ex.message = 'Could not create unit \"' + name + '\" from \"' + definition + '\": ' + ex.message\n throw (ex)\n }\n } else if (definition && definition.type === 'Unit') {\n defUnit = definition.clone()\n }\n\n aliases = aliases || []\n offset = offset || 0\n if (prefixes && prefixes.toUpperCase) { prefixes = PREFIXES[prefixes.toUpperCase()] || PREFIXES.NONE } else { prefixes = PREFIXES.NONE }\n\n // If defUnit is null, it is because the user did not\n // specify a defintion. So create a new base dimension.\n let newUnit = {}\n if (!defUnit) {\n // Add a new base dimension\n baseName = baseName || name + '_STUFF' // foo --> foo_STUFF, or the essence of foo\n if (BASE_DIMENSIONS.indexOf(baseName) >= 0) {\n throw new Error('Cannot create new base unit \"' + name + '\": a base unit with that name already exists (and cannot be overridden)')\n }\n BASE_DIMENSIONS.push(baseName)\n\n // Push 0 onto existing base units\n for (const b in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, b)) {\n BASE_UNITS[b].dimensions[BASE_DIMENSIONS.length - 1] = 0\n }\n }\n\n // Add the new base unit\n const newBaseUnit = { dimensions: [] }\n for (let i = 0; i < BASE_DIMENSIONS.length; i++) {\n newBaseUnit.dimensions[i] = 0\n }\n newBaseUnit.dimensions[BASE_DIMENSIONS.length - 1] = 1\n newBaseUnit.key = baseName\n BASE_UNITS[baseName] = newBaseUnit\n\n newUnit = {\n name: name,\n value: 1,\n dimensions: BASE_UNITS[baseName].dimensions.slice(0),\n prefixes: prefixes,\n offset: offset,\n base: BASE_UNITS[baseName]\n }\n\n currentUnitSystem[baseName] = {\n unit: newUnit,\n prefix: PREFIXES.NONE['']\n }\n } else {\n newUnit = {\n name: name,\n value: defUnit.value,\n dimensions: defUnit.dimensions.slice(0),\n prefixes: prefixes,\n offset: offset\n }\n\n // Create a new base if no matching base exists\n let anyMatch = false\n for (const i in BASE_UNITS) {\n if (hasOwnProperty(BASE_UNITS, i)) {\n let match = true\n for (let j = 0; j < BASE_DIMENSIONS.length; j++) {\n if (Math.abs((newUnit.dimensions[j] || 0) - (BASE_UNITS[i].dimensions[j] || 0)) > 1e-12) {\n match = false\n break\n }\n }\n if (match) {\n anyMatch = true\n newUnit.base = BASE_UNITS[i]\n break\n }\n }\n }\n if (!anyMatch) {\n baseName = baseName || name + '_STUFF' // foo --> foo_STUFF, or the essence of foo\n // Add the new base unit\n const newBaseUnit = { dimensions: defUnit.dimensions.slice(0) }\n newBaseUnit.key = baseName\n BASE_UNITS[baseName] = newBaseUnit\n\n currentUnitSystem[baseName] = {\n unit: newUnit,\n prefix: PREFIXES.NONE['']\n }\n\n newUnit.base = BASE_UNITS[baseName]\n }\n }\n\n Unit.UNITS[name] = newUnit\n\n for (let i = 0; i < aliases.length; i++) {\n const aliasName = aliases[i]\n const alias = {}\n for (const key in newUnit) {\n if (hasOwnProperty(newUnit, key)) {\n alias[key] = newUnit[key]\n }\n }\n alias.name = aliasName\n Unit.UNITS[aliasName] = alias\n }\n // delete the memoization cache, since adding a new unit to the array\n // invalidates all old results\n delete _findUnit.cache\n\n return new Unit(null, name)\n }\n\n Unit.deleteUnit = function (name) {\n delete Unit.UNITS[name]\n }\n\n // expose arrays with prefixes, dimensions, units, systems\n Unit.PREFIXES = PREFIXES\n Unit.BASE_DIMENSIONS = BASE_DIMENSIONS\n Unit.BASE_UNITS = BASE_UNITS\n Unit.UNIT_SYSTEMS = UNIT_SYSTEMS\n Unit.UNITS = UNITS\n\n return Unit\n}, { isClass: true })\n","import { factory } from '../../../utils/factory.js'\nimport { deepMap } from '../../../utils/collection.js'\n\nconst name = 'unit'\nconst dependencies = ['typed', 'Unit']\n\n// This function is named createUnitFunction to prevent a naming conflict with createUnit\nexport const createUnitFunction = /* #__PURE__ */ factory(name, dependencies, ({ typed, Unit }) => {\n /**\n * Create a unit. Depending on the passed arguments, the function\n * will create and return a new math.Unit object.\n * When a matrix is provided, all elements will be converted to units.\n *\n * Syntax:\n *\n * math.unit(unit : string)\n * math.unit(value : number, unit : string)\n *\n * Examples:\n *\n * const a = math.unit(5, 'cm') // returns Unit 50 mm\n * const b = math.unit('23 kg') // returns Unit 23 kg\n * a.to('m') // returns Unit 0.05 m\n *\n * See also:\n *\n * bignumber, boolean, complex, index, matrix, number, string, createUnit\n *\n * @param {* | Array | Matrix} args A number and unit.\n * @return {Unit | Array | Matrix} The created unit\n */\n\n return typed(name, {\n Unit: function (x) {\n return x.clone()\n },\n\n string: function (x) {\n if (Unit.isValuelessUnit(x)) {\n return new Unit(null, x) // a pure unit\n }\n\n return Unit.parse(x, { allowNoUnits: true }) // a unit with value, like '5cm'\n },\n\n 'number | BigNumber | Fraction | Complex, string': function (value, unit) {\n return new Unit(value, unit)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'sparse'\nconst dependencies = ['typed', 'SparseMatrix']\n\nexport const createSparse = /* #__PURE__ */ factory(name, dependencies, ({ typed, SparseMatrix }) => {\n /**\n * Create a Sparse Matrix. The function creates a new `math.Matrix` object from\n * an `Array`. A Matrix has utility functions to manipulate the data in the\n * matrix, like getting the size and getting or setting values in the matrix.\n *\n * Syntax:\n *\n * math.sparse() // creates an empty sparse matrix.\n * math.sparse(data) // creates a sparse matrix with initial data.\n * math.sparse(data, 'number') // creates a sparse matrix with initial data, number datatype.\n *\n * Examples:\n *\n * let m = math.sparse([[1, 2], [3, 4]])\n * m.size() // Array [2, 2]\n * m.resize([3, 2], 5)\n * m.valueOf() // Array [[1, 2], [3, 4], [5, 5]]\n * m.get([1, 0]) // number 3\n *\n * See also:\n *\n * bignumber, boolean, complex, index, number, string, unit, matrix\n *\n * @param {Array | Matrix} [data] A two dimensional array\n *\n * @return {Matrix} The created matrix\n */\n return typed(name, {\n '': function () {\n return new SparseMatrix([])\n },\n\n string: function (datatype) {\n return new SparseMatrix([], datatype)\n },\n\n 'Array | Matrix': function (data) {\n return new SparseMatrix(data)\n },\n\n 'Array | Matrix, string': function (data, datatype) {\n return new SparseMatrix(data, datatype)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'createUnit'\nconst dependencies = ['typed', 'Unit']\n\nexport const createCreateUnit = /* #__PURE__ */ factory(name, dependencies, ({ typed, Unit }) => {\n /**\n * Create a user-defined unit and register it with the Unit type.\n *\n * Syntax:\n *\n * math.createUnit({\n * baseUnit1: {\n * aliases: [string, ...]\n * prefixes: object\n * },\n * unit2: {\n * definition: string,\n * aliases: [string, ...]\n * prefixes: object,\n * offset: number\n * },\n * unit3: string // Shortcut\n * })\n *\n * // Another shortcut:\n * math.createUnit(string, unit : string, [object])\n *\n * Examples:\n *\n * math.createUnit('foo')\n * math.createUnit('knot', {definition: '0.514444444 m/s', aliases: ['knots', 'kt', 'kts']})\n * math.createUnit('mph', '1 mile/hour')\n *\n * @param {string} name The name of the new unit. Must be unique. Example: 'knot'\n * @param {string, Unit} definition Definition of the unit in terms of existing units. For example, '0.514444444 m / s'.\n * @param {Object} options (optional) An object containing any of the following properties:\n * - `prefixes {string}` \"none\", \"short\", \"long\", \"binary_short\", or \"binary_long\". The default is \"none\".\n * - `aliases {Array}` Array of strings. Example: ['knots', 'kt', 'kts']\n * - `offset {Numeric}` An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.\n *\n * See also:\n *\n * unit\n *\n * @return {Unit} The new unit\n */\n return typed(name, {\n\n // General function signature. First parameter is an object where each property is the definition of a new unit. The object keys are the unit names and the values are the definitions. The values can be objects, strings, or Units. If a property is an empty object or an empty string, a new base unit is created. The second parameter is the options.\n 'Object, Object': function (obj, options) {\n return Unit.createUnit(obj, options)\n },\n\n // Same as above but without the options.\n Object: function (obj) {\n return Unit.createUnit(obj, {})\n },\n\n // Shortcut method for creating one unit.\n 'string, Unit | string | Object, Object': function (name, def, options) {\n const obj = {}\n obj[name] = def\n return Unit.createUnit(obj, options)\n },\n\n // Same as above but without the options.\n 'string, Unit | string | Object': function (name, def) {\n const obj = {}\n obj[name] = def\n return Unit.createUnit(obj, {})\n },\n\n // Without a definition, creates a base unit.\n string: function (name) {\n const obj = {}\n obj[name] = {}\n return Unit.createUnit(obj, {})\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'acos'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAcos = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the inverse cosine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acos(x)\n *\n * Examples:\n *\n * math.acos(0.5) // returns number 1.0471975511965979\n * math.acos(math.cos(1.5)) // returns number 1.5\n *\n * math.acos(2) // returns Complex 0 + 1.3169578969248166 i\n *\n * See also:\n *\n * cos, atan, asin\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc cosine of x\n */\n return typed(name, {\n number: function (x) {\n if ((x >= -1 && x <= 1) || config.predictable) {\n return Math.acos(x)\n } else {\n return new Complex(x, 0).acos()\n }\n },\n\n Complex: function (x) {\n return x.acos()\n },\n\n BigNumber: function (x) {\n return x.acos()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { acosh, asinh, atanh, cosh, sign, sinh, tanh } from '../../utils/number.js'\n\nconst n1 = 'number'\nconst n2 = 'number, number'\n\nexport function acosNumber (x) {\n return Math.acos(x)\n}\nacosNumber.signature = n1\n\nexport function acoshNumber (x) {\n return acosh(x)\n}\nacoshNumber.signature = n1\n\nexport function acotNumber (x) {\n return Math.atan(1 / x)\n}\nacotNumber.signature = n1\n\nexport function acothNumber (x) {\n return isFinite(x)\n ? (Math.log((x + 1) / x) + Math.log(x / (x - 1))) / 2\n : 0\n}\nacothNumber.signature = n1\n\nexport function acscNumber (x) {\n return Math.asin(1 / x)\n}\nacscNumber.signature = n1\n\nexport function acschNumber (x) {\n const xInv = 1 / x\n return Math.log(xInv + Math.sqrt(xInv * xInv + 1))\n}\nacschNumber.signature = n1\n\nexport function asecNumber (x) {\n return Math.acos(1 / x)\n}\nasecNumber.signature = n1\n\nexport function asechNumber (x) {\n const xInv = 1 / x\n const ret = Math.sqrt(xInv * xInv - 1)\n return Math.log(ret + xInv)\n}\nasechNumber.signature = n1\n\nexport function asinNumber (x) {\n return Math.asin(x)\n}\nasinNumber.signature = n1\n\nexport function asinhNumber (x) {\n return asinh(x)\n}\nasinhNumber.signature = n1\n\nexport function atanNumber (x) {\n return Math.atan(x)\n}\natanNumber.signature = n1\n\nexport function atan2Number (y, x) {\n return Math.atan2(y, x)\n}\natan2Number.signature = n2\n\nexport function atanhNumber (x) {\n return atanh(x)\n}\natanhNumber.signature = n1\n\nexport function cosNumber (x) {\n return Math.cos(x)\n}\ncosNumber.signature = n1\n\nexport function coshNumber (x) {\n return cosh(x)\n}\ncoshNumber.signature = n1\n\nexport function cotNumber (x) {\n return 1 / Math.tan(x)\n}\ncotNumber.signature = n1\n\nexport function cothNumber (x) {\n const e = Math.exp(2 * x)\n return (e + 1) / (e - 1)\n}\ncothNumber.signature = n1\n\nexport function cscNumber (x) {\n return 1 / Math.sin(x)\n}\ncscNumber.signature = n1\n\nexport function cschNumber (x) {\n // consider values close to zero (+/-)\n if (x === 0) {\n return Number.POSITIVE_INFINITY\n } else {\n return Math.abs(2 / (Math.exp(x) - Math.exp(-x))) * sign(x)\n }\n}\ncschNumber.signature = n1\n\nexport function secNumber (x) {\n return 1 / Math.cos(x)\n}\nsecNumber.signature = n1\n\nexport function sechNumber (x) {\n return 2 / (Math.exp(x) + Math.exp(-x))\n}\nsechNumber.signature = n1\n\nexport function sinNumber (x) {\n return Math.sin(x)\n}\nsinNumber.signature = n1\n\nexport function sinhNumber (x) {\n return sinh(x)\n}\nsinhNumber.signature = n1\n\nexport function tanNumber (x) {\n return Math.tan(x)\n}\ntanNumber.signature = n1\n\nexport function tanhNumber (x) {\n return tanh(x)\n}\ntanhNumber.signature = n1\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acoshNumber } from '../../plain/number/index.js'\n\nconst name = 'acosh'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAcosh = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the hyperbolic arccos of a value,\n * defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acosh(x)\n *\n * Examples:\n *\n * math.acosh(1.5) // returns 0.9624236501192069\n *\n * See also:\n *\n * cosh, asinh, atanh\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccosine of x\n */\n return typed(name, {\n number: function (x) {\n if (x >= 1 || config.predictable) {\n return acoshNumber(x)\n }\n if (x <= -1) {\n return new Complex(Math.log(Math.sqrt(x * x - 1) - x), Math.PI)\n }\n return new Complex(x, 0).acosh()\n },\n\n Complex: function (x) {\n return x.acosh()\n },\n\n BigNumber: function (x) {\n return x.acosh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acotNumber } from '../../plain/number/index.js'\n\nconst name = 'acot'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createAcot = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the inverse cotangent of a value, defined as `acot(x) = atan(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acot(x)\n *\n * Examples:\n *\n * math.acot(0.5) // returns number 0.4636476090008061\n * math.acot(math.cot(1.5)) // returns number 1.5\n *\n * math.acot(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * cot, atan\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc cotangent of x\n */\n return typed(name, {\n number: acotNumber,\n\n Complex: function (x) {\n return x.acot()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).atan()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acothNumber } from '../../plain/number/index.js'\n\nconst name = 'acoth'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAcoth = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the hyperbolic arccotangent of a value,\n * defined as `acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acoth(x)\n *\n * Examples:\n *\n * math.acoth(0.5) // returns 0.8047189562170503\n *\n * See also:\n *\n * acsch, asech\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccotangent of x\n */\n return typed(name, {\n number: function (x) {\n if (x >= 1 || x <= -1 || config.predictable) {\n return acothNumber(x)\n }\n return new Complex(x, 0).acoth()\n },\n\n Complex: function (x) {\n return x.acoth()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).atanh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acscNumber } from '../../plain/number/index.js'\n\nconst name = 'acsc'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAcsc = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the inverse cosecant of a value, defined as `acsc(x) = asin(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acsc(x)\n *\n * Examples:\n *\n * math.acsc(0.5) // returns number 0.5235987755982989\n * math.acsc(math.csc(1.5)) // returns number ~1.5\n *\n * math.acsc(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * csc, asin, asec\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc cosecant of x\n */\n return typed(name, {\n number: function (x) {\n if (x <= -1 || x >= 1 || config.predictable) {\n return acscNumber(x)\n }\n return new Complex(x, 0).acsc()\n },\n\n Complex: function (x) {\n return x.acsc()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).asin()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { acschNumber } from '../../plain/number/index.js'\n\nconst name = 'acsch'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createAcsch = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic arccosecant of a value,\n * defined as `acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.acsch(x)\n *\n * Examples:\n *\n * math.acsch(0.5) // returns 1.4436354751788103\n *\n * See also:\n *\n * asech, acoth\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arccosecant of x\n */\n return typed(name, {\n number: acschNumber,\n\n Complex: function (x) {\n return x.acsch()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).asinh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asecNumber } from '../../plain/number/index.js'\n\nconst name = 'asec'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAsec = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the inverse secant of a value. Defined as `asec(x) = acos(1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asec(x)\n *\n * Examples:\n *\n * math.asec(0.5) // returns 1.0471975511965979\n * math.asec(math.sec(1.5)) // returns 1.5\n *\n * math.asec(2) // returns 0 + 1.3169578969248166 i\n *\n * See also:\n *\n * acos, acot, acsc\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} The arc secant of x\n */\n return typed(name, {\n number: function (x) {\n if (x <= -1 || x >= 1 || config.predictable) {\n return asecNumber(x)\n }\n return new Complex(x, 0).asec()\n },\n\n Complex: function (x) {\n return x.asec()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).acos()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asechNumber } from '../../plain/number/index.js'\n\nconst name = 'asech'\nconst dependencies = ['typed', 'config', 'Complex', 'BigNumber']\n\nexport const createAsech = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex, BigNumber }) => {\n /**\n * Calculate the hyperbolic arcsecant of a value,\n * defined as `asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asech(x)\n *\n * Examples:\n *\n * math.asech(0.5) // returns 1.3169578969248166\n *\n * See also:\n *\n * acsch, acoth\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arcsecant of x\n */\n return typed(name, {\n number: function (x) {\n if ((x <= 1 && x >= -1) || config.predictable) {\n const xInv = 1 / x\n if (xInv > 0 || config.predictable) {\n return asechNumber(x)\n }\n\n const ret = Math.sqrt(xInv * xInv - 1)\n return new Complex(Math.log(ret - xInv), Math.PI)\n }\n\n return new Complex(x, 0).asech()\n },\n\n Complex: function (x) {\n return x.asech()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x).acosh()\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'asin'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAsin = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the inverse sine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asin(x)\n *\n * Examples:\n *\n * math.asin(0.5) // returns number 0.5235987755982989\n * math.asin(math.sin(1.5)) // returns number ~1.5\n *\n * math.asin(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * sin, atan, acos\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc sine of x\n */\n return typed(name, {\n number: function (x) {\n if ((x >= -1 && x <= 1) || config.predictable) {\n return Math.asin(x)\n } else {\n return new Complex(x, 0).asin()\n }\n },\n\n Complex: function (x) {\n return x.asin()\n },\n\n BigNumber: function (x) {\n return x.asin()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since asin(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { asinhNumber } from '../../plain/number/index.js'\n\nconst name = 'asinh'\nconst dependencies = ['typed']\n\nexport const createAsinh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic arcsine of a value,\n * defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.asinh(x)\n *\n * Examples:\n *\n * math.asinh(0.5) // returns 0.48121182505960347\n *\n * See also:\n *\n * acosh, atanh\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arcsine of x\n */\n return typed('asinh', {\n number: asinhNumber,\n\n Complex: function (x) {\n return x.asinh()\n },\n\n BigNumber: function (x) {\n return x.asinh()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since asinh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'atan'\nconst dependencies = ['typed']\n\nexport const createAtan = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the inverse tangent of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atan(x)\n *\n * Examples:\n *\n * math.atan(0.5) // returns number 0.4636476090008061\n * math.atan(math.tan(1.5)) // returns number 1.5\n *\n * math.atan(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * tan, asin, acos\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} The arc tangent of x\n */\n return typed('atan', {\n number: function (x) {\n return Math.atan(x)\n },\n\n Complex: function (x) {\n return x.atan()\n },\n\n BigNumber: function (x) {\n return x.atan()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since atan(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js'\nimport { createAlgorithm03 } from '../../type/matrix/utils/algorithm03.js'\nimport { createAlgorithm09 } from '../../type/matrix/utils/algorithm09.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm12 } from '../../type/matrix/utils/algorithm12.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'atan2'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'equalScalar',\n 'BigNumber',\n 'DenseMatrix'\n]\n\nexport const createAtan2 = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, equalScalar, BigNumber, DenseMatrix }) => {\n const algorithm02 = createAlgorithm02({ typed, equalScalar })\n const algorithm03 = createAlgorithm03({ typed })\n const algorithm09 = createAlgorithm09({ typed, equalScalar })\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm12 = createAlgorithm12({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Calculate the inverse tangent function with two arguments, y/x.\n * By providing two arguments, the right quadrant of the computed angle can be\n * determined.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atan2(y, x)\n *\n * Examples:\n *\n * math.atan2(2, 2) / math.pi // returns number 0.25\n *\n * const angle = math.unit(60, 'deg') // returns Unit 60 deg\n * const x = math.cos(angle)\n * const y = math.sin(angle)\n *\n * math.atan(2) // returns Complex 1.5707963267948966 -1.3169578969248166 i\n *\n * See also:\n *\n * tan, atan, sin, cos\n *\n * @param {number | Array | Matrix} y Second dimension\n * @param {number | Array | Matrix} x First dimension\n * @return {number | Array | Matrix} Four-quadrant inverse tangent\n */\n return typed(name, {\n\n 'number, number': Math.atan2,\n\n // Complex numbers doesn't seem to have a reasonable implementation of\n // atan2(). Even Matlab removed the support, after they only calculated\n // the atan only on base of the real part of the numbers and ignored the imaginary.\n\n 'BigNumber, BigNumber': function (y, x) {\n return BigNumber.atan2(y, x)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm09(x, y, this, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n // mind the order of y and x!\n return algorithm02(y, x, this, true)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm03(x, y, this, false)\n },\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, this)\n },\n\n 'Array, Array': function (x, y) {\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n return this(x, matrix(y))\n },\n\n 'SparseMatrix, number | BigNumber': function (x, y) {\n return algorithm11(x, y, this, false)\n },\n\n 'DenseMatrix, number | BigNumber': function (x, y) {\n return algorithm14(x, y, this, false)\n },\n\n 'number | BigNumber, SparseMatrix': function (x, y) {\n // mind the order of y and x\n return algorithm12(y, x, this, true)\n },\n\n 'number | BigNumber, DenseMatrix': function (x, y) {\n // mind the order of y and x\n return algorithm14(y, x, this, true)\n },\n\n 'Array, number | BigNumber': function (x, y) {\n return algorithm14(matrix(x), y, this, false).valueOf()\n },\n\n 'number | BigNumber, Array': function (x, y) {\n return algorithm14(matrix(y), x, this, true).valueOf()\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { atanhNumber } from '../../plain/number/index.js'\n\nconst name = 'atanh'\nconst dependencies = ['typed', 'config', 'Complex']\n\nexport const createAtanh = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, Complex }) => {\n /**\n * Calculate the hyperbolic arctangent of a value,\n * defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.atanh(x)\n *\n * Examples:\n *\n * math.atanh(0.5) // returns 0.5493061443340549\n *\n * See also:\n *\n * acosh, asinh\n *\n * @param {number | Complex | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic arctangent of x\n */\n return typed(name, {\n number: function (x) {\n if ((x <= 1 && x >= -1) || config.predictable) {\n return atanhNumber(x)\n }\n return new Complex(x, 0).atanh()\n },\n\n Complex: function (x) {\n return x.atanh()\n },\n\n BigNumber: function (x) {\n return x.atanh()\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since atanh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'cos'\nconst dependencies = ['typed']\n\nexport const createCos = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the cosine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cos(x)\n *\n * Examples:\n *\n * math.cos(2) // returns number -0.4161468365471422\n * math.cos(math.pi / 4) // returns number 0.7071067811865475\n * math.cos(math.unit(180, 'deg')) // returns number -1\n * math.cos(math.unit(60, 'deg')) // returns number 0.5\n *\n * const angle = 0.2\n * math.pow(math.sin(angle), 2) + math.pow(math.cos(angle), 2) // returns number ~1\n *\n * See also:\n *\n * cos, tan\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Cosine of x\n */\n return typed(name, {\n number: Math.cos,\n\n Complex: function (x) {\n return x.cos()\n },\n\n BigNumber: function (x) {\n return x.cos()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cos is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cosh as coshNumber } from '../../utils/number.js'\n\nconst name = 'cosh'\nconst dependencies = ['typed']\n\nexport const createCosh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic cosine of a value,\n * defined as `cosh(x) = 1/2 * (exp(x) + exp(-x))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cosh(x)\n *\n * Examples:\n *\n * math.cosh(0.5) // returns number 1.1276259652063807\n *\n * See also:\n *\n * sinh, tanh\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic cosine of x\n */\n return typed(name, {\n number: coshNumber,\n\n Complex: function (x) {\n return x.cosh()\n },\n\n BigNumber: function (x) {\n return x.cosh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cosh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cotNumber } from '../../plain/number/index.js'\n\nconst name = 'cot'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCot = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the cotangent of a value. Defined as `cot(x) = 1 / tan(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.cot(x)\n *\n * Examples:\n *\n * math.cot(2) // returns number -0.45765755436028577\n * 1 / math.tan(2) // returns number -0.45765755436028577\n *\n * See also:\n *\n * tan, sec, csc\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Cotangent of x\n */\n return typed(name, {\n number: cotNumber,\n\n Complex: function (x) {\n return x.cot()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.tan())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function cot is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cothNumber } from '../../plain/number/index.js'\n\nconst name = 'coth'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCoth = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic cotangent of a value,\n * defined as `coth(x) = 1 / tanh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.coth(x)\n *\n * Examples:\n *\n * // coth(x) = 1 / tanh(x)\n * math.coth(2) // returns 1.0373147207275482\n * 1 / math.tanh(2) // returns 1.0373147207275482\n *\n * See also:\n *\n * sinh, tanh, cosh\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic cotangent of x\n */\n return typed(name, {\n number: cothNumber,\n\n Complex: function (x) {\n return x.coth()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.tanh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function coth is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cscNumber } from '../../plain/number/index.js'\n\nconst name = 'csc'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCsc = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the cosecant of a value, defined as `csc(x) = 1/sin(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.csc(x)\n *\n * Examples:\n *\n * math.csc(2) // returns number 1.099750170294617\n * 1 / math.sin(2) // returns number 1.099750170294617\n *\n * See also:\n *\n * sin, sec, cot\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Cosecant of x\n */\n return typed(name, {\n number: cscNumber,\n\n Complex: function (x) {\n return x.csc()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.sin())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function csc is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { cschNumber } from '../../plain/number/index.js'\n\nconst name = 'csch'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createCsch = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic cosecant of a value,\n * defined as `csch(x) = 1 / sinh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.csch(x)\n *\n * Examples:\n *\n * // csch(x) = 1/ sinh(x)\n * math.csch(0.5) // returns 1.9190347513349437\n * 1 / math.sinh(0.5) // returns 1.9190347513349437\n *\n * See also:\n *\n * sinh, sech, coth\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic cosecant of x\n */\n return typed(name, {\n number: cschNumber,\n\n Complex: function (x) {\n return x.csch()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.sinh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function csch is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { secNumber } from '../../plain/number/index.js'\n\nconst name = 'sec'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createSec = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the secant of a value, defined as `sec(x) = 1/cos(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sec(x)\n *\n * Examples:\n *\n * math.sec(2) // returns number -2.4029979617223822\n * 1 / math.cos(2) // returns number -2.4029979617223822\n *\n * See also:\n *\n * cos, csc, cot\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Secant of x\n */\n return typed(name, {\n number: secNumber,\n\n Complex: function (x) {\n return x.sec()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.cos())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sec is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { sechNumber } from '../../plain/number/index.js'\n\nconst name = 'sech'\nconst dependencies = ['typed', 'BigNumber']\n\nexport const createSech = /* #__PURE__ */ factory(name, dependencies, ({ typed, BigNumber }) => {\n /**\n * Calculate the hyperbolic secant of a value,\n * defined as `sech(x) = 1 / cosh(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sech(x)\n *\n * Examples:\n *\n * // sech(x) = 1/ cosh(x)\n * math.sech(0.5) // returns 0.886818883970074\n * 1 / math.cosh(0.5) // returns 0.886818883970074\n *\n * See also:\n *\n * cosh, csch, coth\n *\n * @param {number | Complex | Unit | Array | Matrix} x Function input\n * @return {number | Complex | Array | Matrix} Hyperbolic secant of x\n */\n return typed(name, {\n number: sechNumber,\n\n Complex: function (x) {\n return x.sech()\n },\n\n BigNumber: function (x) {\n return new BigNumber(1).div(x.cosh())\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sech is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n return deepMap(x, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'sin'\nconst dependencies = ['typed']\n\nexport const createSin = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the sine of a value.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sin(x)\n *\n * Examples:\n *\n * math.sin(2) // returns number 0.9092974268256813\n * math.sin(math.pi / 4) // returns number 0.7071067811865475\n * math.sin(math.unit(90, 'deg')) // returns number 1\n * math.sin(math.unit(30, 'deg')) // returns number 0.5\n *\n * const angle = 0.2\n * math.pow(math.sin(angle), 2) + math.pow(math.cos(angle), 2) // returns number ~1\n *\n * See also:\n *\n * cos, tan\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Sine of x\n */\n return typed(name, {\n number: Math.sin,\n\n Complex: function (x) {\n return x.sin()\n },\n\n BigNumber: function (x) {\n return x.sin()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sin is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sin(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { sinhNumber } from '../../plain/number/index.js'\n\nconst name = 'sinh'\nconst dependencies = ['typed']\n\nexport const createSinh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic sine of a value,\n * defined as `sinh(x) = 1/2 * (exp(x) - exp(-x))`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.sinh(x)\n *\n * Examples:\n *\n * math.sinh(0.5) // returns number 0.5210953054937474\n *\n * See also:\n *\n * cosh, tanh\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic sine of x\n */\n return typed(name, {\n number: sinhNumber,\n\n Complex: function (x) {\n return x.sinh()\n },\n\n BigNumber: function (x) {\n return x.sinh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function sinh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since sinh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\n\nconst name = 'tan'\nconst dependencies = ['typed']\n\nexport const createTan = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the tangent of a value. `tan(x)` is equal to `sin(x) / cos(x)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.tan(x)\n *\n * Examples:\n *\n * math.tan(0.5) // returns number 0.5463024898437905\n * math.sin(0.5) / math.cos(0.5) // returns number 0.5463024898437905\n * math.tan(math.pi / 4) // returns number 1\n * math.tan(math.unit(45, 'deg')) // returns number 1\n *\n * See also:\n *\n * atan, sin, cos\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Tangent of x\n */\n return typed(name, {\n number: Math.tan,\n\n Complex: function (x) {\n return x.tan()\n },\n\n BigNumber: function (x) {\n return x.tan()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function tan is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since tan(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { deepMap } from '../../utils/collection.js'\nimport { tanh as _tanh } from '../../utils/number.js'\n\nconst name = 'tanh'\nconst dependencies = ['typed']\n\nexport const createTanh = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Calculate the hyperbolic tangent of a value,\n * defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.tanh(x)\n *\n * Examples:\n *\n * // tanh(x) = sinh(x) / cosh(x) = 1 / coth(x)\n * math.tanh(0.5) // returns 0.46211715726000974\n * math.sinh(0.5) / math.cosh(0.5) // returns 0.46211715726000974\n * 1 / math.coth(0.5) // returns 0.46211715726000974\n *\n * See also:\n *\n * sinh, cosh, coth\n *\n * @param {number | BigNumber | Complex | Unit | Array | Matrix} x Function input\n * @return {number | BigNumber | Complex | Array | Matrix} Hyperbolic tangent of x\n */\n return typed('tanh', {\n number: _tanh,\n\n Complex: function (x) {\n return x.tanh()\n },\n\n BigNumber: function (x) {\n return x.tanh()\n },\n\n Unit: function (x) {\n if (!x.hasBase(x.constructor.BASE_UNITS.ANGLE)) {\n throw new TypeError('Unit in function tanh is no angle')\n }\n return this(x.value)\n },\n\n 'Array | Matrix': function (x) {\n // deep map collection, skip zeros since tanh(0) = 0\n return deepMap(x, this, true)\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setCartesian'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetCartesian = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the cartesian product of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setCartesian(set1, set2)\n *\n * Examples:\n *\n * math.setCartesian([1, 2], [3, 4]) // returns [[1, 3], [1, 4], [2, 3], [2, 4]]\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference, setPowerset\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The cartesian product of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result = []\n\n if (subset(size(a1), new Index(0)) !== 0 && subset(size(a2), new Index(0)) !== 0) { // if any of them is empty, return empty\n const b1 = flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural)\n const b2 = flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural)\n result = []\n for (let i = 0; i < b1.length; i++) {\n for (let j = 0; j < b2.length; j++) {\n result.push([b1[i], b2[j]])\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return result\n }\n // return a matrix otherwise\n return new DenseMatrix(result)\n }\n })\n})\n","import { flatten, generalize, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setDifference'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetDifference = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the difference of two (multi)sets: every element of set1, that is not the element of set2.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setDifference(set1, set2)\n *\n * Examples:\n *\n * math.setDifference([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2]\n * math.setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2]\n *\n * See also:\n *\n * setUnion, setIntersect, setSymDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The difference of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result\n if (subset(size(a1), new Index(0)) === 0) { // empty-anything=empty\n result = []\n } else if (subset(size(a2), new Index(0)) === 0) { // anything-empty=anything\n return flatten(a1.toArray())\n } else {\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n result = []\n let inb2\n for (let i = 0; i < b1.length; i++) {\n inb2 = false\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n inb2 = true\n break\n }\n }\n if (!inb2) {\n result.push(b1[i])\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return generalize(result)\n }\n // return a matrix otherwise\n return new DenseMatrix(generalize(result))\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setDistinct'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetDistinct = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Collect the distinct elements of a multiset.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setDistinct(set)\n *\n * Examples:\n *\n * math.setDistinct([1, 1, 1, 2, 2, 3]) // returns [1, 2, 3]\n *\n * See also:\n *\n * setMultiplicity\n *\n * @param {Array | Matrix} a A multiset\n * @return {Array | Matrix} A set containing the distinc elements of the multiset\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n let result\n if (subset(size(a), new Index(0)) === 0) { // if empty, return empty\n result = []\n } else {\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n result = []\n result.push(b[0])\n for (let i = 1; i < b.length; i++) {\n if (compareNatural(b[i], b[i - 1]) !== 0) {\n result.push(b[i])\n }\n }\n }\n // return an array, if the input was an array\n if (Array.isArray(a)) {\n return result\n }\n // return a matrix otherwise\n return new DenseMatrix(result)\n }\n })\n})\n","import { flatten, generalize, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setIntersect'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index', 'DenseMatrix']\n\nexport const createSetIntersect = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index, DenseMatrix }) => {\n /**\n * Create the intersection of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setIntersect(set1, set2)\n *\n * Examples:\n *\n * math.setIntersect([1, 2, 3, 4], [3, 4, 5, 6]) // returns [3, 4]\n * math.setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [3, 4]\n *\n * See also:\n *\n * setUnion, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The intersection of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n let result\n if (subset(size(a1), new Index(0)) === 0 || subset(size(a2), new Index(0)) === 0) { // of any of them is empty, return empty\n result = []\n } else {\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n result = []\n for (let i = 0; i < b1.length; i++) {\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n result.push(b1[i])\n break\n }\n }\n }\n }\n // return an array, if both inputs were arrays\n if (Array.isArray(a1) && Array.isArray(a2)) {\n return generalize(result)\n }\n // return a matrix otherwise\n return new DenseMatrix(generalize(result))\n }\n })\n})\n","import { flatten, identify } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setIsSubset'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetIsSubset = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Check whether a (multi)set is a subset of another (multi)set. (Every element of set1 is the element of set2.)\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setIsSubset(set1, set2)\n *\n * Examples:\n *\n * math.setIsSubset([1, 2], [3, 4, 5, 6]) // returns false\n * math.setIsSubset([3, 4], [3, 4, 5, 6]) // returns true\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {boolean} true | false\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // empty is a subset of anything\n return true\n } else if (subset(size(a2), new Index(0)) === 0) { // anything is not a subset of empty\n return false\n }\n const b1 = identify(flatten(Array.isArray(a1) ? a1 : a1.toArray()).sort(compareNatural))\n const b2 = identify(flatten(Array.isArray(a2) ? a2 : a2.toArray()).sort(compareNatural))\n let inb2\n for (let i = 0; i < b1.length; i++) {\n inb2 = false\n for (let j = 0; j < b2.length; j++) {\n if (compareNatural(b1[i].value, b2[j].value) === 0 && b1[i].identifier === b2[j].identifier) { // the identifier is always a decimal int\n inb2 = true\n break\n }\n }\n if (inb2 === false) {\n return false\n }\n }\n return true\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setMultiplicity'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetMultiplicity = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Count the multiplicity of an element in a multiset.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setMultiplicity(element, set)\n *\n * Examples:\n *\n * math.setMultiplicity(1, [1, 2, 2, 4]) // returns 1\n * math.setMultiplicity(2, [1, 2, 2, 4]) // returns 2\n *\n * See also:\n *\n * setDistinct, setSize\n *\n * @param {number | BigNumber | Fraction | Complex} e An element in the multiset\n * @param {Array | Matrix} a A multiset\n * @return {number} The number of how many times the multiset contains the element\n */\n return typed(name, {\n 'number | BigNumber | Fraction | Complex, Array | Matrix': function (e, a) {\n if (subset(size(a), new Index(0)) === 0) { // if empty, return 0\n return 0\n }\n const b = flatten(Array.isArray(a) ? a : a.toArray())\n let count = 0\n for (let i = 0; i < b.length; i++) {\n if (compareNatural(b[i], e) === 0) {\n count++\n }\n }\n return count\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setPowerset'\nconst dependencies = ['typed', 'size', 'subset', 'compareNatural', 'Index']\n\nexport const createSetPowerset = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, subset, compareNatural, Index }) => {\n /**\n * Create the powerset of a (multi)set. (The powerset contains very possible subsets of a (multi)set.)\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setPowerset(set)\n *\n * Examples:\n *\n * math.setPowerset([1, 2, 3]) // returns [[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]\n *\n * See also:\n *\n * setCartesian\n *\n * @param {Array | Matrix} a A (multi)set\n * @return {Array} The powerset of the (multi)set\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n if (subset(size(a), new Index(0)) === 0) { // if empty, return empty\n return []\n }\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n const result = []\n let number = 0\n while (number.toString(2).length <= b.length) {\n result.push(_subset(b, number.toString(2).split('').reverse()))\n number++\n }\n // can not return a matrix, because of the different size of the subarrays\n return _sort(result)\n }\n })\n\n // create subset\n function _subset (array, bitarray) {\n const result = []\n for (let i = 0; i < bitarray.length; i++) {\n if (bitarray[i] === '1') {\n result.push(array[i])\n }\n }\n return result\n }\n\n // sort subsests by length\n function _sort (array) {\n let temp = []\n for (let i = array.length - 1; i > 0; i--) {\n for (let j = 0; j < i; j++) {\n if (array[j].length > array[j + 1].length) {\n temp = array[j]\n array[j] = array[j + 1]\n array[j + 1] = temp\n }\n }\n }\n return array\n }\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setSize'\nconst dependencies = ['typed', 'compareNatural']\n\nexport const createSetSize = /* #__PURE__ */ factory(name, dependencies, ({ typed, compareNatural }) => {\n /**\n * Count the number of elements of a (multi)set. When a second parameter is 'true', count only the unique values.\n * A multi-dimension array will be converted to a single-dimension array before the operation.\n *\n * Syntax:\n *\n * math.setSize(set)\n * math.setSize(set, unique)\n *\n * Examples:\n *\n * math.setSize([1, 2, 2, 4]) // returns 4\n * math.setSize([1, 2, 2, 4], true) // returns 3\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a A multiset\n * @return {number} The number of elements of the (multi)set\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n return Array.isArray(a) ? flatten(a).length : flatten(a.toArray()).length\n },\n 'Array | Matrix, boolean': function (a, unique) {\n if (unique === false || a.length === 0) {\n return Array.isArray(a) ? flatten(a).length : flatten(a.toArray()).length\n } else {\n const b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural)\n let count = 1\n for (let i = 1; i < b.length; i++) {\n if (compareNatural(b[i], b[i - 1]) !== 0) {\n count++\n }\n }\n return count\n }\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setSymDifference'\nconst dependencies = ['typed', 'size', 'concat', 'subset', 'setDifference', 'Index']\n\nexport const createSetSymDifference = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, concat, subset, setDifference, Index }) => {\n /**\n * Create the symmetric difference of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setSymDifference(set1, set2)\n *\n * Examples:\n *\n * math.setSymDifference([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2, 5, 6]\n * math.setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2, 5, 6]\n *\n * See also:\n *\n * setUnion, setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The symmetric difference of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // if any of them is empty, return the other one\n return flatten(a2)\n } else if (subset(size(a2), new Index(0)) === 0) {\n return flatten(a1)\n }\n const b1 = flatten(a1)\n const b2 = flatten(a2)\n return concat(setDifference(b1, b2), setDifference(b2, b1))\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'setUnion'\nconst dependencies = ['typed', 'size', 'concat', 'subset', 'setIntersect', 'setSymDifference', 'Index']\n\nexport const createSetUnion = /* #__PURE__ */ factory(name, dependencies, ({ typed, size, concat, subset, setIntersect, setSymDifference, Index }) => {\n /**\n * Create the union of two (multi)sets.\n * Multi-dimension arrays will be converted to single-dimension arrays before the operation.\n *\n * Syntax:\n *\n * math.setUnion(set1, set2)\n *\n * Examples:\n *\n * math.setUnion([1, 2, 3, 4], [3, 4, 5, 6]) // returns [1, 2, 3, 4, 5, 6]\n * math.setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]]) // returns [1, 2, 3, 4, 5, 6]\n *\n * See also:\n *\n * setIntersect, setDifference\n *\n * @param {Array | Matrix} a1 A (multi)set\n * @param {Array | Matrix} a2 A (multi)set\n * @return {Array | Matrix} The union of two (multi)sets\n */\n return typed(name, {\n 'Array | Matrix, Array | Matrix': function (a1, a2) {\n if (subset(size(a1), new Index(0)) === 0) { // if any of them is empty, return the other one\n return flatten(a2)\n } else if (subset(size(a2), new Index(0)) === 0) {\n return flatten(a1)\n }\n const b1 = flatten(a1)\n const b2 = flatten(a2)\n return concat(setSymDifference(b1, b2), setIntersect(b1, b2))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { extend } from '../../utils/object.js'\nimport { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js'\nimport { createAlgorithm04 } from '../../type/matrix/utils/algorithm04.js'\nimport { createAlgorithm10 } from '../../type/matrix/utils/algorithm10.js'\nimport { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'add'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'addScalar',\n 'equalScalar',\n 'DenseMatrix',\n 'SparseMatrix'\n]\n\nexport const createAdd = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, addScalar, equalScalar, DenseMatrix, SparseMatrix }) => {\n const algorithm01 = createAlgorithm01({ typed })\n const algorithm04 = createAlgorithm04({ typed, equalScalar })\n const algorithm10 = createAlgorithm10({ typed, DenseMatrix })\n const algorithm13 = createAlgorithm13({ typed })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Add two or more values, `x + y`.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.add(x, y)\n * math.add(x, y, z, ...)\n *\n * Examples:\n *\n * math.add(2, 3) // returns number 5\n * math.add(2, 3, 4) // returns number 9\n *\n * const a = math.complex(2, 3)\n * const b = math.complex(-4, 1)\n * math.add(a, b) // returns Complex -2 + 4i\n *\n * math.add([1, 2, 3], 4) // returns Array [5, 6, 7]\n *\n * const c = math.unit('5 cm')\n * const d = math.unit('2.1 mm')\n * math.add(c, d) // returns Unit 52.1 mm\n *\n * math.add(\"2.3\", \"4\") // returns number 6.3\n *\n * See also:\n *\n * subtract, sum\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to add\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to add\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Sum of `x` and `y`\n */\n return typed(name, extend({\n // we extend the signatures of addScalar with signatures dealing with matrices\n\n 'DenseMatrix, DenseMatrix': function (x, y) {\n return algorithm13(x, y, addScalar)\n },\n\n 'DenseMatrix, SparseMatrix': function (x, y) {\n return algorithm01(x, y, addScalar, false)\n },\n\n 'SparseMatrix, DenseMatrix': function (x, y) {\n return algorithm01(y, x, addScalar, true)\n },\n\n 'SparseMatrix, SparseMatrix': function (x, y) {\n return algorithm04(x, y, addScalar)\n },\n\n 'Array, Array': function (x, y) {\n // use matrix implementation\n return this(matrix(x), matrix(y)).valueOf()\n },\n\n 'Array, Matrix': function (x, y) {\n // use matrix implementation\n return this(matrix(x), y)\n },\n\n 'Matrix, Array': function (x, y) {\n // use matrix implementation\n return this(x, matrix(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, addScalar, false)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm10(x, y, addScalar, false)\n },\n\n 'any, DenseMatrix': function (x, y) {\n return algorithm14(y, x, addScalar, true)\n },\n\n 'any, SparseMatrix': function (x, y) {\n return algorithm10(y, x, addScalar, true)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, addScalar, false).valueOf()\n },\n\n 'any, Array': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(y), x, addScalar, true).valueOf()\n },\n\n 'any, any': addScalar,\n\n 'any, any, ...any': function (x, y, rest) {\n let result = this(x, y)\n\n for (let i = 0; i < rest.length; i++) {\n result = this(result, rest[i])\n }\n\n return result\n }\n }, addScalar.signatures))\n})\n","import { factory } from '../../utils/factory.js'\nimport { flatten } from '../../utils/array.js'\n\nconst name = 'hypot'\nconst dependencies = [\n 'typed',\n 'abs',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'sqrt',\n 'smaller',\n 'isPositive'\n]\n\nexport const createHypot = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, addScalar, divideScalar, multiplyScalar, sqrt, smaller, isPositive }) => {\n /**\n * Calculate the hypotenusa of a list with values. The hypotenusa is defined as:\n *\n * hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...)\n *\n * For matrix input, the hypotenusa is calculated for all values in the matrix.\n *\n * Syntax:\n *\n * math.hypot(a, b, ...)\n * math.hypot([a, b, c, ...])\n *\n * Examples:\n *\n * math.hypot(3, 4) // 5\n * math.hypot(3, 4, 5) // 7.0710678118654755\n * math.hypot([3, 4, 5]) // 7.0710678118654755\n * math.hypot(-2) // 2\n *\n * See also:\n *\n * abs, norm\n *\n * @param {... number | BigNumber | Array | Matrix} args A list with numeric values or an Array or Matrix.\n * Matrix and Array input is flattened and returns a\n * single number for the whole matrix.\n * @return {number | BigNumber} Returns the hypothenusa of the input values.\n */\n return typed(name, {\n '... number | BigNumber': _hypot,\n\n Array: function (x) {\n return this.apply(this, flatten(x))\n },\n\n Matrix: function (x) {\n return this.apply(this, flatten(x.toArray()))\n }\n })\n\n /**\n * Calculate the hypotenusa for an Array with values\n * @param {Array.} args\n * @return {number | BigNumber} Returns the result\n * @private\n */\n function _hypot (args) {\n // code based on `hypot` from es6-shim:\n // https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1619-L1633\n let result = 0\n let largest = 0\n\n for (let i = 0; i < args.length; i++) {\n const value = abs(args[i])\n if (smaller(largest, value)) {\n result = multiplyScalar(result,\n multiplyScalar(divideScalar(largest, value), divideScalar(largest, value)))\n result = addScalar(result, 1)\n largest = value\n } else {\n result = addScalar(result, isPositive(value)\n ? multiplyScalar(divideScalar(value, largest), divideScalar(value, largest))\n : value)\n }\n }\n\n return multiplyScalar(largest, sqrt(result))\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'norm'\nconst dependencies = [\n 'typed',\n 'abs',\n 'add',\n 'pow',\n 'conj',\n 'sqrt',\n 'multiply',\n 'equalScalar',\n 'larger',\n 'smaller',\n 'matrix',\n 'ctranspose',\n 'eigs'\n]\n\nexport const createNorm = /* #__PURE__ */ factory(\n name,\n dependencies,\n ({\n typed,\n abs,\n add,\n pow,\n conj,\n sqrt,\n multiply,\n equalScalar,\n larger,\n smaller,\n matrix,\n ctranspose,\n eigs\n }) => {\n /**\n * Calculate the norm of a number, vector or matrix.\n *\n * The second parameter p is optional. If not provided, it defaults to 2.\n *\n * Syntax:\n *\n * math.norm(x)\n * math.norm(x, p)\n *\n * Examples:\n *\n * math.abs(-3.5) // returns 3.5\n * math.norm(-3.5) // returns 3.5\n *\n * math.norm(math.complex(3, -4)) // returns 5\n *\n * math.norm([1, 2, -3], Infinity) // returns 3\n * math.norm([1, 2, -3], -Infinity) // returns 1\n *\n * math.norm([3, 4], 2) // returns 5\n *\n * math.norm([[1, 2], [3, 4]], 1) // returns 6\n * math.norm([[1, 2], [3, 4]], 'inf') // returns 7\n * math.norm([[1, 2], [3, 4]], 'fro') // returns 5.477225575051661\n *\n * See also:\n *\n * abs, hypot\n *\n * @param {number | BigNumber | Complex | Array | Matrix} x\n * Value for which to calculate the norm\n * @param {number | BigNumber | string} [p=2]\n * Vector space.\n * Supported numbers include Infinity and -Infinity.\n * Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm)\n * @return {number | BigNumber} the p-norm\n */\n return typed(name, {\n number: Math.abs,\n\n Complex: function (x) {\n return x.abs()\n },\n\n BigNumber: function (x) {\n // norm(x) = abs(x)\n return x.abs()\n },\n\n boolean: function (x) {\n // norm(x) = abs(x)\n return Math.abs(x)\n },\n\n Array: function (x) {\n return _norm(matrix(x), 2)\n },\n\n Matrix: function (x) {\n return _norm(x, 2)\n },\n\n 'number | Complex | BigNumber | boolean, number | BigNumber | string': function (\n x\n ) {\n // ignore second parameter, TODO: remove the option of second parameter for these types\n return this(x)\n },\n\n 'Array, number | BigNumber | string': function (x, p) {\n return _norm(matrix(x), p)\n },\n\n 'Matrix, number | BigNumber | string': function (x, p) {\n return _norm(x, p)\n }\n })\n\n /**\n * Calculate the plus infinity norm for a vector\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNormPlusInfinity (x) {\n // norm(x, Infinity) = max(abs(x))\n let pinf = 0\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n const v = abs(value)\n if (larger(v, pinf)) {\n pinf = v\n }\n }, true)\n return pinf\n }\n\n /**\n * Calculate the minus infinity norm for a vector\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNormMinusInfinity (x) {\n // norm(x, -Infinity) = min(abs(x))\n let ninf\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n const v = abs(value)\n if (!ninf || smaller(v, ninf)) {\n ninf = v\n }\n }, true)\n return ninf || 0\n }\n\n /**\n * Calculate the norm for a vector\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _vectorNorm (x, p) {\n // check p\n if (p === Number.POSITIVE_INFINITY || p === 'inf') {\n return _vectorNormPlusInfinity(x)\n }\n if (p === Number.NEGATIVE_INFINITY || p === '-inf') {\n return _vectorNormMinusInfinity(x)\n }\n if (p === 'fro') {\n return _norm(x, 2)\n }\n if (typeof p === 'number' && !isNaN(p)) {\n // check p != 0\n if (!equalScalar(p, 0)) {\n // norm(x, p) = sum(abs(xi) ^ p) ^ 1/p\n let n = 0\n // skip zeros since abs(0) === 0\n x.forEach(function (value) {\n n = add(pow(abs(value), p), n)\n }, true)\n return pow(n, 1 / p)\n }\n return Number.POSITIVE_INFINITY\n }\n // invalid parameter value\n throw new Error('Unsupported parameter value')\n }\n\n /**\n * Calculate the Frobenius norm for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormFrobenius (x) {\n // norm(x) = sqrt(sum(diag(x'x)))\n let fro = 0\n x.forEach(function (value, index) {\n fro = add(fro, multiply(value, conj(value)))\n })\n return abs(sqrt(fro))\n }\n\n /**\n * Calculate the norm L1 for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormOne (x) {\n // norm(x) = the largest column sum\n const c = []\n // result\n let maxc = 0\n // skip zeros since abs(0) == 0\n x.forEach(function (value, index) {\n const j = index[1]\n const cj = add(c[j] || 0, abs(value))\n if (larger(cj, maxc)) {\n maxc = cj\n }\n c[j] = cj\n }, true)\n return maxc\n }\n\n /**\n * Calculate the norm L2 for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormTwo (x) {\n // norm(x) = sqrt( max eigenvalue of A*.A)\n const sizeX = x.size()\n if (sizeX[0] !== sizeX[1]) {\n throw new RangeError('Invalid matrix dimensions')\n }\n const tx = ctranspose(x)\n const squaredX = multiply(tx, x)\n const eigenVals = eigs(squaredX).values\n const rho = eigenVals.get([eigenVals.size()[0] - 1])\n return abs(sqrt(rho))\n }\n\n /**\n * Calculate the infinity norm for a matrix\n * @param {Matrix} x\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNormInfinity (x) {\n // norm(x) = the largest row sum\n const r = []\n // result\n let maxr = 0\n // skip zeros since abs(0) == 0\n x.forEach(function (value, index) {\n const i = index[0]\n const ri = add(r[i] || 0, abs(value))\n if (larger(ri, maxr)) {\n maxr = ri\n }\n r[i] = ri\n }, true)\n return maxr\n }\n\n /**\n * Calculate the norm for a 2D Matrix (M*N)\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _matrixNorm (x, p) {\n // check p\n if (p === 1) {\n return _matrixNormOne(x)\n }\n if (p === Number.POSITIVE_INFINITY || p === 'inf') {\n return _matrixNormInfinity(x)\n }\n if (p === 'fro') {\n return _matrixNormFrobenius(x)\n }\n if (p === 2) {\n return _matrixNormTwo(x)\n } // invalid parameter value\n\n throw new Error('Unsupported parameter value ' + p)\n }\n\n /**\n * Calculate the norm for an array\n * @param {Matrix} x\n * @param {number | string} p\n * @returns {number} Returns the norm\n * @private\n */\n function _norm (x, p) {\n // size\n const sizeX = x.size()\n\n // check if it is a vector\n if (sizeX.length === 1) {\n return _vectorNorm(x, p)\n }\n // MxN matrix\n if (sizeX.length === 2) {\n if (sizeX[0] && sizeX[1]) {\n return _matrixNorm(x, p)\n } else {\n throw new RangeError('Invalid matrix dimensions')\n }\n }\n }\n }\n)\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'dot'\nconst dependencies = ['typed', 'addScalar', 'multiplyScalar', 'conj', 'size']\n\nexport const createDot = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, multiplyScalar, conj, size }) => {\n /**\n * Calculate the dot product of two vectors. The dot product of\n * `A = [a1, a2, ..., an]` and `B = [b1, b2, ..., bn]` is defined as:\n *\n * dot(A, B) = conj(a1) * b1 + conj(a2) * b2 + ... + conj(an) * bn\n *\n * Syntax:\n *\n * math.dot(x, y)\n *\n * Examples:\n *\n * math.dot([2, 4, 1], [2, 2, 3]) // returns number 15\n * math.multiply([2, 4, 1], [2, 2, 3]) // returns number 15\n *\n * See also:\n *\n * multiply, cross\n *\n * @param {Array | Matrix} x First vector\n * @param {Array | Matrix} y Second vector\n * @return {number} Returns the dot product of `x` and `y`\n */\n return typed(name, {\n 'Array | DenseMatrix, Array | DenseMatrix': _denseDot,\n 'SparseMatrix, SparseMatrix': _sparseDot\n })\n\n function _validateDim (x, y) {\n const xSize = _size(x)\n const ySize = _size(y)\n let xLen, yLen\n\n if (xSize.length === 1) {\n xLen = xSize[0]\n } else if (xSize.length === 2 && xSize[1] === 1) {\n xLen = xSize[0]\n } else {\n throw new RangeError('Expected a column vector, instead got a matrix of size (' + xSize.join(', ') + ')')\n }\n\n if (ySize.length === 1) {\n yLen = ySize[0]\n } else if (ySize.length === 2 && ySize[1] === 1) {\n yLen = ySize[0]\n } else {\n throw new RangeError('Expected a column vector, instead got a matrix of size (' + ySize.join(', ') + ')')\n }\n\n if (xLen !== yLen) throw new RangeError('Vectors must have equal length (' + xLen + ' != ' + yLen + ')')\n if (xLen === 0) throw new RangeError('Cannot calculate the dot product of empty vectors')\n\n return xLen\n }\n\n function _denseDot (a, b) {\n const N = _validateDim(a, b)\n\n const adata = isMatrix(a) ? a._data : a\n const adt = isMatrix(a) ? a._datatype : undefined\n\n const bdata = isMatrix(b) ? b._data : b\n const bdt = isMatrix(b) ? b._datatype : undefined\n\n // are these 2-dimensional column vectors? (as opposed to 1-dimensional vectors)\n const aIsColumn = _size(a).length === 2\n const bIsColumn = _size(b).length === 2\n\n let add = addScalar\n let mul = multiplyScalar\n\n // process data types\n if (adt && bdt && adt === bdt && typeof adt === 'string') {\n const dt = adt\n // find signatures that matches (dt, dt)\n add = typed.find(addScalar, [dt, dt])\n mul = typed.find(multiplyScalar, [dt, dt])\n }\n\n // both vectors 1-dimensional\n if (!aIsColumn && !bIsColumn) {\n let c = mul(conj(adata[0]), bdata[0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i]), bdata[i]))\n }\n return c\n }\n\n // a is 1-dim, b is column\n if (!aIsColumn && bIsColumn) {\n let c = mul(conj(adata[0]), bdata[0][0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i]), bdata[i][0]))\n }\n return c\n }\n\n // a is column, b is 1-dim\n if (aIsColumn && !bIsColumn) {\n let c = mul(conj(adata[0][0]), bdata[0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i][0]), bdata[i]))\n }\n return c\n }\n\n // both vectors are column\n if (aIsColumn && bIsColumn) {\n let c = mul(conj(adata[0][0]), bdata[0][0])\n for (let i = 1; i < N; i++) {\n c = add(c, mul(conj(adata[i][0]), bdata[i][0]))\n }\n return c\n }\n }\n\n function _sparseDot (x, y) {\n _validateDim(x, y)\n\n const xindex = x._index\n const xvalues = x._values\n\n const yindex = y._index\n const yvalues = y._values\n\n // TODO optimize add & mul using datatype\n let c = 0\n const add = addScalar\n const mul = multiplyScalar\n\n let i = 0\n let j = 0\n while (i < xindex.length && j < yindex.length) {\n const I = xindex[i]\n const J = yindex[j]\n\n if (I < J) {\n i++\n continue\n }\n if (I > J) {\n j++\n continue\n }\n if (I === J) {\n c = add(c, mul(xvalues[i], yvalues[j]))\n i++\n j++\n }\n }\n\n return c\n }\n\n // TODO remove this once #1771 is fixed\n function _size (x) {\n return isMatrix(x) ? x.size() : size(x)\n }\n})\n","import { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'trace'\nconst dependencies = ['typed', 'matrix', 'add']\n\nexport const createTrace = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, add }) => {\n /**\n * Calculate the trace of a matrix: the sum of the elements on the main\n * diagonal of a square matrix.\n *\n * Syntax:\n *\n * math.trace(x)\n *\n * Examples:\n *\n * math.trace([[1, 2], [3, 4]]) // returns 5\n *\n * const A = [\n * [1, 2, 3],\n * [-1, 2, 3],\n * [2, 0, 3]\n * ]\n * math.trace(A) // returns 6\n *\n * See also:\n *\n * diag\n *\n * @param {Array | Matrix} x A matrix\n *\n * @return {number} The trace of `x`\n */\n return typed('trace', {\n Array: function _arrayTrace (x) {\n // use dense matrix implementation\n return _denseTrace(matrix(x))\n },\n\n SparseMatrix: _sparseTrace,\n\n DenseMatrix: _denseTrace,\n\n any: clone\n })\n\n function _denseTrace (m) {\n // matrix size & data\n const size = m._size\n const data = m._data\n\n // process dimensions\n switch (size.length) {\n case 1:\n // vector\n if (size[0] === 1) {\n // return data[0]\n return clone(data[0])\n }\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n case 2:\n {\n // two dimensional\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n // calulate sum\n let sum = 0\n // loop diagonal\n for (let i = 0; i < rows; i++) { sum = add(sum, data[i][i]) }\n // return trace\n return sum\n } else {\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n }\n }\n default:\n // multi dimensional\n throw new RangeError('Matrix must be two dimensional (size: ' + format(size) + ')')\n }\n }\n\n function _sparseTrace (m) {\n // matrix arrays\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n const size = m._size\n // check dimensions\n const rows = size[0]\n const columns = size[1]\n // matrix must be square\n if (rows === columns) {\n // calulate sum\n let sum = 0\n // check we have data (avoid looping columns)\n if (values.length > 0) {\n // loop columns\n for (let j = 0; j < columns; j++) {\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // loop k within [k0, k1[\n for (let k = k0; k < k1; k++) {\n // row index\n const i = index[k]\n // check row\n if (i === j) {\n // accumulate value\n sum = add(sum, values[k])\n // exit loop\n break\n }\n if (i > j) {\n // exit loop, no value on the diagonal for column j\n break\n }\n }\n }\n }\n // return trace\n return sum\n }\n throw new RangeError('Matrix must be square (size: ' + format(size) + ')')\n }\n})\n","import { factory } from '../../../utils/factory.js'\nimport { isBigNumber, isMatrix } from '../../../utils/is.js'\n\nconst name = 'index'\nconst dependencies = ['typed', 'Index']\n\nexport const createIndex = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index }) => {\n /**\n * Create an index. An Index can store ranges having start, step, and end\n * for multiple dimensions.\n * Matrix.get, Matrix.set, and math.subset accept an Index as input.\n *\n * Syntax:\n *\n * math.index(range1, range2, ...)\n *\n * Where each range can be any of:\n *\n * - A number\n * - A string for getting/setting an object property\n * - An instance of `Range`\n * - A one-dimensional Array or a Matrix with numbers\n *\n * Indexes must be zero-based, integer numbers.\n *\n * Examples:\n *\n * const b = [1, 2, 3, 4, 5]\n * math.subset(b, math.index([1, 2, 3])) // returns [2, 3, 4]\n *\n * const a = math.matrix([[1, 2], [3, 4]])\n * a.subset(math.index(0, 1)) // returns 2\n *\n * See also:\n *\n * bignumber, boolean, complex, matrix, number, string, unit\n *\n * @param {...*} ranges Zero or more ranges or numbers.\n * @return {Index} Returns the created index\n */\n return typed(name, {\n '...number | string | BigNumber | Range | Array | Matrix': function (args) {\n const ranges = args.map(function (arg) {\n if (isBigNumber(arg)) {\n return arg.toNumber() // convert BigNumber to Number\n } else if (Array.isArray(arg) || isMatrix(arg)) {\n return arg.map(function (elem) {\n // convert BigNumber to Number\n return isBigNumber(elem) ? elem.toNumber() : elem\n })\n } else {\n return arg\n }\n })\n\n const res = new Index()\n Index.apply(res, ranges)\n return res\n }\n })\n})\n","// Reserved keywords not allowed to use in the parser\nexport const keywords = {\n end: true\n}\n","import { isNode } from '../../utils/is.js'\n\nimport { keywords } from '../keywords.js'\nimport { deepStrictEqual, hasOwnProperty } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Node'\nconst dependencies = ['mathWithTransform']\n\nexport const createNode = /* #__PURE__ */ factory(name, dependencies, ({ mathWithTransform }) => {\n /**\n * Node\n */\n function Node () {\n if (!(this instanceof Node)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n }\n\n /**\n * Evaluate the node\n * @param {Object} [scope] Scope to read/write variables\n * @return {*} Returns the result\n */\n Node.prototype.evaluate = function (scope) {\n return this.compile().evaluate(scope)\n }\n\n Node.prototype.type = 'Node'\n\n Node.prototype.isNode = true\n\n Node.prototype.comment = ''\n\n /**\n * Compile the node into an optimized, evauatable JavaScript function\n * @return {{evaluate: function([Object])}} object\n * Returns an object with a function 'evaluate',\n * which can be invoked as expr.evaluate([scope: Object]),\n * where scope is an optional object with\n * variables.\n */\n Node.prototype.compile = function () {\n const expr = this._compile(mathWithTransform, {})\n const args = {}\n const context = null\n\n function evaluate (scope) {\n const s = scope || {}\n _validateScope(s)\n return expr(s, args, context)\n }\n\n return {\n evaluate\n }\n }\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n Node.prototype._compile = function (math, argNames) {\n throw new Error('Method _compile should be implemented by type ' + this.type)\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n Node.prototype.forEach = function (callback) {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot run forEach on a Node interface')\n }\n\n /**\n * Create a new Node having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {OperatorNode} Returns a transformed copy of the node\n */\n Node.prototype.map = function (callback) {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot run map on a Node interface')\n }\n\n /**\n * Validate whether an object is a Node, for use with map\n * @param {Node} node\n * @returns {Node} Returns the input if it's a node, else throws an Error\n * @protected\n */\n Node.prototype._ifNode = function (node) {\n if (!isNode(node)) {\n throw new TypeError('Callback function must return a Node')\n }\n\n return node\n }\n\n /**\n * Recursively traverse all nodes in a node tree. Executes given callback for\n * this node and each of its child nodes.\n * @param {function(node: Node, path: string, parent: Node)} callback\n * A callback called for every node in the node tree.\n */\n Node.prototype.traverse = function (callback) {\n // execute callback for itself\n // eslint-disable-next-line\n callback(this, null, null)\n\n // recursively traverse over all childs of a node\n function _traverse (node, callback) {\n node.forEach(function (child, path, parent) {\n callback(child, path, parent)\n _traverse(child, callback)\n })\n }\n\n _traverse(this, callback)\n }\n\n /**\n * Recursively transform a node tree via a transform function.\n *\n * For example, to replace all nodes of type SymbolNode having name 'x' with a\n * ConstantNode with value 2:\n *\n * const res = Node.transform(function (node, path, parent) {\n * if (node && node.isSymbolNode) && (node.name === 'x')) {\n * return new ConstantNode(2)\n * }\n * else {\n * return node\n * }\n * })\n *\n * @param {function(node: Node, path: string, parent: Node) : Node} callback\n * A mapping function accepting a node, and returning\n * a replacement for the node or the original node.\n * Signature: callback(node: Node, index: string, parent: Node) : Node\n * @return {Node} Returns the original node or its replacement\n */\n Node.prototype.transform = function (callback) {\n function _transform (child, path, parent) {\n const replacement = callback(child, path, parent)\n\n if (replacement !== child) {\n // stop iterating when the node is replaced\n return replacement\n }\n\n return child.map(_transform)\n }\n\n return _transform(this, null, null)\n }\n\n /**\n * Find any node in the node tree matching given filter function. For example, to\n * find all nodes of type SymbolNode having name 'x':\n *\n * const results = Node.filter(function (node) {\n * return (node && node.isSymbolNode) && (node.name === 'x')\n * })\n *\n * @param {function(node: Node, path: string, parent: Node) : Node} callback\n * A test function returning true when a node matches, and false\n * otherwise. Function signature:\n * callback(node: Node, index: string, parent: Node) : boolean\n * @return {Node[]} nodes An array with nodes matching given filter criteria\n */\n Node.prototype.filter = function (callback) {\n const nodes = []\n\n this.traverse(function (node, path, parent) {\n if (callback(node, path, parent)) {\n nodes.push(node)\n }\n })\n\n return nodes\n }\n\n /**\n * Create a shallow clone of this node\n * @return {Node}\n */\n Node.prototype.clone = function () {\n // must be implemented by each of the Node implementations\n throw new Error('Cannot clone a Node interface')\n }\n\n /**\n * Create a deep clone of this node\n * @return {Node}\n */\n Node.prototype.cloneDeep = function () {\n return this.map(function (node) {\n return node.cloneDeep()\n })\n }\n\n /**\n * Deep compare this node with another node.\n * @param {Node} other\n * @return {boolean} Returns true when both nodes are of the same type and\n * contain the same values (as do their childs)\n */\n Node.prototype.equals = function (other) {\n return other\n ? deepStrictEqual(this, other)\n : false\n }\n\n /**\n * Get string representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\"or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toString = function (options) {\n let customString\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customString = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n return this._toString(options)\n }\n\n /**\n * Get a JSON representation of the node\n * Both .toJSON() and the static .fromJSON(json) should be implemented by all\n * implementations of Node\n * @returns {Object}\n */\n Node.prototype.toJSON = function () {\n throw new Error('Cannot serialize object: toJSON not implemented by ' + this.type)\n }\n\n /**\n * Get HTML representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\" or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toHTML = function (options) {\n let customString\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customString = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n return this.toHTML(options)\n }\n\n /**\n * Internal function to generate the string output.\n * This has to be implemented by every Node\n *\n * @throws {Error}\n */\n Node.prototype._toString = function () {\n // must be implemented by each of the Node implementations\n throw new Error('_toString not implemented for ' + this.type)\n }\n\n /**\n * Get LaTeX representation. (wrapper function)\n *\n * This function can get an object of the following form:\n * {\n * handler: //This can be a callback function of the form\n * // \"function callback(node, options)\"or\n * // a map that maps function names (used in FunctionNodes)\n * // to callbacks\n * parenthesis: \"keep\" //the parenthesis option (This is optional)\n * }\n *\n * @param {Object} [options]\n * @return {string}\n */\n Node.prototype.toTex = function (options) {\n let customTex\n if (options && typeof options === 'object') {\n switch (typeof options.handler) {\n case 'object':\n case 'undefined':\n break\n case 'function':\n customTex = options.handler(this, options)\n break\n default:\n throw new TypeError('Object or function expected as callback')\n }\n }\n\n if (typeof customTex !== 'undefined') {\n return customTex\n }\n\n return this._toTex(options)\n }\n\n /**\n * Internal function to generate the LaTeX output.\n * This has to be implemented by every Node\n *\n * @param {Object} [options]\n * @throws {Error}\n */\n Node.prototype._toTex = function (options) {\n // must be implemented by each of the Node implementations\n throw new Error('_toTex not implemented for ' + this.type)\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n Node.prototype.getIdentifier = function () {\n return this.type\n }\n\n /**\n * Get the content of the current Node.\n * @return {Node} node\n **/\n Node.prototype.getContent = function () {\n return this\n }\n\n /**\n * Validate the symbol names of a scope.\n * Throws an error when the scope contains an illegal symbol.\n * @param {Object} scope\n */\n function _validateScope (scope) {\n for (const symbol in scope) {\n if (hasOwnProperty(scope, symbol)) {\n if (symbol in keywords) {\n throw new Error('Scope contains an illegal symbol, \"' + symbol + '\" is a reserved keyword')\n }\n }\n }\n }\n\n return Node\n}, { isClass: true, isNode: true })\n","import { IndexError } from '../../../error/IndexError.js'\n\n/**\n * Transform zero-based indices to one-based indices in errors\n * @param {Error} err\n * @returns {Error | IndexError} Returns the transformed error\n */\nexport function errorTransform (err) {\n if (err && err.isIndexError) {\n return new IndexError(\n err.index + 1,\n err.min + 1,\n err.max !== undefined ? err.max + 1 : undefined)\n }\n\n return err\n}\n","import { errorTransform } from '../../transform/utils/errorTransform.js'\nimport { getSafeProperty } from '../../../utils/customs.js'\n\nexport function accessFactory ({ subset }) {\n /**\n * Retrieve part of an object:\n *\n * - Retrieve a property from an object\n * - Retrieve a part of a string\n * - Retrieve a matrix subset\n *\n * @param {Object | Array | Matrix | string} object\n * @param {Index} index\n * @return {Object | Array | Matrix | string} Returns the subset\n */\n return function access (object, index) {\n try {\n if (Array.isArray(object)) {\n return subset(object, index)\n } else if (object && typeof object.subset === 'function') { // Matrix\n return object.subset(index)\n } else if (typeof object === 'string') {\n // TODO: move getStringSubset into a separate util file, use that\n return subset(object, index)\n } else if (typeof object === 'object') {\n if (!index.isObjectProperty()) {\n throw new TypeError('Cannot apply a numeric index as object property')\n }\n\n return getSafeProperty(object, index.getObjectProperty())\n } else {\n throw new TypeError('Cannot apply index: unsupported type of object')\n }\n } catch (err) {\n throw errorTransform(err)\n }\n }\n}\n","import {\n isAccessorNode,\n isArrayNode,\n isConstantNode,\n isFunctionNode,\n isIndexNode,\n isNode,\n isObjectNode,\n isParenthesisNode,\n isSymbolNode\n} from '../../utils/is.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { accessFactory } from './utils/access.js'\n\nconst name = 'AccessorNode'\nconst dependencies = [\n 'subset',\n 'Node'\n]\n\nexport const createAccessorNode = /* #__PURE__ */ factory(name, dependencies, ({ subset, Node }) => {\n const access = accessFactory({ subset })\n\n /**\n * @constructor AccessorNode\n * @extends {Node}\n * Access an object property or get a matrix subset\n *\n * @param {Node} object The object from which to retrieve\n * a property or subset.\n * @param {IndexNode} index IndexNode containing ranges\n */\n function AccessorNode (object, index) {\n if (!(this instanceof AccessorNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (!isNode(object)) {\n throw new TypeError('Node expected for parameter \"object\"')\n }\n if (!isIndexNode(index)) {\n throw new TypeError('IndexNode expected for parameter \"index\"')\n }\n\n this.object = object || null\n this.index = index\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n if (this.index) {\n return (this.index.isObjectProperty())\n ? this.index.getObjectProperty()\n : ''\n } else {\n return this.object.name || ''\n }\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n AccessorNode.prototype = new Node()\n\n AccessorNode.prototype.type = 'AccessorNode'\n\n AccessorNode.prototype.isAccessorNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n AccessorNode.prototype._compile = function (math, argNames) {\n const evalObject = this.object._compile(math, argNames)\n const evalIndex = this.index._compile(math, argNames)\n\n if (this.index.isObjectProperty()) {\n const prop = this.index.getObjectProperty()\n return function evalAccessorNode (scope, args, context) {\n return getSafeProperty(evalObject(scope, args, context), prop)\n }\n } else {\n return function evalAccessorNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n const index = evalIndex(scope, args, object) // we pass object here instead of context\n return access(object, index)\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n AccessorNode.prototype.forEach = function (callback) {\n callback(this.object, 'object', this)\n callback(this.index, 'index', this)\n }\n\n /**\n * Create a new AccessorNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {AccessorNode} Returns a transformed copy of the node\n */\n AccessorNode.prototype.map = function (callback) {\n return new AccessorNode(\n this._ifNode(callback(this.object, 'object', this)),\n this._ifNode(callback(this.index, 'index', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {AccessorNode}\n */\n AccessorNode.prototype.clone = function () {\n return new AccessorNode(this.object, this.index)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype._toString = function (options) {\n let object = this.object.toString(options)\n if (needParenthesis(this.object)) {\n object = '(' + object + ')'\n }\n\n return object + this.index.toString(options)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype.toHTML = function (options) {\n let object = this.object.toHTML(options)\n if (needParenthesis(this.object)) {\n object = '(' + object + ')'\n }\n\n return object + this.index.toHTML(options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string}\n */\n AccessorNode.prototype._toTex = function (options) {\n let object = this.object.toTex(options)\n if (needParenthesis(this.object)) {\n object = '\\\\left(\\' + object + \\'\\\\right)'\n }\n\n return object + this.index.toTex(options)\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n AccessorNode.prototype.toJSON = function () {\n return {\n mathjs: 'AccessorNode',\n object: this.object,\n index: this.index\n }\n }\n\n /**\n * Instantiate an AccessorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"AccessorNode\", object: ..., index: ...}`,\n * where mathjs is optional\n * @returns {AccessorNode}\n */\n AccessorNode.fromJSON = function (json) {\n return new AccessorNode(json.object, json.index)\n }\n\n /**\n * Are parenthesis needed?\n * @private\n */\n function needParenthesis (node) {\n // TODO: maybe make a method on the nodes which tells whether they need parenthesis?\n return !(\n isAccessorNode(node) ||\n isArrayNode(node) ||\n isConstantNode(node) ||\n isFunctionNode(node) ||\n isObjectNode(node) ||\n isParenthesisNode(node) ||\n isSymbolNode(node))\n }\n\n return AccessorNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ArrayNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createArrayNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ArrayNode\n * @extends {Node}\n * Holds an 1-dimensional array with items\n * @param {Node[]} [items] 1 dimensional array with items\n */\n function ArrayNode (items) {\n if (!(this instanceof ArrayNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.items = items || []\n\n // validate input\n if (!Array.isArray(this.items) || !this.items.every(isNode)) {\n throw new TypeError('Array containing Nodes expected')\n }\n }\n\n ArrayNode.prototype = new Node()\n\n ArrayNode.prototype.type = 'ArrayNode'\n\n ArrayNode.prototype.isArrayNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ArrayNode.prototype._compile = function (math, argNames) {\n const evalItems = map(this.items, function (item) {\n return item._compile(math, argNames)\n })\n\n const asMatrix = (math.config.matrix !== 'Array')\n if (asMatrix) {\n const matrix = math.matrix\n return function evalArrayNode (scope, args, context) {\n return matrix(map(evalItems, function (evalItem) {\n return evalItem(scope, args, context)\n }))\n }\n } else {\n return function evalArrayNode (scope, args, context) {\n return map(evalItems, function (evalItem) {\n return evalItem(scope, args, context)\n })\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ArrayNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.items.length; i++) {\n const node = this.items[i]\n callback(node, 'items[' + i + ']', this)\n }\n }\n\n /**\n * Create a new ArrayNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ArrayNode} Returns a transformed copy of the node\n */\n ArrayNode.prototype.map = function (callback) {\n const items = []\n for (let i = 0; i < this.items.length; i++) {\n items[i] = this._ifNode(callback(this.items[i], 'items[' + i + ']', this))\n }\n return new ArrayNode(items)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ArrayNode}\n */\n ArrayNode.prototype.clone = function () {\n return new ArrayNode(this.items.slice(0))\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ArrayNode.prototype._toString = function (options) {\n const items = this.items.map(function (node) {\n return node.toString(options)\n })\n return '[' + items.join(', ') + ']'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ArrayNode.prototype.toJSON = function () {\n return {\n mathjs: 'ArrayNode',\n items: this.items\n }\n }\n\n /**\n * Instantiate an ArrayNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ArrayNode\", items: [...]}`,\n * where mathjs is optional\n * @returns {ArrayNode}\n */\n ArrayNode.fromJSON = function (json) {\n return new ArrayNode(json.items)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ArrayNode.prototype.toHTML = function (options) {\n const items = this.items.map(function (node) {\n return node.toHTML(options)\n })\n return '[' + items.join(',') + ']'\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ArrayNode.prototype._toTex = function (options) {\n let s = '\\\\begin{bmatrix}'\n\n this.items.forEach(function (node) {\n if (node.items) {\n s += node.items.map(function (childNode) {\n return childNode.toTex(options)\n }).join('&')\n } else {\n s += node.toTex(options)\n }\n\n // new line\n s += '\\\\\\\\'\n })\n s += '\\\\end{bmatrix}'\n return s\n }\n\n return ArrayNode\n}, { isClass: true, isNode: true })\n","// list of identifiers of nodes in order of their precedence\n// also contains information about left/right associativity\n// and which other operator the operator is associative with\n// Example:\n// addition is associative with addition and subtraction, because:\n// (a+b)+c=a+(b+c)\n// (a+b)-c=a+(b-c)\n//\n// postfix operators are left associative, prefix operators\n// are right associative\n//\n// It's also possible to set the following properties:\n// latexParens: if set to false, this node doesn't need to be enclosed\n// in parentheses when using LaTeX\n// latexLeftParens: if set to false, this !OperatorNode's!\n// left argument doesn't need to be enclosed\n// in parentheses\n// latexRightParens: the same for the right argument\nimport { hasOwnProperty } from '../utils/object.js'\n\nexport const properties = [\n { // assignment\n AssignmentNode: {},\n FunctionAssignmentNode: {}\n },\n { // conditional expression\n ConditionalNode: {\n latexLeftParens: false,\n latexRightParens: false,\n latexParens: false\n // conditionals don't need parentheses in LaTeX because\n // they are 2 dimensional\n }\n },\n { // logical or\n 'OperatorNode:or': {\n associativity: 'left',\n associativeWith: []\n }\n\n },\n { // logical xor\n 'OperatorNode:xor': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // logical and\n 'OperatorNode:and': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise or\n 'OperatorNode:bitOr': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise xor\n 'OperatorNode:bitXor': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitwise and\n 'OperatorNode:bitAnd': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // relational operators\n 'OperatorNode:equal': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:unequal': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:smaller': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:larger': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:smallerEq': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:largerEq': {\n associativity: 'left',\n associativeWith: []\n },\n RelationalNode: {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // bitshift operators\n 'OperatorNode:leftShift': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:rightArithShift': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:rightLogShift': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // unit conversion\n 'OperatorNode:to': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // range\n RangeNode: {}\n },\n { // addition, subtraction\n 'OperatorNode:add': {\n associativity: 'left',\n associativeWith: ['OperatorNode:add', 'OperatorNode:subtract']\n },\n 'OperatorNode:subtract': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // multiply, divide, modulus\n 'OperatorNode:multiply': {\n associativity: 'left',\n associativeWith: [\n 'OperatorNode:multiply',\n 'OperatorNode:divide',\n 'Operator:dotMultiply',\n 'Operator:dotDivide'\n ]\n },\n 'OperatorNode:divide': {\n associativity: 'left',\n associativeWith: [],\n latexLeftParens: false,\n latexRightParens: false,\n latexParens: false\n // fractions don't require parentheses because\n // they're 2 dimensional, so parens aren't needed\n // in LaTeX\n },\n 'OperatorNode:dotMultiply': {\n associativity: 'left',\n associativeWith: [\n 'OperatorNode:multiply',\n 'OperatorNode:divide',\n 'OperatorNode:dotMultiply',\n 'OperatorNode:doDivide'\n ]\n },\n 'OperatorNode:dotDivide': {\n associativity: 'left',\n associativeWith: []\n },\n 'OperatorNode:mod': {\n associativity: 'left',\n associativeWith: []\n }\n },\n { // unary prefix operators\n 'OperatorNode:unaryPlus': {\n associativity: 'right'\n },\n 'OperatorNode:unaryMinus': {\n associativity: 'right'\n },\n 'OperatorNode:bitNot': {\n associativity: 'right'\n },\n 'OperatorNode:not': {\n associativity: 'right'\n }\n },\n { // exponentiation\n 'OperatorNode:pow': {\n associativity: 'right',\n associativeWith: [],\n latexRightParens: false\n // the exponent doesn't need parentheses in\n // LaTeX because it's 2 dimensional\n // (it's on top)\n },\n 'OperatorNode:dotPow': {\n associativity: 'right',\n associativeWith: []\n }\n },\n { // factorial\n 'OperatorNode:factorial': {\n associativity: 'left'\n }\n },\n { // matrix transpose\n 'OperatorNode:transpose': {\n associativity: 'left'\n }\n }\n]\n\n/**\n * Get the precedence of a Node.\n * Higher number for higher precedence, starting with 0.\n * Returns null if the precedence is undefined.\n *\n * @param {Node} _node\n * @param {string} parenthesis\n * @return {number | null}\n */\nexport function getPrecedence (_node, parenthesis) {\n let node = _node\n if (parenthesis !== 'keep') {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n node = _node.getContent()\n }\n const identifier = node.getIdentifier()\n for (let i = 0; i < properties.length; i++) {\n if (identifier in properties[i]) {\n return i\n }\n }\n return null\n}\n\n/**\n * Get the associativity of an operator (left or right).\n * Returns a string containing 'left' or 'right' or null if\n * the associativity is not defined.\n *\n * @param {Node} _node\n * @param {string} parenthesis\n * @return {string|null}\n * @throws {Error}\n */\nexport function getAssociativity (_node, parenthesis) {\n let node = _node\n if (parenthesis !== 'keep') {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n node = _node.getContent()\n }\n const identifier = node.getIdentifier()\n const index = getPrecedence(node, parenthesis)\n if (index === null) {\n // node isn't in the list\n return null\n }\n const property = properties[index][identifier]\n\n if (hasOwnProperty(property, 'associativity')) {\n if (property.associativity === 'left') {\n return 'left'\n }\n if (property.associativity === 'right') {\n return 'right'\n }\n // associativity is invalid\n throw Error('\\'' + identifier + '\\' has the invalid associativity \\'' +\n property.associativity + '\\'.')\n }\n\n // associativity is undefined\n return null\n}\n\n/**\n * Check if an operator is associative with another operator.\n * Returns either true or false or null if not defined.\n *\n * @param {Node} nodeA\n * @param {Node} nodeB\n * @param {string} parenthesis\n * @return {boolean | null}\n */\nexport function isAssociativeWith (nodeA, nodeB, parenthesis) {\n // ParenthesisNodes are only ignored when not in 'keep' mode\n const a = (parenthesis !== 'keep') ? nodeA.getContent() : nodeA\n const b = (parenthesis !== 'keep') ? nodeA.getContent() : nodeB\n const identifierA = a.getIdentifier()\n const identifierB = b.getIdentifier()\n const index = getPrecedence(a, parenthesis)\n if (index === null) {\n // node isn't in the list\n return null\n }\n const property = properties[index][identifierA]\n\n if (hasOwnProperty(property, 'associativeWith') &&\n (property.associativeWith instanceof Array)) {\n for (let i = 0; i < property.associativeWith.length; i++) {\n if (property.associativeWith[i] === identifierB) {\n return true\n }\n }\n return false\n }\n\n // associativeWith is not defined\n return null\n}\n","import { isAccessorNode, isIndexNode, isNode, isSymbolNode } from '../../utils/is.js'\nimport { getSafeProperty, setSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { accessFactory } from './utils/access.js'\nimport { assignFactory } from './utils/assign.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'AssignmentNode'\nconst dependencies = [\n 'subset',\n '?matrix', // FIXME: should not be needed at all, should be handled by subset\n 'Node'\n]\n\nexport const createAssignmentNode = /* #__PURE__ */ factory(name, dependencies, ({ subset, matrix, Node }) => {\n const access = accessFactory({ subset })\n const assign = assignFactory({ subset, matrix })\n\n /**\n * @constructor AssignmentNode\n * @extends {Node}\n *\n * Define a symbol, like `a=3.2`, update a property like `a.b=3.2`, or\n * replace a subset of a matrix like `A[2,2]=42`.\n *\n * Syntax:\n *\n * new AssignmentNode(symbol, value)\n * new AssignmentNode(object, index, value)\n *\n * Usage:\n *\n * new AssignmentNode(new SymbolNode('a'), new ConstantNode(2)) // a=2\n * new AssignmentNode(new SymbolNode('a'), new IndexNode('b'), new ConstantNode(2)) // a.b=2\n * new AssignmentNode(new SymbolNode('a'), new IndexNode(1, 2), new ConstantNode(3)) // a[1,2]=3\n *\n * @param {SymbolNode | AccessorNode} object Object on which to assign a value\n * @param {IndexNode} [index=null] Index, property name or matrix\n * index. Optional. If not provided\n * and `object` is a SymbolNode,\n * the property is assigned to the\n * global scope.\n * @param {Node} value The value to be assigned\n */\n function AssignmentNode (object, index, value) {\n if (!(this instanceof AssignmentNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.object = object\n this.index = value ? index : null\n this.value = value || index\n\n // validate input\n if (!isSymbolNode(object) && !isAccessorNode(object)) {\n throw new TypeError('SymbolNode or AccessorNode expected as \"object\"')\n }\n if (isSymbolNode(object) && object.name === 'end') {\n throw new Error('Cannot assign to symbol \"end\"')\n }\n if (this.index && !isIndexNode(this.index)) { // index is optional\n throw new TypeError('IndexNode expected as \"index\"')\n }\n if (!isNode(this.value)) {\n throw new TypeError('Node expected as \"value\"')\n }\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n if (this.index) {\n return (this.index.isObjectProperty())\n ? this.index.getObjectProperty()\n : ''\n } else {\n return this.object.name || ''\n }\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n AssignmentNode.prototype = new Node()\n\n AssignmentNode.prototype.type = 'AssignmentNode'\n\n AssignmentNode.prototype.isAssignmentNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n AssignmentNode.prototype._compile = function (math, argNames) {\n const evalObject = this.object._compile(math, argNames)\n const evalIndex = this.index ? this.index._compile(math, argNames) : null\n const evalValue = this.value._compile(math, argNames)\n const name = this.object.name\n\n if (!this.index) {\n // apply a variable to the scope, for example `a=2`\n if (!isSymbolNode(this.object)) {\n throw new TypeError('SymbolNode expected as object')\n }\n\n return function evalAssignmentNode (scope, args, context) {\n return setSafeProperty(scope, name, evalValue(scope, args, context))\n }\n } else if (this.index.isObjectProperty()) {\n // apply an object property for example `a.b=2`\n const prop = this.index.getObjectProperty()\n\n return function evalAssignmentNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n const value = evalValue(scope, args, context)\n return setSafeProperty(object, prop, value)\n }\n } else if (isSymbolNode(this.object)) {\n // update a matrix subset, for example `a[2]=3`\n return function evalAssignmentNode (scope, args, context) {\n const childObject = evalObject(scope, args, context)\n const value = evalValue(scope, args, context)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n setSafeProperty(scope, name, assign(childObject, index, value))\n return value\n }\n } else { // isAccessorNode(node.object) === true\n // update a matrix subset, for example `a.b[2]=3`\n\n // we will not use the compile function of the AccessorNode, but compile it\n // ourselves here as we need the parent object of the AccessorNode:\n // wee need to apply the updated object to parent object\n const evalParentObject = this.object.object._compile(math, argNames)\n\n if (this.object.index.isObjectProperty()) {\n const parentProp = this.object.index.getObjectProperty()\n\n return function evalAssignmentNode (scope, args, context) {\n const parent = evalParentObject(scope, args, context)\n const childObject = getSafeProperty(parent, parentProp)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n const value = evalValue(scope, args, context)\n setSafeProperty(parent, parentProp, assign(childObject, index, value))\n return value\n }\n } else {\n // if some parameters use the 'end' parameter, we need to calculate the size\n const evalParentIndex = this.object.index._compile(math, argNames)\n\n return function evalAssignmentNode (scope, args, context) {\n const parent = evalParentObject(scope, args, context)\n const parentIndex = evalParentIndex(scope, args, parent) // Important: we pass parent instead of context\n const childObject = access(parent, parentIndex)\n const index = evalIndex(scope, args, childObject) // Important: we pass childObject instead of context\n const value = evalValue(scope, args, context)\n\n assign(parent, parentIndex, assign(childObject, index, value))\n\n return value\n }\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n AssignmentNode.prototype.forEach = function (callback) {\n callback(this.object, 'object', this)\n if (this.index) {\n callback(this.index, 'index', this)\n }\n callback(this.value, 'value', this)\n }\n\n /**\n * Create a new AssignmentNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {AssignmentNode} Returns a transformed copy of the node\n */\n AssignmentNode.prototype.map = function (callback) {\n const object = this._ifNode(callback(this.object, 'object', this))\n const index = this.index\n ? this._ifNode(callback(this.index, 'index', this))\n : null\n const value = this._ifNode(callback(this.value, 'value', this))\n\n return new AssignmentNode(object, index, value)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {AssignmentNode}\n */\n AssignmentNode.prototype.clone = function () {\n return new AssignmentNode(this.object, this.index, this.value)\n }\n\n /*\n * Is parenthesis needed?\n * @param {node} node\n * @param {string} [parenthesis='keep']\n * @private\n */\n function needParenthesis (node, parenthesis) {\n if (!parenthesis) {\n parenthesis = 'keep'\n }\n\n const precedence = getPrecedence(node, parenthesis)\n const exprPrecedence = getPrecedence(node.value, parenthesis)\n return (parenthesis === 'all') ||\n ((exprPrecedence !== null) && (exprPrecedence <= precedence))\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype._toString = function (options) {\n const object = this.object.toString(options)\n const index = this.index ? this.index.toString(options) : ''\n let value = this.value.toString(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = '(' + value + ')'\n }\n\n return object + index + ' = ' + value\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n AssignmentNode.prototype.toJSON = function () {\n return {\n mathjs: 'AssignmentNode',\n object: this.object,\n index: this.index,\n value: this.value\n }\n }\n\n /**\n * Instantiate an AssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"AssignmentNode\", object: ..., index: ..., value: ...}`,\n * where mathjs is optional\n * @returns {AssignmentNode}\n */\n AssignmentNode.fromJSON = function (json) {\n return new AssignmentNode(json.object, json.index, json.value)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype.toHTML = function (options) {\n const object = this.object.toHTML(options)\n const index = this.index ? this.index.toHTML(options) : ''\n let value = this.value.toHTML(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = '(' + value + ')'\n }\n\n return object + index + '=' + value\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string}\n */\n AssignmentNode.prototype._toTex = function (options) {\n const object = this.object.toTex(options)\n const index = this.index ? this.index.toTex(options) : ''\n let value = this.value.toTex(options)\n if (needParenthesis(this, options && options.parenthesis)) {\n value = `\\\\left(${value}\\\\right)`\n }\n\n return object + index + ':=' + value\n }\n\n return AssignmentNode\n}, { isClass: true, isNode: true })\n","import { errorTransform } from '../../transform/utils/errorTransform.js'\nimport { setSafeProperty } from '../../../utils/customs.js'\n\nexport function assignFactory ({ subset, matrix }) {\n /**\n * Replace part of an object:\n *\n * - Assign a property to an object\n * - Replace a part of a string\n * - Replace a matrix subset\n *\n * @param {Object | Array | Matrix | string} object\n * @param {Index} index\n * @param {*} value\n * @return {Object | Array | Matrix | string} Returns the original object\n * except in case of a string\n */\n // TODO: change assign to return the value instead of the object\n return function assign (object, index, value) {\n try {\n if (Array.isArray(object)) {\n // we use matrix.subset here instead of the function subset because we must not clone the contents\n return matrix(object).subset(index, value).valueOf()\n } else if (object && typeof object.subset === 'function') { // Matrix\n return object.subset(index, value)\n } else if (typeof object === 'string') {\n // TODO: move setStringSubset into a separate util file, use that\n return subset(object, index, value)\n } else if (typeof object === 'object') {\n if (!index.isObjectProperty()) {\n throw TypeError('Cannot apply a numeric index as object property')\n }\n setSafeProperty(object, index.getObjectProperty(), value)\n return object\n } else {\n throw new TypeError('Cannot apply index: unsupported type of object')\n }\n } catch (err) {\n throw errorTransform(err)\n }\n }\n}\n","import { isNode } from '../../utils/is.js'\nimport { forEach, map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'BlockNode'\nconst dependencies = [\n 'ResultSet',\n 'Node'\n]\n\nexport const createBlockNode = /* #__PURE__ */ factory(name, dependencies, ({ ResultSet, Node }) => {\n /**\n * @constructor BlockNode\n * @extends {Node}\n * Holds a set with blocks\n * @param {Array.<{node: Node} | {node: Node, visible: boolean}>} blocks\n * An array with blocks, where a block is constructed as an Object\n * with properties block, which is a Node, and visible, which is\n * a boolean. The property visible is optional and is true by default\n */\n function BlockNode (blocks) {\n if (!(this instanceof BlockNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input, copy blocks\n if (!Array.isArray(blocks)) throw new Error('Array expected')\n this.blocks = blocks.map(function (block) {\n const node = block && block.node\n const visible = block && block.visible !== undefined ? block.visible : true\n\n if (!isNode(node)) throw new TypeError('Property \"node\" must be a Node')\n if (typeof visible !== 'boolean') throw new TypeError('Property \"visible\" must be a boolean')\n\n return {\n node: node,\n visible: visible\n }\n })\n }\n\n BlockNode.prototype = new Node()\n\n BlockNode.prototype.type = 'BlockNode'\n\n BlockNode.prototype.isBlockNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n BlockNode.prototype._compile = function (math, argNames) {\n const evalBlocks = map(this.blocks, function (block) {\n return {\n evaluate: block.node._compile(math, argNames),\n visible: block.visible\n }\n })\n\n return function evalBlockNodes (scope, args, context) {\n const results = []\n\n forEach(evalBlocks, function evalBlockNode (block) {\n const result = block.evaluate(scope, args, context)\n if (block.visible) {\n results.push(result)\n }\n })\n\n return new ResultSet(results)\n }\n }\n\n /**\n * Execute a callback for each of the child blocks of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n BlockNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.blocks.length; i++) {\n callback(this.blocks[i].node, 'blocks[' + i + '].node', this)\n }\n }\n\n /**\n * Create a new BlockNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {BlockNode} Returns a transformed copy of the node\n */\n BlockNode.prototype.map = function (callback) {\n const blocks = []\n for (let i = 0; i < this.blocks.length; i++) {\n const block = this.blocks[i]\n const node = this._ifNode(callback(block.node, 'blocks[' + i + '].node', this))\n blocks[i] = {\n node: node,\n visible: block.visible\n }\n }\n return new BlockNode(blocks)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {BlockNode}\n */\n BlockNode.prototype.clone = function () {\n const blocks = this.blocks.map(function (block) {\n return {\n node: block.node,\n visible: block.visible\n }\n })\n\n return new BlockNode(blocks)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n BlockNode.prototype._toString = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toString(options) + (param.visible ? '' : ';')\n }).join('\\n')\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n BlockNode.prototype.toJSON = function () {\n return {\n mathjs: 'BlockNode',\n blocks: this.blocks\n }\n }\n\n /**\n * Instantiate an BlockNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"BlockNode\", blocks: [{node: ..., visible: false}, ...]}`,\n * where mathjs is optional\n * @returns {BlockNode}\n */\n BlockNode.fromJSON = function (json) {\n return new BlockNode(json.blocks)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n BlockNode.prototype.toHTML = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toHTML(options) + (param.visible ? '' : ';')\n }).join('
')\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n BlockNode.prototype._toTex = function (options) {\n return this.blocks.map(function (param) {\n return param.node.toTex(options) + (param.visible ? '' : ';')\n }).join('\\\\;\\\\;\\n')\n }\n\n return BlockNode\n}, { isClass: true, isNode: true })\n","import { isBigNumber, isComplex, isNode, isUnit, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'ConditionalNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createConditionalNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A lazy evaluating conditional operator: 'condition ? trueExpr : falseExpr'\n *\n * @param {Node} condition Condition, must result in a boolean\n * @param {Node} trueExpr Expression evaluated when condition is true\n * @param {Node} falseExpr Expression evaluated when condition is true\n *\n * @constructor ConditionalNode\n * @extends {Node}\n */\n function ConditionalNode (condition, trueExpr, falseExpr) {\n if (!(this instanceof ConditionalNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n if (!isNode(condition)) throw new TypeError('Parameter condition must be a Node')\n if (!isNode(trueExpr)) throw new TypeError('Parameter trueExpr must be a Node')\n if (!isNode(falseExpr)) throw new TypeError('Parameter falseExpr must be a Node')\n\n this.condition = condition\n this.trueExpr = trueExpr\n this.falseExpr = falseExpr\n }\n\n ConditionalNode.prototype = new Node()\n\n ConditionalNode.prototype.type = 'ConditionalNode'\n\n ConditionalNode.prototype.isConditionalNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ConditionalNode.prototype._compile = function (math, argNames) {\n const evalCondition = this.condition._compile(math, argNames)\n const evalTrueExpr = this.trueExpr._compile(math, argNames)\n const evalFalseExpr = this.falseExpr._compile(math, argNames)\n\n return function evalConditionalNode (scope, args, context) {\n return testCondition(evalCondition(scope, args, context))\n ? evalTrueExpr(scope, args, context)\n : evalFalseExpr(scope, args, context)\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ConditionalNode.prototype.forEach = function (callback) {\n callback(this.condition, 'condition', this)\n callback(this.trueExpr, 'trueExpr', this)\n callback(this.falseExpr, 'falseExpr', this)\n }\n\n /**\n * Create a new ConditionalNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ConditionalNode} Returns a transformed copy of the node\n */\n ConditionalNode.prototype.map = function (callback) {\n return new ConditionalNode(\n this._ifNode(callback(this.condition, 'condition', this)),\n this._ifNode(callback(this.trueExpr, 'trueExpr', this)),\n this._ifNode(callback(this.falseExpr, 'falseExpr', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ConditionalNode}\n */\n ConditionalNode.prototype.clone = function () {\n return new ConditionalNode(this.condition, this.trueExpr, this.falseExpr)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n // Enclose Arguments in parentheses if they are an OperatorNode\n // or have lower or equal precedence\n // NOTE: enclosing all OperatorNodes in parentheses is a decision\n // purely based on aesthetics and readability\n let condition = this.condition.toString(options)\n const conditionPrecedence = getPrecedence(this.condition, parenthesis)\n if ((parenthesis === 'all') ||\n (this.condition.type === 'OperatorNode') ||\n ((conditionPrecedence !== null) && (conditionPrecedence <= precedence))) {\n condition = '(' + condition + ')'\n }\n\n let trueExpr = this.trueExpr.toString(options)\n const truePrecedence = getPrecedence(this.trueExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.trueExpr.type === 'OperatorNode') ||\n ((truePrecedence !== null) && (truePrecedence <= precedence))) {\n trueExpr = '(' + trueExpr + ')'\n }\n\n let falseExpr = this.falseExpr.toString(options)\n const falsePrecedence = getPrecedence(this.falseExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.falseExpr.type === 'OperatorNode') ||\n ((falsePrecedence !== null) && (falsePrecedence <= precedence))) {\n falseExpr = '(' + falseExpr + ')'\n }\n return condition + ' ? ' + trueExpr + ' : ' + falseExpr\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ConditionalNode.prototype.toJSON = function () {\n return {\n mathjs: 'ConditionalNode',\n condition: this.condition,\n trueExpr: this.trueExpr,\n falseExpr: this.falseExpr\n }\n }\n\n /**\n * Instantiate an ConditionalNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ConditionalNode\", \"condition\": ..., \"trueExpr\": ..., \"falseExpr\": ...}`,\n * where mathjs is optional\n * @returns {ConditionalNode}\n */\n ConditionalNode.fromJSON = function (json) {\n return new ConditionalNode(json.condition, json.trueExpr, json.falseExpr)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n // Enclose Arguments in parentheses if they are an OperatorNode\n // or have lower or equal precedence\n // NOTE: enclosing all OperatorNodes in parentheses is a decision\n // purely based on aesthetics and readability\n let condition = this.condition.toHTML(options)\n const conditionPrecedence = getPrecedence(this.condition, parenthesis)\n if ((parenthesis === 'all') ||\n (this.condition.type === 'OperatorNode') ||\n ((conditionPrecedence !== null) && (conditionPrecedence <= precedence))) {\n condition = '(' + condition + ')'\n }\n\n let trueExpr = this.trueExpr.toHTML(options)\n const truePrecedence = getPrecedence(this.trueExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.trueExpr.type === 'OperatorNode') ||\n ((truePrecedence !== null) && (truePrecedence <= precedence))) {\n trueExpr = '(' + trueExpr + ')'\n }\n\n let falseExpr = this.falseExpr.toHTML(options)\n const falsePrecedence = getPrecedence(this.falseExpr, parenthesis)\n if ((parenthesis === 'all') ||\n (this.falseExpr.type === 'OperatorNode') ||\n ((falsePrecedence !== null) && (falsePrecedence <= precedence))) {\n falseExpr = '(' + falseExpr + ')'\n }\n return condition + '?' + trueExpr + ':' + falseExpr\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ConditionalNode.prototype._toTex = function (options) {\n return '\\\\begin{cases} {' +\n this.trueExpr.toTex(options) + '}, &\\\\quad{\\\\text{if }\\\\;' +\n this.condition.toTex(options) +\n '}\\\\\\\\{' + this.falseExpr.toTex(options) +\n '}, &\\\\quad{\\\\text{otherwise}}\\\\end{cases}'\n }\n\n /**\n * Test whether a condition is met\n * @param {*} condition\n * @returns {boolean} true if condition is true or non-zero, else false\n */\n function testCondition (condition) {\n if (typeof condition === 'number' ||\n typeof condition === 'boolean' ||\n typeof condition === 'string') {\n return !!condition\n }\n\n if (condition) {\n if (isBigNumber(condition)) {\n return !condition.isZero()\n }\n\n if (isComplex(condition)) {\n return !!((condition.re || condition.im))\n }\n\n if (isUnit(condition)) {\n return !!condition.value\n }\n }\n\n if (condition === null || condition === undefined) {\n return false\n }\n\n throw new TypeError('Unsupported type of condition \"' + typeOf(condition) + '\"')\n }\n\n return ConditionalNode\n}, { isClass: true, isNode: true })\n","/* eslint no-template-curly-in-string: \"off\" */\n\nimport escapeLatexLib from 'escape-latex'\nimport { hasOwnProperty } from './object.js'\n\nexport const latexSymbols = {\n // GREEK LETTERS\n Alpha: 'A',\n alpha: '\\\\alpha',\n Beta: 'B',\n beta: '\\\\beta',\n Gamma: '\\\\Gamma',\n gamma: '\\\\gamma',\n Delta: '\\\\Delta',\n delta: '\\\\delta',\n Epsilon: 'E',\n epsilon: '\\\\epsilon',\n varepsilon: '\\\\varepsilon',\n Zeta: 'Z',\n zeta: '\\\\zeta',\n Eta: 'H',\n eta: '\\\\eta',\n Theta: '\\\\Theta',\n theta: '\\\\theta',\n vartheta: '\\\\vartheta',\n Iota: 'I',\n iota: '\\\\iota',\n Kappa: 'K',\n kappa: '\\\\kappa',\n varkappa: '\\\\varkappa',\n Lambda: '\\\\Lambda',\n lambda: '\\\\lambda',\n Mu: 'M',\n mu: '\\\\mu',\n Nu: 'N',\n nu: '\\\\nu',\n Xi: '\\\\Xi',\n xi: '\\\\xi',\n Omicron: 'O',\n omicron: 'o',\n Pi: '\\\\Pi',\n pi: '\\\\pi',\n varpi: '\\\\varpi',\n Rho: 'P',\n rho: '\\\\rho',\n varrho: '\\\\varrho',\n Sigma: '\\\\Sigma',\n sigma: '\\\\sigma',\n varsigma: '\\\\varsigma',\n Tau: 'T',\n tau: '\\\\tau',\n Upsilon: '\\\\Upsilon',\n upsilon: '\\\\upsilon',\n Phi: '\\\\Phi',\n phi: '\\\\phi',\n varphi: '\\\\varphi',\n Chi: 'X',\n chi: '\\\\chi',\n Psi: '\\\\Psi',\n psi: '\\\\psi',\n Omega: '\\\\Omega',\n omega: '\\\\omega',\n // logic\n true: '\\\\mathrm{True}',\n false: '\\\\mathrm{False}',\n // other\n i: 'i', // TODO use \\i ??\n inf: '\\\\infty',\n Inf: '\\\\infty',\n infinity: '\\\\infty',\n Infinity: '\\\\infty',\n oo: '\\\\infty',\n lim: '\\\\lim',\n undefined: '\\\\mathbf{?}'\n}\n\nexport const latexOperators = {\n transpose: '^\\\\top',\n ctranspose: '^H',\n factorial: '!',\n pow: '^',\n dotPow: '.^\\\\wedge', // TODO find ideal solution\n unaryPlus: '+',\n unaryMinus: '-',\n bitNot: '\\\\~', // TODO find ideal solution\n not: '\\\\neg',\n multiply: '\\\\cdot',\n divide: '\\\\frac', // TODO how to handle that properly?\n dotMultiply: '.\\\\cdot', // TODO find ideal solution\n dotDivide: '.:', // TODO find ideal solution\n mod: '\\\\mod',\n add: '+',\n subtract: '-',\n to: '\\\\rightarrow',\n leftShift: '<<',\n rightArithShift: '>>',\n rightLogShift: '>>>',\n equal: '=',\n unequal: '\\\\neq',\n smaller: '<',\n larger: '>',\n smallerEq: '\\\\leq',\n largerEq: '\\\\geq',\n bitAnd: '\\\\&',\n bitXor: '\\\\underline{|}',\n bitOr: '|',\n and: '\\\\wedge',\n xor: '\\\\veebar',\n or: '\\\\vee'\n}\n\nexport const latexFunctions = {\n // arithmetic\n abs: { 1: '\\\\left|${args[0]}\\\\right|' },\n add: { 2: `\\\\left(\\${args[0]}${latexOperators.add}\\${args[1]}\\\\right)` },\n cbrt: { 1: '\\\\sqrt[3]{${args[0]}}' },\n ceil: { 1: '\\\\left\\\\lceil${args[0]}\\\\right\\\\rceil' },\n cube: { 1: '\\\\left(${args[0]}\\\\right)^3' },\n divide: { 2: '\\\\frac{${args[0]}}{${args[1]}}' },\n dotDivide: { 2: `\\\\left(\\${args[0]}${latexOperators.dotDivide}\\${args[1]}\\\\right)` },\n dotMultiply: { 2: `\\\\left(\\${args[0]}${latexOperators.dotMultiply}\\${args[1]}\\\\right)` },\n dotPow: { 2: `\\\\left(\\${args[0]}${latexOperators.dotPow}\\${args[1]}\\\\right)` },\n exp: { 1: '\\\\exp\\\\left(${args[0]}\\\\right)' },\n expm1: `\\\\left(e${latexOperators.pow}{\\${args[0]}}-1\\\\right)`,\n fix: { 1: '\\\\mathrm{${name}}\\\\left(${args[0]}\\\\right)' },\n floor: { 1: '\\\\left\\\\lfloor${args[0]}\\\\right\\\\rfloor' },\n gcd: '\\\\gcd\\\\left(${args}\\\\right)',\n hypot: '\\\\hypot\\\\left(${args}\\\\right)',\n log: {\n 1: '\\\\ln\\\\left(${args[0]}\\\\right)',\n 2: '\\\\log_{${args[1]}}\\\\left(${args[0]}\\\\right)'\n },\n log10: { 1: '\\\\log_{10}\\\\left(${args[0]}\\\\right)' },\n log1p: {\n 1: '\\\\ln\\\\left(${args[0]}+1\\\\right)',\n 2: '\\\\log_{${args[1]}}\\\\left(${args[0]}+1\\\\right)'\n },\n log2: '\\\\log_{2}\\\\left(${args[0]}\\\\right)',\n mod: { 2: `\\\\left(\\${args[0]}${latexOperators.mod}\\${args[1]}\\\\right)` },\n multiply: { 2: `\\\\left(\\${args[0]}${latexOperators.multiply}\\${args[1]}\\\\right)` },\n norm: {\n 1: '\\\\left\\\\|${args[0]}\\\\right\\\\|',\n 2: undefined // use default template\n },\n nthRoot: { 2: '\\\\sqrt[${args[1]}]{${args[0]}}' },\n nthRoots: { 2: '\\\\{y : $y^{args[1]} = {${args[0]}}\\\\}' },\n pow: { 2: `\\\\left(\\${args[0]}\\\\right)${latexOperators.pow}{\\${args[1]}}` },\n round: {\n 1: '\\\\left\\\\lfloor${args[0]}\\\\right\\\\rceil',\n 2: undefined // use default template\n },\n sign: { 1: '\\\\mathrm{${name}}\\\\left(${args[0]}\\\\right)' },\n sqrt: { 1: '\\\\sqrt{${args[0]}}' },\n square: { 1: '\\\\left(${args[0]}\\\\right)^2' },\n subtract: { 2: `\\\\left(\\${args[0]}${latexOperators.subtract}\\${args[1]}\\\\right)` },\n unaryMinus: { 1: `${latexOperators.unaryMinus}\\\\left(\\${args[0]}\\\\right)` },\n unaryPlus: { 1: `${latexOperators.unaryPlus}\\\\left(\\${args[0]}\\\\right)` },\n\n // bitwise\n bitAnd: { 2: `\\\\left(\\${args[0]}${latexOperators.bitAnd}\\${args[1]}\\\\right)` },\n bitNot: { 1: latexOperators.bitNot + '\\\\left(${args[0]}\\\\right)' },\n bitOr: { 2: `\\\\left(\\${args[0]}${latexOperators.bitOr}\\${args[1]}\\\\right)` },\n bitXor: { 2: `\\\\left(\\${args[0]}${latexOperators.bitXor}\\${args[1]}\\\\right)` },\n leftShift: { 2: `\\\\left(\\${args[0]}${latexOperators.leftShift}\\${args[1]}\\\\right)` },\n rightArithShift: { 2: `\\\\left(\\${args[0]}${latexOperators.rightArithShift}\\${args[1]}\\\\right)` },\n rightLogShift: { 2: `\\\\left(\\${args[0]}${latexOperators.rightLogShift}\\${args[1]}\\\\right)` },\n\n // combinatorics\n bellNumbers: { 1: '\\\\mathrm{B}_{${args[0]}}' },\n catalan: { 1: '\\\\mathrm{C}_{${args[0]}}' },\n stirlingS2: { 2: '\\\\mathrm{S}\\\\left(${args}\\\\right)' },\n\n // complex\n arg: { 1: '\\\\arg\\\\left(${args[0]}\\\\right)' },\n conj: { 1: '\\\\left(${args[0]}\\\\right)^*' },\n im: { 1: '\\\\Im\\\\left\\\\lbrace${args[0]}\\\\right\\\\rbrace' },\n re: { 1: '\\\\Re\\\\left\\\\lbrace${args[0]}\\\\right\\\\rbrace' },\n\n // logical\n and: { 2: `\\\\left(\\${args[0]}${latexOperators.and}\\${args[1]}\\\\right)` },\n not: { 1: latexOperators.not + '\\\\left(${args[0]}\\\\right)' },\n or: { 2: `\\\\left(\\${args[0]}${latexOperators.or}\\${args[1]}\\\\right)` },\n xor: { 2: `\\\\left(\\${args[0]}${latexOperators.xor}\\${args[1]}\\\\right)` },\n\n // matrix\n cross: { 2: '\\\\left(${args[0]}\\\\right)\\\\times\\\\left(${args[1]}\\\\right)' },\n ctranspose: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.ctranspose}` },\n det: { 1: '\\\\det\\\\left(${args[0]}\\\\right)' },\n dot: { 2: '\\\\left(${args[0]}\\\\cdot${args[1]}\\\\right)' },\n expm: { 1: '\\\\exp\\\\left(${args[0]}\\\\right)' },\n inv: { 1: '\\\\left(${args[0]}\\\\right)^{-1}' },\n sqrtm: { 1: `{\\${args[0]}}${latexOperators.pow}{\\\\frac{1}{2}}` },\n trace: { 1: '\\\\mathrm{tr}\\\\left(${args[0]}\\\\right)' },\n transpose: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.transpose}` },\n\n // probability\n combinations: { 2: '\\\\binom{${args[0]}}{${args[1]}}' },\n combinationsWithRep: { 2: '\\\\left(\\\\!\\\\!{\\\\binom{${args[0]}}{${args[1]}}}\\\\!\\\\!\\\\right)' },\n factorial: { 1: `\\\\left(\\${args[0]}\\\\right)${latexOperators.factorial}` },\n gamma: { 1: '\\\\Gamma\\\\left(${args[0]}\\\\right)' },\n\n // relational\n equal: { 2: `\\\\left(\\${args[0]}${latexOperators.equal}\\${args[1]}\\\\right)` },\n larger: { 2: `\\\\left(\\${args[0]}${latexOperators.larger}\\${args[1]}\\\\right)` },\n largerEq: { 2: `\\\\left(\\${args[0]}${latexOperators.largerEq}\\${args[1]}\\\\right)` },\n smaller: { 2: `\\\\left(\\${args[0]}${latexOperators.smaller}\\${args[1]}\\\\right)` },\n smallerEq: { 2: `\\\\left(\\${args[0]}${latexOperators.smallerEq}\\${args[1]}\\\\right)` },\n unequal: { 2: `\\\\left(\\${args[0]}${latexOperators.unequal}\\${args[1]}\\\\right)` },\n\n // special\n erf: { 1: 'erf\\\\left(${args[0]}\\\\right)' },\n\n // statistics\n max: '\\\\max\\\\left(${args}\\\\right)',\n min: '\\\\min\\\\left(${args}\\\\right)',\n variance: '\\\\mathrm{Var}\\\\left(${args}\\\\right)',\n\n // trigonometry\n acos: { 1: '\\\\cos^{-1}\\\\left(${args[0]}\\\\right)' },\n acosh: { 1: '\\\\cosh^{-1}\\\\left(${args[0]}\\\\right)' },\n acot: { 1: '\\\\cot^{-1}\\\\left(${args[0]}\\\\right)' },\n acoth: { 1: '\\\\coth^{-1}\\\\left(${args[0]}\\\\right)' },\n acsc: { 1: '\\\\csc^{-1}\\\\left(${args[0]}\\\\right)' },\n acsch: { 1: '\\\\mathrm{csch}^{-1}\\\\left(${args[0]}\\\\right)' },\n asec: { 1: '\\\\sec^{-1}\\\\left(${args[0]}\\\\right)' },\n asech: { 1: '\\\\mathrm{sech}^{-1}\\\\left(${args[0]}\\\\right)' },\n asin: { 1: '\\\\sin^{-1}\\\\left(${args[0]}\\\\right)' },\n asinh: { 1: '\\\\sinh^{-1}\\\\left(${args[0]}\\\\right)' },\n atan: { 1: '\\\\tan^{-1}\\\\left(${args[0]}\\\\right)' },\n atan2: { 2: '\\\\mathrm{atan2}\\\\left(${args}\\\\right)' },\n atanh: { 1: '\\\\tanh^{-1}\\\\left(${args[0]}\\\\right)' },\n cos: { 1: '\\\\cos\\\\left(${args[0]}\\\\right)' },\n cosh: { 1: '\\\\cosh\\\\left(${args[0]}\\\\right)' },\n cot: { 1: '\\\\cot\\\\left(${args[0]}\\\\right)' },\n coth: { 1: '\\\\coth\\\\left(${args[0]}\\\\right)' },\n csc: { 1: '\\\\csc\\\\left(${args[0]}\\\\right)' },\n csch: { 1: '\\\\mathrm{csch}\\\\left(${args[0]}\\\\right)' },\n sec: { 1: '\\\\sec\\\\left(${args[0]}\\\\right)' },\n sech: { 1: '\\\\mathrm{sech}\\\\left(${args[0]}\\\\right)' },\n sin: { 1: '\\\\sin\\\\left(${args[0]}\\\\right)' },\n sinh: { 1: '\\\\sinh\\\\left(${args[0]}\\\\right)' },\n tan: { 1: '\\\\tan\\\\left(${args[0]}\\\\right)' },\n tanh: { 1: '\\\\tanh\\\\left(${args[0]}\\\\right)' },\n\n // unit\n to: { 2: `\\\\left(\\${args[0]}${latexOperators.to}\\${args[1]}\\\\right)` },\n\n // utils\n numeric: function (node, options) {\n // Not sure if this is strictly right but should work correctly for the vast majority of use cases.\n return node.args[0].toTex()\n },\n\n // type\n number: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(\\\\left(${args[0]}\\\\right)${args[1]}\\\\right)'\n },\n string: {\n 0: '\\\\mathtt{\"\"}',\n 1: '\\\\mathrm{string}\\\\left(${args[0]}\\\\right)'\n },\n bignumber: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)'\n },\n complex: {\n 0: '0',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: `\\\\left(\\\\left(\\${args[0]}\\\\right)+${latexSymbols.i}\\\\cdot\\\\left(\\${args[1]}\\\\right)\\\\right)`\n },\n matrix: {\n 0: '\\\\begin{bmatrix}\\\\end{bmatrix}',\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(${args[0]}\\\\right)'\n },\n sparse: {\n 0: '\\\\begin{bsparse}\\\\end{bsparse}',\n 1: '\\\\left(${args[0]}\\\\right)'\n },\n unit: {\n 1: '\\\\left(${args[0]}\\\\right)',\n 2: '\\\\left(\\\\left(${args[0]}\\\\right)${args[1]}\\\\right)'\n }\n\n}\n\nexport const defaultTemplate = '\\\\mathrm{${name}}\\\\left(${args}\\\\right)'\n\nconst latexUnits = {\n deg: '^\\\\circ'\n}\n\nexport function escapeLatex (string) {\n return escapeLatexLib(string, { preserveFormatting: true })\n}\n\n// @param {string} name\n// @param {boolean} isUnit\nexport function toSymbol (name, isUnit) {\n isUnit = typeof isUnit === 'undefined' ? false : isUnit\n if (isUnit) {\n if (hasOwnProperty(latexUnits, name)) {\n return latexUnits[name]\n }\n\n return '\\\\mathrm{' + escapeLatex(name) + '}'\n }\n\n if (hasOwnProperty(latexSymbols, name)) {\n return latexSymbols[name]\n }\n\n return escapeLatex(name)\n}\n","import { format } from '../../utils/string.js'\nimport { typeOf } from '../../utils/is.js'\nimport { escapeLatex } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ConstantNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createConstantNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A ConstantNode holds a constant value like a number or string.\n *\n * Usage:\n *\n * new ConstantNode(2.3)\n * new ConstantNode('hello')\n *\n * @param {*} value Value can be any type (number, BigNumber, string, ...)\n * @constructor ConstantNode\n * @extends {Node}\n */\n function ConstantNode (value) {\n if (!(this instanceof ConstantNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.value = value\n }\n\n ConstantNode.prototype = new Node()\n\n ConstantNode.prototype.type = 'ConstantNode'\n\n ConstantNode.prototype.isConstantNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ConstantNode.prototype._compile = function (math, argNames) {\n const value = this.value\n\n return function evalConstantNode () {\n return value\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ConstantNode.prototype.forEach = function (callback) {\n // nothing to do, we don't have childs\n }\n\n /**\n * Create a new ConstantNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {ConstantNode} Returns a clone of the node\n */\n ConstantNode.prototype.map = function (callback) {\n return this.clone()\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ConstantNode}\n */\n ConstantNode.prototype.clone = function () {\n return new ConstantNode(this.value)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype._toString = function (options) {\n return format(this.value, options)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype.toHTML = function (options) {\n const value = this._toString(options)\n\n switch (typeOf(this.value)) {\n case 'number':\n case 'BigNumber':\n case 'Fraction':\n return '' + value + ''\n case 'string':\n return '' + value + ''\n case 'boolean':\n return '' + value + ''\n case 'null':\n return '' + value + ''\n case 'undefined':\n return '' + value + ''\n\n default:\n return '' + value + ''\n }\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ConstantNode.prototype.toJSON = function () {\n return {\n mathjs: 'ConstantNode',\n value: this.value\n }\n }\n\n /**\n * Instantiate a ConstantNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SymbolNode\", value: 2.3}`,\n * where mathjs is optional\n * @returns {ConstantNode}\n */\n ConstantNode.fromJSON = function (json) {\n return new ConstantNode(json.value)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ConstantNode.prototype._toTex = function (options) {\n const value = this._toString(options)\n\n switch (typeOf(this.value)) {\n case 'string':\n return '\\\\mathtt{' + escapeLatex(value) + '}'\n\n case 'number':\n case 'BigNumber':\n {\n if (!isFinite(this.value)) {\n return (this.value.valueOf() < 0)\n ? '-\\\\infty'\n : '\\\\infty'\n }\n\n const index = value.toLowerCase().indexOf('e')\n if (index !== -1) {\n return value.substring(0, index) + '\\\\cdot10^{' +\n value.substring(index + 1) + '}'\n }\n }\n return value\n case 'Fraction':\n return this.value.toLatex()\n\n default:\n return value\n }\n }\n\n return ConstantNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\n\nimport { keywords } from '../keywords.js'\nimport { escape } from '../../utils/string.js'\nimport { forEach, join } from '../../utils/array.js'\nimport { toSymbol } from '../../utils/latex.js'\nimport { getPrecedence } from '../operators.js'\nimport { setSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'FunctionAssignmentNode'\nconst dependencies = [\n 'typed',\n 'Node'\n]\n\nexport const createFunctionAssignmentNode = /* #__PURE__ */ factory(name, dependencies, ({ typed, Node }) => {\n /**\n * @constructor FunctionAssignmentNode\n * @extends {Node}\n * Function assignment\n *\n * @param {string} name Function name\n * @param {string[] | Array.<{name: string, type: string}>} params\n * Array with function parameter names, or an\n * array with objects containing the name\n * and type of the parameter\n * @param {Node} expr The function expression\n */\n function FunctionAssignmentNode (name, params, expr) {\n if (!(this instanceof FunctionAssignmentNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof name !== 'string') throw new TypeError('String expected for parameter \"name\"')\n if (!Array.isArray(params)) throw new TypeError('Array containing strings or objects expected for parameter \"params\"')\n if (!isNode(expr)) throw new TypeError('Node expected for parameter \"expr\"')\n if (name in keywords) throw new Error('Illegal function name, \"' + name + '\" is a reserved keyword')\n\n this.name = name\n this.params = params.map(function (param) {\n return (param && param.name) || param\n })\n this.types = params.map(function (param) {\n return (param && param.type) || 'any'\n })\n this.expr = expr\n }\n\n FunctionAssignmentNode.prototype = new Node()\n\n FunctionAssignmentNode.prototype.type = 'FunctionAssignmentNode'\n\n FunctionAssignmentNode.prototype.isFunctionAssignmentNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n FunctionAssignmentNode.prototype._compile = function (math, argNames) {\n const childArgNames = Object.create(argNames)\n forEach(this.params, function (param) {\n childArgNames[param] = true\n })\n\n // compile the function expression with the child args\n const evalExpr = this.expr._compile(math, childArgNames)\n const name = this.name\n const params = this.params\n const signature = join(this.types, ',')\n const syntax = name + '(' + join(this.params, ', ') + ')'\n\n return function evalFunctionAssignmentNode (scope, args, context) {\n const signatures = {}\n signatures[signature] = function () {\n const childArgs = Object.create(args)\n\n for (let i = 0; i < params.length; i++) {\n childArgs[params[i]] = arguments[i]\n }\n\n return evalExpr(scope, childArgs, context)\n }\n const fn = typed(name, signatures)\n fn.syntax = syntax\n\n setSafeProperty(scope, name, fn)\n\n return fn\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n FunctionAssignmentNode.prototype.forEach = function (callback) {\n callback(this.expr, 'expr', this)\n }\n\n /**\n * Create a new FunctionAssignmentNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {FunctionAssignmentNode} Returns a transformed copy of the node\n */\n FunctionAssignmentNode.prototype.map = function (callback) {\n const expr = this._ifNode(callback(this.expr, 'expr', this))\n\n return new FunctionAssignmentNode(this.name, this.params.slice(0), expr)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {FunctionAssignmentNode}\n */\n FunctionAssignmentNode.prototype.clone = function () {\n return new FunctionAssignmentNode(this.name, this.params.slice(0), this.expr)\n }\n\n /**\n * Is parenthesis needed?\n * @param {Node} node\n * @param {Object} parenthesis\n * @private\n */\n function needParenthesis (node, parenthesis) {\n const precedence = getPrecedence(node, parenthesis)\n const exprPrecedence = getPrecedence(node.expr, parenthesis)\n\n return (parenthesis === 'all') ||\n ((exprPrecedence !== null) && (exprPrecedence <= precedence))\n }\n\n /**\n * get string representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n let expr = this.expr.toString(options)\n if (needParenthesis(this, parenthesis)) {\n expr = '(' + expr + ')'\n }\n return this.name + '(' + this.params.join(', ') + ') = ' + expr\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n FunctionAssignmentNode.prototype.toJSON = function () {\n const types = this.types\n\n return {\n mathjs: 'FunctionAssignmentNode',\n name: this.name,\n params: this.params.map(function (param, index) {\n return {\n name: param,\n type: types[index]\n }\n }),\n expr: this.expr\n }\n }\n\n /**\n * Instantiate an FunctionAssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"FunctionAssignmentNode\", name: ..., params: ..., expr: ...}`,\n * where mathjs is optional\n * @returns {FunctionAssignmentNode}\n */\n FunctionAssignmentNode.fromJSON = function (json) {\n return new FunctionAssignmentNode(json.name, json.params, json.expr)\n }\n\n /**\n * get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const params = []\n for (let i = 0; i < this.params.length; i++) {\n params.push('' + escape(this.params[i]) + '')\n }\n let expr = this.expr.toHTML(options)\n if (needParenthesis(this, parenthesis)) {\n expr = '(' + expr + ')'\n }\n return '' + escape(this.name) + '' + '(' + params.join(',') + ')=' + expr\n }\n\n /**\n * get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionAssignmentNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n let expr = this.expr.toTex(options)\n if (needParenthesis(this, parenthesis)) {\n expr = `\\\\left(${expr}\\\\right)`\n }\n\n return '\\\\mathrm{' + this.name +\n '}\\\\left(' + this.params.map(toSymbol).join(',') + '\\\\right):=' + expr\n }\n\n return FunctionAssignmentNode\n}, { isClass: true, isNode: true })\n","import { isBigNumber, isConstantNode, isNode, isRangeNode, isSymbolNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { escape } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\nimport { getSafeProperty } from '../../utils/customs.js'\n\nconst name = 'IndexNode'\nconst dependencies = [\n 'Range',\n 'Node',\n 'size'\n]\n\nexport const createIndexNode = /* #__PURE__ */ factory(name, dependencies, ({ Range, Node, size }) => {\n /**\n * @constructor IndexNode\n * @extends Node\n *\n * Describes a subset of a matrix or an object property.\n * Cannot be used on its own, needs to be used within an AccessorNode or\n * AssignmentNode.\n *\n * @param {Node[]} dimensions\n * @param {boolean} [dotNotation=false] Optional property describing whether\n * this index was written using dot\n * notation like `a.b`, or using bracket\n * notation like `a[\"b\"]` (default).\n * Used to stringify an IndexNode.\n */\n function IndexNode (dimensions, dotNotation) {\n if (!(this instanceof IndexNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.dimensions = dimensions\n this.dotNotation = dotNotation || false\n\n // validate input\n if (!Array.isArray(dimensions) || !dimensions.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"dimensions\"')\n }\n if (this.dotNotation && !this.isObjectProperty()) {\n throw new Error('dotNotation only applicable for object properties')\n }\n }\n\n IndexNode.prototype = new Node()\n\n IndexNode.prototype.type = 'IndexNode'\n\n IndexNode.prototype.isIndexNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n IndexNode.prototype._compile = function (math, argNames) {\n // TODO: implement support for bignumber (currently bignumbers are silently\n // reduced to numbers when changing the value to zero-based)\n\n // TODO: Optimization: when the range values are ConstantNodes,\n // we can beforehand resolve the zero-based value\n\n // optimization for a simple object property\n const evalDimensions = map(this.dimensions, function (range, i) {\n if (isRangeNode(range)) {\n if (range.needsEnd()) {\n // create a range containing end (like '4:end')\n const childArgNames = Object.create(argNames)\n childArgNames.end = true\n\n const evalStart = range.start._compile(math, childArgNames)\n const evalEnd = range.end._compile(math, childArgNames)\n const evalStep = range.step\n ? range.step._compile(math, childArgNames)\n : function () { return 1 }\n\n return function evalDimension (scope, args, context) {\n const s = size(context).valueOf()\n const childArgs = Object.create(args)\n childArgs.end = s[i]\n\n return createRange(\n evalStart(scope, childArgs, context),\n evalEnd(scope, childArgs, context),\n evalStep(scope, childArgs, context)\n )\n }\n } else {\n // create range\n const evalStart = range.start._compile(math, argNames)\n const evalEnd = range.end._compile(math, argNames)\n const evalStep = range.step\n ? range.step._compile(math, argNames)\n : function () { return 1 }\n\n return function evalDimension (scope, args, context) {\n return createRange(\n evalStart(scope, args, context),\n evalEnd(scope, args, context),\n evalStep(scope, args, context)\n )\n }\n }\n } else if (isSymbolNode(range) && range.name === 'end') {\n // SymbolNode 'end'\n const childArgNames = Object.create(argNames)\n childArgNames.end = true\n\n const evalRange = range._compile(math, childArgNames)\n\n return function evalDimension (scope, args, context) {\n const s = size(context).valueOf()\n const childArgs = Object.create(args)\n childArgs.end = s[i]\n\n return evalRange(scope, childArgs, context)\n }\n } else {\n // ConstantNode\n const evalRange = range._compile(math, argNames)\n return function evalDimension (scope, args, context) {\n return evalRange(scope, args, context)\n }\n }\n })\n\n const index = getSafeProperty(math, 'index')\n\n return function evalIndexNode (scope, args, context) {\n const dimensions = map(evalDimensions, function (evalDimension) {\n return evalDimension(scope, args, context)\n })\n\n return index(...dimensions)\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n IndexNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.dimensions.length; i++) {\n callback(this.dimensions[i], 'dimensions[' + i + ']', this)\n }\n }\n\n /**\n * Create a new IndexNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {IndexNode} Returns a transformed copy of the node\n */\n IndexNode.prototype.map = function (callback) {\n const dimensions = []\n for (let i = 0; i < this.dimensions.length; i++) {\n dimensions[i] = this._ifNode(callback(this.dimensions[i], 'dimensions[' + i + ']', this))\n }\n\n return new IndexNode(dimensions, this.dotNotation)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {IndexNode}\n */\n IndexNode.prototype.clone = function () {\n return new IndexNode(this.dimensions.slice(0), this.dotNotation)\n }\n\n /**\n * Test whether this IndexNode contains a single property name\n * @return {boolean}\n */\n IndexNode.prototype.isObjectProperty = function () {\n return this.dimensions.length === 1 &&\n isConstantNode(this.dimensions[0]) &&\n typeof this.dimensions[0].value === 'string'\n }\n\n /**\n * Returns the property name if IndexNode contains a property.\n * If not, returns null.\n * @return {string | null}\n */\n IndexNode.prototype.getObjectProperty = function () {\n return this.isObjectProperty() ? this.dimensions[0].value : null\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype._toString = function (options) {\n // format the parameters like \"[1, 0:5]\"\n return this.dotNotation\n ? ('.' + this.getObjectProperty())\n : ('[' + this.dimensions.join(', ') + ']')\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n IndexNode.prototype.toJSON = function () {\n return {\n mathjs: 'IndexNode',\n dimensions: this.dimensions,\n dotNotation: this.dotNotation\n }\n }\n\n /**\n * Instantiate an IndexNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"IndexNode\", dimensions: [...], dotNotation: false}`,\n * where mathjs is optional\n * @returns {IndexNode}\n */\n IndexNode.fromJSON = function (json) {\n return new IndexNode(json.dimensions, json.dotNotation)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype.toHTML = function (options) {\n // format the parameters like \"[1, 0:5]\"\n const dimensions = []\n for (let i = 0; i < this.dimensions.length; i++) {\n dimensions[i] = this.dimensions[i].toHTML()\n }\n if (this.dotNotation) {\n return '.' + '' + escape(this.getObjectProperty()) + ''\n } else {\n return '[' + dimensions.join(',') + ']'\n }\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n IndexNode.prototype._toTex = function (options) {\n const dimensions = this.dimensions.map(function (range) {\n return range.toTex(options)\n })\n\n return this.dotNotation\n ? ('.' + this.getObjectProperty() + '')\n : ('_{' + dimensions.join(',') + '}')\n }\n\n // helper function to create a Range from start, step and end\n function createRange (start, end, step) {\n return new Range(\n isBigNumber(start) ? start.toNumber() : start,\n isBigNumber(end) ? end.toNumber() : end,\n isBigNumber(step) ? step.toNumber() : step\n )\n }\n\n return IndexNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { escape, stringify } from '../../utils/string.js'\nimport { isSafeProperty } from '../../utils/customs.js'\nimport { hasOwnProperty } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ObjectNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createObjectNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ObjectNode\n * @extends {Node}\n * Holds an object with keys/values\n * @param {Object.} [properties] object with key/value pairs\n */\n function ObjectNode (properties) {\n if (!(this instanceof ObjectNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n this.properties = properties || {}\n\n // validate input\n if (properties) {\n if (!(typeof properties === 'object') || !Object.keys(properties).every(function (key) {\n return isNode(properties[key])\n })) {\n throw new TypeError('Object containing Nodes expected')\n }\n }\n }\n\n ObjectNode.prototype = new Node()\n\n ObjectNode.prototype.type = 'ObjectNode'\n\n ObjectNode.prototype.isObjectNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ObjectNode.prototype._compile = function (math, argNames) {\n const evalEntries = {}\n\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n // we stringify/parse the key here to resolve unicode characters,\n // so you cannot create a key like {\"co\\\\u006Estructor\": null}\n const stringifiedKey = stringify(key)\n const parsedKey = JSON.parse(stringifiedKey)\n if (!isSafeProperty(this.properties, parsedKey)) {\n throw new Error('No access to property \"' + parsedKey + '\"')\n }\n\n evalEntries[parsedKey] = this.properties[key]._compile(math, argNames)\n }\n }\n\n return function evalObjectNode (scope, args, context) {\n const obj = {}\n\n for (const key in evalEntries) {\n if (hasOwnProperty(evalEntries, key)) {\n obj[key] = evalEntries[key](scope, args, context)\n }\n }\n\n return obj\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ObjectNode.prototype.forEach = function (callback) {\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n callback(this.properties[key], 'properties[' + stringify(key) + ']', this)\n }\n }\n }\n\n /**\n * Create a new ObjectNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {ObjectNode} Returns a transformed copy of the node\n */\n ObjectNode.prototype.map = function (callback) {\n const properties = {}\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n properties[key] = this._ifNode(callback(this.properties[key],\n 'properties[' + stringify(key) + ']', this))\n }\n }\n return new ObjectNode(properties)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ObjectNode}\n */\n ObjectNode.prototype.clone = function () {\n const properties = {}\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n properties[key] = this.properties[key]\n }\n }\n return new ObjectNode(properties)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ObjectNode.prototype._toString = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push(stringify(key) + ': ' + this.properties[key].toString(options))\n }\n }\n return '{' + entries.join(', ') + '}'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ObjectNode.prototype.toJSON = function () {\n return {\n mathjs: 'ObjectNode',\n properties: this.properties\n }\n }\n\n /**\n * Instantiate an OperatorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ObjectNode\", \"properties\": {...}}`,\n * where mathjs is optional\n * @returns {ObjectNode}\n */\n ObjectNode.fromJSON = function (json) {\n return new ObjectNode(json.properties)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ObjectNode.prototype.toHTML = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push('' + escape(key) + '' + ':' + this.properties[key].toHTML(options))\n }\n }\n return '{' + entries.join(',') + '}'\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n ObjectNode.prototype._toTex = function (options) {\n const entries = []\n for (const key in this.properties) {\n if (hasOwnProperty(this.properties, key)) {\n entries.push('\\\\mathbf{' + key + ':} & ' + this.properties[key].toTex(options) + '\\\\\\\\')\n }\n }\n return `\\\\left\\\\{\\\\begin{array}{ll}${entries.join('\\n')}\\\\end{array}\\\\right\\\\}`\n }\n\n return ObjectNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { map } from '../../utils/array.js'\nimport { escape } from '../../utils/string.js'\nimport { getSafeProperty, isSafeMethod } from '../../utils/customs.js'\nimport { getAssociativity, getPrecedence, isAssociativeWith, properties } from '../operators.js'\nimport { latexOperators } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'OperatorNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createOperatorNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor OperatorNode\n * @extends {Node}\n * An operator with two arguments, like 2+3\n *\n * @param {string} op Operator name, for example '+'\n * @param {string} fn Function name, for example 'add'\n * @param {Node[]} args Operator arguments\n * @param {boolean} [implicit] Is this an implicit multiplication?\n */\n function OperatorNode (op, fn, args, implicit) {\n if (!(this instanceof OperatorNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof op !== 'string') {\n throw new TypeError('string expected for parameter \"op\"')\n }\n if (typeof fn !== 'string') {\n throw new TypeError('string expected for parameter \"fn\"')\n }\n if (!Array.isArray(args) || !args.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"args\"')\n }\n\n this.implicit = (implicit === true)\n this.op = op\n this.fn = fn\n this.args = args || []\n }\n\n OperatorNode.prototype = new Node()\n\n OperatorNode.prototype.type = 'OperatorNode'\n\n OperatorNode.prototype.isOperatorNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n OperatorNode.prototype._compile = function (math, argNames) {\n // validate fn\n if (typeof this.fn !== 'string' || !isSafeMethod(math, this.fn)) {\n if (!math[this.fn]) {\n throw new Error('Function ' + this.fn + ' missing in provided namespace \"math\"')\n } else {\n throw new Error('No access to function \"' + this.fn + '\"')\n }\n }\n\n const fn = getSafeProperty(math, this.fn)\n const evalArgs = map(this.args, function (arg) {\n return arg._compile(math, argNames)\n })\n\n if (evalArgs.length === 1) {\n const evalArg0 = evalArgs[0]\n return function evalOperatorNode (scope, args, context) {\n return fn(evalArg0(scope, args, context))\n }\n } else if (evalArgs.length === 2) {\n const evalArg0 = evalArgs[0]\n const evalArg1 = evalArgs[1]\n return function evalOperatorNode (scope, args, context) {\n return fn(evalArg0(scope, args, context), evalArg1(scope, args, context))\n }\n } else {\n return function evalOperatorNode (scope, args, context) {\n return fn.apply(null, map(evalArgs, function (evalArg) {\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n OperatorNode.prototype.forEach = function (callback) {\n for (let i = 0; i < this.args.length; i++) {\n callback(this.args[i], 'args[' + i + ']', this)\n }\n }\n\n /**\n * Create a new OperatorNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {OperatorNode} Returns a transformed copy of the node\n */\n OperatorNode.prototype.map = function (callback) {\n const args = []\n for (let i = 0; i < this.args.length; i++) {\n args[i] = this._ifNode(callback(this.args[i], 'args[' + i + ']', this))\n }\n return new OperatorNode(this.op, this.fn, args, this.implicit)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {OperatorNode}\n */\n OperatorNode.prototype.clone = function () {\n return new OperatorNode(this.op, this.fn, this.args.slice(0), this.implicit)\n }\n\n /**\n * Check whether this is an unary OperatorNode:\n * has exactly one argument, like `-a`.\n * @return {boolean} Returns true when an unary operator node, false otherwise.\n */\n OperatorNode.prototype.isUnary = function () {\n return this.args.length === 1\n }\n\n /**\n * Check whether this is a binary OperatorNode:\n * has exactly two arguments, like `a + b`.\n * @return {boolean} Returns true when a binary operator node, false otherwise.\n */\n OperatorNode.prototype.isBinary = function () {\n return this.args.length === 2\n }\n\n /**\n * Calculate which parentheses are necessary. Gets an OperatorNode\n * (which is the root of the tree) and an Array of Nodes\n * (this.args) and returns an array where 'true' means that an argument\n * has to be enclosed in parentheses whereas 'false' means the opposite.\n *\n * @param {OperatorNode} root\n * @param {string} parenthesis\n * @param {Node[]} args\n * @param {boolean} latex\n * @return {boolean[]}\n * @private\n */\n function calculateNecessaryParentheses (root, parenthesis, implicit, args, latex) {\n // precedence of the root OperatorNode\n const precedence = getPrecedence(root, parenthesis)\n const associativity = getAssociativity(root, parenthesis)\n\n if ((parenthesis === 'all') || ((args.length > 2) && (root.getIdentifier() !== 'OperatorNode:add') && (root.getIdentifier() !== 'OperatorNode:multiply'))) {\n return args.map(function (arg) {\n switch (arg.getContent().type) { // Nodes that don't need extra parentheses\n case 'ArrayNode':\n case 'ConstantNode':\n case 'SymbolNode':\n case 'ParenthesisNode':\n return false\n default:\n return true\n }\n })\n }\n\n let result\n switch (args.length) {\n case 0:\n result = []\n break\n\n case 1: // unary operators\n {\n // precedence of the operand\n const operandPrecedence = getPrecedence(args[0], parenthesis)\n\n // handle special cases for LaTeX, where some of the parentheses aren't needed\n if (latex && (operandPrecedence !== null)) {\n let operandIdentifier\n let rootIdentifier\n if (parenthesis === 'keep') {\n operandIdentifier = args[0].getIdentifier()\n rootIdentifier = root.getIdentifier()\n } else {\n // Ignore Parenthesis Nodes when not in 'keep' mode\n operandIdentifier = args[0].getContent().getIdentifier()\n rootIdentifier = root.getContent().getIdentifier()\n }\n if (properties[precedence][rootIdentifier].latexLeftParens === false) {\n result = [false]\n break\n }\n\n if (properties[operandPrecedence][operandIdentifier].latexParens === false) {\n result = [false]\n break\n }\n }\n\n if (operandPrecedence === null) {\n // if the operand has no defined precedence, no parens are needed\n result = [false]\n break\n }\n\n if (operandPrecedence <= precedence) {\n // if the operands precedence is lower, parens are needed\n result = [true]\n break\n }\n\n // otherwise, no parens needed\n result = [false]\n }\n break\n case 2: // binary operators\n {\n let lhsParens // left hand side needs parenthesis?\n // precedence of the left hand side\n const lhsPrecedence = getPrecedence(args[0], parenthesis)\n // is the root node associative with the left hand side\n const assocWithLhs = isAssociativeWith(root, args[0], parenthesis)\n\n if (lhsPrecedence === null) {\n // if the left hand side has no defined precedence, no parens are needed\n // FunctionNode for example\n lhsParens = false\n } else if ((lhsPrecedence === precedence) && (associativity === 'right') && !assocWithLhs) {\n // In case of equal precedence, if the root node is left associative\n // parens are **never** necessary for the left hand side.\n // If it is right associative however, parens are necessary\n // if the root node isn't associative with the left hand side\n lhsParens = true\n } else if (lhsPrecedence < precedence) {\n lhsParens = true\n } else {\n lhsParens = false\n }\n\n let rhsParens // right hand side needs parenthesis?\n // precedence of the right hand side\n const rhsPrecedence = getPrecedence(args[1], parenthesis)\n // is the root node associative with the right hand side?\n const assocWithRhs = isAssociativeWith(root, args[1], parenthesis)\n\n if (rhsPrecedence === null) {\n // if the right hand side has no defined precedence, no parens are needed\n // FunctionNode for example\n rhsParens = false\n } else if ((rhsPrecedence === precedence) && (associativity === 'left') && !assocWithRhs) {\n // In case of equal precedence, if the root node is right associative\n // parens are **never** necessary for the right hand side.\n // If it is left associative however, parens are necessary\n // if the root node isn't associative with the right hand side\n rhsParens = true\n } else if (rhsPrecedence < precedence) {\n rhsParens = true\n } else {\n rhsParens = false\n }\n\n // handle special cases for LaTeX, where some of the parentheses aren't needed\n if (latex) {\n let rootIdentifier\n let lhsIdentifier\n let rhsIdentifier\n if (parenthesis === 'keep') {\n rootIdentifier = root.getIdentifier()\n lhsIdentifier = root.args[0].getIdentifier()\n rhsIdentifier = root.args[1].getIdentifier()\n } else {\n // Ignore ParenthesisNodes when not in 'keep' mode\n rootIdentifier = root.getContent().getIdentifier()\n lhsIdentifier = root.args[0].getContent().getIdentifier()\n rhsIdentifier = root.args[1].getContent().getIdentifier()\n }\n\n if (lhsPrecedence !== null) {\n if (properties[precedence][rootIdentifier].latexLeftParens === false) {\n lhsParens = false\n }\n\n if (properties[lhsPrecedence][lhsIdentifier].latexParens === false) {\n lhsParens = false\n }\n }\n\n if (rhsPrecedence !== null) {\n if (properties[precedence][rootIdentifier].latexRightParens === false) {\n rhsParens = false\n }\n\n if (properties[rhsPrecedence][rhsIdentifier].latexParens === false) {\n rhsParens = false\n }\n }\n }\n\n result = [lhsParens, rhsParens]\n }\n break\n\n default:\n if ((root.getIdentifier() === 'OperatorNode:add') || (root.getIdentifier() === 'OperatorNode:multiply')) {\n result = args.map(function (arg) {\n const argPrecedence = getPrecedence(arg, parenthesis)\n const assocWithArg = isAssociativeWith(root, arg, parenthesis)\n const argAssociativity = getAssociativity(arg, parenthesis)\n if (argPrecedence === null) {\n // if the argument has no defined precedence, no parens are needed\n return false\n } else if ((precedence === argPrecedence) && (associativity === argAssociativity) && !assocWithArg) {\n return true\n } else if (argPrecedence < precedence) {\n return true\n }\n\n return false\n })\n }\n break\n }\n\n // handles an edge case of 'auto' parentheses with implicit multiplication of ConstantNode\n // In that case print parentheses for ParenthesisNodes even though they normally wouldn't be\n // printed.\n if ((args.length >= 2) && (root.getIdentifier() === 'OperatorNode:multiply') && root.implicit && (parenthesis === 'auto') && (implicit === 'hide')) {\n result = args.map(function (arg, index) {\n const isParenthesisNode = (arg.getIdentifier() === 'ParenthesisNode')\n if (result[index] || isParenthesisNode) { // put in parenthesis?\n return true\n }\n\n return false\n })\n }\n\n return result\n }\n\n /**\n * Get string representation.\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, false)\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toString(options)\n if (parens[0]) {\n operand = '(' + operand + ')'\n }\n\n // for example for \"not\", we want a space between operand and argument\n const opIsNamed = /[a-zA-Z]+/.test(this.op)\n\n if (assoc === 'right') { // prefix operator\n return this.op + (opIsNamed ? ' ' : '') + operand\n } else if (assoc === 'left') { // postfix\n return operand + (opIsNamed ? ' ' : '') + this.op\n }\n\n // fall back to postfix\n return operand + this.op\n } else if (args.length === 2) {\n let lhs = args[0].toString(options) // left hand side\n let rhs = args[1].toString(options) // right hand side\n if (parens[0]) { // left hand side in parenthesis?\n lhs = '(' + lhs + ')'\n }\n if (parens[1]) { // right hand side in parenthesis?\n rhs = '(' + rhs + ')'\n }\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return lhs + ' ' + rhs\n }\n\n return lhs + ' ' + this.op + ' ' + rhs\n } else if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n const stringifiedArgs = args.map(function (arg, index) {\n arg = arg.toString(options)\n if (parens[index]) { // put in parenthesis?\n arg = '(' + arg + ')'\n }\n\n return arg\n })\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return stringifiedArgs.join(' ')\n }\n\n return stringifiedArgs.join(' ' + this.op + ' ')\n } else {\n // fallback to formatting as a function call\n return this.fn + '(' + this.args.join(', ') + ')'\n }\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n OperatorNode.prototype.toJSON = function () {\n return {\n mathjs: 'OperatorNode',\n op: this.op,\n fn: this.fn,\n args: this.args,\n implicit: this.implicit\n }\n }\n\n /**\n * Instantiate an OperatorNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"OperatorNode\", \"op\": \"+\", \"fn\": \"add\", \"args\": [...], \"implicit\": false}`,\n * where mathjs is optional\n * @returns {OperatorNode}\n */\n OperatorNode.fromJSON = function (json) {\n return new OperatorNode(json.op, json.fn, json.args, json.implicit)\n }\n\n /**\n * Get HTML representation.\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, false)\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toHTML(options)\n if (parens[0]) {\n operand = '(' + operand + ')'\n }\n\n if (assoc === 'right') { // prefix operator\n return '' + escape(this.op) + '' + operand\n } else { // postfix when assoc === 'left' or undefined\n return operand + '' + escape(this.op) + ''\n }\n } else if (args.length === 2) { // binary operatoes\n let lhs = args[0].toHTML(options) // left hand side\n let rhs = args[1].toHTML(options) // right hand side\n if (parens[0]) { // left hand side in parenthesis?\n lhs = '(' + lhs + ')'\n }\n if (parens[1]) { // right hand side in parenthesis?\n rhs = '(' + rhs + ')'\n }\n\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return lhs + '' + rhs\n }\n\n return lhs + '' + escape(this.op) + '' + rhs\n } else {\n const stringifiedArgs = args.map(function (arg, index) {\n arg = arg.toHTML(options)\n if (parens[index]) { // put in parenthesis?\n arg = '(' + arg + ')'\n }\n\n return arg\n })\n\n if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n if (this.implicit && (this.getIdentifier() === 'OperatorNode:multiply') && (implicit === 'hide')) {\n return stringifiedArgs.join('')\n }\n\n return stringifiedArgs.join('' + escape(this.op) + '')\n } else {\n // fallback to formatting as a function call\n return '' + escape(this.fn) + '(' + stringifiedArgs.join(',') + ')'\n }\n }\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n OperatorNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const implicit = (options && options.implicit) ? options.implicit : 'hide'\n const args = this.args\n const parens = calculateNecessaryParentheses(this, parenthesis, implicit, args, true)\n let op = latexOperators[this.fn]\n op = typeof op === 'undefined' ? this.op : op // fall back to using this.op\n\n if (args.length === 1) { // unary operators\n const assoc = getAssociativity(this, parenthesis)\n\n let operand = args[0].toTex(options)\n if (parens[0]) {\n operand = `\\\\left(${operand}\\\\right)`\n }\n\n if (assoc === 'right') { // prefix operator\n return op + operand\n } else if (assoc === 'left') { // postfix operator\n return operand + op\n }\n\n // fall back to postfix\n return operand + op\n } else if (args.length === 2) { // binary operators\n const lhs = args[0] // left hand side\n let lhsTex = lhs.toTex(options)\n if (parens[0]) {\n lhsTex = `\\\\left(${lhsTex}\\\\right)`\n }\n\n const rhs = args[1] // right hand side\n let rhsTex = rhs.toTex(options)\n if (parens[1]) {\n rhsTex = `\\\\left(${rhsTex}\\\\right)`\n }\n\n // handle some exceptions (due to the way LaTeX works)\n let lhsIdentifier\n if (parenthesis === 'keep') {\n lhsIdentifier = lhs.getIdentifier()\n } else {\n // Ignore ParenthesisNodes if in 'keep' mode\n lhsIdentifier = lhs.getContent().getIdentifier()\n }\n switch (this.getIdentifier()) {\n case 'OperatorNode:divide':\n // op contains '\\\\frac' at this point\n return op + '{' + lhsTex + '}' + '{' + rhsTex + '}'\n case 'OperatorNode:pow':\n lhsTex = '{' + lhsTex + '}'\n rhsTex = '{' + rhsTex + '}'\n switch (lhsIdentifier) {\n case 'ConditionalNode': //\n case 'OperatorNode:divide':\n lhsTex = `\\\\left(${lhsTex}\\\\right)`\n }\n break\n case 'OperatorNode:multiply':\n if (this.implicit && (implicit === 'hide')) {\n return lhsTex + '~' + rhsTex\n }\n }\n return lhsTex + op + rhsTex\n } else if ((args.length > 2) && ((this.getIdentifier() === 'OperatorNode:add') || (this.getIdentifier() === 'OperatorNode:multiply'))) {\n const texifiedArgs = args.map(function (arg, index) {\n arg = arg.toTex(options)\n if (parens[index]) {\n arg = `\\\\left(${arg}\\\\right)`\n }\n return arg\n })\n\n if ((this.getIdentifier() === 'OperatorNode:multiply') && this.implicit) {\n return texifiedArgs.join('~')\n }\n\n return texifiedArgs.join(op)\n } else {\n // fall back to formatting as a function call\n // as this is a fallback, it doesn't use\n // fancy function names\n return '\\\\mathrm{' + this.fn + '}\\\\left(' +\n args.map(function (arg) {\n return arg.toTex(options)\n }).join(',') + '\\\\right)'\n }\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n OperatorNode.prototype.getIdentifier = function () {\n return this.type + ':' + this.fn\n }\n\n return OperatorNode\n}, { isClass: true, isNode: true })\n","import { isNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'ParenthesisNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createParenthesisNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor ParenthesisNode\n * @extends {Node}\n * A parenthesis node describes manual parenthesis from the user input\n * @param {Node} content\n * @extends {Node}\n */\n function ParenthesisNode (content) {\n if (!(this instanceof ParenthesisNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (!isNode(content)) {\n throw new TypeError('Node expected for parameter \"content\"')\n }\n\n this.content = content\n }\n\n ParenthesisNode.prototype = new Node()\n\n ParenthesisNode.prototype.type = 'ParenthesisNode'\n\n ParenthesisNode.prototype.isParenthesisNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n ParenthesisNode.prototype._compile = function (math, argNames) {\n return this.content._compile(math, argNames)\n }\n\n /**\n * Get the content of the current Node.\n * @return {Node} content\n * @override\n **/\n ParenthesisNode.prototype.getContent = function () {\n return this.content.getContent()\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n ParenthesisNode.prototype.forEach = function (callback) {\n callback(this.content, 'content', this)\n }\n\n /**\n * Create a new ParenthesisNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {ParenthesisNode} Returns a clone of the node\n */\n ParenthesisNode.prototype.map = function (callback) {\n const content = callback(this.content, 'content', this)\n return new ParenthesisNode(content)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {ParenthesisNode}\n */\n ParenthesisNode.prototype.clone = function () {\n return new ParenthesisNode(this.content)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype._toString = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return '(' + this.content.toString(options) + ')'\n }\n return this.content.toString(options)\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n ParenthesisNode.prototype.toJSON = function () {\n return {\n mathjs: 'ParenthesisNode',\n content: this.content\n }\n }\n\n /**\n * Instantiate an ParenthesisNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"ParenthesisNode\", \"content\": ...}`,\n * where mathjs is optional\n * @returns {ParenthesisNode}\n */\n ParenthesisNode.fromJSON = function (json) {\n return new ParenthesisNode(json.content)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype.toHTML = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return '(' + this.content.toHTML(options) + ')'\n }\n return this.content.toHTML(options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n ParenthesisNode.prototype._toTex = function (options) {\n if ((!options) || (options && !options.parenthesis) || (options && options.parenthesis === 'keep')) {\n return `\\\\left(${this.content.toTex(options)}\\\\right)`\n }\n return this.content.toTex(options)\n }\n\n return ParenthesisNode\n}, { isClass: true, isNode: true })\n","import { isNode, isSymbolNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { getPrecedence } from '../operators.js'\n\nconst name = 'RangeNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createRangeNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * @constructor RangeNode\n * @extends {Node}\n * create a range\n * @param {Node} start included lower-bound\n * @param {Node} end included upper-bound\n * @param {Node} [step] optional step\n */\n function RangeNode (start, end, step) {\n if (!(this instanceof RangeNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate inputs\n if (!isNode(start)) throw new TypeError('Node expected')\n if (!isNode(end)) throw new TypeError('Node expected')\n if (step && !isNode(step)) throw new TypeError('Node expected')\n if (arguments.length > 3) throw new Error('Too many arguments')\n\n this.start = start // included lower-bound\n this.end = end // included upper-bound\n this.step = step || null // optional step\n }\n\n RangeNode.prototype = new Node()\n\n RangeNode.prototype.type = 'RangeNode'\n\n RangeNode.prototype.isRangeNode = true\n\n /**\n * Check whether the RangeNode needs the `end` symbol to be defined.\n * This end is the size of the Matrix in current dimension.\n * @return {boolean}\n */\n RangeNode.prototype.needsEnd = function () {\n // find all `end` symbols in this RangeNode\n const endSymbols = this.filter(function (node) {\n return isSymbolNode(node) && (node.name === 'end')\n })\n\n return endSymbols.length > 0\n }\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n RangeNode.prototype._compile = function (math, argNames) {\n const range = math.range\n const evalStart = this.start._compile(math, argNames)\n const evalEnd = this.end._compile(math, argNames)\n\n if (this.step) {\n const evalStep = this.step._compile(math, argNames)\n\n return function evalRangeNode (scope, args, context) {\n return range(\n evalStart(scope, args, context),\n evalEnd(scope, args, context),\n evalStep(scope, args, context)\n )\n }\n } else {\n return function evalRangeNode (scope, args, context) {\n return range(\n evalStart(scope, args, context),\n evalEnd(scope, args, context)\n )\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n RangeNode.prototype.forEach = function (callback) {\n callback(this.start, 'start', this)\n callback(this.end, 'end', this)\n if (this.step) {\n callback(this.step, 'step', this)\n }\n }\n\n /**\n * Create a new RangeNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {RangeNode} Returns a transformed copy of the node\n */\n RangeNode.prototype.map = function (callback) {\n return new RangeNode(\n this._ifNode(callback(this.start, 'start', this)),\n this._ifNode(callback(this.end, 'end', this)),\n this.step && this._ifNode(callback(this.step, 'step', this))\n )\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {RangeNode}\n */\n RangeNode.prototype.clone = function () {\n return new RangeNode(this.start, this.end, this.step && this.step)\n }\n\n /**\n * Calculate the necessary parentheses\n * @param {Node} node\n * @param {string} parenthesis\n * @return {Object} parentheses\n * @private\n */\n function calculateNecessaryParentheses (node, parenthesis) {\n const precedence = getPrecedence(node, parenthesis)\n const parens = {}\n\n const startPrecedence = getPrecedence(node.start, parenthesis)\n parens.start = ((startPrecedence !== null) && (startPrecedence <= precedence)) ||\n (parenthesis === 'all')\n\n if (node.step) {\n const stepPrecedence = getPrecedence(node.step, parenthesis)\n parens.step = ((stepPrecedence !== null) && (stepPrecedence <= precedence)) ||\n (parenthesis === 'all')\n }\n\n const endPrecedence = getPrecedence(node.end, parenthesis)\n parens.end = ((endPrecedence !== null) && (endPrecedence <= precedence)) ||\n (parenthesis === 'all')\n\n return parens\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n RangeNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n // format string as start:step:stop\n let str\n\n let start = this.start.toString(options)\n if (parens.start) {\n start = '(' + start + ')'\n }\n str = start\n\n if (this.step) {\n let step = this.step.toString(options)\n if (parens.step) {\n step = '(' + step + ')'\n }\n str += ':' + step\n }\n\n let end = this.end.toString(options)\n if (parens.end) {\n end = '(' + end + ')'\n }\n str += ':' + end\n\n return str\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n RangeNode.prototype.toJSON = function () {\n return {\n mathjs: 'RangeNode',\n start: this.start,\n end: this.end,\n step: this.step\n }\n }\n\n /**\n * Instantiate an RangeNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"RangeNode\", \"start\": ..., \"end\": ..., \"step\": ...}`,\n * where mathjs is optional\n * @returns {RangeNode}\n */\n RangeNode.fromJSON = function (json) {\n return new RangeNode(json.start, json.end, json.step)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n RangeNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n // format string as start:step:stop\n let str\n\n let start = this.start.toHTML(options)\n if (parens.start) {\n start = '(' + start + ')'\n }\n str = start\n\n if (this.step) {\n let step = this.step.toHTML(options)\n if (parens.step) {\n step = '(' + step + ')'\n }\n str += ':' + step\n }\n\n let end = this.end.toHTML(options)\n if (parens.end) {\n end = '(' + end + ')'\n }\n str += ':' + end\n\n return str\n }\n\n /**\n * Get LaTeX representation\n * @params {Object} options\n * @return {string} str\n */\n RangeNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const parens = calculateNecessaryParentheses(this, parenthesis)\n\n let str = this.start.toTex(options)\n if (parens.start) {\n str = `\\\\left(${str}\\\\right)`\n }\n\n if (this.step) {\n let step = this.step.toTex(options)\n if (parens.step) {\n step = `\\\\left(${step}\\\\right)`\n }\n str += ':' + step\n }\n\n let end = this.end.toTex(options)\n if (parens.end) {\n end = `\\\\left(${end}\\\\right)`\n }\n str += ':' + end\n\n return str\n }\n\n return RangeNode\n}, { isClass: true, isNode: true })\n","import { getPrecedence } from '../operators.js'\nimport { escape } from '../../utils/string.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { latexOperators } from '../../utils/latex.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'RelationalNode'\nconst dependencies = [\n 'Node'\n]\n\nexport const createRelationalNode = /* #__PURE__ */ factory(name, dependencies, ({ Node }) => {\n /**\n * A node representing a chained conditional expression, such as 'x > y > z'\n *\n * @param {String[]} conditionals An array of conditional operators used to compare the parameters\n * @param {Node[]} params The parameters that will be compared\n *\n * @constructor RelationalNode\n * @extends {Node}\n */\n function RelationalNode (conditionals, params) {\n if (!(this instanceof RelationalNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n if (!Array.isArray(conditionals)) throw new TypeError('Parameter conditionals must be an array')\n if (!Array.isArray(params)) throw new TypeError('Parameter params must be an array')\n if (conditionals.length !== params.length - 1) throw new TypeError('Parameter params must contain exactly one more element than parameter conditionals')\n\n this.conditionals = conditionals\n this.params = params\n }\n\n RelationalNode.prototype = new Node()\n\n RelationalNode.prototype.type = 'RelationalNode'\n\n RelationalNode.prototype.isRelationalNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n RelationalNode.prototype._compile = function (math, argNames) {\n const self = this\n\n const compiled = this.params.map(p => p._compile(math, argNames))\n\n return function evalRelationalNode (scope, args, context) {\n let evalLhs\n let evalRhs = compiled[0](scope, args, context)\n\n for (let i = 0; i < self.conditionals.length; i++) {\n evalLhs = evalRhs\n evalRhs = compiled[i + 1](scope, args, context)\n const condFn = getSafeProperty(math, self.conditionals[i])\n if (!condFn(evalLhs, evalRhs)) {\n return false\n }\n }\n return true\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n RelationalNode.prototype.forEach = function (callback) {\n this.params.forEach((n, i) => callback(n, 'params[' + i + ']', this), this)\n }\n\n /**\n * Create a new RelationalNode having its childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {RelationalNode} Returns a transformed copy of the node\n */\n RelationalNode.prototype.map = function (callback) {\n return new RelationalNode(this.conditionals.slice(), this.params.map((n, i) => this._ifNode(callback(n, 'params[' + i + ']', this)), this))\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {RelationalNode}\n */\n RelationalNode.prototype.clone = function () {\n return new RelationalNode(this.conditionals, this.params)\n }\n\n /**\n * Get string representation.\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype._toString = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '(' + p.toString(options) + ')'\n : p.toString(options)\n })\n\n const operatorMap = {\n equal: '==',\n unequal: '!=',\n smaller: '<',\n larger: '>',\n smallerEq: '<=',\n largerEq: '>='\n }\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += ' ' + operatorMap[this.conditionals[i]] + ' ' + paramStrings[i + 1]\n }\n\n return ret\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n RelationalNode.prototype.toJSON = function () {\n return {\n mathjs: 'RelationalNode',\n conditionals: this.conditionals,\n params: this.params\n }\n }\n\n /**\n * Instantiate a RelationalNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"RelationalNode\", \"condition\": ..., \"trueExpr\": ..., \"falseExpr\": ...}`,\n * where mathjs is optional\n * @returns {RelationalNode}\n */\n RelationalNode.fromJSON = function (json) {\n return new RelationalNode(json.conditionals, json.params)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype.toHTML = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '(' + p.toHTML(options) + ')'\n : p.toHTML(options)\n })\n\n const operatorMap = {\n equal: '==',\n unequal: '!=',\n smaller: '<',\n larger: '>',\n smallerEq: '<=',\n largerEq: '>='\n }\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += '' + escape(operatorMap[this.conditionals[i]]) + '' + paramStrings[i + 1]\n }\n\n return ret\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n RelationalNode.prototype._toTex = function (options) {\n const parenthesis = (options && options.parenthesis) ? options.parenthesis : 'keep'\n const precedence = getPrecedence(this, parenthesis)\n\n const paramStrings = this.params.map(function (p, index) {\n const paramPrecedence = getPrecedence(p, parenthesis)\n return (parenthesis === 'all' || (paramPrecedence !== null && paramPrecedence <= precedence))\n ? '\\\\left(' + p.toTex(options) + '\\right)'\n : p.toTex(options)\n })\n\n let ret = paramStrings[0]\n for (let i = 0; i < this.conditionals.length; i++) {\n ret += latexOperators[this.conditionals[i]] + paramStrings[i + 1]\n }\n\n return ret\n }\n\n return RelationalNode\n}, { isClass: true, isNode: true })\n","import { escape } from '../../utils/string.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { toSymbol } from '../../utils/latex.js'\n\nconst name = 'SymbolNode'\nconst dependencies = [\n 'math',\n '?Unit',\n 'Node'\n]\n\nexport const createSymbolNode = /* #__PURE__ */ factory(name, dependencies, ({ math, Unit, Node }) => {\n /**\n * Check whether some name is a valueless unit like \"inch\".\n * @param {string} name\n * @return {boolean}\n */\n function isValuelessUnit (name) {\n return Unit ? Unit.isValuelessUnit(name) : false\n }\n\n /**\n * @constructor SymbolNode\n * @extends {Node}\n * A symbol node can hold and resolve a symbol\n * @param {string} name\n * @extends {Node}\n */\n function SymbolNode (name) {\n if (!(this instanceof SymbolNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n // validate input\n if (typeof name !== 'string') throw new TypeError('String expected for parameter \"name\"')\n\n this.name = name\n }\n\n SymbolNode.prototype = new Node()\n\n SymbolNode.prototype.type = 'SymbolNode'\n\n SymbolNode.prototype.isSymbolNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n SymbolNode.prototype._compile = function (math, argNames) {\n const name = this.name\n\n if (argNames[name] === true) {\n // this is a FunctionAssignment argument\n // (like an x when inside the expression of a function assignment `f(x) = ...`)\n return function (scope, args, context) {\n return args[name]\n }\n } else if (name in math) {\n return function (scope, args, context) {\n return name in scope\n ? getSafeProperty(scope, name)\n : getSafeProperty(math, name)\n }\n } else {\n const isUnit = isValuelessUnit(name)\n\n return function (scope, args, context) {\n return name in scope\n ? getSafeProperty(scope, name)\n : isUnit\n ? new Unit(null, name)\n : undef(name)\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n SymbolNode.prototype.forEach = function (callback) {\n // nothing to do, we don't have childs\n }\n\n /**\n * Create a new SymbolNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node) : Node} callback\n * @returns {SymbolNode} Returns a clone of the node\n */\n SymbolNode.prototype.map = function (callback) {\n return this.clone()\n }\n\n /**\n * Throws an error 'Undefined symbol {name}'\n * @param {string} name\n */\n function undef (name) {\n throw new Error('Undefined symbol ' + name)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {SymbolNode}\n */\n SymbolNode.prototype.clone = function () {\n return new SymbolNode(this.name)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype._toString = function (options) {\n return this.name\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype.toHTML = function (options) {\n const name = escape(this.name)\n\n if (name === 'true' || name === 'false') {\n return '' + name + ''\n } else if (name === 'i') {\n return '' + name + ''\n } else if (name === 'Infinity') {\n return '' + name + ''\n } else if (name === 'NaN') {\n return '' + name + ''\n } else if (name === 'null') {\n return '' + name + ''\n } else if (name === 'undefined') {\n return '' + name + ''\n }\n\n return '' + name + ''\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n SymbolNode.prototype.toJSON = function () {\n return {\n mathjs: 'SymbolNode',\n name: this.name\n }\n }\n\n /**\n * Instantiate a SymbolNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"SymbolNode\", name: \"x\"}`,\n * where mathjs is optional\n * @returns {SymbolNode}\n */\n SymbolNode.fromJSON = function (json) {\n return new SymbolNode(json.name)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n * @override\n */\n SymbolNode.prototype._toTex = function (options) {\n let isUnit = false\n if ((typeof math[this.name] === 'undefined') && isValuelessUnit(this.name)) {\n isUnit = true\n }\n const symbol = toSymbol(this.name, isUnit)\n if (symbol[0] === '\\\\') {\n // no space needed if the symbol starts with '\\'\n return symbol\n }\n // the space prevents symbols from breaking stuff like '\\cdot' if it's written right before the symbol\n return ' ' + symbol\n }\n\n return SymbolNode\n}, { isClass: true, isNode: true })\n","import { isAccessorNode, isFunctionAssignmentNode, isIndexNode, isNode, isSymbolNode } from '../../utils/is.js'\n\nimport { escape } from '../../utils/string.js'\nimport { hasOwnProperty } from '../../utils/object.js'\nimport { map } from '../../utils/array.js'\nimport { getSafeProperty, validateSafeMethod } from '../../utils/customs.js'\nimport { factory } from '../../utils/factory.js'\nimport { defaultTemplate, latexFunctions } from '../../utils/latex.js'\n\nconst name = 'FunctionNode'\nconst dependencies = [\n 'math',\n 'Node',\n 'SymbolNode'\n]\n\nexport const createFunctionNode = /* #__PURE__ */ factory(name, dependencies, ({ math, Node, SymbolNode }) => {\n /**\n * @constructor FunctionNode\n * @extends {./Node}\n * invoke a list with arguments on a node\n * @param {./Node | string} fn Node resolving with a function on which to invoke\n * the arguments, typically a SymboNode or AccessorNode\n * @param {./Node[]} args\n */\n function FunctionNode (fn, args) {\n if (!(this instanceof FunctionNode)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (typeof fn === 'string') {\n fn = new SymbolNode(fn)\n }\n\n // validate input\n if (!isNode(fn)) throw new TypeError('Node expected as parameter \"fn\"')\n if (!Array.isArray(args) || !args.every(isNode)) {\n throw new TypeError('Array containing Nodes expected for parameter \"args\"')\n }\n\n this.fn = fn\n this.args = args || []\n\n // readonly property name\n Object.defineProperty(this, 'name', {\n get: function () {\n return this.fn.name || ''\n }.bind(this),\n set: function () {\n throw new Error('Cannot assign a new name, name is read-only')\n }\n })\n }\n\n FunctionNode.prototype = new Node()\n\n FunctionNode.prototype.type = 'FunctionNode'\n\n FunctionNode.prototype.isFunctionNode = true\n\n /**\n * Compile a node into a JavaScript function.\n * This basically pre-calculates as much as possible and only leaves open\n * calculations which depend on a dynamic scope with variables.\n * @param {Object} math Math.js namespace with functions and constants.\n * @param {Object} argNames An object with argument names as key and `true`\n * as value. Used in the SymbolNode to optimize\n * for arguments from user assigned functions\n * (see FunctionAssignmentNode) or special symbols\n * like `end` (see IndexNode).\n * @return {function} Returns a function which can be called like:\n * evalNode(scope: Object, args: Object, context: *)\n */\n FunctionNode.prototype._compile = function (math, argNames) {\n if (!(this instanceof FunctionNode)) {\n throw new TypeError('No valid FunctionNode')\n }\n\n // compile arguments\n const evalArgs = map(this.args, function (arg) {\n return arg._compile(math, argNames)\n })\n\n if (isSymbolNode(this.fn)) {\n // we can statically determine whether the function has an rawArgs property\n const name = this.fn.name\n const fn = name in math ? getSafeProperty(math, name) : undefined\n const isRaw = (typeof fn === 'function') && (fn.rawArgs === true)\n\n if (isRaw) {\n // pass unevaluated parameters (nodes) to the function\n // \"raw\" evaluation\n const rawArgs = this.args\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(rawArgs, math, Object.assign({}, scope, args))\n }\n } else {\n // \"regular\" evaluation\n if (evalArgs.length === 1) {\n const evalArg0 = evalArgs[0]\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(evalArg0(scope, args, context))\n }\n } else if (evalArgs.length === 2) {\n const evalArg0 = evalArgs[0]\n const evalArg1 = evalArgs[1]\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn)(evalArg0(scope, args, context), evalArg1(scope, args, context))\n }\n } else {\n return function evalFunctionNode (scope, args, context) {\n return (name in scope ? getSafeProperty(scope, name) : fn).apply(null, map(evalArgs, function (evalArg) {\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n } else if (isAccessorNode(this.fn) &&\n isIndexNode(this.fn.index) && this.fn.index.isObjectProperty()) {\n // execute the function with the right context: the object of the AccessorNode\n\n const evalObject = this.fn.object._compile(math, argNames)\n const prop = this.fn.index.getObjectProperty()\n const rawArgs = this.args\n\n return function evalFunctionNode (scope, args, context) {\n const object = evalObject(scope, args, context)\n validateSafeMethod(object, prop)\n const isRaw = object[prop] && object[prop].rawArgs\n\n return isRaw\n ? object[prop](rawArgs, math, Object.assign({}, scope, args)) // \"raw\" evaluation\n : object[prop].apply(object, map(evalArgs, function (evalArg) { // \"regular\" evaluation\n return evalArg(scope, args, context)\n }))\n }\n } else { // node.fn.isAccessorNode && !node.fn.index.isObjectProperty()\n // we have to dynamically determine whether the function has a rawArgs property\n const evalFn = this.fn._compile(math, argNames)\n const rawArgs = this.args\n\n return function evalFunctionNode (scope, args, context) {\n const fn = evalFn(scope, args, context)\n const isRaw = fn && fn.rawArgs\n\n return isRaw\n ? fn(rawArgs, math, Object.assign({}, scope, args)) // \"raw\" evaluation\n : fn.apply(fn, map(evalArgs, function (evalArg) { // \"regular\" evaluation\n return evalArg(scope, args, context)\n }))\n }\n }\n }\n\n /**\n * Execute a callback for each of the child nodes of this node\n * @param {function(child: Node, path: string, parent: Node)} callback\n */\n FunctionNode.prototype.forEach = function (callback) {\n callback(this.fn, 'fn', this)\n\n for (let i = 0; i < this.args.length; i++) {\n callback(this.args[i], 'args[' + i + ']', this)\n }\n }\n\n /**\n * Create a new FunctionNode having it's childs be the results of calling\n * the provided callback function for each of the childs of the original node.\n * @param {function(child: Node, path: string, parent: Node): Node} callback\n * @returns {FunctionNode} Returns a transformed copy of the node\n */\n FunctionNode.prototype.map = function (callback) {\n const fn = this._ifNode(callback(this.fn, 'fn', this))\n const args = []\n for (let i = 0; i < this.args.length; i++) {\n args[i] = this._ifNode(callback(this.args[i], 'args[' + i + ']', this))\n }\n return new FunctionNode(fn, args)\n }\n\n /**\n * Create a clone of this node, a shallow copy\n * @return {FunctionNode}\n */\n FunctionNode.prototype.clone = function () {\n return new FunctionNode(this.fn, this.args.slice(0))\n }\n\n // backup Node's toString function\n // @private\n const nodeToString = FunctionNode.prototype.toString\n\n /**\n * Get string representation. (wrapper function)\n * This overrides parts of Node's toString function.\n * If callback is an object containing callbacks, it\n * calls the correct callback for the current node,\n * otherwise it falls back to calling Node's toString\n * function.\n *\n * @param {Object} options\n * @return {string} str\n * @override\n */\n FunctionNode.prototype.toString = function (options) {\n let customString\n const name = this.fn.toString(options)\n if (options && (typeof options.handler === 'object') && hasOwnProperty(options.handler, name)) {\n // callback is a map of callback functions\n customString = options.handler[name](this, options)\n }\n\n if (typeof customString !== 'undefined') {\n return customString\n }\n\n // fall back to Node's toString\n return nodeToString.call(this, options)\n }\n\n /**\n * Get string representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype._toString = function (options) {\n const args = this.args.map(function (arg) {\n return arg.toString(options)\n })\n\n const fn = isFunctionAssignmentNode(this.fn)\n ? ('(' + this.fn.toString(options) + ')')\n : this.fn.toString(options)\n\n // format the arguments like \"add(2, 4.2)\"\n return fn + '(' + args.join(', ') + ')'\n }\n\n /**\n * Get a JSON representation of the node\n * @returns {Object}\n */\n FunctionNode.prototype.toJSON = function () {\n return {\n mathjs: 'FunctionNode',\n fn: this.fn,\n args: this.args\n }\n }\n\n /**\n * Instantiate an AssignmentNode from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"FunctionNode\", fn: ..., args: ...}`,\n * where mathjs is optional\n * @returns {FunctionNode}\n */\n FunctionNode.fromJSON = function (json) {\n return new FunctionNode(json.fn, json.args)\n }\n\n /**\n * Get HTML representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype.toHTML = function (options) {\n const args = this.args.map(function (arg) {\n return arg.toHTML(options)\n })\n\n // format the arguments like \"add(2, 4.2)\"\n return '' + escape(this.fn) + '(' + args.join(',') + ')'\n }\n\n /*\n * Expand a LaTeX template\n *\n * @param {string} template\n * @param {Node} node\n * @param {Object} options\n * @private\n **/\n function expandTemplate (template, node, options) {\n let latex = ''\n\n // Match everything of the form ${identifier} or ${identifier[2]} or $$\n // while submatching identifier and 2 (in the second case)\n const regex = /\\$(?:\\{([a-z_][a-z_0-9]*)(?:\\[([0-9]+)\\])?\\}|\\$)/gi\n\n let inputPos = 0 // position in the input string\n let match\n while ((match = regex.exec(template)) !== null) { // go through all matches\n // add everything in front of the match to the LaTeX string\n latex += template.substring(inputPos, match.index)\n inputPos = match.index\n\n if (match[0] === '$$') { // escaped dollar sign\n latex += '$'\n inputPos++\n } else { // template parameter\n inputPos += match[0].length\n const property = node[match[1]]\n if (!property) {\n throw new ReferenceError('Template: Property ' + match[1] + ' does not exist.')\n }\n if (match[2] === undefined) { // no square brackets\n switch (typeof property) {\n case 'string':\n latex += property\n break\n case 'object':\n if (isNode(property)) {\n latex += property.toTex(options)\n } else if (Array.isArray(property)) {\n // make array of Nodes into comma separated list\n latex += property.map(function (arg, index) {\n if (isNode(arg)) {\n return arg.toTex(options)\n }\n throw new TypeError('Template: ' + match[1] + '[' + index + '] is not a Node.')\n }).join(',')\n } else {\n throw new TypeError('Template: ' + match[1] + ' has to be a Node, String or array of Nodes')\n }\n break\n default:\n throw new TypeError('Template: ' + match[1] + ' has to be a Node, String or array of Nodes')\n }\n } else { // with square brackets\n if (isNode(property[match[2]] && property[match[2]])) {\n latex += property[match[2]].toTex(options)\n } else {\n throw new TypeError('Template: ' + match[1] + '[' + match[2] + '] is not a Node.')\n }\n }\n }\n }\n latex += template.slice(inputPos) // append rest of the template\n\n return latex\n }\n\n // backup Node's toTex function\n // @private\n const nodeToTex = FunctionNode.prototype.toTex\n\n /**\n * Get LaTeX representation. (wrapper function)\n * This overrides parts of Node's toTex function.\n * If callback is an object containing callbacks, it\n * calls the correct callback for the current node,\n * otherwise it falls back to calling Node's toTex\n * function.\n *\n * @param {Object} options\n * @return {string}\n */\n FunctionNode.prototype.toTex = function (options) {\n let customTex\n if (options && (typeof options.handler === 'object') && hasOwnProperty(options.handler, this.name)) {\n // callback is a map of callback functions\n customTex = options.handler[this.name](this, options)\n }\n\n if (typeof customTex !== 'undefined') {\n return customTex\n }\n\n // fall back to Node's toTex\n return nodeToTex.call(this, options)\n }\n\n /**\n * Get LaTeX representation\n * @param {Object} options\n * @return {string} str\n */\n FunctionNode.prototype._toTex = function (options) {\n const args = this.args.map(function (arg) { // get LaTeX of the arguments\n return arg.toTex(options)\n })\n\n let latexConverter\n\n if (latexFunctions[this.name]) {\n latexConverter = latexFunctions[this.name]\n }\n\n // toTex property on the function itself\n if (math[this.name] &&\n ((typeof math[this.name].toTex === 'function') ||\n (typeof math[this.name].toTex === 'object') ||\n (typeof math[this.name].toTex === 'string'))\n ) {\n // .toTex is a callback function\n latexConverter = math[this.name].toTex\n }\n\n let customToTex\n switch (typeof latexConverter) {\n case 'function': // a callback function\n customToTex = latexConverter(this, options)\n break\n case 'string': // a template string\n customToTex = expandTemplate(latexConverter, this, options)\n break\n case 'object': // an object with different \"converters\" for different numbers of arguments\n switch (typeof latexConverter[args.length]) {\n case 'function':\n customToTex = latexConverter[args.length](this, options)\n break\n case 'string':\n customToTex = expandTemplate(latexConverter[args.length], this, options)\n break\n }\n }\n\n if (typeof customToTex !== 'undefined') {\n return customToTex\n }\n\n return expandTemplate(defaultTemplate, this, options)\n }\n\n /**\n * Get identifier.\n * @return {string}\n */\n FunctionNode.prototype.getIdentifier = function () {\n return this.type + ':' + this.name\n }\n\n return FunctionNode\n}, { isClass: true, isNode: true })\n","import { factory } from '../utils/factory.js'\nimport { isAccessorNode, isConstantNode, isFunctionNode, isOperatorNode, isSymbolNode } from '../utils/is.js'\nimport { deepMap } from '../utils/collection.js'\nimport { hasOwnProperty } from '../utils/object.js'\n\nconst name = 'parse'\nconst dependencies = [\n 'typed',\n 'numeric',\n 'config',\n 'AccessorNode',\n 'ArrayNode',\n 'AssignmentNode',\n 'BlockNode',\n 'ConditionalNode',\n 'ConstantNode',\n 'FunctionAssignmentNode',\n 'FunctionNode',\n 'IndexNode',\n 'ObjectNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'RangeNode',\n 'RelationalNode',\n 'SymbolNode'\n]\n\nexport const createParse = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n numeric,\n config,\n AccessorNode,\n ArrayNode,\n AssignmentNode,\n BlockNode,\n ConditionalNode,\n ConstantNode,\n FunctionAssignmentNode,\n FunctionNode,\n IndexNode,\n ObjectNode,\n OperatorNode,\n ParenthesisNode,\n RangeNode,\n RelationalNode,\n SymbolNode\n}) => {\n /**\n * Parse an expression. Returns a node tree, which can be evaluated by\n * invoking node.evaluate().\n *\n * Note the evaluating arbitrary expressions may involve security risks,\n * see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.\n *\n * Syntax:\n *\n * math.parse(expr)\n * math.parse(expr, options)\n * math.parse([expr1, expr2, expr3, ...])\n * math.parse([expr1, expr2, expr3, ...], options)\n *\n * Example:\n *\n * const node1 = math.parse('sqrt(3^2 + 4^2)')\n * node1.compile().evaluate() // 5\n *\n * let scope = {a:3, b:4}\n * const node2 = math.parse('a * b') // 12\n * const code2 = node2.compile()\n * code2.evaluate(scope) // 12\n * scope.a = 5\n * code2.evaluate(scope) // 20\n *\n * const nodes = math.parse(['a = 3', 'b = 4', 'a * b'])\n * nodes[2].compile().evaluate() // 12\n *\n * See also:\n *\n * evaluate, compile\n *\n * @param {string | string[] | Matrix} expr Expression to be parsed\n * @param {{nodes: Object}} [options] Available options:\n * - `nodes` a set of custom nodes\n * @return {Node | Node[]} node\n * @throws {Error}\n */\n const parse = typed(name, {\n string: function (expression) {\n return parseStart(expression, {})\n },\n 'Array | Matrix': function (expressions) {\n return parseMultiple(expressions, {})\n },\n 'string, Object': function (expression, options) {\n const extraNodes = options.nodes !== undefined ? options.nodes : {}\n\n return parseStart(expression, extraNodes)\n },\n 'Array | Matrix, Object': parseMultiple\n })\n\n function parseMultiple (expressions, options = {}) {\n const extraNodes = options.nodes !== undefined ? options.nodes : {}\n\n // parse an array or matrix with expressions\n return deepMap(expressions, function (elem) {\n if (typeof elem !== 'string') throw new TypeError('String expected')\n\n return parseStart(elem, extraNodes)\n })\n }\n\n // token types enumeration\n const TOKENTYPE = {\n NULL: 0,\n DELIMITER: 1,\n NUMBER: 2,\n SYMBOL: 3,\n UNKNOWN: 4\n }\n\n // map with all delimiters\n const DELIMITERS = {\n ',': true,\n '(': true,\n ')': true,\n '[': true,\n ']': true,\n '{': true,\n '}': true,\n '\"': true,\n '\\'': true,\n ';': true,\n\n '+': true,\n '-': true,\n '*': true,\n '.*': true,\n '/': true,\n './': true,\n '%': true,\n '^': true,\n '.^': true,\n '~': true,\n '!': true,\n '&': true,\n '|': true,\n '^|': true,\n '=': true,\n ':': true,\n '?': true,\n\n '==': true,\n '!=': true,\n '<': true,\n '>': true,\n '<=': true,\n '>=': true,\n\n '<<': true,\n '>>': true,\n '>>>': true\n }\n\n // map with all named delimiters\n const NAMED_DELIMITERS = {\n mod: true,\n to: true,\n in: true,\n and: true,\n xor: true,\n or: true,\n not: true\n }\n\n const CONSTANTS = {\n true: true,\n false: false,\n null: null,\n undefined: undefined\n }\n\n const NUMERIC_CONSTANTS = [\n 'NaN',\n 'Infinity'\n ]\n\n function initialState () {\n return {\n extraNodes: {}, // current extra nodes, must be careful not to mutate\n expression: '', // current expression\n comment: '', // last parsed comment\n index: 0, // current index in expr\n token: '', // current token\n tokenType: TOKENTYPE.NULL, // type of the token\n nestingLevel: 0, // level of nesting inside parameters, used to ignore newline characters\n conditionalLevel: null // when a conditional is being parsed, the level of the conditional is stored here\n }\n }\n\n /**\n * View upto `length` characters of the expression starting at the current character.\n *\n * @param {Object} state\n * @param {number} [length=1] Number of characters to view\n * @returns {string}\n * @private\n */\n function currentString (state, length) {\n return state.expression.substr(state.index, length)\n }\n\n /**\n * View the current character. Returns '' if end of expression is reached.\n *\n * @param {Object} state\n * @returns {string}\n * @private\n */\n function currentCharacter (state) {\n return currentString(state, 1)\n }\n\n /**\n * Get the next character from the expression.\n * The character is stored into the char c. If the end of the expression is\n * reached, the function puts an empty string in c.\n * @private\n */\n function next (state) {\n state.index++\n }\n\n /**\n * Preview the previous character from the expression.\n * @return {string} cNext\n * @private\n */\n function prevCharacter (state) {\n return state.expression.charAt(state.index - 1)\n }\n\n /**\n * Preview the next character from the expression.\n * @return {string} cNext\n * @private\n */\n function nextCharacter (state) {\n return state.expression.charAt(state.index + 1)\n }\n\n /**\n * Get next token in the current string expr.\n * The token and token type are available as token and tokenType\n * @private\n */\n function getToken (state) {\n state.tokenType = TOKENTYPE.NULL\n state.token = ''\n state.comment = ''\n\n // skip over whitespaces\n // space, tab, and newline when inside parameters\n while (parse.isWhitespace(currentCharacter(state), state.nestingLevel)) {\n next(state)\n }\n\n // skip comment\n if (currentCharacter(state) === '#') {\n while (currentCharacter(state) !== '\\n' && currentCharacter(state) !== '') {\n state.comment += currentCharacter(state)\n next(state)\n }\n }\n\n // check for end of expression\n if (currentCharacter(state) === '') {\n // token is still empty\n state.tokenType = TOKENTYPE.DELIMITER\n return\n }\n\n // check for new line character\n if (currentCharacter(state) === '\\n' && !state.nestingLevel) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = currentCharacter(state)\n next(state)\n return\n }\n\n const c1 = currentCharacter(state)\n const c2 = currentString(state, 2)\n const c3 = currentString(state, 3)\n if (c3.length === 3 && DELIMITERS[c3]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c3\n next(state)\n next(state)\n next(state)\n return\n }\n\n // check for delimiters consisting of 2 characters\n if (c2.length === 2 && DELIMITERS[c2]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c2\n next(state)\n next(state)\n return\n }\n\n // check for delimiters consisting of 1 character\n if (DELIMITERS[c1]) {\n state.tokenType = TOKENTYPE.DELIMITER\n state.token = c1\n next(state)\n return\n }\n\n // check for a number\n if (parse.isDigitDot(c1)) {\n state.tokenType = TOKENTYPE.NUMBER\n\n // check for binary, octal, or hex\n const c2 = currentString(state, 2)\n if (c2 === '0b' || c2 === '0o' || c2 === '0x') {\n state.token += currentCharacter(state)\n next(state)\n state.token += currentCharacter(state)\n next(state)\n while (parse.isHexDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n // check for word size suffix\n const sign = currentCharacter(state)\n if (sign === 'i') {\n state.token += sign\n next(state)\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n }\n return\n }\n\n // get number, can have a single dot\n if (currentCharacter(state) === '.') {\n state.token += currentCharacter(state)\n next(state)\n\n if (!parse.isDigit(currentCharacter(state))) {\n // this is no number, it is just a dot (can be dot notation)\n state.tokenType = TOKENTYPE.DELIMITER\n }\n } else {\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n }\n\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n // check for exponential notation like \"2.3e-4\", \"1.23e50\" or \"2e+4\"\n if (currentCharacter(state) === 'E' || currentCharacter(state) === 'e') {\n if (parse.isDigit(nextCharacter(state)) || nextCharacter(state) === '-' || nextCharacter(state) === '+') {\n state.token += currentCharacter(state)\n next(state)\n\n if (currentCharacter(state) === '+' || currentCharacter(state) === '-') {\n state.token += currentCharacter(state)\n next(state)\n }\n // Scientific notation MUST be followed by an exponent\n if (!parse.isDigit(currentCharacter(state))) {\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n\n while (parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n\n if (parse.isDecimalMark(currentCharacter(state), nextCharacter(state))) {\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n } else if (nextCharacter(state) === '.') {\n next(state)\n throw createSyntaxError(state, 'Digit expected, got \"' + currentCharacter(state) + '\"')\n }\n }\n\n return\n }\n\n // check for variables, functions, named operators\n if (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state))) {\n while (parse.isAlpha(currentCharacter(state), prevCharacter(state), nextCharacter(state)) || parse.isDigit(currentCharacter(state))) {\n state.token += currentCharacter(state)\n next(state)\n }\n\n if (hasOwnProperty(NAMED_DELIMITERS, state.token)) {\n state.tokenType = TOKENTYPE.DELIMITER\n } else {\n state.tokenType = TOKENTYPE.SYMBOL\n }\n\n return\n }\n\n // something unknown is found, wrong characters -> a syntax error\n state.tokenType = TOKENTYPE.UNKNOWN\n while (currentCharacter(state) !== '') {\n state.token += currentCharacter(state)\n next(state)\n }\n throw createSyntaxError(state, 'Syntax error in part \"' + state.token + '\"')\n }\n\n /**\n * Get next token and skip newline tokens\n */\n function getTokenSkipNewline (state) {\n do {\n getToken(state)\n }\n while (state.token === '\\n') // eslint-disable-line no-unmodified-loop-condition\n }\n\n /**\n * Open parameters.\n * New line characters will be ignored until closeParams(state) is called\n */\n function openParams (state) {\n state.nestingLevel++\n }\n\n /**\n * Close parameters.\n * New line characters will no longer be ignored\n */\n function closeParams (state) {\n state.nestingLevel--\n }\n\n /**\n * Checks whether the current character `c` is a valid alpha character:\n *\n * - A latin letter (upper or lower case) Ascii: a-z, A-Z\n * - An underscore Ascii: _\n * - A dollar sign Ascii: $\n * - A latin letter with accents Unicode: \\u00C0 - \\u02AF\n * - A greek letter Unicode: \\u0370 - \\u03FF\n * - A mathematical alphanumeric symbol Unicode: \\u{1D400} - \\u{1D7FF} excluding invalid code points\n *\n * The previous and next characters are needed to determine whether\n * this character is part of a unicode surrogate pair.\n *\n * @param {string} c Current character in the expression\n * @param {string} cPrev Previous character\n * @param {string} cNext Next character\n * @return {boolean}\n */\n parse.isAlpha = function isAlpha (c, cPrev, cNext) {\n return parse.isValidLatinOrGreek(c) ||\n parse.isValidMathSymbol(c, cNext) ||\n parse.isValidMathSymbol(cPrev, c)\n }\n\n /**\n * Test whether a character is a valid latin, greek, or letter-like character\n * @param {string} c\n * @return {boolean}\n */\n parse.isValidLatinOrGreek = function isValidLatinOrGreek (c) {\n return /^[a-zA-Z_$\\u00C0-\\u02AF\\u0370-\\u03FF\\u2100-\\u214F]$/.test(c)\n }\n\n /**\n * Test whether two given 16 bit characters form a surrogate pair of a\n * unicode math symbol.\n *\n * https://unicode-table.com/en/\n * https://www.wikiwand.com/en/Mathematical_operators_and_symbols_in_Unicode\n *\n * Note: In ES6 will be unicode aware:\n * https://stackoverflow.com/questions/280712/javascript-unicode-regexes\n * https://mathiasbynens.be/notes/es6-unicode-regex\n *\n * @param {string} high\n * @param {string} low\n * @return {boolean}\n */\n parse.isValidMathSymbol = function isValidMathSymbol (high, low) {\n return /^[\\uD835]$/.test(high) &&\n /^[\\uDC00-\\uDFFF]$/.test(low) &&\n /^[^\\uDC55\\uDC9D\\uDCA0\\uDCA1\\uDCA3\\uDCA4\\uDCA7\\uDCA8\\uDCAD\\uDCBA\\uDCBC\\uDCC4\\uDD06\\uDD0B\\uDD0C\\uDD15\\uDD1D\\uDD3A\\uDD3F\\uDD45\\uDD47-\\uDD49\\uDD51\\uDEA6\\uDEA7\\uDFCC\\uDFCD]$/.test(low)\n }\n\n /**\n * Check whether given character c is a white space character: space, tab, or enter\n * @param {string} c\n * @param {number} nestingLevel\n * @return {boolean}\n */\n parse.isWhitespace = function isWhitespace (c, nestingLevel) {\n // TODO: also take '\\r' carriage return as newline? Or does that give problems on mac?\n return c === ' ' || c === '\\t' || (c === '\\n' && nestingLevel > 0)\n }\n\n /**\n * Test whether the character c is a decimal mark (dot).\n * This is the case when it's not the start of a delimiter '.*', './', or '.^'\n * @param {string} c\n * @param {string} cNext\n * @return {boolean}\n */\n parse.isDecimalMark = function isDecimalMark (c, cNext) {\n return c === '.' && cNext !== '/' && cNext !== '*' && cNext !== '^'\n }\n\n /**\n * checks if the given char c is a digit or dot\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isDigitDot = function isDigitDot (c) {\n return ((c >= '0' && c <= '9') || c === '.')\n }\n\n /**\n * checks if the given char c is a digit\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isDigit = function isDigit (c) {\n return (c >= '0' && c <= '9')\n }\n\n /**\n * checks if the given char c is a hex digit\n * @param {string} c a string with one character\n * @return {boolean}\n */\n parse.isHexDigit = function isHexDigit (c) {\n return ((c >= '0' && c <= '9') ||\n (c >= 'a' && c <= 'f') ||\n (c >= 'A' && c <= 'F'))\n }\n\n /**\n * Start of the parse levels below, in order of precedence\n * @return {Node} node\n * @private\n */\n function parseStart (expression, extraNodes) {\n const state = initialState()\n Object.assign(state, { expression, extraNodes })\n getToken(state)\n\n const node = parseBlock(state)\n\n // check for garbage at the end of the expression\n // an expression ends with a empty character '' and tokenType DELIMITER\n if (state.token !== '') {\n if (state.tokenType === TOKENTYPE.DELIMITER) {\n // user entered a not existing operator like \"//\"\n\n // TODO: give hints for aliases, for example with \"<>\" give as hint \" did you mean !== ?\"\n throw createError(state, 'Unexpected operator ' + state.token)\n } else {\n throw createSyntaxError(state, 'Unexpected part \"' + state.token + '\"')\n }\n }\n\n return node\n }\n\n /**\n * Parse a block with expressions. Expressions can be separated by a newline\n * character '\\n', or by a semicolon ';'. In case of a semicolon, no output\n * of the preceding line is returned.\n * @return {Node} node\n * @private\n */\n function parseBlock (state) {\n let node\n const blocks = []\n let visible\n\n if (state.token !== '' && state.token !== '\\n' && state.token !== ';') {\n node = parseAssignment(state)\n node.comment = state.comment\n }\n\n // TODO: simplify this loop\n while (state.token === '\\n' || state.token === ';') { // eslint-disable-line no-unmodified-loop-condition\n if (blocks.length === 0 && node) {\n visible = (state.token !== ';')\n blocks.push({\n node: node,\n visible: visible\n })\n }\n\n getToken(state)\n if (state.token !== '\\n' && state.token !== ';' && state.token !== '') {\n node = parseAssignment(state)\n node.comment = state.comment\n\n visible = (state.token !== ';')\n blocks.push({\n node: node,\n visible: visible\n })\n }\n }\n\n if (blocks.length > 0) {\n return new BlockNode(blocks)\n } else {\n if (!node) {\n node = new ConstantNode(undefined)\n node.comment = state.comment\n }\n\n return node\n }\n }\n\n /**\n * Assignment of a function or variable,\n * - can be a variable like 'a=2.3'\n * - or a updating an existing variable like 'matrix(2,3:5)=[6,7,8]'\n * - defining a function like 'f(x) = x^2'\n * @return {Node} node\n * @private\n */\n function parseAssignment (state) {\n let name, args, value, valid\n\n const node = parseConditional(state)\n\n if (state.token === '=') {\n if (isSymbolNode(node)) {\n // parse a variable assignment like 'a = 2/3'\n name = node.name\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new AssignmentNode(new SymbolNode(name), value)\n } else if (isAccessorNode(node)) {\n // parse a matrix subset assignment like 'A[1,2] = 4'\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new AssignmentNode(node.object, node.index, value)\n } else if (isFunctionNode(node) && isSymbolNode(node.fn)) {\n // parse function assignment like 'f(x) = x^2'\n valid = true\n args = []\n\n name = node.name\n node.args.forEach(function (arg, index) {\n if (isSymbolNode(arg)) {\n args[index] = arg.name\n } else {\n valid = false\n }\n })\n\n if (valid) {\n getTokenSkipNewline(state)\n value = parseAssignment(state)\n return new FunctionAssignmentNode(name, args, value)\n }\n }\n\n throw createSyntaxError(state, 'Invalid left hand side of assignment operator =')\n }\n\n return node\n }\n\n /**\n * conditional operation\n *\n * condition ? truePart : falsePart\n *\n * Note: conditional operator is right-associative\n *\n * @return {Node} node\n * @private\n */\n function parseConditional (state) {\n let node = parseLogicalOr(state)\n\n while (state.token === '?') { // eslint-disable-line no-unmodified-loop-condition\n // set a conditional level, the range operator will be ignored as long\n // as conditionalLevel === state.nestingLevel.\n const prev = state.conditionalLevel\n state.conditionalLevel = state.nestingLevel\n getTokenSkipNewline(state)\n\n const condition = node\n const trueExpr = parseAssignment(state)\n\n if (state.token !== ':') throw createSyntaxError(state, 'False part of conditional expression expected')\n\n state.conditionalLevel = null\n getTokenSkipNewline(state)\n\n const falseExpr = parseAssignment(state) // Note: check for conditional operator again, right associativity\n\n node = new ConditionalNode(condition, trueExpr, falseExpr)\n\n // restore the previous conditional level\n state.conditionalLevel = prev\n }\n\n return node\n }\n\n /**\n * logical or, 'x or y'\n * @return {Node} node\n * @private\n */\n function parseLogicalOr (state) {\n let node = parseLogicalXor(state)\n\n while (state.token === 'or') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('or', 'or', [node, parseLogicalXor(state)])\n }\n\n return node\n }\n\n /**\n * logical exclusive or, 'x xor y'\n * @return {Node} node\n * @private\n */\n function parseLogicalXor (state) {\n let node = parseLogicalAnd(state)\n\n while (state.token === 'xor') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('xor', 'xor', [node, parseLogicalAnd(state)])\n }\n\n return node\n }\n\n /**\n * logical and, 'x and y'\n * @return {Node} node\n * @private\n */\n function parseLogicalAnd (state) {\n let node = parseBitwiseOr(state)\n\n while (state.token === 'and') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('and', 'and', [node, parseBitwiseOr(state)])\n }\n\n return node\n }\n\n /**\n * bitwise or, 'x | y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseOr (state) {\n let node = parseBitwiseXor(state)\n\n while (state.token === '|') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('|', 'bitOr', [node, parseBitwiseXor(state)])\n }\n\n return node\n }\n\n /**\n * bitwise exclusive or (xor), 'x ^| y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseXor (state) {\n let node = parseBitwiseAnd(state)\n\n while (state.token === '^|') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('^|', 'bitXor', [node, parseBitwiseAnd(state)])\n }\n\n return node\n }\n\n /**\n * bitwise and, 'x & y'\n * @return {Node} node\n * @private\n */\n function parseBitwiseAnd (state) {\n let node = parseRelational(state)\n\n while (state.token === '&') { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n node = new OperatorNode('&', 'bitAnd', [node, parseRelational(state)])\n }\n\n return node\n }\n\n /**\n * Parse a chained conditional, like 'a > b >= c'\n * @return {Node} node\n */\n function parseRelational (state) {\n const params = [parseShift(state)]\n const conditionals = []\n\n const operators = {\n '==': 'equal',\n '!=': 'unequal',\n '<': 'smaller',\n '>': 'larger',\n '<=': 'smallerEq',\n '>=': 'largerEq'\n }\n\n while (hasOwnProperty(operators, state.token)) { // eslint-disable-line no-unmodified-loop-condition\n const cond = { name: state.token, fn: operators[state.token] }\n conditionals.push(cond)\n getTokenSkipNewline(state)\n params.push(parseShift(state))\n }\n\n if (params.length === 1) {\n return params[0]\n } else if (params.length === 2) {\n return new OperatorNode(conditionals[0].name, conditionals[0].fn, params)\n } else {\n return new RelationalNode(conditionals.map(c => c.fn), params)\n }\n }\n\n /**\n * Bitwise left shift, bitwise right arithmetic shift, bitwise right logical shift\n * @return {Node} node\n * @private\n */\n function parseShift (state) {\n let node, name, fn, params\n\n node = parseConversion(state)\n\n const operators = {\n '<<': 'leftShift',\n '>>': 'rightArithShift',\n '>>>': 'rightLogShift'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n params = [node, parseConversion(state)]\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * conversion operators 'to' and 'in'\n * @return {Node} node\n * @private\n */\n function parseConversion (state) {\n let node, name, fn, params\n\n node = parseRange(state)\n\n const operators = {\n to: 'to',\n in: 'to' // alias of 'to'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n\n if (name === 'in' && state.token === '') {\n // end of expression -> this is the unit 'in' ('inch')\n node = new OperatorNode('*', 'multiply', [node, new SymbolNode('in')], true)\n } else {\n // operator 'a to b' or 'a in b'\n params = [node, parseRange(state)]\n node = new OperatorNode(name, fn, params)\n }\n }\n\n return node\n }\n\n /**\n * parse range, \"start:end\", \"start:step:end\", \":\", \"start:\", \":end\", etc\n * @return {Node} node\n * @private\n */\n function parseRange (state) {\n let node\n const params = []\n\n if (state.token === ':') {\n // implicit start=1 (one-based)\n node = new ConstantNode(1)\n } else {\n // explicit start\n node = parseAddSubtract(state)\n }\n\n if (state.token === ':' && (state.conditionalLevel !== state.nestingLevel)) {\n // we ignore the range operator when a conditional operator is being processed on the same level\n params.push(node)\n\n // parse step and end\n while (state.token === ':' && params.length < 3) { // eslint-disable-line no-unmodified-loop-condition\n getTokenSkipNewline(state)\n\n if (state.token === ')' || state.token === ']' || state.token === ',' || state.token === '') {\n // implicit end\n params.push(new SymbolNode('end'))\n } else {\n // explicit end\n params.push(parseAddSubtract(state))\n }\n }\n\n if (params.length === 3) {\n // params = [start, step, end]\n node = new RangeNode(params[0], params[2], params[1]) // start, end, step\n } else { // length === 2\n // params = [start, end]\n node = new RangeNode(params[0], params[1]) // start, end\n }\n }\n\n return node\n }\n\n /**\n * add or subtract\n * @return {Node} node\n * @private\n */\n function parseAddSubtract (state) {\n let node, name, fn, params\n\n node = parseMultiplyDivide(state)\n\n const operators = {\n '+': 'add',\n '-': 'subtract'\n }\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n params = [node, parseMultiplyDivide(state)]\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * multiply, divide, modulus\n * @return {Node} node\n * @private\n */\n function parseMultiplyDivide (state) {\n let node, last, name, fn\n\n node = parseImplicitMultiplication(state)\n last = node\n\n const operators = {\n '*': 'multiply',\n '.*': 'dotMultiply',\n '/': 'divide',\n './': 'dotDivide',\n '%': 'mod',\n mod: 'mod'\n }\n\n while (true) {\n if (hasOwnProperty(operators, state.token)) {\n // explicit operators\n name = state.token\n fn = operators[name]\n\n getTokenSkipNewline(state)\n\n last = parseImplicitMultiplication(state)\n node = new OperatorNode(name, fn, [node, last])\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * implicit multiplication\n * @return {Node} node\n * @private\n */\n function parseImplicitMultiplication (state) {\n let node, last\n\n node = parseRule2(state)\n last = node\n\n while (true) {\n if ((state.tokenType === TOKENTYPE.SYMBOL) ||\n (state.token === 'in' && isConstantNode(node)) ||\n (state.tokenType === TOKENTYPE.NUMBER &&\n !isConstantNode(last) &&\n (!isOperatorNode(last) || last.op === '!')) ||\n (state.token === '(')) {\n // parse implicit multiplication\n //\n // symbol: implicit multiplication like '2a', '(2+3)a', 'a b'\n // number: implicit multiplication like '(2+3)2'\n // parenthesis: implicit multiplication like '2(3+4)', '(3+4)(1+2)'\n last = parseRule2(state)\n node = new OperatorNode('*', 'multiply', [node, last], true /* implicit */)\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * Infamous \"rule 2\" as described in https://github.com/josdejong/mathjs/issues/792#issuecomment-361065370\n * Explicit division gets higher precedence than implicit multiplication\n * when the division matches this pattern: [number] / [number] [symbol]\n * @return {Node} node\n * @private\n */\n function parseRule2 (state) {\n let node = parseUnary(state)\n let last = node\n const tokenStates = []\n\n while (true) {\n // Match the \"number /\" part of the pattern \"number / number symbol\"\n if (state.token === '/' && isConstantNode(last)) {\n // Look ahead to see if the next token is a number\n tokenStates.push(Object.assign({}, state))\n getTokenSkipNewline(state)\n\n // Match the \"number / number\" part of the pattern\n if (state.tokenType === TOKENTYPE.NUMBER) {\n // Look ahead again\n tokenStates.push(Object.assign({}, state))\n getTokenSkipNewline(state)\n\n // Match the \"symbol\" part of the pattern, or a left parenthesis\n if (state.tokenType === TOKENTYPE.SYMBOL || state.token === '(') {\n // We've matched the pattern \"number / number symbol\".\n // Rewind once and build the \"number / number\" node; the symbol will be consumed later\n Object.assign(state, tokenStates.pop())\n tokenStates.pop()\n last = parseUnary(state)\n node = new OperatorNode('/', 'divide', [node, last])\n } else {\n // Not a match, so rewind\n tokenStates.pop()\n Object.assign(state, tokenStates.pop())\n break\n }\n } else {\n // Not a match, so rewind\n Object.assign(state, tokenStates.pop())\n break\n }\n } else {\n break\n }\n }\n\n return node\n }\n\n /**\n * Unary plus and minus, and logical and bitwise not\n * @return {Node} node\n * @private\n */\n function parseUnary (state) {\n let name, params, fn\n const operators = {\n '-': 'unaryMinus',\n '+': 'unaryPlus',\n '~': 'bitNot',\n not: 'not'\n }\n\n if (hasOwnProperty(operators, state.token)) {\n fn = operators[state.token]\n name = state.token\n\n getTokenSkipNewline(state)\n params = [parseUnary(state)]\n\n return new OperatorNode(name, fn, params)\n }\n\n return parsePow(state)\n }\n\n /**\n * power\n * Note: power operator is right associative\n * @return {Node} node\n * @private\n */\n function parsePow (state) {\n let node, name, fn, params\n\n node = parseLeftHandOperators(state)\n\n if (state.token === '^' || state.token === '.^') {\n name = state.token\n fn = (name === '^') ? 'pow' : 'dotPow'\n\n getTokenSkipNewline(state)\n params = [node, parseUnary(state)] // Go back to unary, we can have '2^-3'\n node = new OperatorNode(name, fn, params)\n }\n\n return node\n }\n\n /**\n * Left hand operators: factorial x!, ctranspose x'\n * @return {Node} node\n * @private\n */\n function parseLeftHandOperators (state) {\n let node, name, fn, params\n\n node = parseCustomNodes(state)\n\n const operators = {\n '!': 'factorial',\n '\\'': 'ctranspose'\n }\n\n while (hasOwnProperty(operators, state.token)) {\n name = state.token\n fn = operators[name]\n\n getToken(state)\n params = [node]\n\n node = new OperatorNode(name, fn, params)\n node = parseAccessors(state, node)\n }\n\n return node\n }\n\n /**\n * Parse a custom node handler. A node handler can be used to process\n * nodes in a custom way, for example for handling a plot.\n *\n * A handler must be passed as second argument of the parse function.\n * - must extend math.Node\n * - must contain a function _compile(defs: Object) : string\n * - must contain a function find(filter: Object) : Node[]\n * - must contain a function toString() : string\n * - the constructor is called with a single argument containing all parameters\n *\n * For example:\n *\n * nodes = {\n * 'plot': PlotHandler\n * }\n *\n * The constructor of the handler is called as:\n *\n * node = new PlotHandler(params)\n *\n * The handler will be invoked when evaluating an expression like:\n *\n * node = math.parse('plot(sin(x), x)', nodes)\n *\n * @return {Node} node\n * @private\n */\n function parseCustomNodes (state) {\n let params = []\n\n if (state.tokenType === TOKENTYPE.SYMBOL && hasOwnProperty(state.extraNodes, state.token)) {\n const CustomNode = state.extraNodes[state.token]\n\n getToken(state)\n\n // parse parameters\n if (state.token === '(') {\n params = []\n\n openParams(state)\n getToken(state)\n\n if (state.token !== ')') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n }\n\n // create a new custom node\n // noinspection JSValidateTypes\n return new CustomNode(params)\n }\n\n return parseSymbol(state)\n }\n\n /**\n * parse symbols: functions, variables, constants, units\n * @return {Node} node\n * @private\n */\n function parseSymbol (state) {\n let node, name\n\n if (state.tokenType === TOKENTYPE.SYMBOL ||\n (state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS)) {\n name = state.token\n\n getToken(state)\n\n if (hasOwnProperty(CONSTANTS, name)) { // true, false, null, ...\n node = new ConstantNode(CONSTANTS[name])\n } else if (NUMERIC_CONSTANTS.indexOf(name) !== -1) { // NaN, Infinity\n node = new ConstantNode(numeric(name, 'number'))\n } else {\n node = new SymbolNode(name)\n }\n\n // parse function parameters and matrix index\n node = parseAccessors(state, node)\n return node\n }\n\n return parseDoubleQuotesString(state)\n }\n\n /**\n * parse accessors:\n * - function invocation in round brackets (...), for example sqrt(2)\n * - index enclosed in square brackets [...], for example A[2,3]\n * - dot notation for properties, like foo.bar\n * @param {Object} state\n * @param {Node} node Node on which to apply the parameters. If there\n * are no parameters in the expression, the node\n * itself is returned\n * @param {string[]} [types] Filter the types of notations\n * can be ['(', '[', '.']\n * @return {Node} node\n * @private\n */\n function parseAccessors (state, node, types) {\n let params\n\n while ((state.token === '(' || state.token === '[' || state.token === '.') &&\n (!types || types.indexOf(state.token) !== -1)) { // eslint-disable-line no-unmodified-loop-condition\n params = []\n\n if (state.token === '(') {\n if (isSymbolNode(node) || isAccessorNode(node)) {\n // function invocation like fn(2, 3) or obj.fn(2, 3)\n openParams(state)\n getToken(state)\n\n if (state.token !== ')') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new FunctionNode(node, params)\n } else {\n // implicit multiplication like (2+3)(4+5) or sqrt(2)(1+2)\n // don't parse it here but let it be handled by parseImplicitMultiplication\n // with correct precedence\n return node\n }\n } else if (state.token === '[') {\n // index notation like variable[2, 3]\n openParams(state)\n getToken(state)\n\n if (state.token !== ']') {\n params.push(parseAssignment(state))\n\n // parse a list with parameters\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n params.push(parseAssignment(state))\n }\n }\n\n if (state.token !== ']') {\n throw createSyntaxError(state, 'Parenthesis ] expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new AccessorNode(node, new IndexNode(params))\n } else {\n // dot notation like variable.prop\n getToken(state)\n\n if (state.tokenType !== TOKENTYPE.SYMBOL) {\n throw createSyntaxError(state, 'Property name expected after dot')\n }\n params.push(new ConstantNode(state.token))\n getToken(state)\n\n const dotNotation = true\n node = new AccessorNode(node, new IndexNode(params, dotNotation))\n }\n }\n\n return node\n }\n\n /**\n * Parse a double quotes string.\n * @return {Node} node\n * @private\n */\n function parseDoubleQuotesString (state) {\n let node, str\n\n if (state.token === '\"') {\n str = parseDoubleQuotesStringToken(state)\n\n // create constant\n node = new ConstantNode(str)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseSingleQuotesString(state)\n }\n\n /**\n * Parse a string surrounded by double quotes \"...\"\n * @return {string}\n */\n function parseDoubleQuotesStringToken (state) {\n let str = ''\n\n while (currentCharacter(state) !== '' && currentCharacter(state) !== '\"') {\n if (currentCharacter(state) === '\\\\') {\n // escape character, immediately process the next\n // character to prevent stopping at a next '\\\"'\n str += currentCharacter(state)\n next(state)\n }\n\n str += currentCharacter(state)\n next(state)\n }\n\n getToken(state)\n if (state.token !== '\"') {\n throw createSyntaxError(state, 'End of string \" expected')\n }\n getToken(state)\n\n return JSON.parse('\"' + str + '\"') // unescape escaped characters\n }\n\n /**\n * Parse a single quotes string.\n * @return {Node} node\n * @private\n */\n function parseSingleQuotesString (state) {\n let node, str\n\n if (state.token === '\\'') {\n str = parseSingleQuotesStringToken(state)\n\n // create constant\n node = new ConstantNode(str)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseMatrix(state)\n }\n\n /**\n * Parse a string surrounded by single quotes '...'\n * @return {string}\n */\n function parseSingleQuotesStringToken (state) {\n let str = ''\n\n while (currentCharacter(state) !== '' && currentCharacter(state) !== '\\'') {\n if (currentCharacter(state) === '\\\\') {\n // escape character, immediately process the next\n // character to prevent stopping at a next '\\''\n str += currentCharacter(state)\n next(state)\n }\n\n str += currentCharacter(state)\n next(state)\n }\n\n getToken(state)\n if (state.token !== '\\'') {\n throw createSyntaxError(state, 'End of string \\' expected')\n }\n getToken(state)\n\n return JSON.parse('\"' + str + '\"') // unescape escaped characters\n }\n\n /**\n * parse the matrix\n * @return {Node} node\n * @private\n */\n function parseMatrix (state) {\n let array, params, rows, cols\n\n if (state.token === '[') {\n // matrix [...]\n openParams(state)\n getToken(state)\n\n if (state.token !== ']') {\n // this is a non-empty matrix\n const row = parseRow(state)\n\n if (state.token === ';') {\n // 2 dimensional array\n rows = 1\n params = [row]\n\n // the rows of the matrix are separated by dot-comma's\n while (state.token === ';') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n\n params[rows] = parseRow(state)\n rows++\n }\n\n if (state.token !== ']') {\n throw createSyntaxError(state, 'End of matrix ] expected')\n }\n closeParams(state)\n getToken(state)\n\n // check if the number of columns matches in all rows\n cols = params[0].items.length\n for (let r = 1; r < rows; r++) {\n if (params[r].items.length !== cols) {\n throw createError(state, 'Column dimensions mismatch ' +\n '(' + params[r].items.length + ' !== ' + cols + ')')\n }\n }\n\n array = new ArrayNode(params)\n } else {\n // 1 dimensional vector\n if (state.token !== ']') {\n throw createSyntaxError(state, 'End of matrix ] expected')\n }\n closeParams(state)\n getToken(state)\n\n array = row\n }\n } else {\n // this is an empty matrix \"[ ]\"\n closeParams(state)\n getToken(state)\n array = new ArrayNode([])\n }\n\n return parseAccessors(state, array)\n }\n\n return parseObject(state)\n }\n\n /**\n * Parse a single comma-separated row from a matrix, like 'a, b, c'\n * @return {ArrayNode} node\n */\n function parseRow (state) {\n const params = [parseAssignment(state)]\n let len = 1\n\n while (state.token === ',') { // eslint-disable-line no-unmodified-loop-condition\n getToken(state)\n\n // parse expression\n params[len] = parseAssignment(state)\n len++\n }\n\n return new ArrayNode(params)\n }\n\n /**\n * parse an object, enclosed in angle brackets{...}, for example {value: 2}\n * @return {Node} node\n * @private\n */\n function parseObject (state) {\n if (state.token === '{') {\n openParams(state)\n let key\n\n const properties = {}\n do {\n getToken(state)\n\n if (state.token !== '}') {\n // parse key\n if (state.token === '\"') {\n key = parseDoubleQuotesStringToken(state)\n } else if (state.token === '\\'') {\n key = parseSingleQuotesStringToken(state)\n } else if (state.tokenType === TOKENTYPE.SYMBOL || (state.tokenType === TOKENTYPE.DELIMITER && state.token in NAMED_DELIMITERS)) {\n key = state.token\n getToken(state)\n } else {\n throw createSyntaxError(state, 'Symbol or string expected as object key')\n }\n\n // parse key/value separator\n if (state.token !== ':') {\n throw createSyntaxError(state, 'Colon : expected after object key')\n }\n getToken(state)\n\n // parse key\n properties[key] = parseAssignment(state)\n }\n }\n while (state.token === ',') // eslint-disable-line no-unmodified-loop-condition\n\n if (state.token !== '}') {\n throw createSyntaxError(state, 'Comma , or bracket } expected after object value')\n }\n closeParams(state)\n getToken(state)\n\n let node = new ObjectNode(properties)\n\n // parse index parameters\n node = parseAccessors(state, node)\n\n return node\n }\n\n return parseNumber(state)\n }\n\n /**\n * parse a number\n * @return {Node} node\n * @private\n */\n function parseNumber (state) {\n let numberStr\n\n if (state.tokenType === TOKENTYPE.NUMBER) {\n // this is a number\n numberStr = state.token\n getToken(state)\n\n return new ConstantNode(numeric(numberStr, config.number))\n }\n\n return parseParentheses(state)\n }\n\n /**\n * parentheses\n * @return {Node} node\n * @private\n */\n function parseParentheses (state) {\n let node\n\n // check if it is a parenthesized expression\n if (state.token === '(') {\n // parentheses (...)\n openParams(state)\n getToken(state)\n\n node = parseAssignment(state) // start again\n\n if (state.token !== ')') {\n throw createSyntaxError(state, 'Parenthesis ) expected')\n }\n closeParams(state)\n getToken(state)\n\n node = new ParenthesisNode(node)\n node = parseAccessors(state, node)\n return node\n }\n\n return parseEnd(state)\n }\n\n /**\n * Evaluated when the expression is not yet ended but expected to end\n * @return {Node} res\n * @private\n */\n function parseEnd (state) {\n if (state.token === '') {\n // syntax error or unexpected end of expression\n throw createSyntaxError(state, 'Unexpected end of expression')\n } else {\n throw createSyntaxError(state, 'Value expected')\n }\n }\n\n /**\n * Shortcut for getting the current row value (one based)\n * Returns the line of the currently handled expression\n * @private\n */\n /* TODO: implement keeping track on the row number\n function row () {\n return null\n }\n */\n\n /**\n * Shortcut for getting the current col value (one based)\n * Returns the column (position) where the last state.token starts\n * @private\n */\n function col (state) {\n return state.index - state.token.length + 1\n }\n\n /**\n * Create an error\n * @param {Object} state\n * @param {string} message\n * @return {SyntaxError} instantiated error\n * @private\n */\n function createSyntaxError (state, message) {\n const c = col(state)\n const error = new SyntaxError(message + ' (char ' + c + ')')\n error.char = c\n\n return error\n }\n\n /**\n * Create an error\n * @param {Object} state\n * @param {string} message\n * @return {Error} instantiated error\n * @private\n */\n function createError (state, message) {\n const c = col(state)\n const error = new SyntaxError(message + ' (char ' + c + ')')\n error.char = c\n\n return error\n }\n\n return parse\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'compile'\nconst dependencies = ['typed', 'parse']\n\nexport const createCompile = /* #__PURE__ */ factory(name, dependencies, ({ typed, parse }) => {\n /**\n * Parse and compile an expression.\n * Returns a an object with a function `evaluate([scope])` to evaluate the\n * compiled expression.\n *\n * Syntax:\n *\n * math.compile(expr) // returns one node\n * math.compile([expr1, expr2, expr3, ...]) // returns an array with nodes\n *\n * Examples:\n *\n * const code1 = math.compile('sqrt(3^2 + 4^2)')\n * code1.evaluate() // 5\n *\n * let scope = {a: 3, b: 4}\n * const code2 = math.compile('a * b') // 12\n * code2.evaluate(scope) // 12\n * scope.a = 5\n * code2.evaluate(scope) // 20\n *\n * const nodes = math.compile(['a = 3', 'b = 4', 'a * b'])\n * nodes[2].evaluate() // 12\n *\n * See also:\n *\n * parse, evaluate\n *\n * @param {string | string[] | Array | Matrix} expr\n * The expression to be compiled\n * @return {{evaluate: Function} | Array.<{evaluate: Function}>} code\n * An object with the compiled expression\n * @throws {Error}\n */\n return typed(name, {\n string: function (expr) {\n return parse(expr).compile()\n },\n\n 'Array | Matrix': function (expr) {\n return deepMap(expr, function (entry) {\n return parse(entry).compile()\n })\n }\n })\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'evaluate'\nconst dependencies = ['typed', 'parse']\n\nexport const createEvaluate = /* #__PURE__ */ factory(name, dependencies, ({ typed, parse }) => {\n /**\n * Evaluate an expression.\n *\n * Note the evaluating arbitrary expressions may involve security risks,\n * see [https://mathjs.org/docs/expressions/security.html](https://mathjs.org/docs/expressions/security.html) for more information.\n *\n * Syntax:\n *\n * math.evaluate(expr)\n * math.evaluate(expr, scope)\n * math.evaluate([expr1, expr2, expr3, ...])\n * math.evaluate([expr1, expr2, expr3, ...], scope)\n *\n * Example:\n *\n * math.evaluate('(2+3)/4') // 1.25\n * math.evaluate('sqrt(3^2 + 4^2)') // 5\n * math.evaluate('sqrt(-4)') // 2i\n * math.evaluate(['a=3', 'b=4', 'a*b']) // [3, 4, 12]\n *\n * let scope = {a:3, b:4}\n * math.evaluate('a * b', scope) // 12\n *\n * See also:\n *\n * parse, compile\n *\n * @param {string | string[] | Matrix} expr The expression to be evaluated\n * @param {Object} [scope] Scope to read/write variables\n * @return {*} The result of the expression\n * @throws {Error}\n */\n return typed(name, {\n string: function (expr) {\n const scope = {}\n return parse(expr).compile().evaluate(scope)\n },\n\n 'string, Object': function (expr, scope) {\n return parse(expr).compile().evaluate(scope)\n },\n\n 'Array | Matrix': function (expr) {\n const scope = {}\n return deepMap(expr, function (entry) {\n return parse(entry).compile().evaluate(scope)\n })\n },\n\n 'Array | Matrix, Object': function (expr, scope) {\n return deepMap(expr, function (entry) {\n return parse(entry).compile().evaluate(scope)\n })\n }\n })\n})\n","import { factory } from '../utils/factory.js'\nimport { extend, hasOwnProperty } from '../utils/object.js'\nimport { getSafeProperty, setSafeProperty } from '../utils/customs.js'\n\nconst name = 'Parser'\nconst dependencies = ['parse']\n\nexport const createParserClass = /* #__PURE__ */ factory(name, dependencies, ({ parse }) => {\n /**\n * @constructor Parser\n * Parser contains methods to evaluate or parse expressions, and has a number\n * of convenience methods to get, set, and remove variables from memory. Parser\n * keeps a scope containing variables in memory, which is used for all\n * evaluations.\n *\n * Methods:\n * const result = parser.evaluate(expr) // evaluate an expression\n * const value = parser.get(name) // retrieve a variable from the parser\n * const values = parser.getAll() // retrieve all defined variables\n * parser.set(name, value) // set a variable in the parser\n * parser.remove(name) // clear a variable from the\n * // parsers scope\n * parser.clear() // clear the parsers scope\n *\n * Example usage:\n * const parser = new Parser()\n * // Note: there is a convenience method which can be used instead:\n * // const parser = new math.parser()\n *\n * // evaluate expressions\n * parser.evaluate('sqrt(3^2 + 4^2)') // 5\n * parser.evaluate('sqrt(-4)') // 2i\n * parser.evaluate('2 inch in cm') // 5.08 cm\n * parser.evaluate('cos(45 deg)') // 0.7071067811865476\n *\n * // define variables and functions\n * parser.evaluate('x = 7 / 2') // 3.5\n * parser.evaluate('x + 3') // 6.5\n * parser.evaluate('function f(x, y) = x^y') // f(x, y)\n * parser.evaluate('f(2, 3)') // 8\n *\n * // get and set variables and functions\n * const x = parser.get('x') // 7\n * const f = parser.get('f') // function\n * const g = f(3, 2) // 9\n * parser.set('h', 500)\n * const i = parser.evaluate('h / 2') // 250\n * parser.set('hello', function (name) {\n * return 'hello, ' + name + '!'\n * })\n * parser.evaluate('hello(\"user\")') // \"hello, user!\"\n *\n * // clear defined functions and variables\n * parser.clear()\n *\n */\n function Parser () {\n if (!(this instanceof Parser)) {\n throw new SyntaxError(\n 'Constructor must be called with the new operator')\n }\n this.scope = {}\n }\n\n /**\n * Attach type information\n */\n Parser.prototype.type = 'Parser'\n Parser.prototype.isParser = true\n\n /**\n * Parse and evaluate the given expression\n * @param {string} expr A string containing an expression, for example \"2+3\"\n * @return {*} result The result, or undefined when the expression was empty\n * @throws {Error}\n */\n Parser.prototype.evaluate = function (expr) {\n // TODO: validate arguments\n return parse(expr)\n .compile()\n .evaluate(this.scope)\n }\n\n /**\n * Get a variable (a function or variable) by name from the parsers scope.\n * Returns undefined when not found\n * @param {string} name\n * @return {* | undefined} value\n */\n Parser.prototype.get = function (name) {\n // TODO: validate arguments\n return name in this.scope\n ? getSafeProperty(this.scope, name)\n : undefined\n }\n\n /**\n * Get a map with all defined variables\n * @return {Object} values\n */\n Parser.prototype.getAll = function () {\n return extend({}, this.scope)\n }\n\n /**\n * Set a symbol (a function or variable) by name from the parsers scope.\n * @param {string} name\n * @param {* | undefined} value\n */\n Parser.prototype.set = function (name, value) {\n // TODO: validate arguments\n return setSafeProperty(this.scope, name, value)\n }\n\n /**\n * Remove a variable from the parsers scope\n * @param {string} name\n */\n Parser.prototype.remove = function (name) {\n // TODO: validate arguments\n delete this.scope[name]\n }\n\n /**\n * Clear the scope with variables and functions\n */\n Parser.prototype.clear = function () {\n for (const name in this.scope) {\n if (hasOwnProperty(this.scope, name)) {\n delete this.scope[name]\n }\n }\n }\n\n return Parser\n}, { isClass: true })\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'parser'\nconst dependencies = ['typed', 'Parser']\n\nexport const createParser = /* #__PURE__ */ factory(name, dependencies, ({ typed, Parser }) => {\n /**\n * Create a parser. The function creates a new `math.Parser` object.\n *\n * Syntax:\n *\n * math.parser()\n *\n * Examples:\n *\n * const parser = new math.parser()\n *\n * // evaluate expressions\n * const a = parser.evaluate('sqrt(3^2 + 4^2)') // 5\n * const b = parser.evaluate('sqrt(-4)') // 2i\n * const c = parser.evaluate('2 inch in cm') // 5.08 cm\n * const d = parser.evaluate('cos(45 deg)') // 0.7071067811865476\n *\n * // define variables and functions\n * parser.evaluate('x = 7 / 2') // 3.5\n * parser.evaluate('x + 3') // 6.5\n * parser.evaluate('function f(x, y) = x^y') // f(x, y)\n * parser.evaluate('f(2, 3)') // 8\n *\n * // get and set variables and functions\n * const x = parser.get('x') // 7\n * const f = parser.get('f') // function\n * const g = f(3, 2) // 9\n * parser.set('h', 500)\n * const i = parser.evaluate('h / 2') // 250\n * parser.set('hello', function (name) {\n * return 'hello, ' + name + '!'\n * })\n * parser.evaluate('hello(\"user\")') // \"hello, user!\"\n *\n * // clear defined functions and variables\n * parser.clear()\n *\n * See also:\n *\n * evaluate, compile, parse\n *\n * @return {Parser} Parser\n */\n return typed(name, {\n '': function () {\n return new Parser()\n }\n })\n})\n","import { clone } from '../../../utils/object.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'lup'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'abs',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'larger',\n 'equalScalar',\n 'unaryMinus',\n 'DenseMatrix',\n 'SparseMatrix',\n 'Spa'\n]\n\nexport const createLup = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n matrix,\n abs,\n addScalar,\n divideScalar,\n multiplyScalar,\n subtract,\n larger,\n equalScalar,\n unaryMinus,\n DenseMatrix,\n SparseMatrix,\n Spa\n }\n) => {\n /**\n * Calculate the Matrix LU decomposition with partial pivoting. Matrix `A` is decomposed in two matrices (`L`, `U`) and a\n * row permutation vector `p` where `A[p,:] = L * U`\n *\n * Syntax:\n *\n * math.lup(A)\n *\n * Example:\n *\n * const m = [[2, 1], [1, 4]]\n * const r = math.lup(m)\n * // r = {\n * // L: [[1, 0], [0.5, 1]],\n * // U: [[2, 1], [0, 3.5]],\n * // P: [0, 1]\n * // }\n *\n * See also:\n *\n * slu, lsolve, lusolve, usolve\n *\n * @param {Matrix | Array} A A two dimensional matrix or array for which to get the LUP decomposition.\n *\n * @return {{L: Array | Matrix, U: Array | Matrix, P: Array.}} The lower triangular matrix, the upper triangular matrix and the permutation matrix.\n */\n return typed(name, {\n\n DenseMatrix: function (m) {\n return _denseLUP(m)\n },\n\n SparseMatrix: function (m) {\n return _sparseLUP(m)\n },\n\n Array: function (a) {\n // create dense matrix from array\n const m = matrix(a)\n // lup, use matrix implementation\n const r = _denseLUP(m)\n // result\n return {\n L: r.L.valueOf(),\n U: r.U.valueOf(),\n p: r.p\n }\n }\n })\n\n function _denseLUP (m) {\n // rows & columns\n const rows = m._size[0]\n const columns = m._size[1]\n // minimum rows and columns\n let n = Math.min(rows, columns)\n // matrix array, clone original data\n const data = clone(m._data)\n // l matrix arrays\n const ldata = []\n const lsize = [rows, n]\n // u matrix arrays\n const udata = []\n const usize = [n, columns]\n // vars\n let i, j, k\n // permutation vector\n const p = []\n for (i = 0; i < rows; i++) { p[i] = i }\n // loop columns\n for (j = 0; j < columns; j++) {\n // skip first column in upper triangular matrix\n if (j > 0) {\n // loop rows\n for (i = 0; i < rows; i++) {\n // min i,j\n const min = Math.min(i, j)\n // v[i, j]\n let s = 0\n // loop up to min\n for (k = 0; k < min; k++) {\n // s = l[i, k] - data[k, j]\n s = addScalar(s, multiplyScalar(data[i][k], data[k][j]))\n }\n data[i][j] = subtract(data[i][j], s)\n }\n }\n // row with larger value in cvector, row >= j\n let pi = j\n let pabsv = 0\n let vjj = 0\n // loop rows\n for (i = j; i < rows; i++) {\n // data @ i, j\n const v = data[i][j]\n // absolute value\n const absv = abs(v)\n // value is greater than pivote value\n if (larger(absv, pabsv)) {\n // store row\n pi = i\n // update max value\n pabsv = absv\n // value @ [j, j]\n vjj = v\n }\n }\n // swap rows (j <-> pi)\n if (j !== pi) {\n // swap values j <-> pi in p\n p[j] = [p[pi], p[pi] = p[j]][0]\n // swap j <-> pi in data\n DenseMatrix._swapRows(j, pi, data)\n }\n // check column is in lower triangular matrix\n if (j < rows) {\n // loop rows (lower triangular matrix)\n for (i = j + 1; i < rows; i++) {\n // value @ i, j\n const vij = data[i][j]\n if (!equalScalar(vij, 0)) {\n // update data\n data[i][j] = divideScalar(data[i][j], vjj)\n }\n }\n }\n }\n // loop columns\n for (j = 0; j < columns; j++) {\n // loop rows\n for (i = 0; i < rows; i++) {\n // initialize row in arrays\n if (j === 0) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i] = []\n }\n // L\n ldata[i] = []\n }\n // check we are in the upper triangular matrix\n if (i < j) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = data[i][j]\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = 0\n }\n continue\n }\n // diagonal value\n if (i === j) {\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = data[i][j]\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = 1\n }\n continue\n }\n // check row exists in upper triangular matrix\n if (i < columns) {\n // U\n udata[i][j] = 0\n }\n // check column exists in lower triangular matrix\n if (j < rows) {\n // L\n ldata[i][j] = data[i][j]\n }\n }\n }\n // l matrix\n const l = new DenseMatrix({\n data: ldata,\n size: lsize\n })\n // u matrix\n const u = new DenseMatrix({\n data: udata,\n size: usize\n })\n // p vector\n const pv = []\n for (i = 0, n = p.length; i < n; i++) { pv[p[i]] = i }\n // return matrices\n return {\n L: l,\n U: u,\n p: pv,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\nP: ' + this.p\n }\n }\n }\n\n function _sparseLUP (m) {\n // rows & columns\n const rows = m._size[0]\n const columns = m._size[1]\n // minimum rows and columns\n const n = Math.min(rows, columns)\n // matrix arrays (will not be modified, thanks to permutation vector)\n const values = m._values\n const index = m._index\n const ptr = m._ptr\n // l matrix arrays\n const lvalues = []\n const lindex = []\n const lptr = []\n const lsize = [rows, n]\n // u matrix arrays\n const uvalues = []\n const uindex = []\n const uptr = []\n const usize = [n, columns]\n // vars\n let i, j, k\n // permutation vectors, (current index -> original index) and (original index -> current index)\n const pvCo = []\n const pvOc = []\n for (i = 0; i < rows; i++) {\n pvCo[i] = i\n pvOc[i] = i\n }\n // swap indices in permutation vectors (condition x < y)!\n const swapIndeces = function (x, y) {\n // find pv indeces getting data from x and y\n const kx = pvOc[x]\n const ky = pvOc[y]\n // update permutation vector current -> original\n pvCo[kx] = y\n pvCo[ky] = x\n // update permutation vector original -> current\n pvOc[x] = ky\n pvOc[y] = kx\n }\n // loop columns\n for (j = 0; j < columns; j++) {\n // sparse accumulator\n const spa = new Spa()\n // check lower triangular matrix has a value @ column j\n if (j < rows) {\n // update ptr\n lptr.push(lvalues.length)\n // first value in j column for lower triangular matrix\n lvalues.push(1)\n lindex.push(j)\n }\n // update ptr\n uptr.push(uvalues.length)\n // k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]\n const k0 = ptr[j]\n const k1 = ptr[j + 1]\n // copy column j into sparse accumulator\n for (k = k0; k < k1; k++) {\n // row\n i = index[k]\n // copy column values into sparse accumulator (use permutation vector)\n spa.set(pvCo[i], values[k])\n }\n // skip first column in upper triangular matrix\n if (j > 0) {\n // loop rows in column j (above diagonal)\n spa.forEach(0, j - 1, function (k, vkj) {\n // loop rows in column k (L)\n SparseMatrix._forEachRow(k, lvalues, lindex, lptr, function (i, vik) {\n // check row is below k\n if (i > k) {\n // update spa value\n spa.accumulate(i, unaryMinus(multiplyScalar(vik, vkj)))\n }\n })\n })\n }\n // row with larger value in spa, row >= j\n let pi = j\n let vjj = spa.get(j)\n let pabsv = abs(vjj)\n // loop values in spa (order by row, below diagonal)\n spa.forEach(j + 1, rows - 1, function (x, v) {\n // absolute value\n const absv = abs(v)\n // value is greater than pivote value\n if (larger(absv, pabsv)) {\n // store row\n pi = x\n // update max value\n pabsv = absv\n // value @ [j, j]\n vjj = v\n }\n })\n // swap rows (j <-> pi)\n if (j !== pi) {\n // swap values j <-> pi in L\n SparseMatrix._swapRows(j, pi, lsize[1], lvalues, lindex, lptr)\n // swap values j <-> pi in U\n SparseMatrix._swapRows(j, pi, usize[1], uvalues, uindex, uptr)\n // swap values in spa\n spa.swap(j, pi)\n // update permutation vector (swap values @ j, pi)\n swapIndeces(j, pi)\n }\n // loop values in spa (order by row)\n spa.forEach(0, rows - 1, function (x, v) {\n // check we are above diagonal\n if (x <= j) {\n // update upper triangular matrix\n uvalues.push(v)\n uindex.push(x)\n } else {\n // update value\n v = divideScalar(v, vjj)\n // check value is non zero\n if (!equalScalar(v, 0)) {\n // update lower triangular matrix\n lvalues.push(v)\n lindex.push(x)\n }\n }\n })\n }\n // update ptrs\n uptr.push(uvalues.length)\n lptr.push(lvalues.length)\n\n // return matrices\n return {\n L: new SparseMatrix({\n values: lvalues,\n index: lindex,\n ptr: lptr,\n size: lsize\n }),\n U: new SparseMatrix({\n values: uvalues,\n index: uindex,\n ptr: uptr,\n size: usize\n }),\n p: pvCo,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\nP: ' + this.p\n }\n }\n }\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'qr'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'zeros',\n 'identity',\n 'isZero',\n 'equal',\n 'sign',\n 'sqrt',\n 'conj',\n 'unaryMinus',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'subtract',\n 'complex'\n]\n\nexport const createQr = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n matrix,\n zeros,\n identity,\n isZero,\n equal,\n sign,\n sqrt,\n conj,\n unaryMinus,\n addScalar,\n divideScalar,\n multiplyScalar,\n subtract,\n complex\n }\n) => {\n /**\n * Calculate the Matrix QR decomposition. Matrix `A` is decomposed in\n * two matrices (`Q`, `R`) where `Q` is an\n * orthogonal matrix and `R` is an upper triangular matrix.\n *\n * Syntax:\n *\n * math.qr(A)\n *\n * Example:\n *\n * const m = [\n * [1, -1, 4],\n * [1, 4, -2],\n * [1, 4, 2],\n * [1, -1, 0]\n * ]\n * const result = math.qr(m)\n * // r = {\n * // Q: [\n * // [0.5, -0.5, 0.5],\n * // [0.5, 0.5, -0.5],\n * // [0.5, 0.5, 0.5],\n * // [0.5, -0.5, -0.5],\n * // ],\n * // R: [\n * // [2, 3, 2],\n * // [0, 5, -2],\n * // [0, 0, 4],\n * // [0, 0, 0]\n * // ]\n * // }\n *\n * See also:\n *\n * lup, lusolve\n *\n * @param {Matrix | Array} A A two dimensional matrix or array\n * for which to get the QR decomposition.\n *\n * @return {{Q: Array | Matrix, R: Array | Matrix}} Q: the orthogonal\n * matrix and R: the upper triangular matrix\n */\n return Object.assign(typed(name, {\n\n DenseMatrix: function (m) {\n return _denseQR(m)\n },\n\n SparseMatrix: function (m) {\n return _sparseQR(m)\n },\n\n Array: function (a) {\n // create dense matrix from array\n const m = matrix(a)\n // lup, use matrix implementation\n const r = _denseQR(m)\n // result\n return {\n Q: r.Q.valueOf(),\n R: r.R.valueOf()\n }\n }\n }), { _denseQRimpl })\n\n function _denseQRimpl (m) {\n // rows & columns (m x n)\n const rows = m._size[0] // m\n const cols = m._size[1] // n\n\n const Q = identity([rows], 'dense')\n const Qdata = Q._data\n\n const R = m.clone()\n const Rdata = R._data\n\n // vars\n let i, j, k\n\n const w = zeros([rows], '')\n\n for (k = 0; k < Math.min(cols, rows); ++k) {\n /*\n * **k-th Household matrix**\n *\n * The matrix I - 2*v*transpose(v)\n * x = first column of A\n * x1 = first element of x\n * alpha = x1 / |x1| * |x|\n * e1 = tranpose([1, 0, 0, ...])\n * u = x - alpha * e1\n * v = u / |u|\n *\n * Household matrix = I - 2 * v * tranpose(v)\n *\n * * Initially Q = I and R = A.\n * * Household matrix is a reflection in a plane normal to v which\n * will zero out all but the top right element in R.\n * * Appplying reflection to both Q and R will not change product.\n * * Repeat this process on the (1,1) minor to get R as an upper\n * triangular matrix.\n * * Reflections leave the magnitude of the columns of Q unchanged\n * so Q remains othoganal.\n *\n */\n\n const pivot = Rdata[k][k]\n const sgn = unaryMinus(equal(pivot, 0) ? 1 : sign(pivot))\n const conjSgn = conj(sgn)\n\n let alphaSquared = 0\n\n for (i = k; i < rows; i++) {\n alphaSquared = addScalar(alphaSquared, multiplyScalar(Rdata[i][k], conj(Rdata[i][k])))\n }\n\n const alpha = multiplyScalar(sgn, sqrt(alphaSquared))\n\n if (!isZero(alpha)) {\n // first element in vector u\n const u1 = subtract(pivot, alpha)\n\n // w = v * u1 / |u| (only elements k to (rows-1) are used)\n w[k] = 1\n\n for (i = k + 1; i < rows; i++) {\n w[i] = divideScalar(Rdata[i][k], u1)\n }\n\n // tau = - conj(u1 / alpha)\n const tau = unaryMinus(conj(divideScalar(u1, alpha)))\n\n let s\n\n /*\n * tau and w have been choosen so that\n *\n * 2 * v * tranpose(v) = tau * w * tranpose(w)\n */\n\n /*\n * -- calculate R = R - tau * w * tranpose(w) * R --\n * Only do calculation with rows k to (rows-1)\n * Additionally columns 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n for (j = k; j < cols; j++) {\n s = 0.0\n\n // calculate jth element of [tranpose(w) * R]\n for (i = k; i < rows; i++) {\n s = addScalar(s, multiplyScalar(conj(w[i]), Rdata[i][j]))\n }\n\n // calculate the jth element of [tau * transpose(w) * R]\n s = multiplyScalar(s, tau)\n\n for (i = k; i < rows; i++) {\n Rdata[i][j] = multiplyScalar(\n subtract(Rdata[i][j], multiplyScalar(w[i], s)),\n conjSgn\n )\n }\n }\n /*\n * -- calculate Q = Q - tau * Q * w * transpose(w) --\n * Q is a square matrix (rows x rows)\n * Only do calculation with columns k to (rows-1)\n * Additionally rows 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n for (i = 0; i < rows; i++) {\n s = 0.0\n\n // calculate ith element of [Q * w]\n for (j = k; j < rows; j++) {\n s = addScalar(s, multiplyScalar(Qdata[i][j], w[j]))\n }\n\n // calculate the ith element of [tau * Q * w]\n s = multiplyScalar(s, tau)\n\n for (j = k; j < rows; ++j) {\n Qdata[i][j] = divideScalar(\n subtract(Qdata[i][j], multiplyScalar(s, conj(w[j]))),\n conjSgn\n )\n }\n }\n }\n }\n\n // return matrices\n return {\n Q: Q,\n R: R,\n toString: function () {\n return 'Q: ' + this.Q.toString() + '\\nR: ' + this.R.toString()\n }\n }\n }\n\n function _denseQR (m) {\n const ret = _denseQRimpl(m)\n const Rdata = ret.R._data\n if (m._data.length > 0) {\n const zero = Rdata[0][0].type === 'Complex' ? complex(0) : 0\n\n for (let i = 0; i < Rdata.length; ++i) {\n for (let j = 0; j < i && j < (Rdata[0] || []).length; ++j) {\n Rdata[i][j] = zero\n }\n }\n }\n\n return ret\n }\n\n function _sparseQR (m) {\n throw new Error('qr not implemented for sparse matrices yet')\n }\n})\n","/**\n * Depth-first search and postorder of a tree rooted at node j\n *\n * @param {Number} j The tree node\n * @param {Number} k\n * @param {Array} w The workspace array\n * @param {Number} head The index offset within the workspace for the head array\n * @param {Number} next The index offset within the workspace for the next array\n * @param {Array} post The post ordering array\n * @param {Number} stack The index offset within the workspace for the stack array\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csTdfs (j, k, w, head, next, post, stack) {\n // variables\n let top = 0\n // place j on the stack\n w[stack] = j\n // while (stack is not empty)\n while (top >= 0) {\n // p = top of stack\n const p = w[stack + top]\n // i = youngest child of p\n const i = w[head + p]\n if (i === -1) {\n // p has no unordered children left\n top--\n // node p is the kth postordered node\n post[k++] = p\n } else {\n // remove i from children of p\n w[head + p] = w[next + i]\n // increment top\n ++top\n // start dfs on child node i\n w[stack + top] = i\n }\n }\n return k\n}\n","/**\n * This function \"flips\" its input about the integer -1.\n *\n * @param {Number} i The value to flip\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csFlip (i) {\n // flip the value\n return -i - 2\n}\n","import { factory } from '../../../utils/factory.js'\nimport { csFkeep } from './csFkeep.js'\nimport { csFlip } from './csFlip.js'\nimport { csTdfs } from './csTdfs.js'\n\nconst name = 'csAmd'\nconst dependencies = [\n 'add',\n 'multiply',\n 'transpose'\n]\n\nexport const createCsAmd = /* #__PURE__ */ factory(name, dependencies, ({ add, multiply, transpose }) => {\n /**\n * Approximate minimum degree ordering. The minimum degree algorithm is a widely used\n * heuristic for finding a permutation P so that P*A*P' has fewer nonzeros in its factorization\n * than A. It is a gready method that selects the sparsest pivot row and column during the course\n * of a right looking sparse Cholesky factorization.\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n *\n * @param {Number} order 0: Natural, 1: Cholesky, 2: LU, 3: QR\n * @param {Matrix} m Sparse Matrix\n */\n return function csAmd (order, a) {\n // check input parameters\n if (!a || order <= 0 || order > 3) { return null }\n // a matrix arrays\n const asize = a._size\n // rows and columns\n const m = asize[0]\n const n = asize[1]\n // initialize vars\n let lemax = 0\n // dense threshold\n let dense = Math.max(16, 10 * Math.sqrt(n))\n dense = Math.min(n - 2, dense)\n // create target matrix C\n const cm = _createTargetMatrix(order, a, m, n, dense)\n // drop diagonal entries\n csFkeep(cm, _diag, null)\n // C matrix arrays\n const cindex = cm._index\n const cptr = cm._ptr\n\n // number of nonzero elements in C\n let cnz = cptr[n]\n\n // allocate result (n+1)\n const P = []\n\n // create workspace (8 * (n + 1))\n const W = []\n const len = 0 // first n + 1 entries\n const nv = n + 1 // next n + 1 entries\n const next = 2 * (n + 1) // next n + 1 entries\n const head = 3 * (n + 1) // next n + 1 entries\n const elen = 4 * (n + 1) // next n + 1 entries\n const degree = 5 * (n + 1) // next n + 1 entries\n const w = 6 * (n + 1) // next n + 1 entries\n const hhead = 7 * (n + 1) // last n + 1 entries\n\n // use P as workspace for last\n const last = P\n\n // initialize quotient graph\n let mark = _initializeQuotientGraph(n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree)\n\n // initialize degree lists\n let nel = _initializeDegreeLists(n, cptr, W, degree, elen, w, dense, nv, head, last, next)\n\n // minimum degree node\n let mindeg = 0\n\n // vars\n let i, j, k, k1, k2, e, pj, ln, nvi, pk, eln, p1, p2, pn, h, d\n\n // while (selecting pivots) do\n while (nel < n) {\n // select node of minimum approximate degree. amd() is now ready to start eliminating the graph. It first\n // finds a node k of minimum degree and removes it from its degree list. The variable nel keeps track of thow\n // many nodes have been eliminated.\n for (k = -1; mindeg < n && (k = W[head + mindeg]) === -1; mindeg++);\n if (W[next + k] !== -1) { last[W[next + k]] = -1 }\n // remove k from degree list\n W[head + mindeg] = W[next + k]\n // elenk = |Ek|\n const elenk = W[elen + k]\n // # of nodes k represents\n let nvk = W[nv + k]\n // W[nv + k] nodes of A eliminated\n nel += nvk\n\n // Construct a new element. The new element Lk is constructed in place if |Ek| = 0. nv[i] is\n // negated for all nodes i in Lk to flag them as members of this set. Each node i is removed from the\n // degree lists. All elements e in Ek are absorved into element k.\n let dk = 0\n // flag k as in Lk\n W[nv + k] = -nvk\n let p = cptr[k]\n // do in place if W[elen + k] === 0\n const pk1 = (elenk === 0) ? p : cnz\n let pk2 = pk1\n for (k1 = 1; k1 <= elenk + 1; k1++) {\n if (k1 > elenk) {\n // search the nodes in k\n e = k\n // list of nodes starts at cindex[pj]\n pj = p\n // length of list of nodes in k\n ln = W[len + k] - elenk\n } else {\n // search the nodes in e\n e = cindex[p++]\n pj = cptr[e]\n // length of list of nodes in e\n ln = W[len + e]\n }\n for (k2 = 1; k2 <= ln; k2++) {\n i = cindex[pj++]\n // check node i dead, or seen\n if ((nvi = W[nv + i]) <= 0) { continue }\n // W[degree + Lk] += size of node i\n dk += nvi\n // negate W[nv + i] to denote i in Lk\n W[nv + i] = -nvi\n // place i in Lk\n cindex[pk2++] = i\n if (W[next + i] !== -1) { last[W[next + i]] = last[i] }\n // check we need to remove i from degree list\n if (last[i] !== -1) { W[next + last[i]] = W[next + i] } else { W[head + W[degree + i]] = W[next + i] }\n }\n if (e !== k) {\n // absorb e into k\n cptr[e] = csFlip(k)\n // e is now a dead element\n W[w + e] = 0\n }\n }\n // cindex[cnz...nzmax] is free\n if (elenk !== 0) { cnz = pk2 }\n // external degree of k - |Lk\\i|\n W[degree + k] = dk\n // element k is in cindex[pk1..pk2-1]\n cptr[k] = pk1\n W[len + k] = pk2 - pk1\n // k is now an element\n W[elen + k] = -2\n\n // Find set differences. The scan1 function now computes the set differences |Le \\ Lk| for all elements e. At the start of the\n // scan, no entry in the w array is greater than or equal to mark.\n\n // clear w if necessary\n mark = _wclear(mark, lemax, W, w, n)\n // scan 1: find |Le\\Lk|\n for (pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check if W[elen + i] empty, skip it\n if ((eln = W[elen + i]) <= 0) { continue }\n // W[nv + i] was negated\n nvi = -W[nv + i]\n const wnvi = mark - nvi\n // scan Ei\n for (p = cptr[i], p1 = cptr[i] + eln - 1; p <= p1; p++) {\n e = cindex[p]\n if (W[w + e] >= mark) {\n // decrement |Le\\Lk|\n W[w + e] -= nvi\n } else if (W[w + e] !== 0) {\n // ensure e is a live element, 1st time e seen in scan 1\n W[w + e] = W[degree + e] + wnvi\n }\n }\n }\n\n // degree update\n // The second pass computes the approximate degree di, prunes the sets Ei and Ai, and computes a hash\n // function h(i) for all nodes in Lk.\n\n // scan2: degree update\n for (pk = pk1; pk < pk2; pk++) {\n // consider node i in Lk\n i = cindex[pk]\n p1 = cptr[i]\n p2 = p1 + W[elen + i] - 1\n pn = p1\n // scan Ei\n for (h = 0, d = 0, p = p1; p <= p2; p++) {\n e = cindex[p]\n // check e is an unabsorbed element\n if (W[w + e] !== 0) {\n // dext = |Le\\Lk|\n const dext = W[w + e] - mark\n if (dext > 0) {\n // sum up the set differences\n d += dext\n // keep e in Ei\n cindex[pn++] = e\n // compute the hash of node i\n h += e\n } else {\n // aggressive absorb. e->k\n cptr[e] = csFlip(k)\n // e is a dead element\n W[w + e] = 0\n }\n }\n }\n // W[elen + i] = |Ei|\n W[elen + i] = pn - p1 + 1\n const p3 = pn\n const p4 = p1 + W[len + i]\n // prune edges in Ai\n for (p = p2 + 1; p < p4; p++) {\n j = cindex[p]\n // check node j dead or in Lk\n const nvj = W[nv + j]\n if (nvj <= 0) { continue }\n // degree(i) += |j|\n d += nvj\n // place j in node list of i\n cindex[pn++] = j\n // compute hash for node i\n h += j\n }\n // check for mass elimination\n if (d === 0) {\n // absorb i into k\n cptr[i] = csFlip(k)\n nvi = -W[nv + i]\n // |Lk| -= |i|\n dk -= nvi\n // |k| += W[nv + i]\n nvk += nvi\n nel += nvi\n W[nv + i] = 0\n // node i is dead\n W[elen + i] = -1\n } else {\n // update degree(i)\n W[degree + i] = Math.min(W[degree + i], d)\n // move first node to end\n cindex[pn] = cindex[p3]\n // move 1st el. to end of Ei\n cindex[p3] = cindex[p1]\n // add k as 1st element in of Ei\n cindex[p1] = k\n // new len of adj. list of node i\n W[len + i] = pn - p1 + 1\n // finalize hash of i\n h = (h < 0 ? -h : h) % n\n // place i in hash bucket\n W[next + i] = W[hhead + h]\n W[hhead + h] = i\n // save hash of i in last[i]\n last[i] = h\n }\n }\n // finalize |Lk|\n W[degree + k] = dk\n lemax = Math.max(lemax, dk)\n // clear w\n mark = _wclear(mark + lemax, lemax, W, w, n)\n\n // Supernode detection. Supernode detection relies on the hash function h(i) computed for each node i.\n // If two nodes have identical adjacency lists, their hash functions wil be identical.\n for (pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check i is dead, skip it\n if (W[nv + i] >= 0) { continue }\n // scan hash bucket of node i\n h = last[i]\n i = W[hhead + h]\n // hash bucket will be empty\n W[hhead + h] = -1\n for (; i !== -1 && W[next + i] !== -1; i = W[next + i], mark++) {\n ln = W[len + i]\n eln = W[elen + i]\n for (p = cptr[i] + 1; p <= cptr[i] + ln - 1; p++) { W[w + cindex[p]] = mark }\n let jlast = i\n // compare i with all j\n for (j = W[next + i]; j !== -1;) {\n let ok = W[len + j] === ln && W[elen + j] === eln\n for (p = cptr[j] + 1; ok && p <= cptr[j] + ln - 1; p++) {\n // compare i and j\n if (W[w + cindex[p]] !== mark) { ok = 0 }\n }\n // check i and j are identical\n if (ok) {\n // absorb j into i\n cptr[j] = csFlip(i)\n W[nv + i] += W[nv + j]\n W[nv + j] = 0\n // node j is dead\n W[elen + j] = -1\n // delete j from hash bucket\n j = W[next + j]\n W[next + jlast] = j\n } else {\n // j and i are different\n jlast = j\n j = W[next + j]\n }\n }\n }\n }\n\n // Finalize new element. The elimination of node k is nearly complete. All nodes i in Lk are scanned one last time.\n // Node i is removed from Lk if it is dead. The flagged status of nv[i] is cleared.\n for (p = pk1, pk = pk1; pk < pk2; pk++) {\n i = cindex[pk]\n // check i is dead, skip it\n if ((nvi = -W[nv + i]) <= 0) { continue }\n // restore W[nv + i]\n W[nv + i] = nvi\n // compute external degree(i)\n d = W[degree + i] + dk - nvi\n d = Math.min(d, n - nel - nvi)\n if (W[head + d] !== -1) { last[W[head + d]] = i }\n // put i back in degree list\n W[next + i] = W[head + d]\n last[i] = -1\n W[head + d] = i\n // find new minimum degree\n mindeg = Math.min(mindeg, d)\n W[degree + i] = d\n // place i in Lk\n cindex[p++] = i\n }\n // # nodes absorbed into k\n W[nv + k] = nvk\n // length of adj list of element k\n if ((W[len + k] = p - pk1) === 0) {\n // k is a root of the tree\n cptr[k] = -1\n // k is now a dead element\n W[w + k] = 0\n }\n if (elenk !== 0) {\n // free unused space in Lk\n cnz = p\n }\n }\n\n // Postordering. The elimination is complete, but no permutation has been computed. All that is left\n // of the graph is the assembly tree (ptr) and a set of dead nodes and elements (i is a dead node if\n // nv[i] is zero and a dead element if nv[i] > 0). It is from this information only that the final permutation\n // is computed. The tree is restored by unflipping all of ptr.\n\n // fix assembly tree\n for (i = 0; i < n; i++) { cptr[i] = csFlip(cptr[i]) }\n for (j = 0; j <= n; j++) { W[head + j] = -1 }\n // place unordered nodes in lists\n for (j = n; j >= 0; j--) {\n // skip if j is an element\n if (W[nv + j] > 0) { continue }\n // place j in list of its parent\n W[next + j] = W[head + cptr[j]]\n W[head + cptr[j]] = j\n }\n // place elements in lists\n for (e = n; e >= 0; e--) {\n // skip unless e is an element\n if (W[nv + e] <= 0) { continue }\n if (cptr[e] !== -1) {\n // place e in list of its parent\n W[next + e] = W[head + cptr[e]]\n W[head + cptr[e]] = e\n }\n }\n // postorder the assembly tree\n for (k = 0, i = 0; i <= n; i++) {\n if (cptr[i] === -1) { k = csTdfs(i, k, W, head, next, P, w) }\n }\n // remove last item in array\n P.splice(P.length - 1, 1)\n // return P\n return P\n }\n\n /**\n * Creates the matrix that will be used by the approximate minimum degree ordering algorithm. The function accepts the matrix M as input and returns a permutation\n * vector P. The amd algorithm operates on a symmetrix matrix, so one of three symmetric matrices is formed.\n *\n * Order: 0\n * A natural ordering P=null matrix is returned.\n *\n * Order: 1\n * Matrix must be square. This is appropriate for a Cholesky or LU factorization.\n * P = M + M'\n *\n * Order: 2\n * Dense columns from M' are dropped, M recreated from M'. This is appropriatefor LU factorization of unsymmetric matrices.\n * P = M' * M\n *\n * Order: 3\n * This is best used for QR factorization or LU factorization is matrix M has no dense rows. A dense row is a row with more than 10*sqr(columns) entries.\n * P = M' * M\n */\n function _createTargetMatrix (order, a, m, n, dense) {\n // compute A'\n const at = transpose(a)\n\n // check order = 1, matrix must be square\n if (order === 1 && n === m) {\n // C = A + A'\n return add(a, at)\n }\n\n // check order = 2, drop dense columns from M'\n if (order === 2) {\n // transpose arrays\n const tindex = at._index\n const tptr = at._ptr\n // new column index\n let p2 = 0\n // loop A' columns (rows)\n for (let j = 0; j < m; j++) {\n // column j of AT starts here\n let p = tptr[j]\n // new column j starts here\n tptr[j] = p2\n // skip dense col j\n if (tptr[j + 1] - p > dense) { continue }\n // map rows in column j of A\n for (const p1 = tptr[j + 1]; p < p1; p++) { tindex[p2++] = tindex[p] }\n }\n // finalize AT\n tptr[m] = p2\n // recreate A from new transpose matrix\n a = transpose(at)\n // use A' * A\n return multiply(at, a)\n }\n\n // use A' * A, square or rectangular matrix\n return multiply(at, a)\n }\n\n /**\n * Initialize quotient graph. There are four kind of nodes and elements that must be represented:\n *\n * - A live node is a node i (or a supernode) that has not been selected as a pivot nad has not been merged into another supernode.\n * - A dead node i is one that has been removed from the graph, having been absorved into r = flip(ptr[i]).\n * - A live element e is one that is in the graph, having been formed when node e was selected as the pivot.\n * - A dead element e is one that has benn absorved into a subsequent element s = flip(ptr[e]).\n */\n function _initializeQuotientGraph (n, cptr, W, len, head, last, next, hhead, nv, w, elen, degree) {\n // Initialize quotient graph\n for (let k = 0; k < n; k++) { W[len + k] = cptr[k + 1] - cptr[k] }\n W[len + n] = 0\n // initialize workspace\n for (let i = 0; i <= n; i++) {\n // degree list i is empty\n W[head + i] = -1\n last[i] = -1\n W[next + i] = -1\n // hash list i is empty\n W[hhead + i] = -1\n // node i is just one node\n W[nv + i] = 1\n // node i is alive\n W[w + i] = 1\n // Ek of node i is empty\n W[elen + i] = 0\n // degree of node i\n W[degree + i] = W[len + i]\n }\n // clear w\n const mark = _wclear(0, 0, W, w, n)\n // n is a dead element\n W[elen + n] = -2\n // n is a root of assembly tree\n cptr[n] = -1\n // n is a dead element\n W[w + n] = 0\n // return mark\n return mark\n }\n\n /**\n * Initialize degree lists. Each node is placed in its degree lists. Nodes of zero degree are eliminated immediately. Nodes with\n * degree >= dense are alsol eliminated and merged into a placeholder node n, a dead element. Thes nodes will appera last in the\n * output permutation p.\n */\n function _initializeDegreeLists (n, cptr, W, degree, elen, w, dense, nv, head, last, next) {\n // result\n let nel = 0\n // loop columns\n for (let i = 0; i < n; i++) {\n // degree @ i\n const d = W[degree + i]\n // check node i is empty\n if (d === 0) {\n // element i is dead\n W[elen + i] = -2\n nel++\n // i is a root of assembly tree\n cptr[i] = -1\n W[w + i] = 0\n } else if (d > dense) {\n // absorb i into element n\n W[nv + i] = 0\n // node i is dead\n W[elen + i] = -1\n nel++\n cptr[i] = csFlip(n)\n W[nv + n]++\n } else {\n const h = W[head + d]\n if (h !== -1) { last[h] = i }\n // put node i in degree list d\n W[next + i] = W[head + d]\n W[head + d] = i\n }\n }\n return nel\n }\n\n function _wclear (mark, lemax, W, w, n) {\n if (mark < 2 || (mark + lemax < 0)) {\n for (let k = 0; k < n; k++) {\n if (W[w + k] !== 0) { W[w + k] = 1 }\n }\n mark = 2\n }\n // at this point, W [0..n-1] < mark holds\n return mark\n }\n\n function _diag (i, j) {\n return i !== j\n }\n})\n","/**\n * Keeps entries in the matrix when the callback function returns true, removes the entry otherwise\n *\n * @param {Matrix} a The sparse matrix\n * @param {function} callback The callback function, function will be invoked with the following args:\n * - The entry row\n * - The entry column\n * - The entry value\n * - The state parameter\n * @param {any} other The state\n *\n * @return The number of nonzero elements in the matrix\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csFkeep (a, callback, other) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n // columns\n const n = asize[1]\n // nonzero items\n let nz = 0\n // loop columns\n for (let j = 0; j < n; j++) {\n // get current location of col j\n let p = aptr[j]\n // record new location of col j\n aptr[j] = nz\n for (; p < aptr[j + 1]; p++) {\n // check we need to keep this item\n if (callback(aindex[p], j, avalues ? avalues[p] : 1, other)) {\n // keep A(i,j)\n aindex[nz] = aindex[p]\n // check we need to process values (pattern only)\n if (avalues) { avalues[nz] = avalues[p] }\n // increment nonzero items\n nz++\n }\n }\n }\n // finalize A\n aptr[n] = nz\n // trim arrays\n aindex.splice(nz, aindex.length - nz)\n // check we need to process values (pattern only)\n if (avalues) { avalues.splice(nz, avalues.length - nz) }\n // return number of nonzero items\n return nz\n}\n","/**\n * This function determines if j is a leaf of the ith row subtree.\n * Consider A(i,j), node j in ith row subtree and return lca(jprev,j)\n *\n * @param {Number} i The ith row subtree\n * @param {Number} j The node to test\n * @param {Array} w The workspace array\n * @param {Number} first The index offset within the workspace for the first array\n * @param {Number} maxfirst The index offset within the workspace for the maxfirst array\n * @param {Number} prevleaf The index offset within the workspace for the prevleaf array\n * @param {Number} ancestor The index offset within the workspace for the ancestor array\n *\n * @return {Object}\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csLeaf (i, j, w, first, maxfirst, prevleaf, ancestor) {\n let s, sparent\n\n // our result\n let jleaf = 0\n let q\n\n // check j is a leaf\n if (i <= j || w[first + j] <= w[maxfirst + i]) { return (-1) }\n // update max first[j] seen so far\n w[maxfirst + i] = w[first + j]\n // jprev = previous leaf of ith subtree\n const jprev = w[prevleaf + i]\n w[prevleaf + i] = j\n\n // check j is first or subsequent leaf\n if (jprev === -1) {\n // 1st leaf, q = root of ith subtree\n jleaf = 1\n q = i\n } else {\n // update jleaf\n jleaf = 2\n // q = least common ancester (jprev,j)\n for (q = jprev; q !== w[ancestor + q]; q = w[ancestor + q]);\n for (s = jprev; s !== q; s = sparent) {\n // path compression\n sparent = w[ancestor + s]\n w[ancestor + s] = q\n }\n }\n return {\n jleaf: jleaf,\n q: q\n }\n}\n","import { factory } from '../../../utils/factory.js'\nimport { csLeaf } from './csLeaf.js'\n\nconst name = 'csCounts'\nconst dependencies = [\n 'transpose'\n]\n\nexport const createCsCounts = /* #__PURE__ */ factory(name, dependencies, ({ transpose }) => {\n /**\n * Computes the column counts using the upper triangular part of A.\n * It transposes A internally, none of the input parameters are modified.\n *\n * @param {Matrix} a The sparse matrix A\n *\n * @param {Matrix} ata Count the columns of A'A instead\n *\n * @return An array of size n of the column counts or null on error\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function (a, parent, post, ata) {\n // check inputs\n if (!a || !parent || !post) { return null }\n // a matrix arrays\n const asize = a._size\n // rows and columns\n const m = asize[0]\n const n = asize[1]\n // variables\n let i, j, k, J, p, p0, p1\n\n // workspace size\n const s = 4 * n + (ata ? (n + m + 1) : 0)\n // allocate workspace\n const w = [] // (s)\n const ancestor = 0 // first n entries\n const maxfirst = n // next n entries\n const prevleaf = 2 * n // next n entries\n const first = 3 * n // next n entries\n const head = 4 * n // next n + 1 entries (used when ata is true)\n const next = 5 * n + 1 // last entries in workspace\n // clear workspace w[0..s-1]\n for (k = 0; k < s; k++) { w[k] = -1 }\n\n // allocate result\n const colcount = [] // (n)\n\n // AT = A'\n const at = transpose(a)\n // at arrays\n const tindex = at._index\n const tptr = at._ptr\n\n // find w[first + j]\n for (k = 0; k < n; k++) {\n j = post[k]\n // colcount[j]=1 if j is a leaf\n colcount[j] = (w[first + j] === -1) ? 1 : 0\n for (; j !== -1 && w[first + j] === -1; j = parent[j]) { w[first + j] = k }\n }\n\n // initialize ata if needed\n if (ata) {\n // invert post\n for (k = 0; k < n; k++) { w[post[k]] = k }\n // loop rows (columns in AT)\n for (i = 0; i < m; i++) {\n // values in column i of AT\n for (k = n, p0 = tptr[i], p1 = tptr[i + 1], p = p0; p < p1; p++) { k = Math.min(k, w[tindex[p]]) }\n // place row i in linked list k\n w[next + i] = w[head + k]\n w[head + k] = i\n }\n }\n\n // each node in its own set\n for (i = 0; i < n; i++) { w[ancestor + i] = i }\n\n for (k = 0; k < n; k++) {\n // j is the kth node in postordered etree\n j = post[k]\n // check j is not a root\n if (parent[j] !== -1) { colcount[parent[j]]-- }\n\n // J=j for LL'=A case\n for (J = (ata ? w[head + k] : j); J !== -1; J = (ata ? w[next + J] : -1)) {\n for (p = tptr[J]; p < tptr[J + 1]; p++) {\n i = tindex[p]\n const r = csLeaf(i, j, w, first, maxfirst, prevleaf, ancestor)\n // check A(i,j) is in skeleton\n if (r.jleaf >= 1) { colcount[j]++ }\n // check account for overlap in q\n if (r.jleaf === 2) { colcount[r.q]-- }\n }\n }\n if (parent[j] !== -1) { w[ancestor + j] = parent[j] }\n }\n // sum up colcount's of each child\n for (j = 0; j < n; j++) {\n if (parent[j] !== -1) { colcount[parent[j]] += colcount[j] }\n }\n return colcount\n }\n})\n","import { csPermute } from './csPermute.js'\nimport { csPost } from './csPost.js'\nimport { csEtree } from './csEtree.js'\nimport { createCsAmd } from './csAmd.js'\nimport { createCsCounts } from './csCounts.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'csSqr'\nconst dependencies = [\n 'add',\n 'multiply',\n 'transpose'\n]\n\nexport const createCsSqr = /* #__PURE__ */ factory(name, dependencies, ({ add, multiply, transpose }) => {\n const csAmd = createCsAmd({ add, multiply, transpose })\n const csCounts = createCsCounts({ transpose })\n\n /**\n * Symbolic ordering and analysis for QR and LU decompositions.\n *\n * @param {Number} order The ordering strategy (see csAmd for more details)\n * @param {Matrix} a The A matrix\n * @param {boolean} qr Symbolic ordering and analysis for QR decomposition (true) or\n * symbolic ordering and analysis for LU decomposition (false)\n *\n * @return {Object} The Symbolic ordering and analysis for matrix A\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csSqr (order, a, qr) {\n // a arrays\n const aptr = a._ptr\n const asize = a._size\n // columns\n const n = asize[1]\n // vars\n let k\n // symbolic analysis result\n const s = {}\n // fill-reducing ordering\n s.q = csAmd(order, a)\n // validate results\n if (order && !s.q) { return null }\n // QR symbolic analysis\n if (qr) {\n // apply permutations if needed\n const c = order ? csPermute(a, null, s.q, 0) : a\n // etree of C'*C, where C=A(:,q)\n s.parent = csEtree(c, 1)\n // post order elimination tree\n const post = csPost(s.parent, n)\n // col counts chol(C'*C)\n s.cp = csCounts(c, s.parent, post, 1)\n // check we have everything needed to calculate number of nonzero elements\n if (c && s.parent && s.cp && _vcount(c, s)) {\n // calculate number of nonzero elements\n for (s.unz = 0, k = 0; k < n; k++) { s.unz += s.cp[k] }\n }\n } else {\n // for LU factorization only, guess nnz(L) and nnz(U)\n s.unz = 4 * (aptr[n]) + n\n s.lnz = s.unz\n }\n // return result S\n return s\n }\n\n /**\n * Compute nnz(V) = s.lnz, s.pinv, s.leftmost, s.m2 from A and s.parent\n */\n function _vcount (a, s) {\n // a arrays\n const aptr = a._ptr\n const aindex = a._index\n const asize = a._size\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n // initialize s arrays\n s.pinv = [] // (m + n)\n s.leftmost = [] // (m)\n // vars\n const parent = s.parent\n const pinv = s.pinv\n const leftmost = s.leftmost\n // workspace, next: first m entries, head: next n entries, tail: next n entries, nque: next n entries\n const w = [] // (m + 3 * n)\n const next = 0\n const head = m\n const tail = m + n\n const nque = m + 2 * n\n // vars\n let i, k, p, p0, p1\n // initialize w\n for (k = 0; k < n; k++) {\n // queue k is empty\n w[head + k] = -1\n w[tail + k] = -1\n w[nque + k] = 0\n }\n // initialize row arrays\n for (i = 0; i < m; i++) { leftmost[i] = -1 }\n // loop columns backwards\n for (k = n - 1; k >= 0; k--) {\n // values & index for column k\n for (p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {\n // leftmost[i] = min(find(A(i,:)))\n leftmost[aindex[p]] = k\n }\n }\n // scan rows in reverse order\n for (i = m - 1; i >= 0; i--) {\n // row i is not yet ordered\n pinv[i] = -1\n k = leftmost[i]\n // check row i is empty\n if (k === -1) { continue }\n // first row in queue k\n if (w[nque + k]++ === 0) { w[tail + k] = i }\n // put i at head of queue k\n w[next + i] = w[head + k]\n w[head + k] = i\n }\n s.lnz = 0\n s.m2 = m\n // find row permutation and nnz(V)\n for (k = 0; k < n; k++) {\n // remove row i from queue k\n i = w[head + k]\n // count V(k,k) as nonzero\n s.lnz++\n // add a fictitious row\n if (i < 0) { i = s.m2++ }\n // associate row i with V(:,k)\n pinv[i] = k\n // skip if V(k+1:m,k) is empty\n if (--nque[k] <= 0) { continue }\n // nque[k] is nnz (V(k+1:m,k))\n s.lnz += w[nque + k]\n // move all rows to parent of k\n const pa = parent[k]\n if (pa !== -1) {\n if (w[nque + pa] === 0) { w[tail + pa] = w[tail + k] }\n w[next + w[tail + k]] = w[head + pa]\n w[head + pa] = w[next + i]\n w[nque + pa] += w[nque + k]\n }\n }\n for (i = 0; i < m; i++) {\n if (pinv[i] < 0) { pinv[i] = k++ }\n }\n return true\n }\n})\n","/**\n * Permutes a sparse matrix C = P * A * Q\n *\n * @param {SparseMatrix} a The Matrix A\n * @param {Array} pinv The row permutation vector\n * @param {Array} q The column permutation vector\n * @param {boolean} values Create a pattern matrix (false), values and pattern otherwise\n *\n * @return {Matrix} C = P * A * Q, null on error\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csPermute (a, pinv, q, values) {\n // a arrays\n const avalues = a._values\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n const adt = a._datatype\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n // c arrays\n const cvalues = values && a._values ? [] : null\n const cindex = [] // (aptr[n])\n const cptr = [] // (n + 1)\n // initialize vars\n let nz = 0\n // loop columns\n for (let k = 0; k < n; k++) {\n // column k of C is column q[k] of A\n cptr[k] = nz\n // apply column permutation\n const j = q ? (q[k]) : k\n // loop values in column j of A\n for (let t0 = aptr[j], t1 = aptr[j + 1], t = t0; t < t1; t++) {\n // row i of A is row pinv[i] of C\n const r = pinv ? pinv[aindex[t]] : aindex[t]\n // index\n cindex[nz] = r\n // check we need to populate values\n if (cvalues) { cvalues[nz] = avalues[t] }\n // increment number of nonzero elements\n nz++\n }\n }\n // finalize the last column of C\n cptr[n] = nz\n // return C matrix\n return a.createSparseMatrix({\n values: cvalues,\n index: cindex,\n ptr: cptr,\n size: [m, n],\n datatype: adt\n })\n}\n","/**\n * Computes the elimination tree of Matrix A (using triu(A)) or the\n * elimination tree of A'A without forming A'A.\n *\n * @param {Matrix} a The A Matrix\n * @param {boolean} ata A value of true the function computes the etree of A'A\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csEtree (a, ata) {\n // check inputs\n if (!a) { return null }\n // a arrays\n const aindex = a._index\n const aptr = a._ptr\n const asize = a._size\n // rows & columns\n const m = asize[0]\n const n = asize[1]\n\n // allocate result\n const parent = [] // (n)\n\n // allocate workspace\n const w = [] // (n + (ata ? m : 0))\n const ancestor = 0 // first n entries in w\n const prev = n // last m entries (ata = true)\n\n let i, inext\n\n // check we are calculating A'A\n if (ata) {\n // initialize workspace\n for (i = 0; i < m; i++) { w[prev + i] = -1 }\n }\n // loop columns\n for (let k = 0; k < n; k++) {\n // node k has no parent yet\n parent[k] = -1\n // nor does k have an ancestor\n w[ancestor + k] = -1\n // values in column k\n for (let p0 = aptr[k], p1 = aptr[k + 1], p = p0; p < p1; p++) {\n // row\n const r = aindex[p]\n // node\n i = ata ? (w[prev + r]) : r\n // traverse from i to k\n for (; i !== -1 && i < k; i = inext) {\n // inext = ancestor of i\n inext = w[ancestor + i]\n // path compression\n w[ancestor + i] = k\n // check no anc., parent is k\n if (inext === -1) { parent[i] = k }\n }\n if (ata) { w[prev + r] = k }\n }\n }\n return parent\n}\n","import { csTdfs } from './csTdfs.js'\n\n/**\n * Post order a tree of forest\n *\n * @param {Array} parent The tree or forest\n * @param {Number} n Number of columns\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csPost (parent, n) {\n // check inputs\n if (!parent) { return null }\n // vars\n let k = 0\n let j\n // allocate result\n const post = [] // (n)\n // workspace, head: first n entries, next: next n entries, stack: last n entries\n const w = [] // (3 * n)\n const head = 0\n const next = n\n const stack = 2 * n\n // initialize workspace\n for (j = 0; j < n; j++) {\n // empty linked lists\n w[head + j] = -1\n }\n // traverse nodes in reverse order\n for (j = n - 1; j >= 0; j--) {\n // check j is a root\n if (parent[j] === -1) { continue }\n // add j to list of its parent\n w[next + j] = w[head + parent[j]]\n w[head + parent[j]] = j\n }\n // loop nodes\n for (j = 0; j < n; j++) {\n // skip j if it is not a root\n if (parent[j] !== -1) { continue }\n // depth-first search\n k = csTdfs(j, k, w, head, next, post, stack)\n }\n return post\n}\n","/**\n * Checks if the node at w[j] is marked\n *\n * @param {Array} w The array\n * @param {Number} j The array index\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csMarked (w, j) {\n // check node is marked\n return w[j] < 0\n}\n","import { csFlip } from './csFlip.js'\n\n/**\n * Marks the node at w[j]\n *\n * @param {Array} w The array\n * @param {Number} j The array index\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csMark (w, j) {\n // mark w[j]\n w[j] = csFlip(w[j])\n}\n","import { csFlip } from './csFlip.js'\n\n/**\n * Flips the value if it is negative of returns the same value otherwise.\n *\n * @param {Number} i The value to flip\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csUnflip (i) {\n // flip the value if it is negative\n return i < 0 ? csFlip(i) : i\n}\n","import { csMarked } from './csMarked.js'\nimport { csMark } from './csMark.js'\nimport { csUnflip } from './csUnflip.js'\n\n/**\n * Depth-first search computes the nonzero pattern xi of the directed graph G (Matrix) starting\n * at nodes in B (see csReach()).\n *\n * @param {Number} j The starting node for the DFS algorithm\n * @param {Matrix} g The G matrix to search, ptr array modified, then restored\n * @param {Number} top Start index in stack xi[top..n-1]\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} pinv The inverse row permutation vector, must be null for L * x = b\n *\n * @return {Number} New value of top\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csDfs (j, g, top, xi, pinv) {\n // g arrays\n const index = g._index\n const ptr = g._ptr\n const size = g._size\n // columns\n const n = size[1]\n // vars\n let i, p, p2\n // initialize head\n let head = 0\n // initialize the recursion stack\n xi[0] = j\n // loop\n while (head >= 0) {\n // get j from the top of the recursion stack\n j = xi[head]\n // apply permutation vector\n const jnew = pinv ? pinv[j] : j\n // check node j is marked\n if (!csMarked(ptr, j)) {\n // mark node j as visited\n csMark(ptr, j)\n // update stack (last n entries in xi)\n xi[n + head] = jnew < 0 ? 0 : csUnflip(ptr[jnew])\n }\n // node j done if no unvisited neighbors\n let done = 1\n // examine all neighbors of j, stack (last n entries in xi)\n for (p = xi[n + head], p2 = jnew < 0 ? 0 : csUnflip(ptr[jnew + 1]); p < p2; p++) {\n // consider neighbor node i\n i = index[p]\n // check we have visited node i, skip it\n if (csMarked(ptr, i)) { continue }\n // pause depth-first search of node j, update stack (last n entries in xi)\n xi[n + head] = p\n // start dfs at node i\n xi[++head] = i\n // node j is not done\n done = 0\n // break, to start dfs(i)\n break\n }\n // check depth-first search at node j is done\n if (done) {\n // remove j from the recursion stack\n head--\n // and place in the output stack\n xi[--top] = j\n }\n }\n return top\n}\n","import { csReach } from './csReach.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'csSpsolve'\nconst dependencies = [\n 'divideScalar',\n 'multiply',\n 'subtract'\n]\n\nexport const createCsSpsolve = /* #__PURE__ */ factory(name, dependencies, ({ divideScalar, multiply, subtract }) => {\n /**\n * The function csSpsolve() computes the solution to G * x = bk, where bk is the\n * kth column of B. When lo is true, the function assumes G = L is lower triangular with the\n * diagonal entry as the first entry in each column. When lo is true, the function assumes G = U\n * is upper triangular with the diagonal entry as the last entry in each column.\n *\n * @param {Matrix} g The G matrix\n * @param {Matrix} b The B matrix\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} x The soluton to the linear system G * x = b\n * @param {Array} pinv The inverse row permutation vector, must be null for L * x = b\n * @param {boolean} lo The lower (true) upper triangular (false) flag\n *\n * @return {Number} The index for the nonzero pattern\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csSpsolve (g, b, k, xi, x, pinv, lo) {\n // g arrays\n const gvalues = g._values\n const gindex = g._index\n const gptr = g._ptr\n const gsize = g._size\n // columns\n const n = gsize[1]\n // b arrays\n const bvalues = b._values\n const bindex = b._index\n const bptr = b._ptr\n // vars\n let p, p0, p1, q\n // xi[top..n-1] = csReach(B(:,k))\n const top = csReach(g, b, k, xi, pinv)\n // clear x\n for (p = top; p < n; p++) { x[xi[p]] = 0 }\n // scatter b\n for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) { x[bindex[p]] = bvalues[p] }\n // loop columns\n for (let px = top; px < n; px++) {\n // x array index for px\n const j = xi[px]\n // apply permutation vector (U x = b), j maps to column J of G\n const J = pinv ? pinv[j] : j\n // check column J is empty\n if (J < 0) { continue }\n // column value indeces in G, p0 <= p < p1\n p0 = gptr[J]\n p1 = gptr[J + 1]\n // x(j) /= G(j,j)\n x[j] = divideScalar(x[j], gvalues[lo ? p0 : (p1 - 1)])\n // first entry L(j,j)\n p = lo ? (p0 + 1) : p0\n q = lo ? (p1) : (p1 - 1)\n // loop\n for (; p < q; p++) {\n // row\n const i = gindex[p]\n // x(i) -= G(i,j) * x(j)\n x[i] = subtract(x[i], multiply(gvalues[p], x[j]))\n }\n }\n // return top of stack\n return top\n }\n})\n","import { csMarked } from './csMarked.js'\nimport { csMark } from './csMark.js'\nimport { csDfs } from './csDfs.js'\n\n/**\n * The csReach function computes X = Reach(B), where B is the nonzero pattern of the n-by-1\n * sparse column of vector b. The function returns the set of nodes reachable from any node in B. The\n * nonzero pattern xi of the solution x to the sparse linear system Lx=b is given by X=Reach(B).\n *\n * @param {Matrix} g The G matrix\n * @param {Matrix} b The B matrix\n * @param {Number} k The kth column in B\n * @param {Array} xi The nonzero pattern xi[top] .. xi[n - 1], an array of size = 2 * n\n * The first n entries is the nonzero pattern, the last n entries is the stack\n * @param {Array} pinv The inverse row permutation vector\n *\n * @return {Number} The index for the nonzero pattern\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\nexport function csReach (g, b, k, xi, pinv) {\n // g arrays\n const gptr = g._ptr\n const gsize = g._size\n // b arrays\n const bindex = b._index\n const bptr = b._ptr\n // columns\n const n = gsize[1]\n // vars\n let p, p0, p1\n // initialize top\n let top = n\n // loop column indeces in B\n for (p0 = bptr[k], p1 = bptr[k + 1], p = p0; p < p1; p++) {\n // node i\n const i = bindex[p]\n // check node i is marked\n if (!csMarked(gptr, i)) {\n // start a dfs at unmarked node i\n top = csDfs(i, g, top, xi, pinv)\n }\n }\n // loop columns from top -> n - 1\n for (p = top; p < n; p++) {\n // restore G\n csMark(gptr, xi[p])\n }\n return top\n}\n","import { factory } from '../../../utils/factory.js'\nimport { createCsSpsolve } from './csSpsolve.js'\n\nconst name = 'csLu'\nconst dependencies = [\n 'abs',\n 'divideScalar',\n 'multiply',\n 'subtract',\n 'larger',\n 'largerEq',\n 'SparseMatrix'\n]\n\nexport const createCsLu = /* #__PURE__ */ factory(name, dependencies, ({ abs, divideScalar, multiply, subtract, larger, largerEq, SparseMatrix }) => {\n const csSpsolve = createCsSpsolve({ divideScalar, multiply, subtract })\n\n /**\n * Computes the numeric LU factorization of the sparse matrix A. Implements a Left-looking LU factorization\n * algorithm that computes L and U one column at a tume. At the kth step, it access columns 1 to k-1 of L\n * and column k of A. Given the fill-reducing column ordering q (see parameter s) computes L, U and pinv so\n * L * U = A(p, q), where p is the inverse of pinv.\n *\n * @param {Matrix} m The A Matrix to factorize\n * @param {Object} s The symbolic analysis from csSqr(). Provides the fill-reducing\n * column ordering q\n * @param {Number} tol Partial pivoting threshold (1 for partial pivoting)\n *\n * @return {Number} The numeric LU factorization of A or null\n *\n * Reference: http://faculty.cse.tamu.edu/davis/publications.html\n */\n return function csLu (m, s, tol) {\n // validate input\n if (!m) { return null }\n // m arrays\n const size = m._size\n // columns\n const n = size[1]\n // symbolic analysis result\n let q\n let lnz = 100\n let unz = 100\n // update symbolic analysis parameters\n if (s) {\n q = s.q\n lnz = s.lnz || lnz\n unz = s.unz || unz\n }\n // L arrays\n const lvalues = [] // (lnz)\n const lindex = [] // (lnz)\n const lptr = [] // (n + 1)\n // L\n const L = new SparseMatrix({\n values: lvalues,\n index: lindex,\n ptr: lptr,\n size: [n, n]\n })\n // U arrays\n const uvalues = [] // (unz)\n const uindex = [] // (unz)\n const uptr = [] // (n + 1)\n // U\n const U = new SparseMatrix({\n values: uvalues,\n index: uindex,\n ptr: uptr,\n size: [n, n]\n })\n // inverse of permutation vector\n const pinv = [] // (n)\n // vars\n let i, p\n // allocate arrays\n const x = [] // (n)\n const xi = [] // (2 * n)\n // initialize variables\n for (i = 0; i < n; i++) {\n // clear workspace\n x[i] = 0\n // no rows pivotal yet\n pinv[i] = -1\n // no cols of L yet\n lptr[i + 1] = 0\n }\n // reset number of nonzero elements in L and U\n lnz = 0\n unz = 0\n // compute L(:,k) and U(:,k)\n for (let k = 0; k < n; k++) {\n // update ptr\n lptr[k] = lnz\n uptr[k] = unz\n // apply column permutations if needed\n const col = q ? q[k] : k\n // solve triangular system, x = L\\A(:,col)\n const top = csSpsolve(L, m, col, xi, x, pinv, 1)\n // find pivot\n let ipiv = -1\n let a = -1\n // loop xi[] from top -> n\n for (p = top; p < n; p++) {\n // x[i] is nonzero\n i = xi[p]\n // check row i is not yet pivotal\n if (pinv[i] < 0) {\n // absolute value of x[i]\n const xabs = abs(x[i])\n // check absoulte value is greater than pivot value\n if (larger(xabs, a)) {\n // largest pivot candidate so far\n a = xabs\n ipiv = i\n }\n } else {\n // x(i) is the entry U(pinv[i],k)\n uindex[unz] = pinv[i]\n uvalues[unz++] = x[i]\n }\n }\n // validate we found a valid pivot\n if (ipiv === -1 || a <= 0) { return null }\n // update actual pivot column, give preference to diagonal value\n if (pinv[col] < 0 && largerEq(abs(x[col]), multiply(a, tol))) { ipiv = col }\n // the chosen pivot\n const pivot = x[ipiv]\n // last entry in U(:,k) is U(k,k)\n uindex[unz] = k\n uvalues[unz++] = pivot\n // ipiv is the kth pivot row\n pinv[ipiv] = k\n // first entry in L(:,k) is L(k,k) = 1\n lindex[lnz] = ipiv\n lvalues[lnz++] = 1\n // L(k+1:n,k) = x / pivot\n for (p = top; p < n; p++) {\n // row\n i = xi[p]\n // check x(i) is an entry in L(:,k)\n if (pinv[i] < 0) {\n // save unpermuted row in L\n lindex[lnz] = i\n // scale pivot column\n lvalues[lnz++] = divideScalar(x[i], pivot)\n }\n // x[0..n-1] = 0 for next k\n x[i] = 0\n }\n }\n // update ptr\n lptr[n] = lnz\n uptr[n] = unz\n // fix row indices of L for final pinv\n for (p = 0; p < lnz; p++) { lindex[p] = pinv[lindex[p]] }\n // trim arrays\n lvalues.splice(lnz, lvalues.length - lnz)\n lindex.splice(lnz, lindex.length - lnz)\n uvalues.splice(unz, uvalues.length - unz)\n uindex.splice(unz, uindex.length - unz)\n // return LU factor\n return {\n L: L,\n U: U,\n pinv: pinv\n }\n }\n})\n","import { isInteger } from '../../../utils/number.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createCsSqr } from '../sparse/csSqr.js'\nimport { createCsLu } from '../sparse/csLu.js'\n\nconst name = 'slu'\nconst dependencies = [\n 'typed',\n 'abs',\n 'add',\n 'multiply',\n 'transpose',\n 'divideScalar',\n 'subtract',\n 'larger',\n 'largerEq',\n 'SparseMatrix'\n]\n\nexport const createSlu = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, multiply, transpose, divideScalar, subtract, larger, largerEq, SparseMatrix }) => {\n const csSqr = createCsSqr({ add, multiply, transpose })\n const csLu = createCsLu({ abs, divideScalar, multiply, subtract, larger, largerEq, SparseMatrix })\n\n /**\n * Calculate the Sparse Matrix LU decomposition with full pivoting. Sparse Matrix `A` is decomposed in two matrices (`L`, `U`) and two permutation vectors (`pinv`, `q`) where\n *\n * `P * A * Q = L * U`\n *\n * Syntax:\n *\n * math.slu(A, order, threshold)\n *\n * Examples:\n *\n * const A = math.sparse([[4,3], [6, 3]])\n * math.slu(A, 1, 0.001)\n * // returns:\n * // {\n * // L: [[1, 0], [1.5, 1]]\n * // U: [[4, 3], [0, -1.5]]\n * // p: [0, 1]\n * // q: [0, 1]\n * // }\n *\n * See also:\n *\n * lup, lsolve, usolve, lusolve\n *\n * @param {SparseMatrix} A A two dimensional sparse matrix for which to get the LU decomposition.\n * @param {Number} order The Symbolic Ordering and Analysis order:\n * 0 - Natural ordering, no permutation vector q is returned\n * 1 - Matrix must be square, symbolic ordering and analisis is performed on M = A + A'\n * 2 - Symbolic ordering and analisis is performed on M = A' * A. Dense columns from A' are dropped, A recreated from A'.\n * This is appropriatefor LU factorization of unsymmetric matrices.\n * 3 - Symbolic ordering and analisis is performed on M = A' * A. This is best used for LU factorization is matrix M has no dense rows.\n * A dense row is a row with more than 10*sqr(columns) entries.\n * @param {Number} threshold Partial pivoting threshold (1 for partial pivoting)\n *\n * @return {Object} The lower triangular matrix, the upper triangular matrix and the permutation vectors.\n */\n return typed(name, {\n\n 'SparseMatrix, number, number': function (a, order, threshold) {\n // verify order\n if (!isInteger(order) || order < 0 || order > 3) { throw new Error('Symbolic Ordering and Analysis order must be an integer number in the interval [0, 3]') }\n // verify threshold\n if (threshold < 0 || threshold > 1) { throw new Error('Partial pivoting threshold must be a number from 0 to 1') }\n\n // perform symbolic ordering and analysis\n const s = csSqr(order, a, false)\n\n // perform lu decomposition\n const f = csLu(a, s, threshold)\n\n // return decomposition\n return {\n L: f.L,\n U: f.U,\n p: f.pinv,\n q: s.q,\n toString: function () {\n return 'L: ' + this.L.toString() + '\\nU: ' + this.U.toString() + '\\np: ' + this.p.toString() + (this.q ? '\\nq: ' + this.q.toString() : '') + '\\n'\n }\n }\n }\n })\n})\n","/**\n * Permutes a vector; x = P'b. In MATLAB notation, x(p)=b.\n *\n * @param {Array} p The permutation vector of length n. null value denotes identity\n * @param {Array} b The input vector\n *\n * @return {Array} The output vector x = P'b\n */\nexport function csIpvec (p, b) {\n // vars\n let k\n const n = b.length\n const x = []\n // check permutation vector was provided, p = null denotes identity\n if (p) {\n // loop vector\n for (k = 0; k < n; k++) {\n // apply permutation\n x[p[k]] = b[k]\n }\n } else {\n // loop vector\n for (k = 0; k < n; k++) {\n // x[i] = b[i]\n x[k] = b[k]\n }\n }\n return x\n}\n","import { isArray, isMatrix } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createSolveValidation } from './utils/solveValidation.js'\nimport { csIpvec } from '../sparse/csIpvec.js'\n\nconst name = 'lusolve'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'lup',\n 'slu',\n 'usolve',\n 'lsolve',\n 'DenseMatrix'\n]\n\nexport const createLusolve = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, lup, slu, usolve, lsolve, DenseMatrix }) => {\n const solveValidation = createSolveValidation({ DenseMatrix })\n\n /**\n * Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.\n *\n * Syntax:\n *\n * math.lusolve(A, b) // returns column vector with the solution to the linear system A * x = b\n * math.lusolve(lup, b) // returns column vector with the solution to the linear system A * x = b, lup = math.lup(A)\n *\n * Examples:\n *\n * const m = [[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]\n *\n * const x = math.lusolve(m, [-1, -1, -1, -1]) // x = [[-1], [-0.5], [-1/3], [-0.25]]\n *\n * const f = math.lup(m)\n * const x1 = math.lusolve(f, [-1, -1, -1, -1]) // x1 = [[-1], [-0.5], [-1/3], [-0.25]]\n * const x2 = math.lusolve(f, [1, 2, 1, -1]) // x2 = [[1], [1], [1/3], [-0.25]]\n *\n * const a = [[-2, 3], [2, 1]]\n * const b = [11, 9]\n * const x = math.lusolve(a, b) // [[2], [5]]\n *\n * See also:\n *\n * lup, slu, lsolve, usolve\n *\n * @param {Matrix | Array | Object} A Invertible Matrix or the Matrix LU decomposition\n * @param {Matrix | Array} b Column Vector\n * @param {number} [order] The Symbolic Ordering and Analysis order, see slu for details. Matrix must be a SparseMatrix\n * @param {Number} [threshold] Partial pivoting threshold (1 for partial pivoting), see slu for details. Matrix must be a SparseMatrix.\n *\n * @return {DenseMatrix | Array} Column vector with the solution to the linear system A * x = b\n */\n return typed(name, {\n\n 'Array, Array | Matrix': function (a, b) {\n a = matrix(a)\n const d = lup(a)\n const x = _lusolve(d.L, d.U, d.p, null, b)\n return x.valueOf()\n },\n\n 'DenseMatrix, Array | Matrix': function (a, b) {\n const d = lup(a)\n return _lusolve(d.L, d.U, d.p, null, b)\n },\n\n 'SparseMatrix, Array | Matrix': function (a, b) {\n const d = lup(a)\n return _lusolve(d.L, d.U, d.p, null, b)\n },\n\n 'SparseMatrix, Array | Matrix, number, number': function (a, b, order, threshold) {\n const d = slu(a, order, threshold)\n return _lusolve(d.L, d.U, d.p, d.q, b)\n },\n\n 'Object, Array | Matrix': function (d, b) {\n return _lusolve(d.L, d.U, d.p, d.q, b)\n }\n })\n\n function _toMatrix (a) {\n if (isMatrix(a)) { return a }\n if (isArray(a)) { return matrix(a) }\n throw new TypeError('Invalid Matrix LU decomposition')\n }\n\n function _lusolve (l, u, p, q, b) {\n // verify decomposition\n l = _toMatrix(l)\n u = _toMatrix(u)\n\n // apply row permutations if needed (b is a DenseMatrix)\n if (p) {\n b = solveValidation(l, b, true)\n b._data = csIpvec(p, b._data)\n }\n\n // use forward substitution to resolve L * y = b\n const y = lsolve(l, b)\n // use backward substitution to resolve U * x = y\n const x = usolve(u, y)\n\n // apply column permutations if needed (x is a DenseMatrix)\n if (q) { x._data = csIpvec(q, x._data) }\n\n return x\n }\n})\n","import { isHelp } from '../utils/is.js'\nimport { clone } from '../utils/object.js'\nimport { format } from '../utils/string.js'\nimport { factory } from '../utils/factory.js'\n\nconst name = 'Help'\nconst dependencies = ['parse']\n\nexport const createHelpClass = /* #__PURE__ */ factory(name, dependencies, ({ parse }) => {\n /**\n * Documentation object\n * @param {Object} doc Object containing properties:\n * {string} name\n * {string} category\n * {string} description\n * {string[]} syntax\n * {string[]} examples\n * {string[]} seealso\n * @constructor\n */\n function Help (doc) {\n if (!(this instanceof Help)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (!doc) throw new Error('Argument \"doc\" missing')\n\n this.doc = doc\n }\n\n /**\n * Attach type information\n */\n Help.prototype.type = 'Help'\n Help.prototype.isHelp = true\n\n /**\n * Generate a string representation of the Help object\n * @return {string} Returns a string\n * @private\n */\n Help.prototype.toString = function () {\n const doc = this.doc || {}\n let desc = '\\n'\n\n if (doc.name) {\n desc += 'Name: ' + doc.name + '\\n\\n'\n }\n if (doc.category) {\n desc += 'Category: ' + doc.category + '\\n\\n'\n }\n if (doc.description) {\n desc += 'Description:\\n ' + doc.description + '\\n\\n'\n }\n if (doc.syntax) {\n desc += 'Syntax:\\n ' + doc.syntax.join('\\n ') + '\\n\\n'\n }\n if (doc.examples) {\n desc += 'Examples:\\n'\n\n const scope = {}\n for (let i = 0; i < doc.examples.length; i++) {\n const expr = doc.examples[i]\n desc += ' ' + expr + '\\n'\n\n let res\n try {\n // note: res can be undefined when `expr` is an empty string\n res = parse(expr).compile().evaluate(scope)\n } catch (e) {\n res = e\n }\n if (res !== undefined && !isHelp(res)) {\n desc += ' ' + format(res, { precision: 14 }) + '\\n'\n }\n }\n desc += '\\n'\n }\n if (doc.seealso && doc.seealso.length) {\n desc += 'See also: ' + doc.seealso.join(', ') + '\\n'\n }\n\n return desc\n }\n\n /**\n * Export the help object to JSON\n */\n Help.prototype.toJSON = function () {\n const obj = clone(this.doc)\n obj.mathjs = 'Help'\n return obj\n }\n\n /**\n * Instantiate a Help object from a JSON object\n * @param {Object} json\n * @returns {Help} Returns a new Help object\n */\n Help.fromJSON = function (json) {\n const doc = {}\n\n Object.keys(json)\n .filter(prop => prop !== 'mathjs')\n .forEach(prop => {\n doc[prop] = json[prop]\n })\n\n return new Help(doc)\n }\n\n /**\n * Returns a string representation of the Help object\n */\n Help.prototype.valueOf = Help.prototype.toString\n\n return Help\n}, { isClass: true })\n","import { isChain } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { hasOwnProperty, lazy } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'Chain'\nconst dependencies = ['?on', 'math']\n\nexport const createChainClass = /* #__PURE__ */ factory(name, dependencies, ({ on, math }) => {\n /**\n * @constructor Chain\n * Wrap any value in a chain, allowing to perform chained operations on\n * the value.\n *\n * All methods available in the math.js library can be called upon the chain,\n * and then will be evaluated with the value itself as first argument.\n * The chain can be closed by executing chain.done(), which will return\n * the final value.\n *\n * The Chain has a number of special functions:\n * - done() Finalize the chained operation and return the\n * chain's value.\n * - valueOf() The same as done()\n * - toString() Returns a string representation of the chain's value.\n *\n * @param {*} [value]\n */\n function Chain (value) {\n if (!(this instanceof Chain)) {\n throw new SyntaxError('Constructor must be called with the new operator')\n }\n\n if (isChain(value)) {\n this.value = value.value\n } else {\n this.value = value\n }\n }\n\n /**\n * Attach type information\n */\n Chain.prototype.type = 'Chain'\n Chain.prototype.isChain = true\n\n /**\n * Close the chain. Returns the final value.\n * Does the same as method valueOf()\n * @returns {*} value\n */\n Chain.prototype.done = function () {\n return this.value\n }\n\n /**\n * Close the chain. Returns the final value.\n * Does the same as method done()\n * @returns {*} value\n */\n Chain.prototype.valueOf = function () {\n return this.value\n }\n\n /**\n * Get a string representation of the value in the chain\n * @returns {string}\n */\n Chain.prototype.toString = function () {\n return format(this.value)\n }\n\n /**\n * Get a JSON representation of the chain\n * @returns {Object}\n */\n Chain.prototype.toJSON = function () {\n return {\n mathjs: 'Chain',\n value: this.value\n }\n }\n\n /**\n * Instantiate a Chain from its JSON representation\n * @param {Object} json An object structured like\n * `{\"mathjs\": \"Chain\", value: ...}`,\n * where mathjs is optional\n * @returns {Chain}\n */\n Chain.fromJSON = function (json) {\n return new Chain(json.value)\n }\n\n /**\n * Create a proxy method for the chain\n * @param {string} name\n * @param {Function} fn The function to be proxied\n * If fn is no function, it is silently ignored.\n * @private\n */\n function createProxy (name, fn) {\n if (typeof fn === 'function') {\n Chain.prototype[name] = chainify(fn)\n }\n }\n\n /**\n * Create a proxy method for the chain\n * @param {string} name\n * @param {function} resolver The function resolving with the\n * function to be proxied\n * @private\n */\n function createLazyProxy (name, resolver) {\n lazy(Chain.prototype, name, function outerResolver () {\n const fn = resolver()\n if (typeof fn === 'function') {\n return chainify(fn)\n }\n\n return undefined // if not a function, ignore\n })\n }\n\n /**\n * Make a function chainable\n * @param {function} fn\n * @return {Function} chain function\n * @private\n */\n function chainify (fn) {\n return function () {\n const args = [this.value] // `this` will be the context of a Chain instance\n for (let i = 0; i < arguments.length; i++) {\n args[i + 1] = arguments[i]\n }\n\n return new Chain(fn.apply(fn, args))\n }\n }\n\n /**\n * Create a proxy for a single method, or an object with multiple methods.\n * Example usage:\n *\n * Chain.createProxy('add', function add (x, y) {...})\n * Chain.createProxy({\n * add: function add (x, y) {...},\n * subtract: function subtract (x, y) {...}\n * }\n *\n * @param {string | Object} arg0 A name (string), or an object with\n * functions\n * @param {*} [arg1] A function, when arg0 is a name\n */\n Chain.createProxy = function (arg0, arg1) {\n if (typeof arg0 === 'string') {\n // createProxy(name, value)\n createProxy(arg0, arg1)\n } else {\n // createProxy(values)\n for (const name in arg0) {\n if (hasOwnProperty(arg0, name) && excludedNames[name] === undefined) {\n createLazyProxy(name, () => arg0[name])\n }\n }\n }\n }\n\n const excludedNames = {\n expression: true,\n docs: true,\n type: true,\n classes: true,\n json: true,\n error: true,\n isChain: true // conflicts with the property isChain of a Chain instance\n }\n\n // create proxy for everything that is in math.js\n Chain.createProxy(math)\n\n // register on the import event, automatically add a proxy for every imported function.\n if (on) {\n on('import', function (name, resolver, path) {\n if (!path) {\n // an imported function (not a data type or something special)\n createLazyProxy(name, resolver)\n }\n })\n }\n\n return Chain\n}, { isClass: true })\n","export const piDocs = {\n name: 'pi',\n category: 'Constants',\n syntax: [\n 'pi'\n ],\n description: 'The number pi is a mathematical constant that is the ratio of a circle\\'s circumference to its diameter, and is approximately equal to 3.14159',\n examples: [\n 'pi',\n 'sin(pi/2)'\n ],\n seealso: ['tau']\n}\n","export const eDocs = {\n name: 'e',\n category: 'Constants',\n syntax: [\n 'e'\n ],\n description: 'Euler\\'s number, the base of the natural logarithm. Approximately equal to 2.71828',\n examples: [\n 'e',\n 'e ^ 2',\n 'exp(2)',\n 'log(e)'\n ],\n seealso: ['exp']\n}\n","import { bignumberDocs } from './construction/bignumber.js'\nimport { typeOfDocs } from './function/utils/typeOf.js'\nimport { isZeroDocs } from './function/utils/isZero.js'\nimport { isPrimeDocs } from './function/utils/isPrime.js'\nimport { isPositiveDocs } from './function/utils/isPositive.js'\nimport { isNumericDocs } from './function/utils/isNumeric.js'\nimport { hasNumericValueDocs } from './function/utils/hasNumericValue.js'\nimport { isNegativeDocs } from './function/utils/isNegative.js'\nimport { isIntegerDocs } from './function/utils/isInteger.js'\nimport { isNaNDocs } from './function/utils/isNaN.js'\nimport { formatDocs } from './function/utils/format.js'\nimport { binDocs } from './function/utils/bin.js'\nimport { octDocs } from './function/utils/oct.js'\nimport { hexDocs } from './function/utils/hex.js'\nimport { cloneDocs } from './function/utils/clone.js'\nimport { toDocs } from './function/units/to.js'\nimport { tanhDocs } from './function/trigonometry/tanh.js'\nimport { tanDocs } from './function/trigonometry/tan.js'\nimport { sinhDocs } from './function/trigonometry/sinh.js'\nimport { sechDocs } from './function/trigonometry/sech.js'\nimport { secDocs } from './function/trigonometry/sec.js'\nimport { cschDocs } from './function/trigonometry/csch.js'\nimport { cscDocs } from './function/trigonometry/csc.js'\nimport { cothDocs } from './function/trigonometry/coth.js'\nimport { cotDocs } from './function/trigonometry/cot.js'\nimport { coshDocs } from './function/trigonometry/cosh.js'\nimport { cosDocs } from './function/trigonometry/cos.js'\nimport { atan2Docs } from './function/trigonometry/atan2.js'\nimport { atanhDocs } from './function/trigonometry/atanh.js'\nimport { atanDocs } from './function/trigonometry/atan.js'\nimport { asinhDocs } from './function/trigonometry/asinh.js'\nimport { asinDocs } from './function/trigonometry/asin.js'\nimport { asechDocs } from './function/trigonometry/asech.js'\nimport { asecDocs } from './function/trigonometry/asec.js'\nimport { acschDocs } from './function/trigonometry/acsch.js'\nimport { acscDocs } from './function/trigonometry/acsc.js'\nimport { acothDocs } from './function/trigonometry/acoth.js'\nimport { acotDocs } from './function/trigonometry/acot.js'\nimport { acoshDocs } from './function/trigonometry/acosh.js'\nimport { acosDocs } from './function/trigonometry/acos.js'\nimport { sumDocs } from './function/statistics/sum.js'\nimport { stdDocs } from './function/statistics/std.js'\nimport { quantileSeqDocs } from './function/statistics/quantileSeq.js'\nimport { prodDocs } from './function/statistics/prod.js'\nimport { modeDocs } from './function/statistics/mode.js'\nimport { minDocs } from './function/statistics/min.js'\nimport { medianDocs } from './function/statistics/median.js'\nimport { meanDocs } from './function/statistics/mean.js'\nimport { maxDocs } from './function/statistics/max.js'\nimport { madDocs } from './function/statistics/mad.js'\nimport { erfDocs } from './function/special/erf.js'\nimport { setUnionDocs } from './function/set/setUnion.js'\nimport { setSymDifferenceDocs } from './function/set/setSymDifference.js'\nimport { setSizeDocs } from './function/set/setSize.js'\nimport { setPowersetDocs } from './function/set/setPowerset.js'\nimport { setMultiplicityDocs } from './function/set/setMultiplicity.js'\nimport { setIsSubsetDocs } from './function/set/setIsSubset.js'\nimport { setIntersectDocs } from './function/set/setIntersect.js'\nimport { setDistinctDocs } from './function/set/setDistinct.js'\nimport { setDifferenceDocs } from './function/set/setDifference.js'\nimport { setCartesianDocs } from './function/set/setCartesian.js'\nimport { unequalDocs } from './function/relational/unequal.js'\nimport { smallerEqDocs } from './function/relational/smallerEq.js'\nimport { smallerDocs } from './function/relational/smaller.js'\nimport { largerEqDocs } from './function/relational/largerEq.js'\nimport { largerDocs } from './function/relational/larger.js'\nimport { equalTextDocs } from './function/relational/equalText.js'\nimport { equalDocs } from './function/relational/equal.js'\nimport { deepEqualDocs } from './function/relational/deepEqual.js'\nimport { compareTextDocs } from './function/relational/compareText.js'\nimport { compareNaturalDocs } from './function/relational/compareNatural.js'\nimport { compareDocs } from './function/relational/compare.js'\nimport { randomIntDocs } from './function/probability/randomInt.js'\nimport { randomDocs } from './function/probability/random.js'\nimport { pickRandomDocs } from './function/probability/pickRandom.js'\nimport { permutationsDocs } from './function/probability/permutations.js'\nimport { multinomialDocs } from './function/probability/multinomial.js'\nimport { kldivergenceDocs } from './function/probability/kldivergence.js'\nimport { gammaDocs } from './function/probability/gamma.js'\nimport { factorialDocs } from './function/probability/factorial.js'\nimport { combinationsDocs } from './function/probability/combinations.js'\nimport { combinationsWithRepDocs } from './function/probability/combinationsWithRep.js'\nimport { zerosDocs } from './function/matrix/zeros.js'\nimport { transposeDocs } from './function/matrix/transpose.js'\nimport { traceDocs } from './function/matrix/trace.js'\nimport { subsetDocs } from './function/matrix/subset.js'\nimport { squeezeDocs } from './function/matrix/squeeze.js'\nimport { sortDocs } from './function/matrix/sort.js'\nimport { sizeDocs } from './function/matrix/size.js'\nimport { diffDocs } from './function/matrix/diff.js'\nimport { reshapeDocs } from './function/matrix/reshape.js'\nimport { resizeDocs } from './function/matrix/resize.js'\nimport { rangeDocs } from './function/matrix/range.js'\nimport { partitionSelectDocs } from './function/matrix/partitionSelect.js'\nimport { onesDocs } from './function/matrix/ones.js'\nimport { mapDocs } from './function/matrix/map.js'\nimport { kronDocs } from './function/matrix/kron.js'\nimport { invDocs } from './function/matrix/inv.js'\nimport { forEachDocs } from './function/matrix/forEach.js'\nimport { flattenDocs } from './function/matrix/flatten.js'\nimport { filterDocs } from './function/matrix/filter.js'\nimport { identityDocs } from './function/matrix/identity.js'\nimport { getMatrixDataTypeDocs } from './function/matrix/getMatrixDataType.js'\nimport { dotDocs } from './function/matrix/dot.js'\nimport { diagDocs } from './function/matrix/diag.js'\nimport { detDocs } from './function/matrix/det.js'\nimport { ctransposeDocs } from './function/matrix/ctranspose.js'\nimport { crossDocs } from './function/matrix/cross.js'\nimport { concatDocs } from './function/matrix/concat.js'\nimport { xorDocs } from './function/logical/xor.js'\nimport { orDocs } from './function/logical/or.js'\nimport { notDocs } from './function/logical/not.js'\nimport { andDocs } from './function/logical/and.js'\nimport { intersectDocs } from './function/geometry/intersect.js'\nimport { distanceDocs } from './function/geometry/distance.js'\nimport { helpDocs } from './function/expression/help.js'\nimport { evaluateDocs } from './function/expression/evaluate.js'\nimport { imDocs } from './function/complex/im.js'\nimport { reDocs } from './function/complex/re.js'\nimport { conjDocs } from './function/complex/conj.js'\nimport { argDocs } from './function/complex/arg.js'\nimport { typedDocs } from './core/typed.js'\nimport { importDocs } from './core/import.js'\nimport { configDocs } from './core/config.js'\nimport { stirlingS2Docs } from './function/combinatorics/stirlingS2.js'\nimport { compositionDocs } from './function/combinatorics/composition.js'\nimport { catalanDocs } from './function/combinatorics/catalan.js'\nimport { bellNumbersDocs } from './function/combinatorics/bellNumbers.js'\nimport { rightLogShiftDocs } from './function/bitwise/rightLogShift.js'\nimport { rightArithShiftDocs } from './function/bitwise/rightArithShift.js'\nimport { leftShiftDocs } from './function/bitwise/leftShift.js'\nimport { bitXorDocs } from './function/bitwise/bitXor.js'\nimport { bitOrDocs } from './function/bitwise/bitOr.js'\nimport { bitNotDocs } from './function/bitwise/bitNot.js'\nimport { bitAndDocs } from './function/bitwise/bitAnd.js'\nimport { xgcdDocs } from './function/arithmetic/xgcd.js'\nimport { unaryPlusDocs } from './function/arithmetic/unaryPlus.js'\nimport { unaryMinusDocs } from './function/arithmetic/unaryMinus.js'\nimport { squareDocs } from './function/arithmetic/square.js'\nimport { sqrtmDocs } from './function/arithmetic/sqrtm.js'\nimport { sqrtDocs } from './function/arithmetic/sqrt.js'\nimport { signDocs } from './function/arithmetic/sign.js'\nimport { roundDocs } from './function/arithmetic/round.js'\nimport { powDocs } from './function/arithmetic/pow.js'\nimport { nthRootsDocs } from './function/arithmetic/nthRoots.js'\nimport { nthRootDocs } from './function/arithmetic/nthRoot.js'\nimport { normDocs } from './function/arithmetic/norm.js'\nimport { multiplyDocs } from './function/arithmetic/multiply.js'\nimport { modDocs } from './function/arithmetic/mod.js'\nimport { log10Docs } from './function/arithmetic/log10.js'\nimport { log1pDocs } from './function/arithmetic/log1p.js'\nimport { log2Docs } from './function/arithmetic/log2.js'\nimport { logDocs } from './function/arithmetic/log.js'\nimport { lcmDocs } from './function/arithmetic/lcm.js'\nimport { hypotDocs } from './function/arithmetic/hypot.js'\nimport { gcdDocs } from './function/arithmetic/gcd.js'\nimport { floorDocs } from './function/arithmetic/floor.js'\nimport { fixDocs } from './function/arithmetic/fix.js'\nimport { expm1Docs } from './function/arithmetic/expm1.js'\nimport { expmDocs } from './function/arithmetic/expm.js'\nimport { eigsDocs } from './function/matrix/eigs.js'\nimport { expDocs } from './function/arithmetic/exp.js'\nimport { dotMultiplyDocs } from './function/arithmetic/dotMultiply.js'\nimport { dotDivideDocs } from './function/arithmetic/dotDivide.js'\nimport { divideDocs } from './function/arithmetic/divide.js'\nimport { cubeDocs } from './function/arithmetic/cube.js'\nimport { ceilDocs } from './function/arithmetic/ceil.js'\nimport { cbrtDocs } from './function/arithmetic/cbrt.js'\nimport { addDocs } from './function/arithmetic/add.js'\nimport { absDocs } from './function/arithmetic/abs.js'\nimport { qrDocs } from './function/algebra/qr.js'\nimport { usolveDocs } from './function/algebra/usolve.js'\nimport { usolveAllDocs } from './function/algebra/usolveAll.js'\nimport { sluDocs } from './function/algebra/slu.js'\nimport { rationalizeDocs } from './function/algebra/rationalize.js'\nimport { simplifyDocs } from './function/algebra/simplify.js'\nimport { lupDocs } from './function/algebra/lup.js'\nimport { lsolveDocs } from './function/algebra/lsolve.js'\nimport { lsolveAllDocs } from './function/algebra/lsolveAll.js'\nimport { derivativeDocs } from './function/algebra/derivative.js'\nimport { versionDocs } from './constants/version.js'\nimport { trueDocs } from './constants/true.js'\nimport { tauDocs } from './constants/tau.js'\nimport { SQRT2Docs } from './constants/SQRT2.js'\nimport { SQRT12Docs } from './constants/SQRT1_2.js'\nimport { phiDocs } from './constants/phi.js'\nimport { piDocs } from './constants/pi.js'\nimport { nullDocs } from './constants/null.js'\nimport { NaNDocs } from './constants/NaN.js'\nimport { LOG10EDocs } from './constants/LOG10E.js'\nimport { LOG2EDocs } from './constants/LOG2E.js'\nimport { LN10Docs } from './constants/LN10.js'\nimport { LN2Docs } from './constants/LN2.js'\nimport { InfinityDocs } from './constants/Infinity.js'\nimport { iDocs } from './constants/i.js'\nimport { falseDocs } from './constants/false.js'\nimport { eDocs } from './constants/e.js'\nimport { unitDocs } from './construction/unit.js'\nimport { stringDocs } from './construction/string.js'\nimport { splitUnitDocs } from './construction/splitUnit.js'\nimport { sparseDocs } from './construction/sparse.js'\nimport { numberDocs } from './construction/number.js'\nimport { matrixDocs } from './construction/matrix.js'\nimport { indexDocs } from './construction/index.js'\nimport { fractionDocs } from './construction/fraction.js'\nimport { createUnitDocs } from './construction/createUnit.js'\nimport { complexDocs } from './construction/complex.js'\nimport { booleanDocs } from './construction/boolean.js'\nimport { dotPowDocs } from './function/arithmetic/dotPow.js'\nimport { lusolveDocs } from './function/algebra/lusolve.js'\nimport { subtractDocs } from './function/arithmetic/subtract.js'\nimport { varianceDocs } from './function/statistics/variance.js'\nimport { sinDocs } from './function/trigonometry/sin.js'\nimport { numericDocs } from './function/utils/numeric.js'\nimport { columnDocs } from './function/matrix/column.js'\nimport { rowDocs } from './function/matrix/row.js'\nimport { rotationMatrixDocs } from './function/matrix/rotationMatrix.js'\nimport { rotateDocs } from './function/matrix/rotate.js'\n\nexport const embeddedDocs = {\n\n // construction functions\n bignumber: bignumberDocs,\n boolean: booleanDocs,\n complex: complexDocs,\n createUnit: createUnitDocs,\n fraction: fractionDocs,\n index: indexDocs,\n matrix: matrixDocs,\n number: numberDocs,\n sparse: sparseDocs,\n splitUnit: splitUnitDocs,\n string: stringDocs,\n unit: unitDocs,\n\n // constants\n e: eDocs,\n E: eDocs,\n false: falseDocs,\n i: iDocs,\n Infinity: InfinityDocs,\n LN2: LN2Docs,\n LN10: LN10Docs,\n LOG2E: LOG2EDocs,\n LOG10E: LOG10EDocs,\n NaN: NaNDocs,\n null: nullDocs,\n pi: piDocs,\n PI: piDocs,\n phi: phiDocs,\n SQRT1_2: SQRT12Docs,\n SQRT2: SQRT2Docs,\n tau: tauDocs,\n true: trueDocs,\n version: versionDocs,\n\n // physical constants\n // TODO: more detailed docs for physical constants\n speedOfLight: { description: 'Speed of light in vacuum', examples: ['speedOfLight'] },\n gravitationConstant: { description: 'Newtonian constant of gravitation', examples: ['gravitationConstant'] },\n planckConstant: { description: 'Planck constant', examples: ['planckConstant'] },\n reducedPlanckConstant: { description: 'Reduced Planck constant', examples: ['reducedPlanckConstant'] },\n\n magneticConstant: { description: 'Magnetic constant (vacuum permeability)', examples: ['magneticConstant'] },\n electricConstant: { description: 'Electric constant (vacuum permeability)', examples: ['electricConstant'] },\n vacuumImpedance: { description: 'Characteristic impedance of vacuum', examples: ['vacuumImpedance'] },\n coulomb: { description: 'Coulomb\\'s constant', examples: ['coulomb'] },\n elementaryCharge: { description: 'Elementary charge', examples: ['elementaryCharge'] },\n bohrMagneton: { description: 'Borh magneton', examples: ['bohrMagneton'] },\n conductanceQuantum: { description: 'Conductance quantum', examples: ['conductanceQuantum'] },\n inverseConductanceQuantum: { description: 'Inverse conductance quantum', examples: ['inverseConductanceQuantum'] },\n // josephson: {description: 'Josephson constant', examples: ['josephson']},\n magneticFluxQuantum: { description: 'Magnetic flux quantum', examples: ['magneticFluxQuantum'] },\n nuclearMagneton: { description: 'Nuclear magneton', examples: ['nuclearMagneton'] },\n klitzing: { description: 'Von Klitzing constant', examples: ['klitzing'] },\n\n bohrRadius: { description: 'Borh radius', examples: ['bohrRadius'] },\n classicalElectronRadius: { description: 'Classical electron radius', examples: ['classicalElectronRadius'] },\n electronMass: { description: 'Electron mass', examples: ['electronMass'] },\n fermiCoupling: { description: 'Fermi coupling constant', examples: ['fermiCoupling'] },\n fineStructure: { description: 'Fine-structure constant', examples: ['fineStructure'] },\n hartreeEnergy: { description: 'Hartree energy', examples: ['hartreeEnergy'] },\n protonMass: { description: 'Proton mass', examples: ['protonMass'] },\n deuteronMass: { description: 'Deuteron Mass', examples: ['deuteronMass'] },\n neutronMass: { description: 'Neutron mass', examples: ['neutronMass'] },\n quantumOfCirculation: { description: 'Quantum of circulation', examples: ['quantumOfCirculation'] },\n rydberg: { description: 'Rydberg constant', examples: ['rydberg'] },\n thomsonCrossSection: { description: 'Thomson cross section', examples: ['thomsonCrossSection'] },\n weakMixingAngle: { description: 'Weak mixing angle', examples: ['weakMixingAngle'] },\n efimovFactor: { description: 'Efimov factor', examples: ['efimovFactor'] },\n\n atomicMass: { description: 'Atomic mass constant', examples: ['atomicMass'] },\n avogadro: { description: 'Avogadro\\'s number', examples: ['avogadro'] },\n boltzmann: { description: 'Boltzmann constant', examples: ['boltzmann'] },\n faraday: { description: 'Faraday constant', examples: ['faraday'] },\n firstRadiation: { description: 'First radiation constant', examples: ['firstRadiation'] },\n loschmidt: { description: 'Loschmidt constant at T=273.15 K and p=101.325 kPa', examples: ['loschmidt'] },\n gasConstant: { description: 'Gas constant', examples: ['gasConstant'] },\n molarPlanckConstant: { description: 'Molar Planck constant', examples: ['molarPlanckConstant'] },\n molarVolume: { description: 'Molar volume of an ideal gas at T=273.15 K and p=101.325 kPa', examples: ['molarVolume'] },\n sackurTetrode: { description: 'Sackur-Tetrode constant at T=1 K and p=101.325 kPa', examples: ['sackurTetrode'] },\n secondRadiation: { description: 'Second radiation constant', examples: ['secondRadiation'] },\n stefanBoltzmann: { description: 'Stefan-Boltzmann constant', examples: ['stefanBoltzmann'] },\n wienDisplacement: { description: 'Wien displacement law constant', examples: ['wienDisplacement'] },\n // spectralRadiance: {description: 'First radiation constant for spectral radiance', examples: ['spectralRadiance']},\n\n molarMass: { description: 'Molar mass constant', examples: ['molarMass'] },\n molarMassC12: { description: 'Molar mass constant of carbon-12', examples: ['molarMassC12'] },\n gravity: { description: 'Standard acceleration of gravity (standard acceleration of free-fall on Earth)', examples: ['gravity'] },\n\n planckLength: { description: 'Planck length', examples: ['planckLength'] },\n planckMass: { description: 'Planck mass', examples: ['planckMass'] },\n planckTime: { description: 'Planck time', examples: ['planckTime'] },\n planckCharge: { description: 'Planck charge', examples: ['planckCharge'] },\n planckTemperature: { description: 'Planck temperature', examples: ['planckTemperature'] },\n\n // functions - algebra\n derivative: derivativeDocs,\n lsolve: lsolveDocs,\n lsolveAll: lsolveAllDocs,\n lup: lupDocs,\n lusolve: lusolveDocs,\n simplify: simplifyDocs,\n rationalize: rationalizeDocs,\n slu: sluDocs,\n usolve: usolveDocs,\n usolveAll: usolveAllDocs,\n qr: qrDocs,\n\n // functions - arithmetic\n abs: absDocs,\n add: addDocs,\n cbrt: cbrtDocs,\n ceil: ceilDocs,\n cube: cubeDocs,\n divide: divideDocs,\n dotDivide: dotDivideDocs,\n dotMultiply: dotMultiplyDocs,\n dotPow: dotPowDocs,\n exp: expDocs,\n expm: expmDocs,\n expm1: expm1Docs,\n fix: fixDocs,\n floor: floorDocs,\n gcd: gcdDocs,\n hypot: hypotDocs,\n lcm: lcmDocs,\n log: logDocs,\n log2: log2Docs,\n log1p: log1pDocs,\n log10: log10Docs,\n mod: modDocs,\n multiply: multiplyDocs,\n norm: normDocs,\n nthRoot: nthRootDocs,\n nthRoots: nthRootsDocs,\n pow: powDocs,\n round: roundDocs,\n sign: signDocs,\n sqrt: sqrtDocs,\n sqrtm: sqrtmDocs,\n square: squareDocs,\n subtract: subtractDocs,\n unaryMinus: unaryMinusDocs,\n unaryPlus: unaryPlusDocs,\n xgcd: xgcdDocs,\n\n // functions - bitwise\n bitAnd: bitAndDocs,\n bitNot: bitNotDocs,\n bitOr: bitOrDocs,\n bitXor: bitXorDocs,\n leftShift: leftShiftDocs,\n rightArithShift: rightArithShiftDocs,\n rightLogShift: rightLogShiftDocs,\n\n // functions - combinatorics\n bellNumbers: bellNumbersDocs,\n catalan: catalanDocs,\n composition: compositionDocs,\n stirlingS2: stirlingS2Docs,\n\n // functions - core\n config: configDocs,\n import: importDocs,\n typed: typedDocs,\n\n // functions - complex\n arg: argDocs,\n conj: conjDocs,\n re: reDocs,\n im: imDocs,\n\n // functions - expression\n evaluate: evaluateDocs,\n help: helpDocs,\n\n // functions - geometry\n distance: distanceDocs,\n intersect: intersectDocs,\n\n // functions - logical\n and: andDocs,\n not: notDocs,\n or: orDocs,\n xor: xorDocs,\n\n // functions - matrix\n concat: concatDocs,\n cross: crossDocs,\n column: columnDocs,\n ctranspose: ctransposeDocs,\n det: detDocs,\n diag: diagDocs,\n diff: diffDocs,\n dot: dotDocs,\n getMatrixDataType: getMatrixDataTypeDocs,\n identity: identityDocs,\n filter: filterDocs,\n flatten: flattenDocs,\n forEach: forEachDocs,\n inv: invDocs,\n eigs: eigsDocs,\n kron: kronDocs,\n map: mapDocs,\n ones: onesDocs,\n partitionSelect: partitionSelectDocs,\n range: rangeDocs,\n resize: resizeDocs,\n reshape: reshapeDocs,\n rotate: rotateDocs,\n rotationMatrix: rotationMatrixDocs,\n row: rowDocs,\n size: sizeDocs,\n sort: sortDocs,\n squeeze: squeezeDocs,\n subset: subsetDocs,\n trace: traceDocs,\n transpose: transposeDocs,\n zeros: zerosDocs,\n\n // functions - probability\n combinations: combinationsDocs,\n combinationsWithRep: combinationsWithRepDocs,\n // distribution: distributionDocs,\n factorial: factorialDocs,\n gamma: gammaDocs,\n kldivergence: kldivergenceDocs,\n multinomial: multinomialDocs,\n permutations: permutationsDocs,\n pickRandom: pickRandomDocs,\n random: randomDocs,\n randomInt: randomIntDocs,\n\n // functions - relational\n compare: compareDocs,\n compareNatural: compareNaturalDocs,\n compareText: compareTextDocs,\n deepEqual: deepEqualDocs,\n equal: equalDocs,\n equalText: equalTextDocs,\n larger: largerDocs,\n largerEq: largerEqDocs,\n smaller: smallerDocs,\n smallerEq: smallerEqDocs,\n unequal: unequalDocs,\n\n // functions - set\n setCartesian: setCartesianDocs,\n setDifference: setDifferenceDocs,\n setDistinct: setDistinctDocs,\n setIntersect: setIntersectDocs,\n setIsSubset: setIsSubsetDocs,\n setMultiplicity: setMultiplicityDocs,\n setPowerset: setPowersetDocs,\n setSize: setSizeDocs,\n setSymDifference: setSymDifferenceDocs,\n setUnion: setUnionDocs,\n\n // functions - special\n erf: erfDocs,\n\n // functions - statistics\n mad: madDocs,\n max: maxDocs,\n mean: meanDocs,\n median: medianDocs,\n min: minDocs,\n mode: modeDocs,\n prod: prodDocs,\n quantileSeq: quantileSeqDocs,\n std: stdDocs,\n sum: sumDocs,\n variance: varianceDocs,\n\n // functions - trigonometry\n acos: acosDocs,\n acosh: acoshDocs,\n acot: acotDocs,\n acoth: acothDocs,\n acsc: acscDocs,\n acsch: acschDocs,\n asec: asecDocs,\n asech: asechDocs,\n asin: asinDocs,\n asinh: asinhDocs,\n atan: atanDocs,\n atanh: atanhDocs,\n atan2: atan2Docs,\n cos: cosDocs,\n cosh: coshDocs,\n cot: cotDocs,\n coth: cothDocs,\n csc: cscDocs,\n csch: cschDocs,\n sec: secDocs,\n sech: sechDocs,\n sin: sinDocs,\n sinh: sinhDocs,\n tan: tanDocs,\n tanh: tanhDocs,\n\n // functions - units\n to: toDocs,\n\n // functions - utils\n clone: cloneDocs,\n format: formatDocs,\n bin: binDocs,\n oct: octDocs,\n hex: hexDocs,\n isNaN: isNaNDocs,\n isInteger: isIntegerDocs,\n isNegative: isNegativeDocs,\n isNumeric: isNumericDocs,\n hasNumericValue: hasNumericValueDocs,\n isPositive: isPositiveDocs,\n isPrime: isPrimeDocs,\n isZero: isZeroDocs,\n // print: printDocs // TODO: add documentation for print as soon as the parser supports objects.\n typeOf: typeOfDocs,\n numeric: numericDocs\n}\n","export const bignumberDocs = {\n name: 'bignumber',\n category: 'Construction',\n syntax: [\n 'bignumber(x)'\n ],\n description:\n 'Create a big number from a number or string.',\n examples: [\n '0.1 + 0.2',\n 'bignumber(0.1) + bignumber(0.2)',\n 'bignumber(\"7.2\")',\n 'bignumber(\"7.2e500\")',\n 'bignumber([0.1, 0.2, 0.3])'\n ],\n seealso: [\n 'boolean', 'complex', 'fraction', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const booleanDocs = {\n name: 'boolean',\n category: 'Construction',\n syntax: [\n 'x',\n 'boolean(x)'\n ],\n description:\n 'Convert a string or number into a boolean.',\n examples: [\n 'boolean(0)',\n 'boolean(1)',\n 'boolean(3)',\n 'boolean(\"true\")',\n 'boolean(\"false\")',\n 'boolean([1, 0, 1, 1])'\n ],\n seealso: [\n 'bignumber', 'complex', 'index', 'matrix', 'number', 'string', 'unit'\n ]\n}\n","export const complexDocs = {\n name: 'complex',\n category: 'Construction',\n syntax: [\n 'complex()',\n 'complex(re, im)',\n 'complex(string)'\n ],\n description:\n 'Create a complex number.',\n examples: [\n 'complex()',\n 'complex(2, 3)',\n 'complex(\"7 - 2i\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'index', 'matrix', 'number', 'string', 'unit'\n ]\n}\n","export const createUnitDocs = {\n name: 'createUnit',\n category: 'Construction',\n syntax: [\n 'createUnit(definitions)',\n 'createUnit(name, definition)'\n ],\n description:\n 'Create a user-defined unit and register it with the Unit type.',\n examples: [\n 'createUnit(\"foo\")',\n 'createUnit(\"knot\", {definition: \"0.514444444 m/s\", aliases: [\"knots\", \"kt\", \"kts\"]})',\n 'createUnit(\"mph\", \"1 mile/hour\")'\n ],\n seealso: [\n 'unit', 'splitUnit'\n ]\n}\n","export const fractionDocs = {\n name: 'fraction',\n category: 'Construction',\n syntax: [\n 'fraction(num)',\n 'fraction(num,den)'\n ],\n description:\n 'Create a fraction from a number or from a numerator and denominator.',\n examples: [\n 'fraction(0.125)',\n 'fraction(1, 3) + fraction(2, 5)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const indexDocs = {\n name: 'index',\n category: 'Construction',\n syntax: [\n '[start]',\n '[start:end]',\n '[start:step:end]',\n '[start1, start 2, ...]',\n '[start1:end1, start2:end2, ...]',\n '[start1:step1:end1, start2:step2:end2, ...]'\n ],\n description:\n 'Create an index to get or replace a subset of a matrix',\n examples: [\n '[]',\n '[1, 2, 3]',\n 'A = [1, 2, 3; 4, 5, 6]',\n 'A[1, :]',\n 'A[1, 2] = 50',\n 'A[0:2, 0:2] = ones(2, 2)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'matrix,', 'number', 'range', 'string', 'unit'\n ]\n}\n","export const matrixDocs = {\n name: 'matrix',\n category: 'Construction',\n syntax: [\n '[]',\n '[a1, b1, ...; a2, b2, ...]',\n 'matrix()',\n 'matrix(\"dense\")',\n 'matrix([...])'\n ],\n description:\n 'Create a matrix.',\n examples: [\n '[]',\n '[1, 2, 3]',\n '[1, 2, 3; 4, 5, 6]',\n 'matrix()',\n 'matrix([3, 4])',\n 'matrix([3, 4; 5, 6], \"sparse\")',\n 'matrix([3, 4; 5, 6], \"sparse\", \"number\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'number', 'string', 'unit', 'sparse'\n ]\n}\n","export const numberDocs = {\n name: 'number',\n category: 'Construction',\n syntax: [\n 'x',\n 'number(x)',\n 'number(unit, valuelessUnit)'\n ],\n description:\n 'Create a number or convert a string or boolean into a number.',\n examples: [\n '2',\n '2e3',\n '4.05',\n 'number(2)',\n 'number(\"7.2\")',\n 'number(true)',\n 'number([true, false, true, true])',\n 'number(unit(\"52cm\"), \"m\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'fraction', 'index', 'matrix', 'string', 'unit'\n ]\n}\n","export const sparseDocs = {\n name: 'sparse',\n category: 'Construction',\n syntax: [\n 'sparse()',\n 'sparse([a1, b1, ...; a1, b2, ...])',\n 'sparse([a1, b1, ...; a1, b2, ...], \"number\")'\n ],\n description:\n 'Create a sparse matrix.',\n examples: [\n 'sparse()',\n 'sparse([3, 4; 5, 6])',\n 'sparse([3, 0; 5, 0], \"number\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'number', 'string', 'unit', 'matrix'\n ]\n}\n","export const splitUnitDocs = {\n name: 'splitUnit',\n category: 'Construction',\n syntax: [\n 'splitUnit(unit: Unit, parts: Unit[])'\n ],\n description:\n 'Split a unit in an array of units whose sum is equal to the original unit.',\n examples: [\n 'splitUnit(1 m, [\"feet\", \"inch\"])'\n ],\n seealso: [\n 'unit', 'createUnit'\n ]\n}\n","export const stringDocs = {\n name: 'string',\n category: 'Construction',\n syntax: [\n '\"text\"',\n 'string(x)'\n ],\n description:\n 'Create a string or convert a value to a string',\n examples: [\n '\"Hello World!\"',\n 'string(4.2)',\n 'string(3 + 2i)'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'number', 'unit'\n ]\n}\n","export const unitDocs = {\n name: 'unit',\n category: 'Construction',\n syntax: [\n 'value unit',\n 'unit(value, unit)',\n 'unit(string)'\n ],\n description:\n 'Create a unit.',\n examples: [\n '5.5 mm',\n '3 inch',\n 'unit(7.1, \"kilogram\")',\n 'unit(\"23 deg\")'\n ],\n seealso: [\n 'bignumber', 'boolean', 'complex', 'index', 'matrix', 'number', 'string'\n ]\n}\n","export const falseDocs = {\n name: 'false',\n category: 'Constants',\n syntax: [\n 'false'\n ],\n description: 'Boolean value false',\n examples: [\n 'false'\n ],\n seealso: ['true']\n}\n","export const iDocs = {\n name: 'i',\n category: 'Constants',\n syntax: [\n 'i'\n ],\n description: 'Imaginary unit, defined as i*i=-1. A complex number is described as a + b*i, where a is the real part, and b is the imaginary part.',\n examples: [\n 'i',\n 'i * i',\n 'sqrt(-1)'\n ],\n seealso: []\n}\n","export const InfinityDocs = {\n name: 'Infinity',\n category: 'Constants',\n syntax: [\n 'Infinity'\n ],\n description: 'Infinity, a number which is larger than the maximum number that can be handled by a floating point number.',\n examples: [\n 'Infinity',\n '1 / 0'\n ],\n seealso: []\n}\n","export const LN2Docs = {\n name: 'LN2',\n category: 'Constants',\n syntax: [\n 'LN2'\n ],\n description: 'Returns the natural logarithm of 2, approximately equal to 0.693',\n examples: [\n 'LN2',\n 'log(2)'\n ],\n seealso: []\n}\n","export const LN10Docs = {\n name: 'LN10',\n category: 'Constants',\n syntax: [\n 'LN10'\n ],\n description: 'Returns the natural logarithm of 10, approximately equal to 2.302',\n examples: [\n 'LN10',\n 'log(10)'\n ],\n seealso: []\n}\n","export const LOG2EDocs = {\n name: 'LOG2E',\n category: 'Constants',\n syntax: [\n 'LOG2E'\n ],\n description: 'Returns the base-2 logarithm of E, approximately equal to 1.442',\n examples: [\n 'LOG2E',\n 'log(e, 2)'\n ],\n seealso: []\n}\n","export const LOG10EDocs = {\n name: 'LOG10E',\n category: 'Constants',\n syntax: [\n 'LOG10E'\n ],\n description: 'Returns the base-10 logarithm of E, approximately equal to 0.434',\n examples: [\n 'LOG10E',\n 'log(e, 10)'\n ],\n seealso: []\n}\n","export const NaNDocs = {\n name: 'NaN',\n category: 'Constants',\n syntax: [\n 'NaN'\n ],\n description: 'Not a number',\n examples: [\n 'NaN',\n '0 / 0'\n ],\n seealso: []\n}\n","export const nullDocs = {\n name: 'null',\n category: 'Constants',\n syntax: [\n 'null'\n ],\n description: 'Value null',\n examples: [\n 'null'\n ],\n seealso: ['true', 'false']\n}\n","export const phiDocs = {\n name: 'phi',\n category: 'Constants',\n syntax: [\n 'phi'\n ],\n description: 'Phi is the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Phi is defined as `(1 + sqrt(5)) / 2` and is approximately 1.618034...',\n examples: [\n 'phi'\n ],\n seealso: []\n}\n","export const SQRT12Docs = {\n name: 'SQRT1_2',\n category: 'Constants',\n syntax: [\n 'SQRT1_2'\n ],\n description: 'Returns the square root of 1/2, approximately equal to 0.707',\n examples: [\n 'SQRT1_2',\n 'sqrt(1/2)'\n ],\n seealso: []\n}\n","export const SQRT2Docs = {\n name: 'SQRT2',\n category: 'Constants',\n syntax: [\n 'SQRT2'\n ],\n description: 'Returns the square root of 2, approximately equal to 1.414',\n examples: [\n 'SQRT2',\n 'sqrt(2)'\n ],\n seealso: []\n}\n","export const tauDocs = {\n name: 'tau',\n category: 'Constants',\n syntax: [\n 'tau'\n ],\n description: 'Tau is the ratio constant of a circle\\'s circumference to radius, equal to 2 * pi, approximately 6.2832.',\n examples: [\n 'tau',\n '2 * pi'\n ],\n seealso: ['pi']\n}\n","export const trueDocs = {\n name: 'true',\n category: 'Constants',\n syntax: [\n 'true'\n ],\n description: 'Boolean value true',\n examples: [\n 'true'\n ],\n seealso: ['false']\n}\n","export const versionDocs = {\n name: 'version',\n category: 'Constants',\n syntax: [\n 'version'\n ],\n description: 'A string with the version number of math.js',\n examples: [\n 'version'\n ],\n seealso: []\n}\n","export const derivativeDocs = {\n name: 'derivative',\n category: 'Algebra',\n syntax: [\n 'derivative(expr, variable)',\n 'derivative(expr, variable, {simplify: boolean})'\n ],\n description: 'Takes the derivative of an expression expressed in parser Nodes. The derivative will be taken over the supplied variable in the second parameter. If there are multiple variables in the expression, it will return a partial derivative.',\n examples: [\n 'derivative(\"2x^3\", \"x\")',\n 'derivative(\"2x^3\", \"x\", {simplify: false})',\n 'derivative(\"2x^2 + 3x + 4\", \"x\")',\n 'derivative(\"sin(2x)\", \"x\")',\n 'f = parse(\"x^2 + x\")',\n 'x = parse(\"x\")',\n 'df = derivative(f, x)',\n 'df.evaluate({x: 3})'\n ],\n seealso: [\n 'simplify', 'parse', 'evaluate'\n ]\n}\n","export const lsolveDocs = {\n name: 'lsolve',\n category: 'Algebra',\n syntax: [\n 'x=lsolve(L, b)'\n ],\n description:\n 'Finds one solution of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lsolve(a, b)'\n ],\n seealso: [\n 'lsolveAll', 'lup', 'lusolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const lsolveAllDocs = {\n name: 'lsolveAll',\n category: 'Algebra',\n syntax: [\n 'x=lsolveAll(L, b)'\n ],\n description:\n 'Finds all solutions of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lsolve(a, b)'\n ],\n seealso: [\n 'lsolve', 'lup', 'lusolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const lupDocs = {\n name: 'lup',\n category: 'Algebra',\n syntax: [\n 'lup(m)'\n ],\n description:\n 'Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U',\n examples: [\n 'lup([[2, 1], [1, 4]])',\n 'lup(matrix([[2, 1], [1, 4]]))',\n 'lup(sparse([[2, 1], [1, 4]]))'\n ],\n seealso: [\n 'lusolve', 'lsolve', 'usolve', 'matrix', 'sparse', 'slu', 'qr'\n ]\n}\n","export const lusolveDocs = {\n name: 'lusolve',\n category: 'Algebra',\n syntax: [\n 'x=lusolve(A, b)',\n 'x=lusolve(lu, b)'\n ],\n description: 'Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.',\n examples: [\n 'a = [-2, 3; 2, 1]',\n 'b = [11, 9]',\n 'x = lusolve(a, b)'\n ],\n seealso: [\n 'lup', 'slu', 'lsolve', 'usolve', 'matrix', 'sparse'\n ]\n}\n","export const simplifyDocs = {\n name: 'simplify',\n category: 'Algebra',\n syntax: [\n 'simplify(expr)',\n 'simplify(expr, rules)'\n ],\n description: 'Simplify an expression tree.',\n examples: [\n 'simplify(\"3 + 2 / 4\")',\n 'simplify(\"2x + x\")',\n 'f = parse(\"x * (x + 2 + x)\")',\n 'simplified = simplify(f)',\n 'simplified.evaluate({x: 2})'\n ],\n seealso: [\n 'derivative', 'parse', 'evaluate'\n ]\n}\n","export const rationalizeDocs = {\n name: 'rationalize',\n category: 'Algebra',\n syntax: [\n 'rationalize(expr)',\n 'rationalize(expr, scope)',\n 'rationalize(expr, scope, detailed)'\n ],\n description: 'Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.',\n examples: [\n 'rationalize(\"2x/y - y/(x+1)\")',\n 'rationalize(\"2x/y - y/(x+1)\", true)'\n ],\n seealso: [\n 'simplify'\n ]\n}\n","export const sluDocs = {\n name: 'slu',\n category: 'Algebra',\n syntax: [\n 'slu(A, order, threshold)'\n ],\n description: 'Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U',\n examples: [\n 'slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)'\n ],\n seealso: [\n 'lusolve', 'lsolve', 'usolve', 'matrix', 'sparse', 'lup', 'qr'\n ]\n}\n","export const usolveDocs = {\n name: 'usolve',\n category: 'Algebra',\n syntax: [\n 'x=usolve(U, b)'\n ],\n description:\n 'Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.',\n examples: [\n 'x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])'\n ],\n seealso: [\n 'usolveAll', 'lup', 'lusolve', 'lsolve', 'matrix', 'sparse'\n ]\n}\n","export const usolveAllDocs = {\n name: 'usolveAll',\n category: 'Algebra',\n syntax: [\n 'x=usolve(U, b)'\n ],\n description:\n 'Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.',\n examples: [\n 'x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])'\n ],\n seealso: [\n 'usolve', 'lup', 'lusolve', 'lsolve', 'matrix', 'sparse'\n ]\n}\n","export const qrDocs = {\n name: 'qr',\n category: 'Algebra',\n syntax: [\n 'qr(A)'\n ],\n description:\n 'Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.',\n examples: [\n 'qr([[1, -1, 4], [1, 4, -2], [1, 4, 2], [1, -1, 0]])'\n ],\n seealso: [\n 'lup', 'slu', 'matrix'\n ]\n}\n","export const absDocs = {\n name: 'abs',\n category: 'Arithmetic',\n syntax: [\n 'abs(x)'\n ],\n description: 'Compute the absolute value.',\n examples: [\n 'abs(3.5)',\n 'abs(-4.2)'\n ],\n seealso: ['sign']\n}\n","export const addDocs = {\n name: 'add',\n category: 'Operators',\n syntax: [\n 'x + y',\n 'add(x, y)'\n ],\n description: 'Add two values.',\n examples: [\n 'a = 2.1 + 3.6',\n 'a - 3.6',\n '3 + 2i',\n '3 cm + 2 inch',\n '\"2.3\" + \"4\"'\n ],\n seealso: [\n 'subtract'\n ]\n}\n","export const cbrtDocs = {\n name: 'cbrt',\n category: 'Arithmetic',\n syntax: [\n 'cbrt(x)',\n 'cbrt(x, allRoots)'\n ],\n description:\n 'Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned',\n examples: [\n 'cbrt(64)',\n 'cube(4)',\n 'cbrt(-8)',\n 'cbrt(2 + 3i)',\n 'cbrt(8i)',\n 'cbrt(8i, true)',\n 'cbrt(27 m^3)'\n ],\n seealso: [\n 'square',\n 'sqrt',\n 'cube',\n 'multiply'\n ]\n}\n","export const ceilDocs = {\n name: 'ceil',\n category: 'Arithmetic',\n syntax: [\n 'ceil(x)'\n ],\n description:\n 'Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.',\n examples: [\n 'ceil(3.2)',\n 'ceil(3.8)',\n 'ceil(-4.2)'\n ],\n seealso: ['floor', 'fix', 'round']\n}\n","export const cubeDocs = {\n name: 'cube',\n category: 'Arithmetic',\n syntax: [\n 'cube(x)'\n ],\n description: 'Compute the cube of a value. The cube of x is x * x * x.',\n examples: [\n 'cube(2)',\n '2^3',\n '2 * 2 * 2'\n ],\n seealso: [\n 'multiply',\n 'square',\n 'pow'\n ]\n}\n","export const divideDocs = {\n name: 'divide',\n category: 'Operators',\n syntax: [\n 'x / y',\n 'divide(x, y)'\n ],\n description: 'Divide two values.',\n examples: [\n 'a = 2 / 3',\n 'a * 3',\n '4.5 / 2',\n '3 + 4 / 2',\n '(3 + 4) / 2',\n '18 km / 4.5'\n ],\n seealso: [\n 'multiply'\n ]\n}\n","export const dotDivideDocs = {\n name: 'dotDivide',\n category: 'Operators',\n syntax: [\n 'x ./ y',\n 'dotDivide(x, y)'\n ],\n description: 'Divide two values element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'b = [2, 1, 1; 3, 2, 5]',\n 'a ./ b'\n ],\n seealso: [\n 'multiply',\n 'dotMultiply',\n 'divide'\n ]\n}\n","export const dotMultiplyDocs = {\n name: 'dotMultiply',\n category: 'Operators',\n syntax: [\n 'x .* y',\n 'dotMultiply(x, y)'\n ],\n description: 'Multiply two values element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'b = [2, 1, 1; 3, 2, 5]',\n 'a .* b'\n ],\n seealso: [\n 'multiply',\n 'divide',\n 'dotDivide'\n ]\n}\n","export const dotPowDocs = {\n name: 'dotPow',\n category: 'Operators',\n syntax: [\n 'x .^ y',\n 'dotPow(x, y)'\n ],\n description:\n 'Calculates the power of x to y element wise.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a .^ 2'\n ],\n seealso: [\n 'pow'\n ]\n}\n","export const expDocs = {\n name: 'exp',\n category: 'Arithmetic',\n syntax: [\n 'exp(x)'\n ],\n description: 'Calculate the exponent of a value.',\n examples: [\n 'exp(1.3)',\n 'e ^ 1.3',\n 'log(exp(1.3))',\n 'x = 2.4',\n '(exp(i*x) == cos(x) + i*sin(x)) # Euler\\'s formula'\n ],\n seealso: [\n 'expm',\n 'expm1',\n 'pow',\n 'log'\n ]\n}\n","export const expmDocs = {\n name: 'expm',\n category: 'Arithmetic',\n syntax: [\n 'exp(x)'\n ],\n description: 'Compute the matrix exponential, expm(A) = e^A. ' +\n 'The matrix must be square. ' +\n 'Not to be confused with exp(a), which performs element-wise exponentiation.',\n examples: [\n 'expm([[0,2],[0,0]])'\n ],\n seealso: [\n 'exp'\n ]\n}\n","export const expm1Docs = {\n name: 'expm1',\n category: 'Arithmetic',\n syntax: [\n 'expm1(x)'\n ],\n description: 'Calculate the value of subtracting 1 from the exponential value.',\n examples: [\n 'expm1(2)',\n 'pow(e, 2) - 1',\n 'log(expm1(2) + 1)'\n ],\n seealso: [\n 'exp',\n 'pow',\n 'log'\n ]\n}\n","export const fixDocs = {\n name: 'fix',\n category: 'Arithmetic',\n syntax: [\n 'fix(x)'\n ],\n description:\n 'Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.',\n examples: [\n 'fix(3.2)',\n 'fix(3.8)',\n 'fix(-4.2)',\n 'fix(-4.8)'\n ],\n seealso: ['ceil', 'floor', 'round']\n}\n","export const floorDocs = {\n name: 'floor',\n category: 'Arithmetic',\n syntax: [\n 'floor(x)'\n ],\n description:\n 'Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.',\n examples: [\n 'floor(3.2)',\n 'floor(3.8)',\n 'floor(-4.2)'\n ],\n seealso: ['ceil', 'fix', 'round']\n}\n","export const gcdDocs = {\n name: 'gcd',\n category: 'Arithmetic',\n syntax: [\n 'gcd(a, b)',\n 'gcd(a, b, c, ...)'\n ],\n description: 'Compute the greatest common divisor.',\n examples: [\n 'gcd(8, 12)',\n 'gcd(-4, 6)',\n 'gcd(25, 15, -10)'\n ],\n seealso: ['lcm', 'xgcd']\n}\n","export const hypotDocs = {\n name: 'hypot',\n category: 'Arithmetic',\n syntax: [\n 'hypot(a, b, c, ...)',\n 'hypot([a, b, c, ...])'\n ],\n description: 'Calculate the hypotenusa of a list with values. ',\n examples: [\n 'hypot(3, 4)',\n 'sqrt(3^2 + 4^2)',\n 'hypot(-2)',\n 'hypot([3, 4, 5])'\n ],\n seealso: ['abs', 'norm']\n}\n","export const lcmDocs = {\n name: 'lcm',\n category: 'Arithmetic',\n syntax: [\n 'lcm(x, y)'\n ],\n description: 'Compute the least common multiple.',\n examples: [\n 'lcm(4, 6)',\n 'lcm(6, 21)',\n 'lcm(6, 21, 5)'\n ],\n seealso: ['gcd']\n}\n","export const logDocs = {\n name: 'log',\n category: 'Arithmetic',\n syntax: [\n 'log(x)',\n 'log(x, base)'\n ],\n description: 'Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).',\n examples: [\n 'log(3.5)',\n 'a = log(2.4)',\n 'exp(a)',\n '10 ^ 4',\n 'log(10000, 10)',\n 'log(10000) / log(10)',\n 'b = log(1024, 2)',\n '2 ^ b'\n ],\n seealso: [\n 'exp',\n 'log1p',\n 'log2',\n 'log10'\n ]\n}\n","export const log2Docs = {\n name: 'log2',\n category: 'Arithmetic',\n syntax: [\n 'log2(x)'\n ],\n description: 'Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.',\n examples: [\n 'log2(0.03125)',\n 'log2(16)',\n 'log2(16) / log2(2)',\n 'pow(2, 4)'\n ],\n seealso: [\n 'exp',\n 'log1p',\n 'log',\n 'log10'\n ]\n}\n","export const log1pDocs = {\n name: 'log1p',\n category: 'Arithmetic',\n syntax: [\n 'log1p(x)',\n 'log1p(x, base)'\n ],\n description: 'Calculate the logarithm of a `value+1`',\n examples: [\n 'log1p(2.5)',\n 'exp(log1p(1.4))',\n 'pow(10, 4)',\n 'log1p(9999, 10)',\n 'log1p(9999) / log(10)'\n ],\n seealso: [\n 'exp',\n 'log',\n 'log2',\n 'log10'\n ]\n}\n","export const log10Docs = {\n name: 'log10',\n category: 'Arithmetic',\n syntax: [\n 'log10(x)'\n ],\n description: 'Compute the 10-base logarithm of a value.',\n examples: [\n 'log10(0.00001)',\n 'log10(10000)',\n '10 ^ 4',\n 'log(10000) / log(10)',\n 'log(10000, 10)'\n ],\n seealso: [\n 'exp',\n 'log'\n ]\n}\n","export const modDocs = {\n name: 'mod',\n category: 'Operators',\n syntax: [\n 'x % y',\n 'x mod y',\n 'mod(x, y)'\n ],\n description:\n 'Calculates the modulus, the remainder of an integer division.',\n examples: [\n '7 % 3',\n '11 % 2',\n '10 mod 4',\n 'isOdd(x) = x % 2',\n 'isOdd(2)',\n 'isOdd(3)'\n ],\n seealso: ['divide']\n}\n","export const multiplyDocs = {\n name: 'multiply',\n category: 'Operators',\n syntax: [\n 'x * y',\n 'multiply(x, y)'\n ],\n description: 'multiply two values.',\n examples: [\n 'a = 2.1 * 3.4',\n 'a / 3.4',\n '2 * 3 + 4',\n '2 * (3 + 4)',\n '3 * 2.1 km'\n ],\n seealso: [\n 'divide'\n ]\n}\n","export const normDocs = {\n name: 'norm',\n category: 'Arithmetic',\n syntax: [\n 'norm(x)',\n 'norm(x, p)'\n ],\n description: 'Calculate the norm of a number, vector or matrix.',\n examples: [\n 'abs(-3.5)',\n 'norm(-3.5)',\n 'norm(3 - 4i)',\n 'norm([1, 2, -3], Infinity)',\n 'norm([1, 2, -3], -Infinity)',\n 'norm([3, 4], 2)',\n 'norm([[1, 2], [3, 4]], 1)',\n 'norm([[1, 2], [3, 4]], \"inf\")',\n 'norm([[1, 2], [3, 4]], \"fro\")'\n ]\n}\n","export const nthRootDocs = {\n name: 'nthRoot',\n category: 'Arithmetic',\n syntax: [\n 'nthRoot(a)',\n 'nthRoot(a, root)'\n ],\n description: 'Calculate the nth root of a value. ' +\n 'The principal nth root of a positive real number A, ' +\n 'is the positive real solution of the equation \"x^root = A\".',\n examples: [\n '4 ^ 3',\n 'nthRoot(64, 3)',\n 'nthRoot(9, 2)',\n 'sqrt(9)'\n ],\n seealso: [\n 'nthRoots',\n 'pow',\n 'sqrt'\n ]\n}\n","export const nthRootsDocs = {\n name: 'nthRoots',\n category: 'Arithmetic',\n syntax: [\n 'nthRoots(A)',\n 'nthRoots(A, root)'\n ],\n description: ('' +\n 'Calculate the nth roots of a value. ' +\n 'An nth root of a positive real number A, ' +\n 'is a positive real solution of the equation \"x^root = A\". ' +\n 'This function returns an array of complex values.'\n ),\n examples: [\n 'nthRoots(1)',\n 'nthRoots(1, 3)'\n ],\n seealso: [\n 'sqrt',\n 'pow',\n 'nthRoot'\n ]\n}\n","export const powDocs = {\n name: 'pow',\n category: 'Operators',\n syntax: [\n 'x ^ y',\n 'pow(x, y)'\n ],\n description:\n 'Calculates the power of x to y, x^y.',\n examples: [\n '2^3',\n '2*2*2',\n '1 + e ^ (pi * i)'\n ],\n seealso: [\n 'multiply',\n 'nthRoot',\n 'nthRoots',\n 'sqrt'\n ]\n}\n","export const roundDocs = {\n name: 'round',\n category: 'Arithmetic',\n syntax: [\n 'round(x)',\n 'round(x, n)'\n ],\n description:\n 'round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.',\n examples: [\n 'round(3.2)',\n 'round(3.8)',\n 'round(-4.2)',\n 'round(-4.8)',\n 'round(pi, 3)',\n 'round(123.45678, 2)'\n ],\n seealso: ['ceil', 'floor', 'fix']\n}\n","export const signDocs = {\n name: 'sign',\n category: 'Arithmetic',\n syntax: [\n 'sign(x)'\n ],\n description:\n 'Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.',\n examples: [\n 'sign(3.5)',\n 'sign(-4.2)',\n 'sign(0)'\n ],\n seealso: [\n 'abs'\n ]\n}\n","export const sqrtDocs = {\n name: 'sqrt',\n category: 'Arithmetic',\n syntax: [\n 'sqrt(x)'\n ],\n description:\n 'Compute the square root value. If x = y * y, then y is the square root of x.',\n examples: [\n 'sqrt(25)',\n '5 * 5',\n 'sqrt(-1)'\n ],\n seealso: [\n 'square',\n 'sqrtm',\n 'multiply',\n 'nthRoot',\n 'nthRoots',\n 'pow'\n ]\n}\n","export const sqrtmDocs = {\n name: 'sqrtm',\n category: 'Arithmetic',\n syntax: [\n 'sqrtm(x)'\n ],\n description:\n 'Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.',\n examples: [\n 'sqrtm([[1, 2], [3, 4]])'\n ],\n seealso: [\n 'sqrt',\n 'abs',\n 'square',\n 'multiply'\n ]\n}\n","export const squareDocs = {\n name: 'square',\n category: 'Arithmetic',\n syntax: [\n 'square(x)'\n ],\n description:\n 'Compute the square of a value. The square of x is x * x.',\n examples: [\n 'square(3)',\n 'sqrt(9)',\n '3^2',\n '3 * 3'\n ],\n seealso: [\n 'multiply',\n 'pow',\n 'sqrt',\n 'cube'\n ]\n}\n","export const subtractDocs = {\n name: 'subtract',\n category: 'Operators',\n syntax: [\n 'x - y',\n 'subtract(x, y)'\n ],\n description: 'subtract two values.',\n examples: [\n 'a = 5.3 - 2',\n 'a + 2',\n '2/3 - 1/6',\n '2 * 3 - 3',\n '2.1 km - 500m'\n ],\n seealso: [\n 'add'\n ]\n}\n","export const unaryMinusDocs = {\n name: 'unaryMinus',\n category: 'Operators',\n syntax: [\n '-x',\n 'unaryMinus(x)'\n ],\n description:\n 'Inverse the sign of a value. Converts booleans and strings to numbers.',\n examples: [\n '-4.5',\n '-(-5.6)',\n '-\"22\"'\n ],\n seealso: [\n 'add', 'subtract', 'unaryPlus'\n ]\n}\n","export const unaryPlusDocs = {\n name: 'unaryPlus',\n category: 'Operators',\n syntax: [\n '+x',\n 'unaryPlus(x)'\n ],\n description:\n 'Converts booleans and strings to numbers.',\n examples: [\n '+true',\n '+\"2\"'\n ],\n seealso: [\n 'add', 'subtract', 'unaryMinus'\n ]\n}\n","export const xgcdDocs = {\n name: 'xgcd',\n category: 'Arithmetic',\n syntax: [\n 'xgcd(a, b)'\n ],\n description: 'Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.',\n examples: [\n 'xgcd(8, 12)',\n 'gcd(8, 12)',\n 'xgcd(36163, 21199)'\n ],\n seealso: ['gcd', 'lcm']\n}\n","export const bitAndDocs = {\n name: 'bitAnd',\n category: 'Bitwise',\n syntax: [\n 'x & y',\n 'bitAnd(x, y)'\n ],\n description: 'Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0',\n examples: [\n '5 & 3',\n 'bitAnd(53, 131)',\n '[1, 12, 31] & 42'\n ],\n seealso: [\n 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitNotDocs = {\n name: 'bitNot',\n category: 'Bitwise',\n syntax: [\n '~x',\n 'bitNot(x)'\n ],\n description: 'Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.',\n examples: [\n '~1',\n '~2',\n 'bitNot([2, -3, 4])'\n ],\n seealso: [\n 'bitAnd', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitOrDocs = {\n name: 'bitOr',\n category: 'Bitwise',\n syntax: [\n 'x | y',\n 'bitOr(x, y)'\n ],\n description: 'Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.',\n examples: [\n '5 | 3',\n 'bitOr([1, 2, 3], 4)'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitXor', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const bitXorDocs = {\n name: 'bitXor',\n category: 'Bitwise',\n syntax: [\n 'bitXor(x, y)'\n ],\n description: 'Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.',\n examples: [\n 'bitOr(1, 2)',\n 'bitXor([2, 3, 4], 4)'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'leftShift', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const leftShiftDocs = {\n name: 'leftShift',\n category: 'Bitwise',\n syntax: [\n 'x << y',\n 'leftShift(x, y)'\n ],\n description: 'Bitwise left logical shift of a value x by y number of bits.',\n examples: [\n '4 << 1',\n '8 >> 1'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'rightArithShift', 'rightLogShift'\n ]\n}\n","export const rightArithShiftDocs = {\n name: 'rightArithShift',\n category: 'Bitwise',\n syntax: [\n 'x >> y',\n 'rightArithShift(x, y)'\n ],\n description: 'Bitwise right arithmetic shift of a value x by y number of bits.',\n examples: [\n '8 >> 1',\n '4 << 1',\n '-12 >> 2'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightLogShift'\n ]\n}\n","export const rightLogShiftDocs = {\n name: 'rightLogShift',\n category: 'Bitwise',\n syntax: [\n 'x >>> y',\n 'rightLogShift(x, y)'\n ],\n description: 'Bitwise right logical shift of a value x by y number of bits.',\n examples: [\n '8 >>> 1',\n '4 << 1',\n '-12 >>> 2'\n ],\n seealso: [\n 'bitAnd', 'bitNot', 'bitOr', 'bitXor', 'leftShift', 'rightArithShift'\n ]\n}\n","export const bellNumbersDocs = {\n name: 'bellNumbers',\n category: 'Combinatorics',\n syntax: [\n 'bellNumbers(n)'\n ],\n description: 'The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.',\n examples: [\n 'bellNumbers(3)',\n 'bellNumbers(8)'\n ],\n seealso: ['stirlingS2']\n}\n","export const catalanDocs = {\n name: 'catalan',\n category: 'Combinatorics',\n syntax: [\n 'catalan(n)'\n ],\n description: 'The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.',\n examples: [\n 'catalan(3)',\n 'catalan(8)'\n ],\n seealso: ['bellNumbers']\n}\n","export const compositionDocs = {\n name: 'composition',\n category: 'Combinatorics',\n syntax: [\n 'composition(n, k)'\n ],\n description: 'The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.',\n examples: [\n 'composition(5, 3)'\n ],\n seealso: ['combinations']\n}\n","export const stirlingS2Docs = {\n name: 'stirlingS2',\n category: 'Combinatorics',\n syntax: [\n 'stirlingS2(n, k)'\n ],\n description: 'he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.',\n examples: [\n 'stirlingS2(5, 3)'\n ],\n seealso: ['bellNumbers']\n}\n","export const configDocs = {\n name: 'config',\n category: 'Core',\n syntax: [\n 'config()',\n 'config(options)'\n ],\n description: 'Get configuration or change configuration.',\n examples: [\n 'config()',\n '1/3 + 1/4',\n 'config({number: \"Fraction\"})',\n '1/3 + 1/4'\n ],\n seealso: []\n}\n","export const importDocs = {\n name: 'import',\n category: 'Core',\n syntax: [\n 'import(functions)',\n 'import(functions, options)'\n ],\n description: 'Import functions or constants from an object.',\n examples: [\n 'import({myFn: f(x)=x^2, myConstant: 32 })',\n 'myFn(2)',\n 'myConstant'\n ],\n seealso: []\n}\n","export const typedDocs = {\n name: 'typed',\n category: 'Core',\n syntax: [\n 'typed(signatures)',\n 'typed(name, signatures)'\n ],\n description: 'Create a typed function.',\n examples: [\n 'double = typed({ \"number, number\": f(x)=x+x })',\n 'double(2)',\n 'double(\"hello\")'\n ],\n seealso: []\n}\n","export const argDocs = {\n name: 'arg',\n category: 'Complex',\n syntax: [\n 'arg(x)'\n ],\n description:\n 'Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).',\n examples: [\n 'arg(2 + 2i)',\n 'atan2(3, 2)',\n 'arg(2 + 3i)'\n ],\n seealso: [\n 're',\n 'im',\n 'conj',\n 'abs'\n ]\n}\n","export const conjDocs = {\n name: 'conj',\n category: 'Complex',\n syntax: [\n 'conj(x)'\n ],\n description:\n 'Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.',\n examples: [\n 'conj(2 + 3i)',\n 'conj(2 - 3i)',\n 'conj(-5.2i)'\n ],\n seealso: [\n 're',\n 'im',\n 'abs',\n 'arg'\n ]\n}\n","export const reDocs = {\n name: 're',\n category: 'Complex',\n syntax: [\n 're(x)'\n ],\n description: 'Get the real part of a complex number.',\n examples: [\n 're(2 + 3i)',\n 'im(2 + 3i)',\n 're(-5.2i)',\n 're(2.4)'\n ],\n seealso: [\n 'im',\n 'conj',\n 'abs',\n 'arg'\n ]\n}\n","export const imDocs = {\n name: 'im',\n category: 'Complex',\n syntax: [\n 'im(x)'\n ],\n description: 'Get the imaginary part of a complex number.',\n examples: [\n 'im(2 + 3i)',\n 're(2 + 3i)',\n 'im(-5.2i)',\n 'im(2.4)'\n ],\n seealso: [\n 're',\n 'conj',\n 'abs',\n 'arg'\n ]\n}\n","export const evaluateDocs = {\n name: 'evaluate',\n category: 'Expression',\n syntax: [\n 'evaluate(expression)',\n 'evaluate([expr1, expr2, expr3, ...])'\n ],\n description: 'Evaluate an expression or an array with expressions.',\n examples: [\n 'evaluate(\"2 + 3\")',\n 'evaluate(\"sqrt(\" + 4 + \")\")'\n ],\n seealso: []\n}\n","export const helpDocs = {\n name: 'help',\n category: 'Expression',\n syntax: [\n 'help(object)',\n 'help(string)'\n ],\n description: 'Display documentation on a function or data type.',\n examples: [\n 'help(sqrt)',\n 'help(\"complex\")'\n ],\n seealso: []\n}\n","export const distanceDocs = {\n name: 'distance',\n category: 'Geometry',\n syntax: [\n 'distance([x1, y1], [x2, y2])',\n 'distance([[x1, y1], [x2, y2]])'\n ],\n description: 'Calculates the Euclidean distance between two points.',\n examples: [\n 'distance([0,0], [4,4])',\n 'distance([[0,0], [4,4]])'\n ],\n seealso: []\n}\n","export const intersectDocs = {\n name: 'intersect',\n category: 'Geometry',\n syntax: [\n 'intersect(expr1, expr2, expr3, expr4)',\n 'intersect(expr1, expr2, expr3)'\n ],\n description: 'Computes the intersection point of lines and/or planes.',\n examples: [\n 'intersect([0, 0], [10, 10], [10, 0], [0, 10])',\n 'intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6])'\n ],\n seealso: []\n}\n","export const andDocs = {\n name: 'and',\n category: 'Logical',\n syntax: [\n 'x and y',\n 'and(x, y)'\n ],\n description: 'Logical and. Test whether two values are both defined with a nonzero/nonempty value.',\n examples: [\n 'true and false',\n 'true and true',\n '2 and 4'\n ],\n seealso: [\n 'not', 'or', 'xor'\n ]\n}\n","export const notDocs = {\n name: 'not',\n category: 'Logical',\n syntax: [\n 'not x',\n 'not(x)'\n ],\n description: 'Logical not. Flips the boolean value of given argument.',\n examples: [\n 'not true',\n 'not false',\n 'not 2',\n 'not 0'\n ],\n seealso: [\n 'and', 'or', 'xor'\n ]\n}\n","export const orDocs = {\n name: 'or',\n category: 'Logical',\n syntax: [\n 'x or y',\n 'or(x, y)'\n ],\n description: 'Logical or. Test if at least one value is defined with a nonzero/nonempty value.',\n examples: [\n 'true or false',\n 'false or false',\n '0 or 4'\n ],\n seealso: [\n 'not', 'and', 'xor'\n ]\n}\n","export const xorDocs = {\n name: 'xor',\n category: 'Logical',\n syntax: [\n 'x xor y',\n 'xor(x, y)'\n ],\n description: 'Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.',\n examples: [\n 'true xor false',\n 'false xor false',\n 'true xor true',\n '0 xor 4'\n ],\n seealso: [\n 'not', 'and', 'or'\n ]\n}\n","export const concatDocs = {\n name: 'concat',\n category: 'Matrix',\n syntax: [\n 'concat(A, B, C, ...)',\n 'concat(A, B, C, ..., dim)'\n ],\n description: 'Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.',\n examples: [\n 'A = [1, 2; 5, 6]',\n 'B = [3, 4; 7, 8]',\n 'concat(A, B)',\n 'concat(A, B, 1)',\n 'concat(A, B, 2)'\n ],\n seealso: [\n 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const crossDocs = {\n name: 'cross',\n category: 'Matrix',\n syntax: [\n 'cross(A, B)'\n ],\n description: 'Calculate the cross product for two vectors in three dimensional space.',\n examples: [\n 'cross([1, 1, 0], [0, 1, 1])',\n 'cross([3, -3, 1], [4, 9, 2])',\n 'cross([2, 3, 4], [5, 6, 7])'\n ],\n seealso: [\n 'multiply',\n 'dot'\n ]\n}\n","export const columnDocs = {\n name: 'column',\n category: 'Matrix',\n syntax: [\n 'column(x, index)'\n ],\n description: 'Return a column from a matrix or array.',\n examples: [\n 'A = [[1, 2], [3, 4]]',\n 'column(A, 1)',\n 'column(A, 2)'\n ],\n seealso: ['row']\n}\n","export const ctransposeDocs = {\n name: 'ctranspose',\n category: 'Matrix',\n syntax: [\n 'x\\'',\n 'ctranspose(x)'\n ],\n description: 'Complex Conjugate and Transpose a matrix',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a\\'',\n 'ctranspose(a)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'zeros'\n ]\n}\n","export const detDocs = {\n name: 'det',\n category: 'Matrix',\n syntax: [\n 'det(x)'\n ],\n description: 'Calculate the determinant of a matrix',\n examples: [\n 'det([1, 2; 3, 4])',\n 'det([-2, 2, 3; -1, 1, 3; 2, 0, -1])'\n ],\n seealso: [\n 'concat', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const diagDocs = {\n name: 'diag',\n category: 'Matrix',\n syntax: [\n 'diag(x)',\n 'diag(x, k)'\n ],\n description: 'Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.',\n examples: [\n 'diag(1:3)',\n 'diag(1:3, 1)',\n 'a = [1, 2, 3; 4, 5, 6; 7, 8, 9]',\n 'diag(a)'\n ],\n seealso: [\n 'concat', 'det', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const diffDocs = {\n name: 'diff',\n category: 'Matrix',\n syntax: [\n 'diff(arr)',\n 'diff(arr, dim)'\n ],\n description: [\n 'Create a new matrix or array with the difference of the passed matrix or array.',\n 'Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference',\n 'If no dimension parameter is passed it is assumed as dimension 0',\n 'Dimension is zero-based in javascript and one-based in the parser',\n 'Arrays must be \\'rectangular\\' meaning arrays like [1, 2]',\n 'If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays'\n ],\n examples: [\n 'diff([1, 2, 4, 7, 0])',\n 'diff([1, 2, 4, 7, 0], 0)',\n 'diff(matrix([1, 2, 4, 7, 0]))',\n 'diff([[1, 2], [3, 4]])',\n 'diff([[1, 2], [3, 4]], 0)',\n 'diff([[1, 2], [3, 4]], 1)',\n 'diff([[1, 2], [3, 4]], bignumber(1))',\n 'diff(matrix([[1, 2], [3, 4]]), 1)',\n 'diff([[1, 2], matrix([3, 4])], 1)'\n\n ],\n seealso: ['subtract', 'partitionSelect']\n}\n","export const dotDocs = {\n name: 'dot',\n category: 'Matrix',\n syntax: [\n 'dot(A, B)',\n 'A * B'\n ],\n description: 'Calculate the dot product of two vectors. ' +\n 'The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] ' +\n 'is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn',\n examples: [\n 'dot([2, 4, 1], [2, 2, 3])',\n '[2, 4, 1] * [2, 2, 3]'\n ],\n seealso: [\n 'multiply',\n 'cross'\n ]\n}\n","export const getMatrixDataTypeDocs = {\n name: 'getMatrixDataType',\n category: 'Matrix',\n syntax: [\n 'getMatrixDataType(x)'\n ],\n description: 'Find the data type of all elements in a matrix or array, ' +\n 'for example \"number\" if all items are a number ' +\n 'and \"Complex\" if all values are complex numbers. ' +\n 'If a matrix contains more than one data type, it will return \"mixed\".',\n examples: [\n 'getMatrixDataType([1, 2, 3])',\n 'getMatrixDataType([[5 cm], [2 inch]])',\n 'getMatrixDataType([1, \"text\"])',\n 'getMatrixDataType([1, bignumber(4)])'\n ],\n seealso: ['matrix', 'sparse', 'typeOf']\n}\n","export const identityDocs = {\n name: 'identity',\n category: 'Matrix',\n syntax: [\n 'identity(n)',\n 'identity(m, n)',\n 'identity([m, n])'\n ],\n description: 'Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.',\n examples: [\n 'identity(3)',\n 'identity(3, 5)',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'identity(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const filterDocs = {\n name: 'filter',\n category: 'Matrix',\n syntax: [\n 'filter(x, test)'\n ],\n description: 'Filter items in a matrix.',\n examples: [\n 'isPositive(x) = x > 0',\n 'filter([6, -2, -1, 4, 3], isPositive)',\n 'filter([6, -2, 0, 1, 0], x != 0)'\n ],\n seealso: ['sort', 'map', 'forEach']\n}\n","export const flattenDocs = {\n name: 'flatten',\n category: 'Matrix',\n syntax: [\n 'flatten(x)'\n ],\n description: 'Flatten a multi dimensional matrix into a single dimensional matrix.',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'size(a)',\n 'b = flatten(a)',\n 'size(b)'\n ],\n seealso: [\n 'concat', 'resize', 'size', 'squeeze'\n ]\n}\n","export const forEachDocs = {\n name: 'forEach',\n category: 'Matrix',\n syntax: [\n 'forEach(x, callback)'\n ],\n description: 'Iterates over all elements of a matrix/array, and executes the given callback function.',\n examples: [\n 'forEach([1, 2, 3], function(val) { console.log(val) })'\n ],\n seealso: ['map', 'sort', 'filter']\n}\n","export const invDocs = {\n name: 'inv',\n category: 'Matrix',\n syntax: [\n 'inv(x)'\n ],\n description: 'Calculate the inverse of a matrix',\n examples: [\n 'inv([1, 2; 3, 4])',\n 'inv(4)',\n '1 / 4'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const eigsDocs = {\n name: 'eigs',\n category: 'Matrix',\n syntax: [\n 'eigs(x)'\n ],\n description: 'Calculate the eigenvalues and eigenvectors of a real symmetric matrix',\n examples: [\n 'eigs([[5, 2.3], [2.3, 1]])'\n ],\n seealso: [\n 'inv'\n ]\n}\n","export const kronDocs = {\n name: 'kron',\n category: 'Matrix',\n syntax: [\n 'kron(x, y)'\n ],\n description: 'Calculates the kronecker product of 2 matrices or vectors.',\n examples: [\n 'kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])',\n 'kron([1,1], [2,3,4])'\n ],\n seealso: [\n 'multiply', 'dot', 'cross'\n ]\n}\n","export const mapDocs = {\n name: 'map',\n category: 'Matrix',\n syntax: [\n 'map(x, callback)'\n ],\n description: 'Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.',\n examples: [\n 'map([1, 2, 3], square)'\n ],\n seealso: ['filter', 'forEach']\n}\n","export const onesDocs = {\n name: 'ones',\n category: 'Matrix',\n syntax: [\n 'ones(m)',\n 'ones(m, n)',\n 'ones(m, n, p, ...)',\n 'ones([m])',\n 'ones([m, n])',\n 'ones([m, n, p, ...])'\n ],\n description: 'Create a matrix containing ones.',\n examples: [\n 'ones(3)',\n 'ones(3, 5)',\n 'ones([2,3]) * 4.5',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'ones(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const partitionSelectDocs = {\n name: 'partitionSelect',\n category: 'Matrix',\n syntax: [\n 'partitionSelect(x, k)',\n 'partitionSelect(x, k, compare)'\n ],\n description: 'Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.',\n examples: [\n 'partitionSelect([5, 10, 1], 2)',\n 'partitionSelect([\"C\", \"B\", \"A\", \"D\"], 1)'\n ],\n seealso: ['sort']\n}\n","export const rangeDocs = {\n name: 'range',\n category: 'Type',\n syntax: [\n 'start:end',\n 'start:step:end',\n 'range(start, end)',\n 'range(start, end, step)',\n 'range(string)'\n ],\n description:\n 'Create a range. Lower bound of the range is included, upper bound is excluded.',\n examples: [\n '1:5',\n '3:-1:-3',\n 'range(3, 7)',\n 'range(0, 12, 2)',\n 'range(\"4:10\")',\n 'a = [1, 2, 3, 4; 5, 6, 7, 8]',\n 'a[1:2, 1:2]'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const resizeDocs = {\n name: 'resize',\n category: 'Matrix',\n syntax: [\n 'resize(x, size)',\n 'resize(x, size, defaultValue)'\n ],\n description: 'Resize a matrix.',\n examples: [\n 'resize([1,2,3,4,5], [3])',\n 'resize([1,2,3], [5])',\n 'resize([1,2,3], [5], -1)',\n 'resize(2, [2, 3])',\n 'resize(\"hello\", [8], \"!\")'\n ],\n seealso: [\n 'size', 'subset', 'squeeze', 'reshape'\n ]\n}\n","export const reshapeDocs = {\n name: 'reshape',\n category: 'Matrix',\n syntax: [\n 'reshape(x, sizes)'\n ],\n description: 'Reshape a multi dimensional array to fit the specified dimensions.',\n examples: [\n 'reshape([1, 2, 3, 4, 5, 6], [2, 3])',\n 'reshape([[1, 2], [3, 4]], [1, 4])',\n 'reshape([[1, 2], [3, 4]], [4])'\n ],\n seealso: [\n 'size', 'squeeze', 'resize'\n ]\n}\n","export const rotateDocs = {\n name: 'rotate',\n category: 'Matrix',\n syntax: [\n 'rotate(w, theta)',\n 'rotate(w, theta, v)'\n ],\n description: 'Returns a 2-D rotation matrix (2x2) for a given angle (in radians). ' +\n 'Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.',\n examples: [\n 'rotate([1, 0], math.pi / 2)',\n 'rotate(matrix([1, 0]), unit(\"35deg\"))',\n 'rotate([1, 0, 0], unit(\"90deg\"), [0, 0, 1])',\n 'rotate(matrix([1, 0, 0]), unit(\"90deg\"), matrix([0, 0, 1]))'\n ],\n seealso: [\n 'matrix', 'rotationMatrix'\n ]\n}\n","export const rotationMatrixDocs = {\n name: 'rotationMatrix',\n category: 'Matrix',\n syntax: [\n 'rotationMatrix(theta)',\n 'rotationMatrix(theta, v)',\n 'rotationMatrix(theta, v, format)'\n ],\n description: 'Returns a 2-D rotation matrix (2x2) for a given angle (in radians). ' +\n 'Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.',\n examples: [\n 'rotationMatrix(pi / 2)',\n 'rotationMatrix(unit(\"45deg\"), [0, 0, 1])',\n 'rotationMatrix(1, matrix([0, 0, 1]), \"sparse\")'\n ],\n seealso: [\n 'cos', 'sin'\n ]\n}\n","export const rowDocs = {\n name: 'row',\n category: 'Matrix',\n syntax: [\n 'row(x, index)'\n ],\n description: 'Return a row from a matrix or array.',\n examples: [\n 'A = [[1, 2], [3, 4]]',\n 'row(A, 1)',\n 'row(A, 2)'\n ],\n seealso: ['column']\n}\n","export const sizeDocs = {\n name: 'size',\n category: 'Matrix',\n syntax: [\n 'size(x)'\n ],\n description: 'Calculate the size of a matrix.',\n examples: [\n 'size(2.3)',\n 'size(\"hello world\")',\n 'a = [1, 2; 3, 4; 5, 6]',\n 'size(a)',\n 'size(1:6)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const sortDocs = {\n name: 'sort',\n category: 'Matrix',\n syntax: [\n 'sort(x)',\n 'sort(x, compare)'\n ],\n description: 'Sort the items in a matrix. Compare can be a string \"asc\", \"desc\", \"natural\", or a custom sort function.',\n examples: [\n 'sort([5, 10, 1])',\n 'sort([\"C\", \"B\", \"A\", \"D\"])',\n 'sortByLength(a, b) = size(a)[1] - size(b)[1]',\n 'sort([\"Langdon\", \"Tom\", \"Sara\"], sortByLength)',\n 'sort([\"10\", \"1\", \"2\"], \"natural\")'\n ],\n seealso: ['map', 'filter', 'forEach']\n}\n","export const squeezeDocs = {\n name: 'squeeze',\n category: 'Matrix',\n syntax: [\n 'squeeze(x)'\n ],\n description: 'Remove inner and outer singleton dimensions from a matrix.',\n examples: [\n 'a = zeros(3,2,1)',\n 'size(squeeze(a))',\n 'b = zeros(1,1,3)',\n 'size(squeeze(b))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'subset', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const subsetDocs = {\n name: 'subset',\n category: 'Matrix',\n syntax: [\n 'value(index)',\n 'value(index) = replacement',\n 'subset(value, [index])',\n 'subset(value, [index], replacement)'\n ],\n description: 'Get or set a subset of a matrix or string. ' +\n 'Indexes are one-based. ' +\n 'Both the ranges lower-bound and upper-bound are included.',\n examples: [\n 'd = [1, 2; 3, 4]',\n 'e = []',\n 'e[1, 1:2] = [5, 6]',\n 'e[2, :] = [7, 8]',\n 'f = d * e',\n 'f[2, 1]',\n 'f[:, 1]'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'trace', 'transpose', 'zeros'\n ]\n}\n","export const traceDocs = {\n name: 'trace',\n category: 'Matrix',\n syntax: [\n 'trace(A)'\n ],\n description: 'Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.',\n examples: [\n 'A = [1, 2, 3; -1, 2, 3; 2, 0, 3]',\n 'trace(A)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'\n ]\n}\n","export const transposeDocs = {\n name: 'transpose',\n category: 'Matrix',\n syntax: [\n 'x\\'',\n 'transpose(x)'\n ],\n description: 'Transpose a matrix',\n examples: [\n 'a = [1, 2, 3; 4, 5, 6]',\n 'a\\'',\n 'transpose(a)'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'zeros'\n ]\n}\n","export const zerosDocs = {\n name: 'zeros',\n category: 'Matrix',\n syntax: [\n 'zeros(m)',\n 'zeros(m, n)',\n 'zeros(m, n, p, ...)',\n 'zeros([m])',\n 'zeros([m, n])',\n 'zeros([m, n, p, ...])'\n ],\n description: 'Create a matrix containing zeros.',\n examples: [\n 'zeros(3)',\n 'zeros(3, 5)',\n 'a = [1, 2, 3; 4, 5, 6]',\n 'zeros(size(a))'\n ],\n seealso: [\n 'concat', 'det', 'diag', 'identity', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose'\n ]\n}\n","export const combinationsDocs = {\n name: 'combinations',\n category: 'Probability',\n syntax: [\n 'combinations(n, k)'\n ],\n description: 'Compute the number of combinations of n items taken k at a time',\n examples: [\n 'combinations(7, 5)'\n ],\n seealso: ['combinationsWithRep', 'permutations', 'factorial']\n}\n","export const combinationsWithRepDocs = {\n name: 'combinationsWithRep',\n category: 'Probability',\n syntax: [\n 'combinationsWithRep(n, k)'\n ],\n description: 'Compute the number of combinations of n items taken k at a time with replacements.',\n examples: [\n 'combinationsWithRep(7, 5)'\n ],\n seealso: ['combinations', 'permutations', 'factorial']\n}\n","export const factorialDocs = {\n name: 'factorial',\n category: 'Probability',\n syntax: [\n 'n!',\n 'factorial(n)'\n ],\n description: 'Compute the factorial of a value',\n examples: [\n '5!',\n '5 * 4 * 3 * 2 * 1',\n '3!'\n ],\n seealso: ['combinations', 'combinationsWithRep', 'permutations', 'gamma']\n}\n","export const gammaDocs = {\n name: 'gamma',\n category: 'Probability',\n syntax: [\n 'gamma(n)'\n ],\n description: 'Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.',\n examples: [\n 'gamma(4)',\n '3!',\n 'gamma(1/2)',\n 'sqrt(pi)'\n ],\n seealso: ['factorial']\n}\n","export const kldivergenceDocs = {\n name: 'kldivergence',\n category: 'Probability',\n syntax: [\n 'kldivergence(x, y)'\n ],\n description: 'Calculate the Kullback-Leibler (KL) divergence between two distributions.',\n examples: [\n 'kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])'\n ],\n seealso: []\n}\n","export const multinomialDocs = {\n name: 'multinomial',\n category: 'Probability',\n syntax: [\n 'multinomial(A)'\n ],\n description: 'Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.',\n examples: [\n 'multinomial([1, 2, 1])'\n ],\n seealso: ['combinations', 'factorial']\n}\n","export const permutationsDocs = {\n name: 'permutations',\n category: 'Probability',\n syntax: [\n 'permutations(n)',\n 'permutations(n, k)'\n ],\n description: 'Compute the number of permutations of n items taken k at a time',\n examples: [\n 'permutations(5)',\n 'permutations(5, 3)'\n ],\n seealso: ['combinations', 'combinationsWithRep', 'factorial']\n}\n","export const pickRandomDocs = {\n name: 'pickRandom',\n category: 'Probability',\n syntax: [\n 'pickRandom(array)',\n 'pickRandom(array, number)',\n 'pickRandom(array, weights)',\n 'pickRandom(array, number, weights)',\n 'pickRandom(array, weights, number)'\n ],\n description:\n 'Pick a random entry from a given array.',\n examples: [\n 'pickRandom(0:10)',\n 'pickRandom([1, 3, 1, 6])',\n 'pickRandom([1, 3, 1, 6], 2)',\n 'pickRandom([1, 3, 1, 6], [2, 3, 2, 1])',\n 'pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])',\n 'pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)'\n ],\n seealso: ['random', 'randomInt']\n}\n","export const randomDocs = {\n name: 'random',\n category: 'Probability',\n syntax: [\n 'random()',\n 'random(max)',\n 'random(min, max)',\n 'random(size)',\n 'random(size, max)',\n 'random(size, min, max)'\n ],\n description:\n 'Return a random number.',\n examples: [\n 'random()',\n 'random(10, 20)',\n 'random([2, 3])'\n ],\n seealso: ['pickRandom', 'randomInt']\n}\n","export const randomIntDocs = {\n name: 'randomInt',\n category: 'Probability',\n syntax: [\n 'randomInt(max)',\n 'randomInt(min, max)',\n 'randomInt(size)',\n 'randomInt(size, max)',\n 'randomInt(size, min, max)'\n ],\n description:\n 'Return a random integer number',\n examples: [\n 'randomInt(10, 20)',\n 'randomInt([2, 3], 10)'\n ],\n seealso: ['pickRandom', 'random']\n}\n","export const compareDocs = {\n name: 'compare',\n category: 'Relational',\n syntax: [\n 'compare(x, y)'\n ],\n description:\n 'Compare two values. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compare(2, 3)',\n 'compare(3, 2)',\n 'compare(2, 2)',\n 'compare(5cm, 40mm)',\n 'compare(2, [1, 2, 3])'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compareNatural', 'compareText'\n ]\n}\n","export const compareNaturalDocs = {\n name: 'compareNatural',\n category: 'Relational',\n syntax: [\n 'compareNatural(x, y)'\n ],\n description:\n 'Compare two values of any type in a deterministic, natural way. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compareNatural(2, 3)',\n 'compareNatural(3, 2)',\n 'compareNatural(2, 2)',\n 'compareNatural(5cm, 40mm)',\n 'compareNatural(\"2\", \"10\")',\n 'compareNatural(2 + 3i, 2 + 4i)',\n 'compareNatural([1, 2, 4], [1, 2, 3])',\n 'compareNatural([1, 5], [1, 2, 3])',\n 'compareNatural([1, 2], [1, 2])',\n 'compareNatural({a: 2}, {a: 4})'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compare', 'compareText'\n ]\n}\n","export const compareTextDocs = {\n name: 'compareText',\n category: 'Relational',\n syntax: [\n 'compareText(x, y)'\n ],\n description:\n 'Compare two strings lexically. Comparison is case sensitive. ' +\n 'Returns 1 when x > y, -1 when x < y, and 0 when x == y.',\n examples: [\n 'compareText(\"B\", \"A\")',\n 'compareText(\"A\", \"B\")',\n 'compareText(\"A\", \"A\")',\n 'compareText(\"2\", \"10\")',\n 'compare(\"2\", \"10\")',\n 'compare(2, 10)',\n 'compareNatural(\"2\", \"10\")',\n 'compareText(\"B\", [\"A\", \"B\", \"C\"])'\n ],\n seealso: [\n 'compare', 'compareNatural'\n ]\n}\n","export const deepEqualDocs = {\n name: 'deepEqual',\n category: 'Relational',\n syntax: [\n 'deepEqual(x, y)'\n ],\n description:\n 'Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.',\n examples: [\n 'deepEqual([1,3,4], [1,3,4])',\n 'deepEqual([1,3,4], [1,3])'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const equalDocs = {\n name: 'equal',\n category: 'Relational',\n syntax: [\n 'x == y',\n 'equal(x, y)'\n ],\n description:\n 'Check equality of two values. Returns true if the values are equal, and false if not.',\n examples: [\n '2+2 == 3',\n '2+2 == 4',\n 'a = 3.2',\n 'b = 6-2.8',\n 'a == b',\n '50cm == 0.5m'\n ],\n seealso: [\n 'unequal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare', 'deepEqual', 'equalText'\n ]\n}\n","export const equalTextDocs = {\n name: 'equalText',\n category: 'Relational',\n syntax: [\n 'equalText(x, y)'\n ],\n description:\n 'Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.',\n examples: [\n 'equalText(\"Hello\", \"Hello\")',\n 'equalText(\"a\", \"A\")',\n 'equal(\"2e3\", \"2000\")',\n 'equalText(\"2e3\", \"2000\")',\n 'equalText(\"B\", [\"A\", \"B\", \"C\"])'\n ],\n seealso: [\n 'compare', 'compareNatural', 'compareText', 'equal'\n ]\n}\n","export const largerDocs = {\n name: 'larger',\n category: 'Relational',\n syntax: [\n 'x > y',\n 'larger(x, y)'\n ],\n description:\n 'Check if value x is larger than y. Returns true if x is larger than y, and false if not.',\n examples: [\n '2 > 3',\n '5 > 2*2',\n 'a = 3.3',\n 'b = 6-2.8',\n '(a > b)',\n '(b < a)',\n '5 cm > 2 inch'\n ],\n seealso: [\n 'equal', 'unequal', 'smaller', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const largerEqDocs = {\n name: 'largerEq',\n category: 'Relational',\n syntax: [\n 'x >= y',\n 'largerEq(x, y)'\n ],\n description:\n 'Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.',\n examples: [\n '2 >= 1+1',\n '2 > 1+1',\n 'a = 3.2',\n 'b = 6-2.8',\n '(a >= b)'\n ],\n seealso: [\n 'equal', 'unequal', 'smallerEq', 'smaller', 'compare'\n ]\n}\n","export const smallerDocs = {\n name: 'smaller',\n category: 'Relational',\n syntax: [\n 'x < y',\n 'smaller(x, y)'\n ],\n description:\n 'Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not.',\n examples: [\n '2 < 3',\n '5 < 2*2',\n 'a = 3.3',\n 'b = 6-2.8',\n '(a < b)',\n '5 cm < 2 inch'\n ],\n seealso: [\n 'equal', 'unequal', 'larger', 'smallerEq', 'largerEq', 'compare'\n ]\n}\n","export const smallerEqDocs = {\n name: 'smallerEq',\n category: 'Relational',\n syntax: [\n 'x <= y',\n 'smallerEq(x, y)'\n ],\n description:\n 'Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.',\n examples: [\n '2 <= 1+1',\n '2 < 1+1',\n 'a = 3.2',\n 'b = 6-2.8',\n '(a <= b)'\n ],\n seealso: [\n 'equal', 'unequal', 'larger', 'smaller', 'largerEq', 'compare'\n ]\n}\n","export const unequalDocs = {\n name: 'unequal',\n category: 'Relational',\n syntax: [\n 'x != y',\n 'unequal(x, y)'\n ],\n description:\n 'Check unequality of two values. Returns true if the values are unequal, and false if they are equal.',\n examples: [\n '2+2 != 3',\n '2+2 != 4',\n 'a = 3.2',\n 'b = 6-2.8',\n 'a != b',\n '50cm != 0.5m',\n '5 cm != 2 inch'\n ],\n seealso: [\n 'equal', 'smaller', 'larger', 'smallerEq', 'largerEq', 'compare', 'deepEqual'\n ]\n}\n","export const setCartesianDocs = {\n name: 'setCartesian',\n category: 'Set',\n syntax: [\n 'setCartesian(set1, set2)'\n ],\n description:\n 'Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setCartesian([1, 2], [3, 4])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference', 'setPowerset'\n ]\n}\n","export const setDifferenceDocs = {\n name: 'setDifference',\n category: 'Set',\n syntax: [\n 'setDifference(set1, set2)'\n ],\n description:\n 'Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setDifference([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setSymDifference'\n ]\n}\n","export const setDistinctDocs = {\n name: 'setDistinct',\n category: 'Set',\n syntax: [\n 'setDistinct(set)'\n ],\n description:\n 'Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setDistinct([1, 1, 1, 2, 2, 3])'\n ],\n seealso: [\n 'setMultiplicity'\n ]\n}\n","export const setIntersectDocs = {\n name: 'setIntersect',\n category: 'Set',\n syntax: [\n 'setIntersect(set1, set2)'\n ],\n description:\n 'Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setIntersect([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setDifference'\n ]\n}\n","export const setIsSubsetDocs = {\n name: 'setIsSubset',\n category: 'Set',\n syntax: [\n 'setIsSubset(set1, set2)'\n ],\n description:\n 'Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setIsSubset([1, 2], [3, 4, 5, 6])',\n 'setIsSubset([3, 4], [3, 4, 5, 6])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setMultiplicityDocs = {\n name: 'setMultiplicity',\n category: 'Set',\n syntax: [\n 'setMultiplicity(element, set)'\n ],\n description:\n 'Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setMultiplicity(1, [1, 2, 2, 4])',\n 'setMultiplicity(2, [1, 2, 2, 4])'\n ],\n seealso: [\n 'setDistinct', 'setSize'\n ]\n}\n","export const setPowersetDocs = {\n name: 'setPowerset',\n category: 'Set',\n syntax: [\n 'setPowerset(set)'\n ],\n description:\n 'Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setPowerset([1, 2, 3])'\n ],\n seealso: [\n 'setCartesian'\n ]\n}\n","export const setSizeDocs = {\n name: 'setSize',\n category: 'Set',\n syntax: [\n 'setSize(set)',\n 'setSize(set, unique)'\n ],\n description:\n 'Count the number of elements of a (multi)set. When the second parameter \"unique\" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',\n examples: [\n 'setSize([1, 2, 2, 4])',\n 'setSize([1, 2, 2, 4], true)'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setSymDifferenceDocs = {\n name: 'setSymDifference',\n category: 'Set',\n syntax: [\n 'setSymDifference(set1, set2)'\n ],\n description:\n 'Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setUnion', 'setIntersect', 'setDifference'\n ]\n}\n","export const setUnionDocs = {\n name: 'setUnion',\n category: 'Set',\n syntax: [\n 'setUnion(set1, set2)'\n ],\n description:\n 'Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.',\n examples: [\n 'setUnion([1, 2, 3, 4], [3, 4, 5, 6])',\n 'setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])'\n ],\n seealso: [\n 'setIntersect', 'setDifference'\n ]\n}\n","export const erfDocs = {\n name: 'erf',\n category: 'Special',\n syntax: [\n 'erf(x)'\n ],\n description: 'Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x',\n examples: [\n 'erf(0.2)',\n 'erf(-0.5)',\n 'erf(4)'\n ],\n seealso: []\n}\n","export const madDocs = {\n name: 'mad',\n category: 'Statistics',\n syntax: [\n 'mad(a, b, c, ...)',\n 'mad(A)'\n ],\n description: 'Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.',\n examples: [\n 'mad(10, 20, 30)',\n 'mad([1, 2, 3])'\n ],\n seealso: [\n 'mean',\n 'median',\n 'std',\n 'abs'\n ]\n}\n","export const maxDocs = {\n name: 'max',\n category: 'Statistics',\n syntax: [\n 'max(a, b, c, ...)',\n 'max(A)',\n 'max(A, dim)'\n ],\n description: 'Compute the maximum value of a list of values.',\n examples: [\n 'max(2, 3, 4, 1)',\n 'max([2, 3, 4, 1])',\n 'max([2, 5; 4, 3])',\n 'max([2, 5; 4, 3], 1)',\n 'max([2, 5; 4, 3], 2)',\n 'max(2.7, 7.1, -4.5, 2.0, 4.1)',\n 'min(2.7, 7.1, -4.5, 2.0, 4.1)'\n ],\n seealso: [\n 'mean',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const meanDocs = {\n name: 'mean',\n category: 'Statistics',\n syntax: [\n 'mean(a, b, c, ...)',\n 'mean(A)',\n 'mean(A, dim)'\n ],\n description: 'Compute the arithmetic mean of a list of values.',\n examples: [\n 'mean(2, 3, 4, 1)',\n 'mean([2, 3, 4, 1])',\n 'mean([2, 5; 4, 3])',\n 'mean([2, 5; 4, 3], 1)',\n 'mean([2, 5; 4, 3], 2)',\n 'mean([1.0, 2.7, 3.2, 4.0])'\n ],\n seealso: [\n 'max',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const medianDocs = {\n name: 'median',\n category: 'Statistics',\n syntax: [\n 'median(a, b, c, ...)',\n 'median(A)'\n ],\n description: 'Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.',\n examples: [\n 'median(5, 2, 7)',\n 'median([3, -1, 5, 7])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance',\n 'quantileSeq'\n ]\n}\n","export const minDocs = {\n name: 'min',\n category: 'Statistics',\n syntax: [\n 'min(a, b, c, ...)',\n 'min(A)',\n 'min(A, dim)'\n ],\n description: 'Compute the minimum value of a list of values.',\n examples: [\n 'min(2, 3, 4, 1)',\n 'min([2, 3, 4, 1])',\n 'min([2, 5; 4, 3])',\n 'min([2, 5; 4, 3], 1)',\n 'min([2, 5; 4, 3], 2)',\n 'min(2.7, 7.1, -4.5, 2.0, 4.1)',\n 'max(2.7, 7.1, -4.5, 2.0, 4.1)'\n ],\n seealso: [\n 'max',\n 'mean',\n 'median',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const modeDocs = {\n name: 'mode',\n category: 'Statistics',\n syntax: [\n 'mode(a, b, c, ...)',\n 'mode(A)',\n 'mode(A, a, b, B, c, ...)'\n ],\n description: 'Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.',\n examples: [\n 'mode(2, 1, 4, 3, 1)',\n 'mode([1, 2.7, 3.2, 4, 2.7])',\n 'mode(1, 4, 6, 1, 6)'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const prodDocs = {\n name: 'prod',\n category: 'Statistics',\n syntax: [\n 'prod(a, b, c, ...)',\n 'prod(A)'\n ],\n description: 'Compute the product of all values.',\n examples: [\n 'prod(2, 3, 4)',\n 'prod([2, 3, 4])',\n 'prod([2, 5; 4, 3])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'min',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const quantileSeqDocs = {\n name: 'quantileSeq',\n category: 'Statistics',\n syntax: [\n 'quantileSeq(A, prob[, sorted])',\n 'quantileSeq(A, [prob1, prob2, ...][, sorted])',\n 'quantileSeq(A, N[, sorted])'\n ],\n description: 'Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. \\n\\nIn case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.',\n examples: [\n 'quantileSeq([3, -1, 5, 7], 0.5)',\n 'quantileSeq([3, -1, 5, 7], [1/3, 2/3])',\n 'quantileSeq([3, -1, 5, 7], 2)',\n 'quantileSeq([-1, 3, 5, 7], 0.5, true)'\n ],\n seealso: [\n 'mean',\n 'median',\n 'min',\n 'max',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const stdDocs = {\n name: 'std',\n category: 'Statistics',\n syntax: [\n 'std(a, b, c, ...)',\n 'std(A)',\n 'std(A, normalization)'\n ],\n description: 'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be \"unbiased\" (default), \"uncorrected\", or \"biased\".',\n examples: [\n 'std(2, 4, 6)',\n 'std([2, 4, 6, 8])',\n 'std([2, 4, 6, 8], \"uncorrected\")',\n 'std([2, 4, 6, 8], \"biased\")',\n 'std([1, 2, 3; 4, 5, 6])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'prod',\n 'sum',\n 'variance'\n ]\n}\n","export const sumDocs = {\n name: 'sum',\n category: 'Statistics',\n syntax: [\n 'sum(a, b, c, ...)',\n 'sum(A)'\n ],\n description: 'Compute the sum of all values.',\n examples: [\n 'sum(2, 3, 4, 1)',\n 'sum([2, 3, 4, 1])',\n 'sum([2, 5; 4, 3])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum',\n 'variance'\n ]\n}\n","export const varianceDocs = {\n name: 'variance',\n category: 'Statistics',\n syntax: [\n 'variance(a, b, c, ...)',\n 'variance(A)',\n 'variance(A, normalization)'\n ],\n description: 'Compute the variance of all values. Optional parameter normalization can be \"unbiased\" (default), \"uncorrected\", or \"biased\".',\n examples: [\n 'variance(2, 4, 6)',\n 'variance([2, 4, 6, 8])',\n 'variance([2, 4, 6, 8], \"uncorrected\")',\n 'variance([2, 4, 6, 8], \"biased\")',\n 'variance([1, 2, 3; 4, 5, 6])'\n ],\n seealso: [\n 'max',\n 'mean',\n 'min',\n 'median',\n 'min',\n 'prod',\n 'std',\n 'sum'\n ]\n}\n","export const acosDocs = {\n name: 'acos',\n category: 'Trigonometry',\n syntax: [\n 'acos(x)'\n ],\n description: 'Compute the inverse cosine of a value in radians.',\n examples: [\n 'acos(0.5)',\n 'acos(cos(2.3))'\n ],\n seealso: [\n 'cos',\n 'atan',\n 'asin'\n ]\n}\n","export const acoshDocs = {\n name: 'acosh',\n category: 'Trigonometry',\n syntax: [\n 'acosh(x)'\n ],\n description: 'Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.',\n examples: [\n 'acosh(1.5)'\n ],\n seealso: [\n 'cosh',\n 'asinh',\n 'atanh'\n ]\n}\n","export const acotDocs = {\n name: 'acot',\n category: 'Trigonometry',\n syntax: [\n 'acot(x)'\n ],\n description: 'Calculate the inverse cotangent of a value.',\n examples: [\n 'acot(0.5)',\n 'acot(cot(0.5))',\n 'acot(2)'\n ],\n seealso: [\n 'cot',\n 'atan'\n ]\n}\n","export const acothDocs = {\n name: 'acoth',\n category: 'Trigonometry',\n syntax: [\n 'acoth(x)'\n ],\n description: 'Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.',\n examples: [\n 'acoth(2)',\n 'acoth(0.5)'\n ],\n seealso: [\n 'acsch',\n 'asech'\n ]\n}\n","export const acscDocs = {\n name: 'acsc',\n category: 'Trigonometry',\n syntax: [\n 'acsc(x)'\n ],\n description: 'Calculate the inverse cotangent of a value.',\n examples: [\n 'acsc(2)',\n 'acsc(csc(0.5))',\n 'acsc(0.5)'\n ],\n seealso: [\n 'csc',\n 'asin',\n 'asec'\n ]\n}\n","export const acschDocs = {\n name: 'acsch',\n category: 'Trigonometry',\n syntax: [\n 'acsch(x)'\n ],\n description: 'Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.',\n examples: [\n 'acsch(0.5)'\n ],\n seealso: [\n 'asech',\n 'acoth'\n ]\n}\n","export const asecDocs = {\n name: 'asec',\n category: 'Trigonometry',\n syntax: [\n 'asec(x)'\n ],\n description: 'Calculate the inverse secant of a value.',\n examples: [\n 'asec(0.5)',\n 'asec(sec(0.5))',\n 'asec(2)'\n ],\n seealso: [\n 'acos',\n 'acot',\n 'acsc'\n ]\n}\n","export const asechDocs = {\n name: 'asech',\n category: 'Trigonometry',\n syntax: [\n 'asech(x)'\n ],\n description: 'Calculate the inverse secant of a value.',\n examples: [\n 'asech(0.5)'\n ],\n seealso: [\n 'acsch',\n 'acoth'\n ]\n}\n","export const asinDocs = {\n name: 'asin',\n category: 'Trigonometry',\n syntax: [\n 'asin(x)'\n ],\n description: 'Compute the inverse sine of a value in radians.',\n examples: [\n 'asin(0.5)',\n 'asin(sin(0.5))'\n ],\n seealso: [\n 'sin',\n 'acos',\n 'atan'\n ]\n}\n","export const asinhDocs = {\n name: 'asinh',\n category: 'Trigonometry',\n syntax: [\n 'asinh(x)'\n ],\n description: 'Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.',\n examples: [\n 'asinh(0.5)'\n ],\n seealso: [\n 'acosh',\n 'atanh'\n ]\n}\n","export const atanDocs = {\n name: 'atan',\n category: 'Trigonometry',\n syntax: [\n 'atan(x)'\n ],\n description: 'Compute the inverse tangent of a value in radians.',\n examples: [\n 'atan(0.5)',\n 'atan(tan(0.5))'\n ],\n seealso: [\n 'tan',\n 'acos',\n 'asin'\n ]\n}\n","export const atanhDocs = {\n name: 'atanh',\n category: 'Trigonometry',\n syntax: [\n 'atanh(x)'\n ],\n description: 'Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.',\n examples: [\n 'atanh(0.5)'\n ],\n seealso: [\n 'acosh',\n 'asinh'\n ]\n}\n","export const atan2Docs = {\n name: 'atan2',\n category: 'Trigonometry',\n syntax: [\n 'atan2(y, x)'\n ],\n description:\n 'Computes the principal value of the arc tangent of y/x in radians.',\n examples: [\n 'atan2(2, 2) / pi',\n 'angle = 60 deg in rad',\n 'x = cos(angle)',\n 'y = sin(angle)',\n 'atan2(y, x)'\n ],\n seealso: [\n 'sin',\n 'cos',\n 'tan'\n ]\n}\n","export const cosDocs = {\n name: 'cos',\n category: 'Trigonometry',\n syntax: [\n 'cos(x)'\n ],\n description: 'Compute the cosine of x in radians.',\n examples: [\n 'cos(2)',\n 'cos(pi / 4) ^ 2',\n 'cos(180 deg)',\n 'cos(60 deg)',\n 'sin(0.2)^2 + cos(0.2)^2'\n ],\n seealso: [\n 'acos',\n 'sin',\n 'tan'\n ]\n}\n","export const coshDocs = {\n name: 'cosh',\n category: 'Trigonometry',\n syntax: [\n 'cosh(x)'\n ],\n description: 'Compute the hyperbolic cosine of x in radians.',\n examples: [\n 'cosh(0.5)'\n ],\n seealso: [\n 'sinh',\n 'tanh',\n 'coth'\n ]\n}\n","export const cotDocs = {\n name: 'cot',\n category: 'Trigonometry',\n syntax: [\n 'cot(x)'\n ],\n description: 'Compute the cotangent of x in radians. Defined as 1/tan(x)',\n examples: [\n 'cot(2)',\n '1 / tan(2)'\n ],\n seealso: [\n 'sec',\n 'csc',\n 'tan'\n ]\n}\n","export const cothDocs = {\n name: 'coth',\n category: 'Trigonometry',\n syntax: [\n 'coth(x)'\n ],\n description: 'Compute the hyperbolic cotangent of x in radians.',\n examples: [\n 'coth(2)',\n '1 / tanh(2)'\n ],\n seealso: [\n 'sech',\n 'csch',\n 'tanh'\n ]\n}\n","export const cscDocs = {\n name: 'csc',\n category: 'Trigonometry',\n syntax: [\n 'csc(x)'\n ],\n description: 'Compute the cosecant of x in radians. Defined as 1/sin(x)',\n examples: [\n 'csc(2)',\n '1 / sin(2)'\n ],\n seealso: [\n 'sec',\n 'cot',\n 'sin'\n ]\n}\n","export const cschDocs = {\n name: 'csch',\n category: 'Trigonometry',\n syntax: [\n 'csch(x)'\n ],\n description: 'Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)',\n examples: [\n 'csch(2)',\n '1 / sinh(2)'\n ],\n seealso: [\n 'sech',\n 'coth',\n 'sinh'\n ]\n}\n","export const secDocs = {\n name: 'sec',\n category: 'Trigonometry',\n syntax: [\n 'sec(x)'\n ],\n description: 'Compute the secant of x in radians. Defined as 1/cos(x)',\n examples: [\n 'sec(2)',\n '1 / cos(2)'\n ],\n seealso: [\n 'cot',\n 'csc',\n 'cos'\n ]\n}\n","export const sechDocs = {\n name: 'sech',\n category: 'Trigonometry',\n syntax: [\n 'sech(x)'\n ],\n description: 'Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)',\n examples: [\n 'sech(2)',\n '1 / cosh(2)'\n ],\n seealso: [\n 'coth',\n 'csch',\n 'cosh'\n ]\n}\n","export const sinDocs = {\n name: 'sin',\n category: 'Trigonometry',\n syntax: [\n 'sin(x)'\n ],\n description: 'Compute the sine of x in radians.',\n examples: [\n 'sin(2)',\n 'sin(pi / 4) ^ 2',\n 'sin(90 deg)',\n 'sin(30 deg)',\n 'sin(0.2)^2 + cos(0.2)^2'\n ],\n seealso: [\n 'asin',\n 'cos',\n 'tan'\n ]\n}\n","export const sinhDocs = {\n name: 'sinh',\n category: 'Trigonometry',\n syntax: [\n 'sinh(x)'\n ],\n description: 'Compute the hyperbolic sine of x in radians.',\n examples: [\n 'sinh(0.5)'\n ],\n seealso: [\n 'cosh',\n 'tanh'\n ]\n}\n","export const tanDocs = {\n name: 'tan',\n category: 'Trigonometry',\n syntax: [\n 'tan(x)'\n ],\n description: 'Compute the tangent of x in radians.',\n examples: [\n 'tan(0.5)',\n 'sin(0.5) / cos(0.5)',\n 'tan(pi / 4)',\n 'tan(45 deg)'\n ],\n seealso: [\n 'atan',\n 'sin',\n 'cos'\n ]\n}\n","export const tanhDocs = {\n name: 'tanh',\n category: 'Trigonometry',\n syntax: [\n 'tanh(x)'\n ],\n description: 'Compute the hyperbolic tangent of x in radians.',\n examples: [\n 'tanh(0.5)',\n 'sinh(0.5) / cosh(0.5)'\n ],\n seealso: [\n 'sinh',\n 'cosh'\n ]\n}\n","export const toDocs = {\n name: 'to',\n category: 'Units',\n syntax: [\n 'x to unit',\n 'to(x, unit)'\n ],\n description: 'Change the unit of a value.',\n examples: [\n '5 inch to cm',\n '3.2kg to g',\n '16 bytes in bits'\n ],\n seealso: []\n}\n","export const cloneDocs = {\n name: 'clone',\n category: 'Utils',\n syntax: [\n 'clone(x)'\n ],\n description: 'Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices',\n examples: [\n 'clone(3.5)',\n 'clone(2 - 4i)',\n 'clone(45 deg)',\n 'clone([1, 2; 3, 4])',\n 'clone(\"hello world\")'\n ],\n seealso: []\n}\n","export const formatDocs = {\n name: 'format',\n category: 'Utils',\n syntax: [\n 'format(value)',\n 'format(value, precision)'\n ],\n description: 'Format a value of any type as string.',\n examples: [\n 'format(2.3)',\n 'format(3 - 4i)',\n 'format([])',\n 'format(pi, 3)'\n ],\n seealso: ['print']\n}\n","export const binDocs = {\n name: 'bin',\n category: 'Utils',\n syntax: [\n 'bin(value)'\n ],\n description: 'Format a number as binary',\n examples: [\n 'bin(2)'\n ],\n seealso: ['oct', 'hex']\n}\n","export const octDocs = {\n name: 'oct',\n category: 'Utils',\n syntax: [\n 'oct(value)'\n ],\n description: 'Format a number as octal',\n examples: [\n 'oct(56)'\n ],\n seealso: ['bin', 'hex']\n}\n","export const hexDocs = {\n name: 'hex',\n category: 'Utils',\n syntax: [\n 'hex(value)'\n ],\n description: 'Format a number as hexadecimal',\n examples: [\n 'hex(240)'\n ],\n seealso: ['bin', 'oct']\n}\n","export const isNaNDocs = {\n name: 'isNaN',\n category: 'Utils',\n syntax: [\n 'isNaN(x)'\n ],\n description: 'Test whether a value is NaN (not a number)',\n examples: [\n 'isNaN(2)',\n 'isNaN(0 / 0)',\n 'isNaN(NaN)',\n 'isNaN(Infinity)'\n ],\n seealso: ['isNegative', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isIntegerDocs = {\n name: 'isInteger',\n category: 'Utils',\n syntax: [\n 'isInteger(x)'\n ],\n description: 'Test whether a value is an integer number.',\n examples: [\n 'isInteger(2)',\n 'isInteger(3.5)',\n 'isInteger([3, 0.5, -2])'\n ],\n seealso: ['isNegative', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isNegativeDocs = {\n name: 'isNegative',\n category: 'Utils',\n syntax: [\n 'isNegative(x)'\n ],\n description: 'Test whether a value is negative: smaller than zero.',\n examples: [\n 'isNegative(2)',\n 'isNegative(0)',\n 'isNegative(-4)',\n 'isNegative([3, 0.5, -2])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isPositive', 'isZero']\n}\n","export const isNumericDocs = {\n name: 'isNumeric',\n category: 'Utils',\n syntax: [\n 'isNumeric(x)'\n ],\n description: 'Test whether a value is a numeric value. ' +\n 'Returns true when the input is a number, BigNumber, Fraction, or boolean.',\n examples: [\n 'isNumeric(2)',\n 'isNumeric(\"2\")',\n 'hasNumericValue(\"2\")',\n 'isNumeric(0)',\n 'isNumeric(bignumber(500))',\n 'isNumeric(fraction(0.125))',\n 'isNumeric(2 + 3i)',\n 'isNumeric([2.3, \"foo\", false])'\n ],\n seealso: ['isInteger', 'isZero', 'isNegative', 'isPositive', 'isNaN', 'hasNumericValue']\n}\n","export const hasNumericValueDocs = {\n name: 'hasNumericValue',\n category: 'Utils',\n syntax: [\n 'hasNumericValue(x)'\n ],\n description: 'Test whether a value is an numeric value. ' +\n 'In case of a string, true is returned if the string contains a numeric value.',\n examples: [\n 'hasNumericValue(2)',\n 'hasNumericValue(\"2\")',\n 'isNumeric(\"2\")',\n 'hasNumericValue(0)',\n 'hasNumericValue(bignumber(500))',\n 'hasNumericValue(fraction(0.125))',\n 'hasNumericValue(2 + 3i)',\n 'hasNumericValue([2.3, \"foo\", false])'\n ],\n seealso: ['isInteger', 'isZero', 'isNegative', 'isPositive', 'isNaN', 'isNumeric']\n}\n","export const isPositiveDocs = {\n name: 'isPositive',\n category: 'Utils',\n syntax: [\n 'isPositive(x)'\n ],\n description: 'Test whether a value is positive: larger than zero.',\n examples: [\n 'isPositive(2)',\n 'isPositive(0)',\n 'isPositive(-4)',\n 'isPositive([3, 0.5, -2])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isZero']\n}\n","export const isPrimeDocs = {\n name: 'isPrime',\n category: 'Utils',\n syntax: [\n 'isPrime(x)'\n ],\n description: 'Test whether a value is prime: has no divisors other than itself and one.',\n examples: [\n 'isPrime(3)',\n 'isPrime(-2)',\n 'isPrime([2, 17, 100])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isZero']\n}\n","export const isZeroDocs = {\n name: 'isZero',\n category: 'Utils',\n syntax: [\n 'isZero(x)'\n ],\n description: 'Test whether a value is zero.',\n examples: [\n 'isZero(2)',\n 'isZero(0)',\n 'isZero(-4)',\n 'isZero([3, 0, -2, 0])'\n ],\n seealso: ['isInteger', 'isNumeric', 'isNegative', 'isPositive']\n}\n","export const typeOfDocs = {\n name: 'typeOf',\n category: 'Utils',\n syntax: [\n 'typeOf(x)'\n ],\n description: 'Get the type of a variable.',\n examples: [\n 'typeOf(3.5)',\n 'typeOf(2 - 4i)',\n 'typeOf(45 deg)',\n 'typeOf(\"hello world\")'\n ],\n seealso: ['getMatrixDataType']\n}\n","export const numericDocs = {\n name: 'numeric',\n category: 'Utils',\n syntax: [\n 'numeric(x)'\n ],\n description: 'Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.',\n examples: [\n 'numeric(\"4\")',\n 'numeric(\"4\", \"number\")',\n 'numeric(\"4\", \"BigNumber\")',\n 'numeric(\"4\", \"Fraction)',\n 'numeric(4, \"Fraction\")',\n 'numeric(fraction(2, 5), \"number)'\n ],\n seealso: ['number', 'fraction', 'bignumber', 'string', 'format']\n}\n","import { factory } from '../../utils/factory.js'\nimport { getSafeProperty } from '../../utils/customs.js'\nimport { embeddedDocs } from '../embeddedDocs/embeddedDocs.js'\nimport { hasOwnProperty } from '../../utils/object.js'\n\nconst name = 'help'\nconst dependencies = ['typed', 'mathWithTransform', 'Help']\n\nexport const createHelp = /* #__PURE__ */ factory(name, dependencies, ({ typed, mathWithTransform, Help }) => {\n /**\n * Retrieve help on a function or data type.\n * Help files are retrieved from the embedded documentation in math.docs.\n *\n * Syntax:\n *\n * math.help(search)\n *\n * Examples:\n *\n * console.log(math.help('sin').toString())\n * console.log(math.help(math.add).toString())\n * console.log(math.help(math.add).toJSON())\n *\n * @param {Function | string | Object} search A function or function name\n * for which to get help\n * @return {Help} A help object\n */\n return typed(name, {\n any: function (search) {\n let prop\n let searchName = search\n\n if (typeof search !== 'string') {\n for (prop in mathWithTransform) {\n // search in functions and constants\n if (hasOwnProperty(mathWithTransform, prop) && (search === mathWithTransform[prop])) {\n searchName = prop\n break\n }\n }\n\n /* TODO: implement help for data types\n if (!text) {\n // search data type\n for (prop in math.type) {\n if (hasOwnProperty(math, prop)) {\n if (search === math.type[prop]) {\n text = prop\n break\n }\n }\n }\n }\n */\n }\n\n const doc = getSafeProperty(embeddedDocs, searchName)\n if (!doc) {\n const searchText = typeof searchName === 'function' ? searchName.name : searchName\n throw new Error('No documentation found on \"' + searchText + '\"')\n }\n return new Help(doc)\n }\n })\n})\n","import { factory } from '../../../utils/factory.js'\n\nconst name = 'chain'\nconst dependencies = ['typed', 'Chain']\n\nexport const createChain = /* #__PURE__ */ factory(name, dependencies, ({ typed, Chain }) => {\n /**\n * Wrap any value in a chain, allowing to perform chained operations on\n * the value.\n *\n * All methods available in the math.js library can be called upon the chain,\n * and then will be evaluated with the value itself as first argument.\n * The chain can be closed by executing `chain.done()`, which returns\n * the final value.\n *\n * The chain has a number of special functions:\n *\n * - `done()` Finalize the chain and return the chain's value.\n * - `valueOf()` The same as `done()`\n * - `toString()` Executes `math.format()` onto the chain's value, returning\n * a string representation of the value.\n *\n * Syntax:\n *\n * math.chain(value)\n *\n * Examples:\n *\n * math.chain(3)\n * .add(4)\n * .subtract(2)\n * .done() // 5\n *\n * math.chain( [[1, 2], [3, 4]] )\n * .subset(math.index(0, 0), 8)\n * .multiply(3)\n * .done() // [[24, 6], [9, 12]]\n *\n * @param {*} [value] A value of any type on which to start a chained operation.\n * @return {math.Chain} The created chain\n */\n return typed(name, {\n '': function () {\n return new Chain()\n },\n\n any: function (value) {\n return new Chain(value)\n }\n })\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { clone } from '../../utils/object.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'det'\nconst dependencies = ['typed', 'matrix', 'subtract', 'multiply', 'unaryMinus', 'lup']\n\nexport const createDet = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, multiply, unaryMinus, lup }) => {\n /**\n * Calculate the determinant of a matrix.\n *\n * Syntax:\n *\n * math.det(x)\n *\n * Examples:\n *\n * math.det([[1, 2], [3, 4]]) // returns -2\n *\n * const A = [\n * [-2, 2, 3],\n * [-1, 1, 3],\n * [2, 0, -1]\n * ]\n * math.det(A) // returns 6\n *\n * See also:\n *\n * inv\n *\n * @param {Array | Matrix} x A matrix\n * @return {number} The determinant of `x`\n */\n return typed(name, {\n any: function (x) {\n return clone(x)\n },\n\n 'Array | Matrix': function det (x) {\n let size\n if (isMatrix(x)) {\n size = x.size()\n } else if (Array.isArray(x)) {\n x = matrix(x)\n size = x.size()\n } else {\n // a scalar\n size = []\n }\n\n switch (size.length) {\n case 0:\n // scalar\n return clone(x)\n\n case 1:\n // vector\n if (size[0] === 1) {\n return clone(x.valueOf()[0])\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n {\n // two dimensional array\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n return _det(x.clone().valueOf(), rows, cols)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n\n default:\n // multi dimensional array\n throw new RangeError('Matrix must be two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n }\n })\n\n /**\n * Calculate the determinant of a matrix\n * @param {Array[]} matrix A square, two dimensional matrix\n * @param {number} rows Number of rows of the matrix (zero-based)\n * @param {number} cols Number of columns of the matrix (zero-based)\n * @returns {number} det\n * @private\n */\n function _det (matrix, rows, cols) {\n if (rows === 1) {\n // this is a 1 x 1 matrix\n return clone(matrix[0][0])\n } else if (rows === 2) {\n // this is a 2 x 2 matrix\n // the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12\n return subtract(\n multiply(matrix[0][0], matrix[1][1]),\n multiply(matrix[1][0], matrix[0][1])\n )\n } else {\n // Compute the LU decomposition\n const decomp = lup(matrix)\n\n // The determinant is the product of the diagonal entries of U (and those of L, but they are all 1)\n let det = decomp.U[0][0]\n for (let i = 1; i < rows; i++) {\n det = multiply(det, decomp.U[i][i])\n }\n\n // The determinant will be multiplied by 1 or -1 depending on the parity of the permutation matrix.\n // This can be determined by counting the cycles. This is roughly a linear time algorithm.\n let evenCycles = 0\n let i = 0\n const visited = []\n while (true) {\n while (visited[i]) {\n i++\n }\n if (i >= rows) break\n let j = i\n let cycleLen = 0\n while (!visited[decomp.p[j]]) {\n visited[decomp.p[j]] = true\n j = decomp.p[j]\n cycleLen++\n }\n if (cycleLen % 2 === 0) {\n evenCycles++\n }\n }\n\n return evenCycles % 2 === 0 ? det : unaryMinus(det)\n }\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { format } from '../../utils/string.js'\n\nconst name = 'inv'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'divideScalar',\n 'addScalar',\n 'multiply',\n 'unaryMinus',\n 'det',\n 'identity',\n 'abs'\n]\n\nexport const createInv = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divideScalar, addScalar, multiply, unaryMinus, det, identity, abs }) => {\n /**\n * Calculate the inverse of a square matrix.\n *\n * Syntax:\n *\n * math.inv(x)\n *\n * Examples:\n *\n * math.inv([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]]\n * math.inv(4) // returns 0.25\n * 1 / 4 // returns 0.25\n *\n * See also:\n *\n * det, transpose\n *\n * @param {number | Complex | Array | Matrix} x Matrix to be inversed\n * @return {number | Complex | Array | Matrix} The inverse of `x`.\n */\n return typed(name, {\n 'Array | Matrix': function (x) {\n const size = isMatrix(x) ? x.size() : arraySize(x)\n switch (size.length) {\n case 1:\n // vector\n if (size[0] === 1) {\n if (isMatrix(x)) {\n return matrix([\n divideScalar(1, x.valueOf()[0])\n ])\n } else {\n return [\n divideScalar(1, x[0])\n ]\n }\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n // two dimensional array\n {\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n if (isMatrix(x)) {\n return matrix(\n _inv(x.valueOf(), rows, cols),\n x.storage()\n )\n } else {\n // return an Array\n return _inv(x, rows, cols)\n }\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n\n default:\n // multi dimensional array\n throw new RangeError('Matrix must be two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n },\n\n any: function (x) {\n // scalar\n return divideScalar(1, x) // FIXME: create a BigNumber one when configured for bignumbers\n }\n })\n\n /**\n * Calculate the inverse of a square matrix\n * @param {Array[]} mat A square matrix\n * @param {number} rows Number of rows\n * @param {number} cols Number of columns, must equal rows\n * @return {Array[]} inv Inverse matrix\n * @private\n */\n function _inv (mat, rows, cols) {\n let r, s, f, value, temp\n\n if (rows === 1) {\n // this is a 1 x 1 matrix\n value = mat[0][0]\n if (value === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n return [[\n divideScalar(1, value)\n ]]\n } else if (rows === 2) {\n // this is a 2 x 2 matrix\n const d = det(mat)\n if (d === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n return [\n [\n divideScalar(mat[1][1], d),\n divideScalar(unaryMinus(mat[0][1]), d)\n ],\n [\n divideScalar(unaryMinus(mat[1][0]), d),\n divideScalar(mat[0][0], d)\n ]\n ]\n } else {\n // this is a matrix of 3 x 3 or larger\n // calculate inverse using gauss-jordan elimination\n // https://en.wikipedia.org/wiki/Gaussian_elimination\n // http://mathworld.wolfram.com/MatrixInverse.html\n // http://math.uww.edu/~mcfarlat/inverse.htm\n\n // make a copy of the matrix (only the arrays, not of the elements)\n const A = mat.concat()\n for (r = 0; r < rows; r++) {\n A[r] = A[r].concat()\n }\n\n // create an identity matrix which in the end will contain the\n // matrix inverse\n const B = identity(rows).valueOf()\n\n // loop over all columns, and perform row reductions\n for (let c = 0; c < cols; c++) {\n // Pivoting: Swap row c with row r, where row r contains the largest element A[r][c]\n let ABig = abs(A[c][c])\n let rBig = c\n r = c + 1\n while (r < rows) {\n if (abs(A[r][c]) > ABig) {\n ABig = abs(A[r][c])\n rBig = r\n }\n r++\n }\n if (ABig === 0) {\n throw Error('Cannot calculate inverse, determinant is zero')\n }\n r = rBig\n if (r !== c) {\n temp = A[c]; A[c] = A[r]; A[r] = temp\n temp = B[c]; B[c] = B[r]; B[r] = temp\n }\n\n // eliminate non-zero values on the other rows at column c\n const Ac = A[c]\n const Bc = B[c]\n for (r = 0; r < rows; r++) {\n const Ar = A[r]\n const Br = B[r]\n if (r !== c) {\n // eliminate value at column c and row r\n if (Ar[c] !== 0) {\n f = divideScalar(unaryMinus(Ar[c]), Ac[c])\n\n // add (f * row c) to row r to eliminate the value\n // at column c\n for (s = c; s < cols; s++) {\n Ar[s] = addScalar(Ar[s], multiply(f, Ac[s]))\n }\n for (s = 0; s < cols; s++) {\n Br[s] = addScalar(Br[s], multiply(f, Bc[s]))\n }\n }\n } else {\n // normalize value at Acc to 1,\n // divide each value on row r with the value at Acc\n f = Ac[c]\n for (s = c; s < cols; s++) {\n Ar[s] = divideScalar(Ar[s], f)\n }\n for (s = 0; s < cols; s++) {\n Br[s] = divideScalar(Br[s], f)\n }\n }\n }\n }\n return B\n }\n }\n})\n","import { clone } from '../../utils/object.js'\nimport { factory } from '../../utils/factory.js'\nimport { format } from '../../utils/string.js'\n\nconst name = 'eigs'\nconst dependencies = ['config', 'typed', 'matrix', 'addScalar', 'equal', 'subtract', 'abs', 'atan', 'cos', 'sin', 'multiplyScalar', 'inv', 'bignumber', 'multiply', 'add']\n\nexport const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, matrix, addScalar, subtract, equal, abs, atan, cos, sin, multiplyScalar, inv, bignumber, multiply, add }) => {\n /**\n * Compute eigenvalue and eigenvector of a real symmetric matrix.\n * Only applicable to two dimensional symmetric matrices. Uses Jacobi\n * Algorithm. Matrix containing mixed type ('number', 'bignumber', 'fraction')\n * of elements are not supported. Input matrix or 2D array should contain all elements\n * of either 'number', 'bignumber' or 'fraction' type. For 'number' and 'fraction', the\n * eigenvalues are of 'number' type. For 'bignumber' the eigenvalues are of ''bignumber' type.\n * Eigenvectors are always of 'number' type.\n *\n * Syntax:\n *\n * math.eigs(x)\n *\n * Examples:\n *\n * const H = [[5, 2.3], [2.3, 1]]\n * const ans = math.eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}\n * const E = ans.values\n * const U = ans.vectors\n * math.multiply(H, math.column(U, 0)) // returns math.multiply(E[0], math.column(U, 0))\n * const UTxHxU = math.multiply(math.transpose(U), H, U) // rotates H to the eigen-representation\n * E[0] == UTxHxU[0][0] // returns true\n * See also:\n *\n * inv\n *\n * @param {Array | Matrix} x Matrix to be diagonalized\n * @return {{values: Array, vectors: Array} | {values: Matrix, vectors: Matrix}} Object containing eigenvalues (Array or Matrix) and eigenvectors (2D Array/Matrix with eigenvectors as columns).\n */\n return typed('eigs', {\n\n Array: function (x) {\n // check array size\n const mat = matrix(x)\n const size = mat.size()\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n // use dense 2D matrix implementation\n const ans = checkAndSubmit(mat, size[0])\n return { values: ans[0], vectors: ans[1] }\n },\n\n Matrix: function (x) {\n // use dense 2D array implementation\n // dense matrix\n const size = x.size()\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n const ans = checkAndSubmit(x, size[0])\n return { values: matrix(ans[0]), vectors: matrix(ans[1]) }\n }\n })\n\n // Is the matrix\n // symmetric ?\n function isSymmetric (x, n) {\n for (let i = 0; i < n; i++) {\n for (let j = i; j < n; j++) {\n // not symmtric\n if (!equal(x[i][j], x[j][i])) {\n throw new TypeError('Input matrix is not symmetric')\n }\n }\n }\n }\n\n // check input for possible problems\n // and perform diagonalization efficiently for\n // specific type of number\n function checkAndSubmit (x, n) {\n let type = x.datatype()\n // type check\n if (type === undefined) {\n type = x.getDataType()\n }\n if (type !== 'number' && type !== 'BigNumber' && type !== 'Fraction') {\n if (type === 'mixed') {\n throw new TypeError('Mixed matrix element type is not supported')\n } else {\n throw new TypeError('Matrix element type not supported (' + type + ')')\n }\n } else {\n isSymmetric(x.toArray(), n)\n }\n\n // perform efficient calculation for 'numbers'\n if (type === 'number') {\n return diag(x.toArray())\n } else if (type === 'Fraction') {\n const xArr = x.toArray()\n // convert fraction to numbers\n for (let i = 0; i < n; i++) {\n for (let j = i; j < n; j++) {\n xArr[i][j] = xArr[i][j].valueOf()\n xArr[j][i] = xArr[i][j]\n }\n }\n return diag(x.toArray())\n } else if (type === 'BigNumber') {\n return diagBig(x.toArray())\n }\n }\n\n // diagonalization implementation for number (efficient)\n function diag (x) {\n const N = x.length\n const e0 = Math.abs(config.epsilon / N)\n let psi\n let Sij = new Array(N)\n // Sij is Identity Matrix\n for (let i = 0; i < N; i++) {\n Sij[i] = createArray(N, 0)\n Sij[i][i] = 1.0\n }\n // initial error\n let Vab = getAij(x)\n while (Math.abs(Vab[1]) >= Math.abs(e0)) {\n const i = Vab[0][0]\n const j = Vab[0][1]\n psi = getTheta(x[i][i], x[j][j], x[i][j])\n x = x1(x, psi, i, j)\n Sij = Sij1(Sij, psi, i, j)\n Vab = getAij(x)\n }\n const Ei = createArray(N, 0) // eigenvalues\n for (let i = 0; i < N; i++) {\n Ei[i] = x[i][i]\n }\n return sorting(clone(Ei), clone(Sij))\n }\n\n // diagonalization implementation for bigNumber\n function diagBig (x) {\n const N = x.length\n const e0 = abs(config.epsilon / N)\n let psi\n let Sij = new Array(N)\n // Sij is Identity Matrix\n for (let i = 0; i < N; i++) {\n Sij[i] = createArray(N, 0)\n Sij[i][i] = 1.0\n }\n // initial error\n let Vab = getAijBig(x)\n while (abs(Vab[1]) >= abs(e0)) {\n const i = Vab[0][0]\n const j = Vab[0][1]\n psi = getThetaBig(x[i][i], x[j][j], x[i][j])\n x = x1Big(x, psi, i, j)\n Sij = Sij1Big(Sij, psi, i, j)\n Vab = getAijBig(x)\n }\n const Ei = createArray(N, 0) // eigenvalues\n for (let i = 0; i < N; i++) {\n Ei[i] = x[i][i]\n }\n // return [clone(Ei), clone(Sij)]\n return sorting(clone(Ei), clone(Sij))\n }\n\n // get angle\n function getTheta (aii, ajj, aij) {\n const denom = (ajj - aii)\n if (Math.abs(denom) <= config.epsilon) {\n return Math.PI / 4\n } else {\n return 0.5 * Math.atan(2 * aij / (ajj - aii))\n }\n }\n\n // get angle\n function getThetaBig (aii, ajj, aij) {\n const denom = subtract(ajj, aii)\n if (abs(denom) <= config.epsilon) {\n return bignumber(-1).acos().div(4)\n } else {\n return multiplyScalar(0.5, atan(multiply(2, aij, inv(denom))))\n }\n }\n\n // update eigvec\n function Sij1 (Sij, theta, i, j) {\n const N = Sij.length\n const c = Math.cos(theta)\n const s = Math.sin(theta)\n const Ski = createArray(N, 0)\n const Skj = createArray(N, 0)\n for (let k = 0; k < N; k++) {\n Ski[k] = c * Sij[k][i] - s * Sij[k][j]\n Skj[k] = s * Sij[k][i] + c * Sij[k][j]\n }\n for (let k = 0; k < N; k++) {\n Sij[k][i] = Ski[k]\n Sij[k][j] = Skj[k]\n }\n return Sij\n }\n // update eigvec for overlap\n function Sij1Big (Sij, theta, i, j) {\n const N = Sij.length\n const c = cos(theta)\n const s = sin(theta)\n const Ski = createArray(N, bignumber(0))\n const Skj = createArray(N, bignumber(0))\n for (let k = 0; k < N; k++) {\n Ski[k] = subtract(multiplyScalar(c, Sij[k][i]), multiplyScalar(s, Sij[k][j]))\n Skj[k] = addScalar(multiplyScalar(s, Sij[k][i]), multiplyScalar(c, Sij[k][j]))\n }\n for (let k = 0; k < N; k++) {\n Sij[k][i] = Ski[k]\n Sij[k][j] = Skj[k]\n }\n return Sij\n }\n\n // update matrix\n function x1Big (Hij, theta, i, j) {\n const N = Hij.length\n const c = bignumber(cos(theta))\n const s = bignumber(sin(theta))\n const c2 = multiplyScalar(c, c)\n const s2 = multiplyScalar(s, s)\n const Aki = createArray(N, bignumber(0))\n const Akj = createArray(N, bignumber(0))\n // 2cs Hij\n const csHij = multiply(bignumber(2), c, s, Hij[i][j])\n // Aii\n const Aii = addScalar(subtract(multiplyScalar(c2, Hij[i][i]), csHij), multiplyScalar(s2, Hij[j][j]))\n const Ajj = add(multiplyScalar(s2, Hij[i][i]), csHij, multiplyScalar(c2, Hij[j][j]))\n // 0 to i\n for (let k = 0; k < N; k++) {\n Aki[k] = subtract(multiplyScalar(c, Hij[i][k]), multiplyScalar(s, Hij[j][k]))\n Akj[k] = addScalar(multiplyScalar(s, Hij[i][k]), multiplyScalar(c, Hij[j][k]))\n }\n // Modify Hij\n Hij[i][i] = Aii\n Hij[j][j] = Ajj\n Hij[i][j] = bignumber(0)\n Hij[j][i] = bignumber(0)\n // 0 to i\n for (let k = 0; k < N; k++) {\n if (k !== i && k !== j) {\n Hij[i][k] = Aki[k]\n Hij[k][i] = Aki[k]\n Hij[j][k] = Akj[k]\n Hij[k][j] = Akj[k]\n }\n }\n return Hij\n }\n\n // update matrix\n function x1 (Hij, theta, i, j) {\n const N = Hij.length\n const c = Math.cos(theta)\n const s = Math.sin(theta)\n const c2 = c * c\n const s2 = s * s\n const Aki = createArray(N, 0)\n const Akj = createArray(N, 0)\n // Aii\n const Aii = c2 * Hij[i][i] - 2 * c * s * Hij[i][j] + s2 * Hij[j][j]\n const Ajj = s2 * Hij[i][i] + 2 * c * s * Hij[i][j] + c2 * Hij[j][j]\n // 0 to i\n for (let k = 0; k < N; k++) {\n Aki[k] = c * Hij[i][k] - s * Hij[j][k]\n Akj[k] = s * Hij[i][k] + c * Hij[j][k]\n }\n // Modify Hij\n Hij[i][i] = Aii\n Hij[j][j] = Ajj\n Hij[i][j] = 0\n Hij[j][i] = 0\n // 0 to i\n for (let k = 0; k < N; k++) {\n if (k !== i && k !== j) {\n Hij[i][k] = Aki[k]\n Hij[k][i] = Aki[k]\n Hij[j][k] = Akj[k]\n Hij[k][j] = Akj[k]\n }\n }\n return Hij\n }\n\n // get max off-diagonal value from Upper Diagonal\n function getAij (Mij) {\n const N = Mij.length\n let maxMij = 0\n let maxIJ = [0, 1]\n for (let i = 0; i < N; i++) {\n for (let j = i + 1; j < N; j++) {\n if (Math.abs(maxMij) < Math.abs(Mij[i][j])) {\n maxMij = Math.abs(Mij[i][j])\n maxIJ = [i, j]\n }\n }\n }\n return [maxIJ, maxMij]\n }\n\n // get max off-diagonal value from Upper Diagonal\n function getAijBig (Mij) {\n const N = Mij.length\n let maxMij = 0\n let maxIJ = [0, 1]\n for (let i = 0; i < N; i++) {\n for (let j = i + 1; j < N; j++) {\n if (abs(maxMij) < abs(Mij[i][j])) {\n maxMij = abs(Mij[i][j])\n maxIJ = [i, j]\n }\n }\n }\n return [maxIJ, maxMij]\n }\n\n // sort results\n function sorting (E, S) {\n const N = E.length\n const Ef = Array(N)\n const Sf = Array(N)\n for (let k = 0; k < N; k++) {\n Sf[k] = Array(N)\n }\n for (let i = 0; i < N; i++) {\n let minID = 0\n let minE = E[0]\n for (let j = 0; j < E.length; j++) {\n if (E[j] < minE) {\n minID = j\n minE = E[minID]\n }\n }\n Ef[i] = E.splice(minID, 1)[0]\n for (let k = 0; k < N; k++) {\n Sf[k][i] = S[k][minID]\n S[k].splice(minID, 1)\n }\n }\n return [clone(Ef), clone(Sf)]\n }\n\n /**\n * Create an array of a certain size and fill all items with an initial value\n * @param {number} size\n * @param {number} value\n * @return {number[]}\n */\n function createArray (size, value) {\n // TODO: as soon as all browsers support Array.fill, use that instead (IE doesn't support it)\n const array = new Array(size)\n\n for (let i = 0; i < size; i++) {\n array[i] = value\n }\n\n return array\n }\n})\n","import { isSparseMatrix } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'expm'\nconst dependencies = ['typed', 'abs', 'add', 'identity', 'inv', 'multiply']\n\nexport const createExpm = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, identity, inv, multiply }) => {\n /**\n * Compute the matrix exponential, expm(A) = e^A. The matrix must be square.\n * Not to be confused with exp(a), which performs element-wise\n * exponentiation.\n *\n * The exponential is calculated using the Padé approximant with scaling and\n * squaring; see \"Nineteen Dubious Ways to Compute the Exponential of a\n * Matrix,\" by Moler and Van Loan.\n *\n * Syntax:\n *\n * math.expm(x)\n *\n * Examples:\n *\n * const A = [[0,2],[0,0]]\n * math.expm(A) // returns [[1,2],[0,1]]\n *\n * See also:\n *\n * exp\n *\n * @param {Matrix} x A square Matrix\n * @return {Matrix} The exponential of x\n */\n return typed(name, {\n\n Matrix: function (A) {\n // Check matrix size\n const size = A.size()\n\n if (size.length !== 2 || size[0] !== size[1]) {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n const n = size[0]\n\n // Desired accuracy of the approximant (The actual accuracy\n // will be affected by round-off error)\n const eps = 1e-15\n\n // The Padé approximant is not so accurate when the values of A\n // are \"large\", so scale A by powers of two. Then compute the\n // exponential, and square the result repeatedly according to\n // the identity e^A = (e^(A/m))^m\n\n // Compute infinity-norm of A, ||A||, to see how \"big\" it is\n const infNorm = infinityNorm(A)\n\n // Find the optimal scaling factor and number of terms in the\n // Padé approximant to reach the desired accuracy\n const params = findParams(infNorm, eps)\n const q = params.q\n const j = params.j\n\n // The Pade approximation to e^A is:\n // Rqq(A) = Dqq(A) ^ -1 * Nqq(A)\n // where\n // Nqq(A) = sum(i=0, q, (2q-i)!p! / [ (2q)!i!(q-i)! ] A^i\n // Dqq(A) = sum(i=0, q, (2q-i)!q! / [ (2q)!i!(q-i)! ] (-A)^i\n\n // Scale A by 1 / 2^j\n const Apos = multiply(A, Math.pow(2, -j))\n\n // The i=0 term is just the identity matrix\n let N = identity(n)\n let D = identity(n)\n\n // Initialization (i=0)\n let factor = 1\n\n // Initialization (i=1)\n let AposToI = Apos // Cloning not necessary\n let alternate = -1\n\n for (let i = 1; i <= q; i++) {\n if (i > 1) {\n AposToI = multiply(AposToI, Apos)\n alternate = -alternate\n }\n factor = factor * (q - i + 1) / ((2 * q - i + 1) * i)\n\n N = add(N, multiply(factor, AposToI))\n D = add(D, multiply(factor * alternate, AposToI))\n }\n\n let R = multiply(inv(D), N)\n\n // Square j times\n for (let i = 0; i < j; i++) {\n R = multiply(R, R)\n }\n\n return isSparseMatrix(A)\n ? A.createSparseMatrix(R)\n : R\n }\n\n })\n\n function infinityNorm (A) {\n const n = A.size()[0]\n let infNorm = 0\n for (let i = 0; i < n; i++) {\n let rowSum = 0\n for (let j = 0; j < n; j++) {\n rowSum += abs(A.get([i, j]))\n }\n infNorm = Math.max(rowSum, infNorm)\n }\n return infNorm\n }\n\n /**\n * Find the best parameters for the Pade approximant given\n * the matrix norm and desired accuracy. Returns the first acceptable\n * combination in order of increasing computational load.\n */\n function findParams (infNorm, eps) {\n const maxSearchSize = 30\n for (let k = 0; k < maxSearchSize; k++) {\n for (let q = 0; q <= k; q++) {\n const j = k - q\n if (errorEstimate(infNorm, q, j) < eps) {\n return { q: q, j: j }\n }\n }\n }\n throw new Error('Could not find acceptable parameters to compute the matrix exponential (try increasing maxSearchSize in expm.js)')\n }\n\n /**\n * Returns the estimated error of the Pade approximant for the given\n * parameters.\n */\n function errorEstimate (infNorm, q, j) {\n let qfac = 1\n for (let i = 2; i <= q; i++) {\n qfac *= i\n }\n let twoqfac = qfac\n for (let i = q + 1; i <= 2 * q; i++) {\n twoqfac *= i\n }\n const twoqp1fac = twoqfac * (2 * q + 1)\n\n return 8.0 *\n Math.pow(infNorm / Math.pow(2, j), 2 * q) *\n qfac * qfac / (twoqfac * twoqp1fac)\n }\n})\n","import { isMatrix } from '../../utils/is.js'\nimport { format } from '../../utils/string.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'sqrtm'\nconst dependencies = ['typed', 'abs', 'add', 'multiply', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity']\n\nexport const createSqrtm = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, add, multiply, sqrt, subtract, inv, size, max, identity }) => {\n const _maxIterations = 1e3\n const _tolerance = 1e-6\n\n /**\n * Calculate the principal square root matrix using the Denman–Beavers iterative method\n *\n * https://en.wikipedia.org/wiki/Square_root_of_a_matrix#By_Denman–Beavers_iteration\n *\n * @param {Array | Matrix} A The square matrix `A`\n * @return {Array | Matrix} The principal square root of matrix `A`\n * @private\n */\n function _denmanBeavers (A) {\n let error\n let iterations = 0\n\n let Y = A\n let Z = identity(size(A))\n\n do {\n const Yk = Y\n Y = multiply(0.5, add(Yk, inv(Z)))\n Z = multiply(0.5, add(Z, inv(Yk)))\n\n error = max(abs(subtract(Y, Yk)))\n\n if (error > _tolerance && ++iterations > _maxIterations) {\n throw new Error('computing square root of matrix: iterative method could not converge')\n }\n } while (error > _tolerance)\n\n return Y\n }\n\n /**\n * Calculate the principal square root of a square matrix.\n * The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.\n *\n * https://en.wikipedia.org/wiki/Square_root_of_a_matrix\n *\n * Syntax:\n *\n * X = math.sqrtm(A)\n *\n * Examples:\n *\n * math.sqrtm([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]]\n *\n * See also:\n *\n * sqrt, pow\n *\n * @param {Array | Matrix} A The square matrix `A`\n * @return {Array | Matrix} The principal square root of matrix `A`\n */\n return typed(name, {\n 'Array | Matrix': function (A) {\n const size = isMatrix(A) ? A.size() : arraySize(A)\n switch (size.length) {\n case 1:\n // Single element Array | Matrix\n if (size[0] === 1) {\n return sqrt(A)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n\n case 2:\n {\n // Two-dimensional Array | Matrix\n const rows = size[0]\n const cols = size[1]\n if (rows === cols) {\n return _denmanBeavers(A)\n } else {\n throw new RangeError('Matrix must be square ' +\n '(size: ' + format(size) + ')')\n }\n }\n default:\n // Multi dimensional array\n throw new RangeError('Matrix must be at most two dimensional ' +\n '(size: ' + format(size) + ')')\n }\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\nimport { extend } from '../../utils/object.js'\nimport { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js'\nimport { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js'\n\nconst name = 'divide'\nconst dependencies = [\n 'typed',\n 'matrix',\n 'multiply',\n 'equalScalar',\n 'divideScalar',\n 'inv'\n]\n\nexport const createDivide = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, multiply, equalScalar, divideScalar, inv }) => {\n const algorithm11 = createAlgorithm11({ typed, equalScalar })\n const algorithm14 = createAlgorithm14({ typed })\n\n /**\n * Divide two values, `x / y`.\n * To divide matrices, `x` is multiplied with the inverse of `y`: `x * inv(y)`.\n *\n * Syntax:\n *\n * math.divide(x, y)\n *\n * Examples:\n *\n * math.divide(2, 3) // returns number 0.6666666666666666\n *\n * const a = math.complex(5, 14)\n * const b = math.complex(4, 1)\n * math.divide(a, b) // returns Complex 2 + 3i\n *\n * const c = [[7, -6], [13, -4]]\n * const d = [[1, 2], [4, 3]]\n * math.divide(c, d) // returns Array [[-9, 4], [-11, 6]]\n *\n * const e = math.unit('18 km')\n * math.divide(e, 4.5) // returns Unit 4 km\n *\n * See also:\n *\n * multiply\n *\n * @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x Numerator\n * @param {number | BigNumber | Fraction | Complex | Array | Matrix} y Denominator\n * @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Quotient, `x / y`\n */\n return typed('divide', extend({\n // we extend the signatures of divideScalar with signatures dealing with matrices\n\n 'Array | Matrix, Array | Matrix': function (x, y) {\n // TODO: implement matrix right division using pseudo inverse\n // https://www.mathworks.nl/help/matlab/ref/mrdivide.html\n // https://www.gnu.org/software/octave/doc/interpreter/Arithmetic-Ops.html\n // https://stackoverflow.com/questions/12263932/how-does-gnu-octave-matrix-division-work-getting-unexpected-behaviour\n return multiply(x, inv(y))\n },\n\n 'DenseMatrix, any': function (x, y) {\n return algorithm14(x, y, divideScalar, false)\n },\n\n 'SparseMatrix, any': function (x, y) {\n return algorithm11(x, y, divideScalar, false)\n },\n\n 'Array, any': function (x, y) {\n // use matrix implementation\n return algorithm14(matrix(x), y, divideScalar, false).valueOf()\n },\n\n 'any, Array | Matrix': function (x, y) {\n return multiply(x, inv(y))\n }\n }, divideScalar.signatures))\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'distance'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'subtract',\n 'divideScalar',\n 'multiplyScalar',\n 'unaryMinus',\n 'sqrt',\n 'abs'\n]\n\nexport const createDistance = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, subtract, multiplyScalar, divideScalar, unaryMinus, sqrt, abs }) => {\n /**\n * Calculates:\n * The eucledian distance between two points in N-dimensional spaces.\n * Distance between point and a line in 2 and 3 dimensional spaces.\n * Pairwise distance between a set of 2D or 3D points\n * NOTE:\n * When substituting coefficients of a line(a, b and c), use ax + by + c = 0 instead of ax + by = c\n * For parametric equation of a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b, c)\n *\n * Syntax:\n * math.distance([x1, y1], [x2, y2])\n *- math.distance({pointOneX: 4, pointOneY: 5}, {pointTwoX: 2, pointTwoY: 7})\n * math.distance([x1, y1, z1], [x2, y2, z2])\n * math.distance({pointOneX: 4, pointOneY: 5, pointOneZ: 8}, {pointTwoX: 2, pointTwoY: 7, pointTwoZ: 9})\n * math.distance([x1, y1, ... , N1], [x2, y2, ... , N2])\n * math.distance([[A], [B], [C]...])\n * math.distance([x1, y1], [LinePtX1, LinePtY1], [LinePtX2, LinePtY2])\n * math.distance({pointX: 1, pointY: 4}, {lineOnePtX: 6, lineOnePtY: 3}, {lineTwoPtX: 2, lineTwoPtY: 8})\n * math.distance([x1, y1, z1], [LinePtX1, LinePtY1, LinePtZ1], [LinePtX2, LinePtY2, LinePtZ2])\n * math.distance({pointX: 1, pointY: 4, pointZ: 7}, {lineOnePtX: 6, lineOnePtY: 3, lineOnePtZ: 4}, {lineTwoPtX: 2, lineTwoPtY: 8, lineTwoPtZ: 5})\n * math.distance([x1, y1], [xCoeffLine, yCoeffLine, constant])\n * math.distance({pointX: 10, pointY: 10}, {xCoeffLine: 8, yCoeffLine: 1, constant: 3})\n * math.distance([x1, y1, z1], [x0, y0, z0, a-tCoeff, b-tCoeff, c-tCoeff]) point and parametric equation of 3D line\n * math.distance([x, y, z], [x0, y0, z0, a, b, c])\n * math.distance({pointX: 2, pointY: 5, pointZ: 9}, {x0: 4, y0: 6, z0: 3, a: 4, b: 2, c: 0})\n *\n * Examples:\n * math.distance([0,0], [4,4]) // Returns 5.6569\n * math.distance(\n * {pointOneX: 0, pointOneY: 0},\n * {pointTwoX: 10, pointTwoY: 10}) // Returns 14.142135623730951\n * math.distance([1, 0, 1], [4, -2, 2]) // Returns 3.74166\n * math.distance(\n * {pointOneX: 4, pointOneY: 5, pointOneZ: 8},\n * {pointTwoX: 2, pointTwoY: 7, pointTwoZ: 9}) // Returns 3\n * math.distance([1, 0, 1, 0], [0, -1, 0, -1]) // Returns 2\n * math.distance([[1, 2], [1, 2], [1, 3]]) // Returns [0, 1, 1]\n * math.distance([[1,2,4], [1,2,6], [8,1,3]]) // Returns [2, 7.14142842854285, 7.681145747868608]\n * math.distance([10, 10], [8, 1, 3]) // Returns 11.535230316796387\n * math.distance([10, 10], [2, 3], [-8, 0]) // Returns 8.759953130362847\n * math.distance(\n * {pointX: 1, pointY: 4},\n * {lineOnePtX: 6, lineOnePtY: 3},\n * {lineTwoPtX: 2, lineTwoPtY: 8}) // Returns 2.720549372624744\n * math.distance([2, 3, 1], [1, 1, 2, 5, 0, 1]) // Returns 2.3204774044612857\n * math.distance(\n * {pointX: 2, pointY: 3, pointZ: 1},\n * {x0: 1, y0: 1, z0: 2, a: 5, b: 0, c: 1} // Returns 2.3204774044612857\n *\n * @param {Array | Matrix | Object} x Co-ordinates of first point\n * @param {Array | Matrix | Object} y Co-ordinates of second point\n * @return {Number | BigNumber} Returns the distance from two/three points\n */\n return typed(name, {\n 'Array, Array, Array': function (x, y, z) {\n // Point to Line 2D (x=Point, y=LinePoint1, z=LinePoint2)\n if (x.length === 2 && y.length === 2 && z.length === 2) {\n if (!_2d(x)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument') }\n if (!_2d(y)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument') }\n if (!_2d(z)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument') }\n const m = divideScalar(subtract(z[1], z[0]), subtract(y[1], y[0]))\n const xCoeff = multiplyScalar(multiplyScalar(m, m), y[0])\n const yCoeff = unaryMinus(multiplyScalar(m, y[0]))\n const constant = x[1]\n\n return _distancePointLine2D(x[0], x[1], xCoeff, yCoeff, constant)\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Object, Object, Object': function (x, y, z) {\n if (Object.keys(x).length === 2 && Object.keys(y).length === 2 && Object.keys(z).length === 2) {\n if (!_2d(x)) { throw new TypeError('Values of pointX and pointY should be numbers or BigNumbers') }\n if (!_2d(y)) { throw new TypeError('Values of lineOnePtX and lineOnePtY should be numbers or BigNumbers') }\n if (!_2d(z)) { throw new TypeError('Values of lineTwoPtX and lineTwoPtY should be numbers or BigNumbers') }\n if ('pointX' in x && 'pointY' in x && 'lineOnePtX' in y &&\n 'lineOnePtY' in y && 'lineTwoPtX' in z && 'lineTwoPtY' in z) {\n const m = divideScalar(subtract(z.lineTwoPtY, z.lineTwoPtX), subtract(y.lineOnePtY, y.lineOnePtX))\n const xCoeff = multiplyScalar(multiplyScalar(m, m), y.lineOnePtX)\n const yCoeff = unaryMinus(multiplyScalar(m, y.lineOnePtX))\n const constant = x.pointX\n\n return _distancePointLine2D(x.pointX, x.pointY, xCoeff, yCoeff, constant)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Array, Array': function (x, y) {\n // Point to Line 2D (x=[pointX, pointY], y=[x-coeff, y-coeff, const])\n if (x.length === 2 && y.length === 3) {\n if (!_2d(x)) {\n throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument')\n }\n if (!_3d(y)) {\n throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument')\n }\n\n return _distancePointLine2D(x[0], x[1], y[0], y[1], y[2])\n } else if (x.length === 3 && y.length === 6) {\n // Point to Line 3D\n if (!_3d(x)) {\n throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument')\n }\n if (!_parametricLine(y)) {\n throw new TypeError('Array with 6 numbers or BigNumbers expected for second argument')\n }\n\n return _distancePointLine3D(x[0], x[1], x[2], y[0], y[1], y[2], y[3], y[4], y[5])\n } else if (x.length === y.length && x.length > 0) {\n // Point to Point N-dimensions\n if (!_containsOnlyNumbers(x)) {\n throw new TypeError('All values of an array should be numbers or BigNumbers')\n }\n if (!_containsOnlyNumbers(y)) {\n throw new TypeError('All values of an array should be numbers or BigNumbers')\n }\n\n return _euclideanDistance(x, y)\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n 'Object, Object': function (x, y) {\n if (Object.keys(x).length === 2 && Object.keys(y).length === 3) {\n if (!_2d(x)) {\n throw new TypeError('Values of pointX and pointY should be numbers or BigNumbers')\n }\n if (!_3d(y)) {\n throw new TypeError('Values of xCoeffLine, yCoeffLine and constant should be numbers or BigNumbers')\n }\n if ('pointX' in x && 'pointY' in x && 'xCoeffLine' in y && 'yCoeffLine' in y && 'constant' in y) {\n return _distancePointLine2D(x.pointX, x.pointY, y.xCoeffLine, y.yCoeffLine, y.constant)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 3 && Object.keys(y).length === 6) {\n // Point to Line 3D\n if (!_3d(x)) {\n throw new TypeError('Values of pointX, pointY and pointZ should be numbers or BigNumbers')\n }\n if (!_parametricLine(y)) {\n throw new TypeError('Values of x0, y0, z0, a, b and c should be numbers or BigNumbers')\n }\n if ('pointX' in x && 'pointY' in x && 'x0' in y && 'y0' in y && 'z0' in y && 'a' in y && 'b' in y && 'c' in y) {\n return _distancePointLine3D(x.pointX, x.pointY, x.pointZ, y.x0, y.y0, y.z0, y.a, y.b, y.c)\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 2 && Object.keys(y).length === 2) {\n // Point to Point 2D\n if (!_2d(x)) {\n throw new TypeError('Values of pointOneX and pointOneY should be numbers or BigNumbers')\n }\n if (!_2d(y)) {\n throw new TypeError('Values of pointTwoX and pointTwoY should be numbers or BigNumbers')\n }\n if ('pointOneX' in x && 'pointOneY' in x && 'pointTwoX' in y && 'pointTwoY' in y) {\n return _euclideanDistance([x.pointOneX, x.pointOneY], [y.pointTwoX, y.pointTwoY])\n } else {\n throw new TypeError('Key names do not match')\n }\n } else if (Object.keys(x).length === 3 && Object.keys(y).length === 3) {\n // Point to Point 3D\n if (!_3d(x)) {\n throw new TypeError('Values of pointOneX, pointOneY and pointOneZ should be numbers or BigNumbers')\n }\n if (!_3d(y)) {\n throw new TypeError('Values of pointTwoX, pointTwoY and pointTwoZ should be numbers or BigNumbers')\n }\n if ('pointOneX' in x && 'pointOneY' in x && 'pointOneZ' in x &&\n 'pointTwoX' in y && 'pointTwoY' in y && 'pointTwoZ' in y\n ) {\n return _euclideanDistance([x.pointOneX, x.pointOneY, x.pointOneZ], [y.pointTwoX, y.pointTwoY, y.pointTwoZ])\n } else {\n throw new TypeError('Key names do not match')\n }\n } else {\n throw new TypeError('Invalid Arguments: Try again')\n }\n },\n Array: function (arr) {\n if (!_pairwise(arr)) { throw new TypeError('Incorrect array format entered for pairwise distance calculation') }\n\n return _distancePairwise(arr)\n }\n })\n\n function _isNumber (a) {\n // distance supports numbers and bignumbers\n return (typeof a === 'number' || isBigNumber(a))\n }\n\n function _2d (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1])\n }\n\n function _3d (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1]) && _isNumber(a[2])\n }\n\n function _containsOnlyNumbers (a) {\n // checks if the number of arguments are correct in count and are valid (should be numbers)\n if (!Array.isArray(a)) {\n a = _objectToArray(a)\n }\n return a.every(_isNumber)\n }\n\n function _parametricLine (a) {\n if (a.constructor !== Array) {\n a = _objectToArray(a)\n }\n return _isNumber(a[0]) && _isNumber(a[1]) && _isNumber(a[2]) &&\n _isNumber(a[3]) && _isNumber(a[4]) && _isNumber(a[5])\n }\n\n function _objectToArray (o) {\n const keys = Object.keys(o)\n const a = []\n for (let i = 0; i < keys.length; i++) {\n a.push(o[keys[i]])\n }\n return a\n }\n\n function _pairwise (a) {\n // checks for valid arguments passed to _distancePairwise(Array)\n if (a[0].length === 2 && _isNumber(a[0][0]) && _isNumber(a[0][1])) {\n if (a.some(aI => aI.length !== 2 || !_isNumber(aI[0]) || !_isNumber(aI[1]))) {\n return false\n }\n } else if (a[0].length === 3 && _isNumber(a[0][0]) && _isNumber(a[0][1]) && _isNumber(a[0][2])) {\n if (a.some(aI => aI.length !== 3 || !_isNumber(aI[0]) || !_isNumber(aI[1]) || !_isNumber(aI[2]))) {\n return false\n }\n } else {\n return false\n }\n return true\n }\n\n function _distancePointLine2D (x, y, a, b, c) {\n const num = abs(addScalar(addScalar(multiplyScalar(a, x), multiplyScalar(b, y)), c))\n const den = sqrt(addScalar(multiplyScalar(a, a), multiplyScalar(b, b)))\n return divideScalar(num, den)\n }\n\n function _distancePointLine3D (x, y, z, x0, y0, z0, a, b, c) {\n let num = [subtract(multiplyScalar(subtract(y0, y), c), multiplyScalar(subtract(z0, z), b)),\n subtract(multiplyScalar(subtract(z0, z), a), multiplyScalar(subtract(x0, x), c)),\n subtract(multiplyScalar(subtract(x0, x), b), multiplyScalar(subtract(y0, y), a))]\n num = sqrt(addScalar(addScalar(multiplyScalar(num[0], num[0]), multiplyScalar(num[1], num[1])), multiplyScalar(num[2], num[2])))\n const den = sqrt(addScalar(addScalar(multiplyScalar(a, a), multiplyScalar(b, b)), multiplyScalar(c, c)))\n return divideScalar(num, den)\n }\n\n function _euclideanDistance (x, y) {\n const vectorSize = x.length\n let result = 0\n let diff = 0\n for (let i = 0; i < vectorSize; i++) {\n diff = subtract(x[i], y[i])\n result = addScalar(multiplyScalar(diff, diff), result)\n }\n return sqrt(result)\n }\n\n function _distancePairwise (a) {\n const result = []\n let pointA = []\n let pointB = []\n for (let i = 0; i < a.length - 1; i++) {\n for (let j = i + 1; j < a.length; j++) {\n if (a[0].length === 2) {\n pointA = [a[i][0], a[i][1]]\n pointB = [a[j][0], a[j][1]]\n } else if (a[0].length === 3) {\n pointA = [a[i][0], a[i][1], a[i][2]]\n pointB = [a[j][0], a[j][1], a[j][2]]\n }\n result.push(_euclideanDistance(pointA, pointB))\n }\n }\n return result\n }\n})\n","import { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'intersect'\nconst dependencies = [\n 'typed', 'config', 'abs', 'add', 'addScalar', 'matrix', 'multiply', 'multiplyScalar', 'divideScalar', 'subtract', 'smaller', 'equalScalar'\n]\n\nexport const createIntersect = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, abs, add, addScalar, matrix, multiply, multiplyScalar, divideScalar, subtract, smaller, equalScalar }) => {\n /**\n * Calculates the point of intersection of two lines in two or three dimensions\n * and of a line and a plane in three dimensions. The inputs are in the form of\n * arrays or 1 dimensional matrices. The line intersection functions return null\n * if the lines do not meet.\n *\n * Note: Fill the plane coefficients as `x + y + z = c` and not as `x + y + z + c = 0`.\n *\n * Syntax:\n *\n * math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)\n * math.intersect(endPoint1, endPoint2, planeCoefficients)\n *\n * Examples:\n *\n * math.intersect([0, 0], [10, 10], [10, 0], [0, 10]) // Returns [5, 5]\n * math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]) // Returns [5, 5, 0]\n * math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]) // Returns [7, -4, 3]\n *\n * @param {Array | Matrix} w Co-ordinates of first end-point of first line\n * @param {Array | Matrix} x Co-ordinates of second end-point of first line\n * @param {Array | Matrix} y Co-ordinates of first end-point of second line\n * OR Co-efficients of the plane's equation\n * @param {Array | Matrix} z Co-ordinates of second end-point of second line\n * OR null if the calculation is for line and plane\n * @return {Array} Returns the point of intersection of lines/lines-planes\n */\n return typed('intersect', {\n 'Array, Array, Array': function (x, y, plane) {\n if (!_3d(x)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument') }\n if (!_3d(y)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument') }\n if (!_4d(plane)) { throw new TypeError('Array with 4 numbers expected as third argument') }\n\n return _intersectLinePlane(x[0], x[1], x[2], y[0], y[1], y[2], plane[0], plane[1], plane[2], plane[3])\n },\n\n 'Array, Array, Array, Array': function (w, x, y, z) {\n if (w.length === 2) {\n if (!_2d(w)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for first argument') }\n if (!_2d(x)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for second argument') }\n if (!_2d(y)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for third argument') }\n if (!_2d(z)) { throw new TypeError('Array with 2 numbers or BigNumbers expected for fourth argument') }\n\n return _intersect2d(w, x, y, z)\n } else if (w.length === 3) {\n if (!_3d(w)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for first argument') }\n if (!_3d(x)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for second argument') }\n if (!_3d(y)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for third argument') }\n if (!_3d(z)) { throw new TypeError('Array with 3 numbers or BigNumbers expected for fourth argument') }\n\n return _intersect3d(w[0], w[1], w[2], x[0], x[1], x[2], y[0], y[1], y[2], z[0], z[1], z[2])\n } else {\n throw new TypeError('Arrays with two or thee dimensional points expected')\n }\n },\n\n 'Matrix, Matrix, Matrix': function (x, y, plane) {\n return matrix(this(x.valueOf(), y.valueOf(), plane.valueOf()))\n },\n\n 'Matrix, Matrix, Matrix, Matrix': function (w, x, y, z) {\n // TODO: output matrix type should match input matrix type\n return matrix(this(w.valueOf(), x.valueOf(), y.valueOf(), z.valueOf()))\n }\n })\n\n function _isNumeric (a) {\n // intersect supports numbers and bignumbers\n return (typeof a === 'number' || isBigNumber(a))\n }\n\n function _2d (x) {\n return x.length === 2 && _isNumeric(x[0]) && _isNumeric(x[1])\n }\n\n function _3d (x) {\n return x.length === 3 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2])\n }\n\n function _4d (x) {\n return x.length === 4 && _isNumeric(x[0]) && _isNumeric(x[1]) && _isNumeric(x[2]) && _isNumeric(x[3])\n }\n\n function _intersect2d (p1a, p1b, p2a, p2b) {\n const o1 = p1a\n const o2 = p2a\n const d1 = subtract(o1, p1b)\n const d2 = subtract(o2, p2b)\n const det = subtract(multiplyScalar(d1[0], d2[1]), multiplyScalar(d2[0], d1[1]))\n if (smaller(abs(det), config.epsilon)) {\n return null\n }\n const d20o11 = multiplyScalar(d2[0], o1[1])\n const d21o10 = multiplyScalar(d2[1], o1[0])\n const d20o21 = multiplyScalar(d2[0], o2[1])\n const d21o20 = multiplyScalar(d2[1], o2[0])\n const t = divideScalar(addScalar(subtract(subtract(d20o11, d21o10), d20o21), d21o20), det)\n return add(multiply(d1, t), o1)\n }\n\n function _intersect3dHelper (a, b, c, d, e, f, g, h, i, j, k, l) {\n // (a - b)*(c - d) + (e - f)*(g - h) + (i - j)*(k - l)\n const add1 = multiplyScalar(subtract(a, b), subtract(c, d))\n const add2 = multiplyScalar(subtract(e, f), subtract(g, h))\n const add3 = multiplyScalar(subtract(i, j), subtract(k, l))\n return addScalar(addScalar(add1, add2), add3)\n }\n\n function _intersect3d (x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4) {\n const d1343 = _intersect3dHelper(x1, x3, x4, x3, y1, y3, y4, y3, z1, z3, z4, z3)\n const d4321 = _intersect3dHelper(x4, x3, x2, x1, y4, y3, y2, y1, z4, z3, z2, z1)\n const d1321 = _intersect3dHelper(x1, x3, x2, x1, y1, y3, y2, y1, z1, z3, z2, z1)\n const d4343 = _intersect3dHelper(x4, x3, x4, x3, y4, y3, y4, y3, z4, z3, z4, z3)\n const d2121 = _intersect3dHelper(x2, x1, x2, x1, y2, y1, y2, y1, z2, z1, z2, z1)\n const ta = divideScalar(\n subtract(multiplyScalar(d1343, d4321), multiplyScalar(d1321, d4343)),\n subtract(multiplyScalar(d2121, d4343), multiplyScalar(d4321, d4321)))\n const tb = divideScalar(addScalar(d1343, multiplyScalar(ta, d4321)), d4343)\n\n const pax = addScalar(x1, multiplyScalar(ta, subtract(x2, x1)))\n const pay = addScalar(y1, multiplyScalar(ta, subtract(y2, y1)))\n const paz = addScalar(z1, multiplyScalar(ta, subtract(z2, z1)))\n const pbx = addScalar(x3, multiplyScalar(tb, subtract(x4, x3)))\n const pby = addScalar(y3, multiplyScalar(tb, subtract(y4, y3)))\n const pbz = addScalar(z3, multiplyScalar(tb, subtract(z4, z3)))\n if (equalScalar(pax, pbx) && equalScalar(pay, pby) && equalScalar(paz, pbz)) {\n return [pax, pay, paz]\n } else {\n return null\n }\n }\n\n function _intersectLinePlane (x1, y1, z1, x2, y2, z2, x, y, z, c) {\n const x1x = multiplyScalar(x1, x)\n const x2x = multiplyScalar(x2, x)\n const y1y = multiplyScalar(y1, y)\n const y2y = multiplyScalar(y2, y)\n const z1z = multiplyScalar(z1, z)\n const z2z = multiplyScalar(z2, z)\n const t = divideScalar(\n subtract(subtract(subtract(c, x1x), y1y), z1z),\n subtract(subtract(subtract(addScalar(addScalar(x2x, y2y), z2z), x1x), y1y), z1z))\n const px = addScalar(x1, multiplyScalar(t, subtract(x2, x1)))\n const py = addScalar(y1, multiplyScalar(t, subtract(y2, y1)))\n const pz = addScalar(z1, multiplyScalar(t, subtract(z2, z1)))\n return [px, py, pz]\n // TODO: Add cases when line is parallel to the plane:\n // (a) no intersection,\n // (b) line contained in plane\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'sum'\nconst dependencies = ['typed', 'config', 'add', 'numeric']\n\nexport const createSum = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, add, numeric }) => {\n /**\n * Compute the sum of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the sum of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.sum(a, b, c, ...)\n * math.sum(A)\n *\n * Examples:\n *\n * math.sum(2, 1, 4, 3) // returns 10\n * math.sum([2, 1, 4, 3]) // returns 10\n * math.sum([[2, 5], [4, 3], [1, 7]]) // returns 22\n *\n * See also:\n *\n * mean, median, min, max, prod, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The sum of all values\n */\n return typed(name, {\n // sum([a, b, c, d, ...])\n 'Array | Matrix': _sum,\n\n // sum([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': _nsumDim,\n\n // sum(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function sum')\n }\n\n return _sum(args)\n }\n })\n\n /**\n * Recursively calculate the sum of an n-dimensional array\n * @param {Array | Matrix} array\n * @return {number} sum\n * @private\n */\n function _sum (array) {\n let sum\n\n deepForEach(array, function (value) {\n try {\n sum = (sum === undefined) ? value : add(sum, value)\n } catch (err) {\n throw improveErrorMessage(err, 'sum', value)\n }\n })\n\n // make sure returning numeric value: parse a string into a numeric value\n if (sum === undefined) {\n sum = numeric(0, config.number)\n }\n if (typeof sum === 'string') {\n sum = numeric(sum, config.number)\n }\n\n return sum\n }\n\n function _nsumDim (array, dim) {\n try {\n const sum = reduce(array, dim, add)\n return sum\n } catch (err) {\n throw improveErrorMessage(err, 'sum')\n }\n }\n})\n","import { containsCollections, deepForEach, reduce } from '../../utils/collection.js'\nimport { arraySize } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'mean'\nconst dependencies = ['typed', 'add', 'divide']\n\nexport const createMean = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide }) => {\n /**\n * Compute the mean value of matrix or a list with values.\n * In case of a multi dimensional array, the mean of the flattened array\n * will be calculated. When `dim` is provided, the maximum over the selected\n * dimension will be calculated. Parameter `dim` is zero-based.\n *\n * Syntax:\n *\n * math.mean(a, b, c, ...)\n * math.mean(A)\n * math.mean(A, dim)\n *\n * Examples:\n *\n * math.mean(2, 1, 4, 3) // returns 2.5\n * math.mean([1, 2.7, 3.2, 4]) // returns 2.725\n *\n * math.mean([[2, 5], [6, 3], [1, 7]], 0) // returns [3, 5]\n * math.mean([[2, 5], [6, 3], [1, 7]], 1) // returns [3.5, 4.5, 4]\n *\n * See also:\n *\n * median, min, max, sum, prod, std, variance\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The mean of all values\n */\n return typed(name, {\n // mean([a, b, c, d, ...])\n 'Array | Matrix': _mean,\n\n // mean([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': _nmeanDim,\n\n // mean(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function mean')\n }\n\n return _mean(args)\n }\n })\n\n /**\n * Calculate the mean value in an n-dimensional array, returning a\n * n-1 dimensional array\n * @param {Array} array\n * @param {number} dim\n * @return {number} mean\n * @private\n */\n function _nmeanDim (array, dim) {\n try {\n const sum = reduce(array, dim, add)\n const s = Array.isArray(array) ? arraySize(array) : array.size()\n return divide(sum, s[dim])\n } catch (err) {\n throw improveErrorMessage(err, 'mean')\n }\n }\n\n /**\n * Recursively calculate the mean value in an n-dimensional array\n * @param {Array} array\n * @return {number} mean\n * @private\n */\n function _mean (array) {\n let sum\n let num = 0\n\n deepForEach(array, function (value) {\n try {\n sum = sum === undefined ? value : add(sum, value)\n num++\n } catch (err) {\n throw improveErrorMessage(err, 'mean', value)\n }\n })\n\n if (num === 0) {\n throw new Error('Cannot calculate the mean of an empty array')\n }\n return divide(sum, num)\n }\n})\n","import { containsCollections } from '../../utils/collection.js'\nimport { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'median'\nconst dependencies = ['typed', 'add', 'divide', 'compare', 'partitionSelect']\n\nexport const createMedian = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, compare, partitionSelect }) => {\n /**\n * Recursively calculate the median of an n-dimensional array\n * @param {Array} array\n * @return {Number} median\n * @private\n */\n function _median (array) {\n try {\n array = flatten(array.valueOf())\n\n const num = array.length\n if (num === 0) {\n throw new Error('Cannot calculate median of an empty array')\n }\n\n if (num % 2 === 0) {\n // even: return the average of the two middle values\n const mid = num / 2 - 1\n const right = partitionSelect(array, mid + 1)\n\n // array now partitioned at mid + 1, take max of left part\n let left = array[mid]\n for (let i = 0; i < mid; ++i) {\n if (compare(array[i], left) > 0) {\n left = array[i]\n }\n }\n\n return middle2(left, right)\n } else {\n // odd: return the middle value\n const m = partitionSelect(array, (num - 1) / 2)\n\n return middle(m)\n }\n } catch (err) {\n throw improveErrorMessage(err, 'median')\n }\n }\n\n // helper function to type check the middle value of the array\n const middle = typed({\n 'number | BigNumber | Complex | Unit': function (value) {\n return value\n }\n })\n\n // helper function to type check the two middle value of the array\n const middle2 = typed({\n 'number | BigNumber | Complex | Unit, number | BigNumber | Complex | Unit': function (left, right) {\n return divide(add(left, right), 2)\n }\n })\n\n /**\n * Compute the median of a matrix or a list with values. The values are\n * sorted and the middle value is returned. In case of an even number of\n * values, the average of the two middle values is returned.\n * Supported types of values are: Number, BigNumber, Unit\n *\n * In case of a (multi dimensional) array or matrix, the median of all\n * elements will be calculated.\n *\n * Syntax:\n *\n * math.median(a, b, c, ...)\n * math.median(A)\n *\n * Examples:\n *\n * math.median(5, 2, 7) // returns 5\n * math.median([3, -1, 5, 7]) // returns 4\n *\n * See also:\n *\n * mean, min, max, sum, prod, std, variance, quantileSeq\n *\n * @param {... *} args A single matrix or or multiple scalar values\n * @return {*} The median\n */\n return typed(name, {\n // median([a, b, c, d, ...])\n 'Array | Matrix': _median,\n\n // median([a, b, c, d, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n // TODO: implement median(A, dim)\n throw new Error('median(A, dim) is not yet supported')\n // return reduce(arguments[0], arguments[1], ...)\n },\n\n // median(a, b, c, d, ...)\n '...': function (args) {\n if (containsCollections(args)) {\n throw new TypeError('Scalar values expected in function median')\n }\n\n return _median(args)\n }\n })\n})\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst name = 'mad'\nconst dependencies = ['typed', 'abs', 'map', 'median', 'subtract']\n\nexport const createMad = /* #__PURE__ */ factory(name, dependencies, ({ typed, abs, map, median, subtract }) => {\n /**\n * Compute the median absolute deviation of a matrix or a list with values.\n * The median absolute deviation is defined as the median of the absolute\n * deviations from the median.\n *\n * Syntax:\n *\n * math.mad(a, b, c, ...)\n * math.mad(A)\n *\n * Examples:\n *\n * math.mad(10, 20, 30) // returns 10\n * math.mad([1, 2, 3]) // returns 1\n * math.mad([[1, 2, 3], [4, 5, 6]]) // returns 1.5\n *\n * See also:\n *\n * median, mean, std, abs\n *\n * @param {Array | Matrix} array\n * A single matrix or multiple scalar values.\n * @return {*} The median absolute deviation.\n */\n return typed(name, {\n // mad([a, b, c, d, ...])\n 'Array | Matrix': _mad,\n\n // mad(a, b, c, d, ...)\n '...': function (args) {\n return _mad(args)\n }\n })\n\n function _mad (array) {\n array = flatten(array.valueOf())\n\n if (array.length === 0) {\n throw new Error('Cannot calculate median absolute deviation (mad) of an empty array')\n }\n\n try {\n const med = median(array)\n return median(map(array, function (value) {\n return abs(subtract(value, med))\n }))\n } catch (err) {\n if (err instanceof TypeError && err.message.indexOf('median') !== -1) {\n throw new TypeError(err.message.replace('median', 'mad'))\n } else {\n throw improveErrorMessage(err, 'mad')\n }\n }\n }\n})\n","import { deepForEach } from '../../utils/collection.js'\nimport { isBigNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { improveErrorMessage } from './utils/improveErrorMessage.js'\n\nconst DEFAULT_NORMALIZATION = 'unbiased'\n\nconst name = 'variance'\nconst dependencies = ['typed', 'add', 'subtract', 'multiply', 'divide', 'apply', 'isNaN']\n\nexport const createVariance = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, subtract, multiply, divide, apply, isNaN }) => {\n /**\n * Compute the variance of a matrix or a list with values.\n * In case of a (multi dimensional) array or matrix, the variance over all\n * elements will be calculated.\n *\n * Additionally, it is possible to compute the variance along the rows\n * or columns of a matrix by specifying the dimension as the second argument.\n *\n * Optionally, the type of normalization can be specified as the final\n * parameter. The parameter `normalization` can be one of the following values:\n *\n * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n *\n *\n * Note that older browser may not like the variable name `var`. In that\n * case, the function can be called as `math['var'](...)` instead of\n * `math.var(...)`.\n *\n * Syntax:\n *\n * math.variance(a, b, c, ...)\n * math.variance(A)\n * math.variance(A, normalization)\n * math.variance(A, dimension)\n * math.variance(A, dimension, normalization)\n *\n * Examples:\n *\n * math.variance(2, 4, 6) // returns 4\n * math.variance([2, 4, 6, 8]) // returns 6.666666666666667\n * math.variance([2, 4, 6, 8], 'uncorrected') // returns 5\n * math.variance([2, 4, 6, 8], 'biased') // returns 4\n *\n * math.variance([[1, 2, 3], [4, 5, 6]]) // returns 3.5\n * math.variance([[1, 2, 3], [4, 6, 8]], 0) // returns [4.5, 8, 12.5]\n * math.variance([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 4]\n * math.variance([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.5, 2]\n *\n * See also:\n *\n * mean, median, max, min, prod, std, sum\n *\n * @param {Array | Matrix} array\n * A single matrix or or multiple scalar values\n * @param {string} [normalization='unbiased']\n * Determines how to normalize the variance.\n * Choose 'unbiased' (default), 'uncorrected', or 'biased'.\n * @param dimension {number | BigNumber}\n * Determines the axis to compute the variance for a matrix\n * @return {*} The variance\n */\n return typed(name, {\n // variance([a, b, c, d, ...])\n 'Array | Matrix': function (array) {\n return _var(array, DEFAULT_NORMALIZATION)\n },\n\n // variance([a, b, c, d, ...], normalization)\n 'Array | Matrix, string': _var,\n\n // variance([a, b, c, c, ...], dim)\n 'Array | Matrix, number | BigNumber': function (array, dim) {\n return _varDim(array, dim, DEFAULT_NORMALIZATION)\n },\n\n // variance([a, b, c, c, ...], dim, normalization)\n 'Array | Matrix, number | BigNumber, string': _varDim,\n\n // variance(a, b, c, d, ...)\n '...': function (args) {\n return _var(args, DEFAULT_NORMALIZATION)\n }\n })\n\n /**\n * Recursively calculate the variance of an n-dimensional array\n * @param {Array} array\n * @param {string} normalization\n * Determines how to normalize the variance:\n * - 'unbiased' The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n * @return {number | BigNumber} variance\n * @private\n */\n function _var (array, normalization) {\n let sum\n let num = 0\n\n if (array.length === 0) {\n throw new SyntaxError('Function variance requires one or more parameters (0 provided)')\n }\n\n // calculate the mean and number of elements\n deepForEach(array, function (value) {\n try {\n sum = sum === undefined ? value : add(sum, value)\n num++\n } catch (err) {\n throw improveErrorMessage(err, 'variance', value)\n }\n })\n if (num === 0) throw new Error('Cannot calculate variance of an empty array')\n\n const mean = divide(sum, num)\n\n // calculate the variance\n sum = undefined\n deepForEach(array, function (value) {\n const diff = subtract(value, mean)\n sum = sum === undefined ? multiply(diff, diff) : add(sum, multiply(diff, diff))\n })\n\n if (isNaN(sum)) {\n return sum\n }\n\n switch (normalization) {\n case 'uncorrected':\n return divide(sum, num)\n\n case 'biased':\n return divide(sum, num + 1)\n\n case 'unbiased':\n {\n const zero = isBigNumber(sum) ? sum.mul(0) : 0\n return (num === 1) ? zero : divide(sum, num - 1)\n }\n\n default:\n throw new Error('Unknown normalization \"' + normalization + '\". ' +\n 'Choose \"unbiased\" (default), \"uncorrected\", or \"biased\".')\n }\n }\n\n function _varDim (array, dim, normalization) {\n try {\n if (array.length === 0) {\n throw new SyntaxError('Function variance requires one or more parameters (0 provided)')\n }\n return apply(array, dim, (x) => _var(x, normalization))\n } catch (err) {\n throw improveErrorMessage(err, 'variance')\n }\n }\n})\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { isInteger } from '../../utils/number.js'\nimport { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'quantileSeq'\nconst dependencies = ['typed', 'add', 'multiply', 'partitionSelect', 'compare']\n\nexport const createQuantileSeq = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, multiply, partitionSelect, compare }) => {\n /**\n * Compute the prob order quantile of a matrix or a list with values.\n * The sequence is sorted and the middle value is returned.\n * Supported types of sequence values are: Number, BigNumber, Unit\n * Supported types of probability are: Number, BigNumber\n *\n * In case of a (multi dimensional) array or matrix, the prob order quantile\n * of all elements will be calculated.\n *\n * Syntax:\n *\n * math.quantileSeq(A, prob[, sorted])\n * math.quantileSeq(A, [prob1, prob2, ...][, sorted])\n * math.quantileSeq(A, N[, sorted])\n *\n * Examples:\n *\n * math.quantileSeq([3, -1, 5, 7], 0.5) // returns 4\n * math.quantileSeq([3, -1, 5, 7], [1/3, 2/3]) // returns [3, 5]\n * math.quantileSeq([3, -1, 5, 7], 2) // returns [3, 5]\n * math.quantileSeq([-1, 3, 5, 7], 0.5, true) // returns 4\n *\n * See also:\n *\n * median, mean, min, max, sum, prod, std, variance\n *\n * @param {Array, Matrix} data A single matrix or Array\n * @param {Number, BigNumber, Array} probOrN prob is the order of the quantile, while N is\n * the amount of evenly distributed steps of\n * probabilities; only one of these options can\n * be provided\n * @param {Boolean} sorted=false is data sorted in ascending order\n * @return {Number, BigNumber, Unit, Array} Quantile(s)\n */\n function quantileSeq (data, probOrN, sorted) {\n let probArr, dataArr, one\n\n if (arguments.length < 2 || arguments.length > 3) {\n throw new SyntaxError('Function quantileSeq requires two or three parameters')\n }\n\n if (isCollection(data)) {\n sorted = sorted || false\n if (typeof sorted === 'boolean') {\n dataArr = data.valueOf()\n if (isNumber(probOrN)) {\n if (probOrN < 0) {\n throw new Error('N/prob must be non-negative')\n }\n\n if (probOrN <= 1) {\n // quantileSeq([a, b, c, d, ...], prob[,sorted])\n return _quantileSeq(dataArr, probOrN, sorted)\n }\n\n if (probOrN > 1) {\n // quantileSeq([a, b, c, d, ...], N[,sorted])\n if (!isInteger(probOrN)) {\n throw new Error('N must be a positive integer')\n }\n\n const nPlusOne = probOrN + 1\n probArr = new Array(probOrN)\n for (let i = 0; i < probOrN;) {\n probArr[i] = _quantileSeq(dataArr, (++i) / nPlusOne, sorted)\n }\n return probArr\n }\n }\n\n if (isBigNumber(probOrN)) {\n const BigNumber = probOrN.constructor\n\n if (probOrN.isNegative()) {\n throw new Error('N/prob must be non-negative')\n }\n\n one = new BigNumber(1)\n\n if (probOrN.lte(one)) {\n // quantileSeq([a, b, c, d, ...], prob[,sorted])\n return new BigNumber(_quantileSeq(dataArr, probOrN, sorted))\n }\n\n if (probOrN.gt(one)) {\n // quantileSeq([a, b, c, d, ...], N[,sorted])\n if (!probOrN.isInteger()) {\n throw new Error('N must be a positive integer')\n }\n\n // largest possible Array length is 2^32-1\n // 2^32 < 10^15, thus safe conversion guaranteed\n const intN = probOrN.toNumber()\n if (intN > 4294967295) {\n throw new Error('N must be less than or equal to 2^32-1, as that is the maximum length of an Array')\n }\n\n const nPlusOne = new BigNumber(intN + 1)\n probArr = new Array(intN)\n for (let i = 0; i < intN;) {\n probArr[i] = new BigNumber(_quantileSeq(dataArr, new BigNumber(++i).div(nPlusOne), sorted))\n }\n return probArr\n }\n }\n\n if (Array.isArray(probOrN)) {\n // quantileSeq([a, b, c, d, ...], [prob1, prob2, ...][,sorted])\n probArr = new Array(probOrN.length)\n for (let i = 0; i < probArr.length; ++i) {\n const currProb = probOrN[i]\n if (isNumber(currProb)) {\n if (currProb < 0 || currProb > 1) {\n throw new Error('Probability must be between 0 and 1, inclusive')\n }\n } else if (isBigNumber(currProb)) {\n one = new currProb.constructor(1)\n if (currProb.isNegative() || currProb.gt(one)) {\n throw new Error('Probability must be between 0 and 1, inclusive')\n }\n } else {\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n probArr[i] = _quantileSeq(dataArr, currProb, sorted)\n }\n return probArr\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n throw new TypeError('Unexpected type of argument in function quantileSeq') // FIXME: becomes redundant when converted to typed-function\n }\n\n /**\n * Calculate the prob order quantile of an n-dimensional array.\n *\n * @param {Array} array\n * @param {Number, BigNumber} prob\n * @param {Boolean} sorted\n * @return {Number, BigNumber, Unit} prob order quantile\n * @private\n */\n function _quantileSeq (array, prob, sorted) {\n const flat = flatten(array)\n const len = flat.length\n if (len === 0) {\n throw new Error('Cannot calculate quantile of an empty sequence')\n }\n\n if (isNumber(prob)) {\n const index = prob * (len - 1)\n const fracPart = index % 1\n if (fracPart === 0) {\n const value = sorted ? flat[index] : partitionSelect(flat, index)\n\n validate(value)\n\n return value\n }\n\n const integerPart = Math.floor(index)\n\n let left\n let right\n if (sorted) {\n left = flat[integerPart]\n right = flat[integerPart + 1]\n } else {\n right = partitionSelect(flat, integerPart + 1)\n\n // max of partition is kth largest\n left = flat[integerPart]\n for (let i = 0; i < integerPart; ++i) {\n if (compare(flat[i], left) > 0) {\n left = flat[i]\n }\n }\n }\n\n validate(left)\n validate(right)\n\n // Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]\n return add(multiply(left, 1 - fracPart), multiply(right, fracPart))\n }\n\n // If prob is a BigNumber\n let index = prob.times(len - 1)\n if (index.isInteger()) {\n index = index.toNumber()\n const value = sorted ? flat[index] : partitionSelect(flat, index)\n\n validate(value)\n\n return value\n }\n\n const integerPart = index.floor()\n const fracPart = index.minus(integerPart)\n const integerPartNumber = integerPart.toNumber()\n\n let left\n let right\n if (sorted) {\n left = flat[integerPartNumber]\n right = flat[integerPartNumber + 1]\n } else {\n right = partitionSelect(flat, integerPartNumber + 1)\n\n // max of partition is kth largest\n left = flat[integerPartNumber]\n for (let i = 0; i < integerPartNumber; ++i) {\n if (compare(flat[i], left) > 0) {\n left = flat[i]\n }\n }\n }\n\n validate(left)\n validate(right)\n\n // Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]\n const one = new fracPart.constructor(1)\n return add(multiply(left, one.minus(fracPart)), multiply(right, fracPart))\n }\n\n /**\n * Check if array value types are valid, throw error otherwise.\n * @param {number | BigNumber | Unit} x\n * @param {number | BigNumber | Unit} x\n * @private\n */\n const validate = typed({\n 'number | BigNumber | Unit': function (x) {\n return x\n }\n })\n\n return quantileSeq\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'std'\nconst dependencies = ['typed', 'sqrt', 'variance']\n\nexport const createStd = /* #__PURE__ */ factory(name, dependencies, ({ typed, sqrt, variance }) => {\n /**\n * Compute the standard deviation of a matrix or a list with values.\n * The standard deviations is defined as the square root of the variance:\n * `std(A) = sqrt(variance(A))`.\n * In case of a (multi dimensional) array or matrix, the standard deviation\n * over all elements will be calculated by default, unless an axis is specified\n * in which case the standard deviation will be computed along that axis.\n *\n * Additionally, it is possible to compute the standard deviation along the rows\n * or columns of a matrix by specifying the dimension as the second argument.\n *\n * Optionally, the type of normalization can be specified as the final\n * parameter. The parameter `normalization` can be one of the following values:\n *\n * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)\n * - 'uncorrected' The sum of squared errors is divided by n\n * - 'biased' The sum of squared errors is divided by (n + 1)\n *\n *\n * Syntax:\n *\n * math.std(a, b, c, ...)\n * math.std(A)\n * math.std(A, normalization)\n * math.std(A, dimension)\n * math.std(A, dimension, normalization)\n *\n * Examples:\n *\n * math.std(2, 4, 6) // returns 2\n * math.std([2, 4, 6, 8]) // returns 2.581988897471611\n * math.std([2, 4, 6, 8], 'uncorrected') // returns 2.23606797749979\n * math.std([2, 4, 6, 8], 'biased') // returns 2\n *\n * math.std([[1, 2, 3], [4, 5, 6]]) // returns 1.8708286933869707\n * math.std([[1, 2, 3], [4, 6, 8]], 0) // returns [2.1213203435596424, 2.8284271247461903, 3.5355339059327378]\n * math.std([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 2]\n * math.std([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.7071067811865476, 1.4142135623730951]\n *\n * See also:\n *\n * mean, median, max, min, prod, sum, variance\n *\n * @param {Array | Matrix} array\n * A single matrix or or multiple scalar values\n * @param {string} [normalization='unbiased']\n * Determines how to normalize the variance.\n * Choose 'unbiased' (default), 'uncorrected', or 'biased'.\n * @param dimension {number | BigNumber}\n * Determines the axis to compute the standard deviation for a matrix\n * @return {*} The standard deviation\n */\n return typed(name, {\n // std([a, b, c, d, ...])\n 'Array | Matrix': _std,\n\n // std([a, b, c, d, ...], normalization)\n 'Array | Matrix, string': _std,\n\n // std([a, b, c, c, ...], dim)\n 'Array | Matrix, number | BigNumber': _std,\n\n // std([a, b, c, c, ...], dim, normalization)\n 'Array | Matrix, number | BigNumber, string': _std,\n\n // std(a, b, c, d, ...)\n '...': function (args) {\n return _std(args)\n }\n })\n\n function _std (array, normalization) {\n if (array.length === 0) {\n throw new SyntaxError('Function std requires one or more parameters (0 provided)')\n }\n\n try {\n return sqrt(variance.apply(null, arguments))\n } catch (err) {\n if (err instanceof TypeError && err.message.indexOf(' variance') !== -1) {\n throw new TypeError(err.message.replace(' variance', ' std'))\n } else {\n throw err\n }\n }\n }\n})\n","/** @param {number} i\n * @param {number} n\n * @returns {number} product of i to n\n */\nexport function product (i, n) {\n if (n < i) {\n return 1\n }\n\n if (n === i) {\n return n\n }\n\n const half = (n + i) >> 1 // divide (n + i) by 2 and truncate to integer\n return product(i, half) * product(half + 1, n)\n}\n","import { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nexport function combinationsNumber (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (k > n) {\n throw new TypeError('k must be less than or equal to n')\n }\n\n const nMinusk = n - k\n\n let prodrange\n if (k < nMinusk) {\n prodrange = product(nMinusk + 1, n)\n return prodrange / product(1, k)\n }\n prodrange = product(k + 1, n)\n return prodrange / product(1, nMinusk)\n}\ncombinationsNumber.signature = 'number, number'\n","import { factory } from '../../utils/factory.js'\nimport { combinationsNumber } from '../../plain/number/combinations.js'\n\nconst name = 'combinations'\nconst dependencies = ['typed']\n\nexport const createCombinations = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the number of ways of picking `k` unordered outcomes from `n`\n * possibilities.\n *\n * Combinations only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.combinations(n, k)\n *\n * Examples:\n *\n * math.combinations(7, 5) // returns 21\n *\n * See also:\n *\n * combinationsWithRep, permutations, factorial\n *\n * @param {number | BigNumber} n Total number of objects in the set\n * @param {number | BigNumber} k Number of objects in the subset\n * @return {number | BigNumber} Number of possible combinations.\n */\n return typed(name, {\n 'number, number': combinationsNumber,\n\n 'BigNumber, BigNumber': function (n, k) {\n const BigNumber = n.constructor\n let result, i\n const nMinusk = n.minus(k)\n const one = new BigNumber(1)\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function combinations')\n }\n if (k.gt(n)) {\n throw new TypeError('k must be less than n in function combinations')\n }\n\n result = one\n if (k.lt(nMinusk)) {\n for (i = one; i.lte(nMinusk); i = i.plus(one)) {\n result = result.times(k.plus(i)).dividedBy(i)\n }\n } else {\n for (i = one; i.lte(k); i = i.plus(one)) {\n result = result.times(nMinusk.plus(i)).dividedBy(i)\n }\n }\n\n return result\n }\n\n // TODO: implement support for collection in combinations\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","import { factory } from '../../utils/factory.js'\nimport { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nconst name = 'combinationsWithRep'\nconst dependencies = ['typed']\n\nexport const createCombinationsWithRep = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Compute the number of ways of picking `k` unordered outcomes from `n`\n * possibilities, allowing individual outcomes to be repeated more than once.\n *\n * CombinationsWithRep only takes integer arguments.\n * The following condition must be enforced: k <= n + k -1.\n *\n * Syntax:\n *\n * math.combinationsWithRep(n, k)\n *\n * Examples:\n *\n * math.combinationsWithRep(7, 5) // returns 462\n *\n * See also:\n *\n * combinations, permutations, factorial\n *\n * @param {number | BigNumber} n Total number of objects in the set\n * @param {number | BigNumber} k Number of objects in the subset\n * @return {number | BigNumber} Number of possible combinations with replacement.\n */\n return typed(name, {\n 'number, number': function (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (n < 1) {\n throw new TypeError('k must be less than or equal to n + k - 1')\n }\n\n if (k < n - 1) {\n const prodrange = product(n, n + k - 1)\n return prodrange / product(1, k)\n }\n const prodrange = product(k + 1, n + k - 1)\n return prodrange / product(1, n - 1)\n },\n\n 'BigNumber, BigNumber': function (n, k) {\n const BigNumber = n.constructor\n let result, i\n const one = new BigNumber(1)\n const nMinusOne = n.minus(one)\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function combinationsWithRep')\n }\n if (n.lt(one)) {\n throw new TypeError('k must be less than or equal to n + k - 1 in function combinationsWithRep')\n }\n\n result = one\n if (k.lt(nMinusOne)) {\n for (i = one; i.lte(nMinusOne); i = i.plus(one)) {\n result = result.times(k.plus(i)).dividedBy(i)\n }\n } else {\n for (i = one; i.lte(k); i = i.plus(one)) {\n result = result.times(nMinusOne.plus(i)).dividedBy(i)\n }\n }\n\n return result\n }\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","/* eslint-disable no-loss-of-precision */\n\nimport { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\n\nexport function gammaNumber (n) {\n let x\n\n if (isInteger(n)) {\n if (n <= 0) {\n return isFinite(n) ? Infinity : NaN\n }\n\n if (n > 171) {\n return Infinity // Will overflow\n }\n\n return product(1, n - 1)\n }\n\n if (n < 0.5) {\n return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n))\n }\n\n if (n >= 171.35) {\n return Infinity // will overflow\n }\n\n if (n > 85.0) { // Extended Stirling Approx\n const twoN = n * n\n const threeN = twoN * n\n const fourN = threeN * n\n const fiveN = fourN * n\n return Math.sqrt(2 * Math.PI / n) * Math.pow((n / Math.E), n) *\n (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) -\n 571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) +\n 5246819 / (75246796800 * fiveN * n))\n }\n\n --n\n x = gammaP[0]\n for (let i = 1; i < gammaP.length; ++i) {\n x += gammaP[i] / (n + i)\n }\n\n const t = n + gammaG + 0.5\n return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x\n}\ngammaNumber.signature = 'number'\n\n// TODO: comment on the variables g and p\n\nexport const gammaG = 4.7421875\n\nexport const gammaP = [\n 0.99999999999999709182,\n 57.156235665862923517,\n -59.597960355475491248,\n 14.136097974741747174,\n -0.49191381609762019978,\n 0.33994649984811888699e-4,\n 0.46523628927048575665e-4,\n -0.98374475304879564677e-4,\n 0.15808870322491248884e-3,\n -0.21026444172410488319e-3,\n 0.21743961811521264320e-3,\n -0.16431810653676389022e-3,\n 0.84418223983852743293e-4,\n -0.26190838401581408670e-4,\n 0.36899182659531622704e-5\n]\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\nimport { gammaG, gammaNumber, gammaP } from '../../plain/number/index.js'\n\nconst name = 'gamma'\nconst dependencies = ['typed', 'config', 'multiplyScalar', 'pow', 'BigNumber', 'Complex']\n\nexport const createGamma = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, multiplyScalar, pow, BigNumber, Complex }) => {\n /**\n * Compute the gamma function of a value using Lanczos approximation for\n * small values, and an extended Stirling approximation for large values.\n *\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.gamma(n)\n *\n * Examples:\n *\n * math.gamma(5) // returns 24\n * math.gamma(-0.5) // returns -3.5449077018110335\n * math.gamma(math.i) // returns -0.15494982830180973 - 0.49801566811835596i\n *\n * See also:\n *\n * combinations, factorial, permutations\n *\n * @param {number | Array | Matrix} n A real or complex number\n * @return {number | Array | Matrix} The gamma of `n`\n */\n\n return typed(name, {\n\n number: gammaNumber,\n\n Complex: function (n) {\n if (n.im === 0) {\n return this(n.re)\n }\n\n n = new Complex(n.re - 1, n.im)\n const x = new Complex(gammaP[0], 0)\n for (let i = 1; i < gammaP.length; ++i) {\n const real = n.re + i // x += p[i]/(n+i)\n const den = real * real + n.im * n.im\n if (den !== 0) {\n x.re += gammaP[i] * real / den\n x.im += -(gammaP[i] * n.im) / den\n } else {\n x.re = gammaP[i] < 0\n ? -Infinity\n : Infinity\n }\n }\n\n const t = new Complex(n.re + gammaG + 0.5, n.im)\n const twoPiSqrt = Math.sqrt(2 * Math.PI)\n\n n.re += 0.5\n const result = pow(t, n)\n if (result.im === 0) { // sqrt(2*PI)*result\n result.re *= twoPiSqrt\n } else if (result.re === 0) {\n result.im *= twoPiSqrt\n } else {\n result.re *= twoPiSqrt\n result.im *= twoPiSqrt\n }\n\n const r = Math.exp(-t.re) // exp(-t)\n t.re = r * Math.cos(-t.im)\n t.im = r * Math.sin(-t.im)\n\n return multiplyScalar(multiplyScalar(result, t), x)\n },\n\n BigNumber: function (n) {\n if (n.isInteger()) {\n return (n.isNegative() || n.isZero())\n ? new BigNumber(Infinity)\n : bigFactorial(n.minus(1))\n }\n\n if (!n.isFinite()) {\n return new BigNumber(n.isNegative() ? NaN : Infinity)\n }\n\n throw new Error('Integer BigNumber expected')\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n })\n\n /**\n * Calculate factorial for a BigNumber\n * @param {BigNumber} n\n * @returns {BigNumber} Returns the factorial of n\n */\n function bigFactorial (n) {\n if (n < 8) {\n return new BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n])\n }\n\n const precision = config.precision + (Math.log(n.toNumber()) | 0)\n const Big = BigNumber.clone({ precision: precision })\n\n if (n % 2 === 1) {\n return n.times(bigFactorial(new BigNumber(n - 1)))\n }\n\n let p = n\n let prod = new Big(n)\n let sum = n.toNumber()\n\n while (p > 2) {\n p -= 2\n sum += p\n prod = prod.times(sum)\n }\n\n return new BigNumber(prod.toPrecision(BigNumber.precision))\n }\n})\n","import { deepMap } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'factorial'\nconst dependencies = ['typed', 'gamma']\n\nexport const createFactorial = /* #__PURE__ */ factory(name, dependencies, ({ typed, gamma }) => {\n /**\n * Compute the factorial of a value\n *\n * Factorial only supports an integer value as argument.\n * For matrices, the function is evaluated element wise.\n *\n * Syntax:\n *\n * math.factorial(n)\n *\n * Examples:\n *\n * math.factorial(5) // returns 120\n * math.factorial(3) // returns 6\n *\n * See also:\n *\n * combinations, combinationsWithRep, gamma, permutations\n *\n * @param {number | BigNumber | Array | Matrix} n An integer number\n * @return {number | BigNumber | Array | Matrix} The factorial of `n`\n */\n return typed(name, {\n number: function (n) {\n if (n < 0) {\n throw new Error('Value must be non-negative')\n }\n\n return gamma(n + 1)\n },\n\n BigNumber: function (n) {\n if (n.isNegative()) {\n throw new Error('Value must be non-negative')\n }\n\n return gamma(n.plus(1))\n },\n\n 'Array | Matrix': function (n) {\n return deepMap(n, this)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'kldivergence'\nconst dependencies = ['typed', 'matrix', 'divide', 'sum', 'multiply', 'dotDivide', 'log', 'isNumeric']\n\nexport const createKldivergence = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, divide, sum, multiply, dotDivide, log, isNumeric }) => {\n /**\n * Calculate the Kullback-Leibler (KL) divergence between two distributions\n *\n * Syntax:\n *\n * math.kldivergence(x, y)\n *\n * Examples:\n *\n * math.kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5]) //returns 0.24376698773121153\n *\n *\n * @param {Array | Matrix} q First vector\n * @param {Array | Matrix} p Second vector\n * @return {number} Returns distance between q and p\n */\n return typed(name, {\n 'Array, Array': function (q, p) {\n return _kldiv(matrix(q), matrix(p))\n },\n\n 'Matrix, Array': function (q, p) {\n return _kldiv(q, matrix(p))\n },\n\n 'Array, Matrix': function (q, p) {\n return _kldiv(matrix(q), p)\n },\n\n 'Matrix, Matrix': function (q, p) {\n return _kldiv(q, p)\n }\n\n })\n\n function _kldiv (q, p) {\n const plength = p.size().length\n const qlength = q.size().length\n if (plength > 1) {\n throw new Error('first object must be one dimensional')\n }\n\n if (qlength > 1) {\n throw new Error('second object must be one dimensional')\n }\n\n if (plength !== qlength) {\n throw new Error('Length of two vectors must be equal')\n }\n\n // Before calculation, apply normalization\n const sumq = sum(q)\n if (sumq === 0) {\n throw new Error('Sum of elements in first object must be non zero')\n }\n\n const sump = sum(p)\n if (sump === 0) {\n throw new Error('Sum of elements in second object must be non zero')\n }\n const qnorm = divide(q, sum(q))\n const pnorm = divide(p, sum(p))\n\n const result = sum(multiply(qnorm, log(dotDivide(qnorm, pnorm))))\n if (isNumeric(result)) {\n return result\n } else {\n return Number.NaN\n }\n }\n})\n","import { deepForEach } from '../../utils/collection.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'multinomial'\nconst dependencies = ['typed', 'add', 'divide', 'multiply', 'factorial', 'isInteger', 'isPositive']\n\nexport const createMultinomial = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, multiply, factorial, isInteger, isPositive }) => {\n /**\n * Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities.\n *\n * multinomial takes one array of integers as an argument.\n * The following condition must be enforced: every ai <= 0\n *\n * Syntax:\n *\n * math.multinomial(a) // a is an array type\n *\n * Examples:\n *\n * math.multinomial([1,2,1]) // returns 12\n *\n * See also:\n *\n * combinations, factorial\n *\n * @param {number[] | BigNumber[]} a Integer numbers of objects in the subset\n * @return {Number | BigNumber} Multinomial coefficient.\n */\n return typed(name, {\n 'Array | Matrix': function (a) {\n let sum = 0\n let denom = 1\n\n deepForEach(a, function (ai) {\n if (!isInteger(ai) || !isPositive(ai)) {\n throw new TypeError('Positive integer value expected in function multinomial')\n }\n sum = add(sum, ai)\n denom = multiply(denom, factorial(ai))\n })\n\n return divide(factorial(sum), denom)\n }\n })\n})\n","import { isInteger } from '../../utils/number.js'\nimport { product } from '../../utils/product.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'permutations'\nconst dependencies = ['typed', 'factorial']\n\nexport const createPermutations = /* #__PURE__ */ factory(name, dependencies, ({ typed, factorial }) => {\n /**\n * Compute the number of ways of obtaining an ordered subset of `k` elements\n * from a set of `n` elements.\n *\n * Permutations only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.permutations(n)\n * math.permutations(n, k)\n *\n * Examples:\n *\n * math.permutations(5) // 120\n * math.permutations(5, 3) // 60\n *\n * See also:\n *\n * combinations, combinationsWithRep, factorial\n *\n * @param {number | BigNumber} n The number of objects in total\n * @param {number | BigNumber} [k] The number of objects in the subset\n * @return {number | BigNumber} The number of permutations\n */\n return typed(name, {\n 'number | BigNumber': factorial,\n 'number, number': function (n, k) {\n if (!isInteger(n) || n < 0) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (!isInteger(k) || k < 0) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (k > n) {\n throw new TypeError('second argument k must be less than or equal to first argument n')\n }\n // Permute n objects, k at a time\n return product((n - k) + 1, n)\n },\n\n 'BigNumber, BigNumber': function (n, k) {\n let result, i\n\n if (!isPositiveInteger(n) || !isPositiveInteger(k)) {\n throw new TypeError('Positive integer value expected in function permutations')\n }\n if (k.gt(n)) {\n throw new TypeError('second argument k must be less than or equal to first argument n')\n }\n\n const one = n.mul(0).add(1)\n result = one\n for (i = n.minus(k).plus(1); i.lte(n); i = i.plus(1)) {\n result = result.times(i)\n }\n\n return result\n }\n\n // TODO: implement support for collection in permutations\n })\n})\n\n/**\n * Test whether BigNumber n is a positive integer\n * @param {BigNumber} n\n * @returns {boolean} isPositiveInteger\n */\nfunction isPositiveInteger (n) {\n return n.isInteger() && n.gte(0)\n}\n","import seedrandom from 'seedrandom'\n\nconst singletonRandom = /* #__PURE__ */ seedrandom(Date.now())\n\nexport function createRng (randomSeed) {\n let random\n\n // create a new random generator with given seed\n function setSeed (seed) {\n random = seed === null ? singletonRandom : seedrandom(String(seed))\n }\n\n // initialize a seeded pseudo random number generator with config's random seed\n setSeed(randomSeed)\n\n // wrapper function so the rng can be updated via generator\n function rng () {\n return random()\n }\n\n return rng\n}\n","import { flatten } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { isMatrix, isNumber } from '../../utils/is.js'\nimport { createRng } from './util/seededRNG.js'\n\nconst name = 'pickRandom'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createPickRandom = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Random pick one or more values from a one dimensional array.\n * Array elements are picked using a random function with uniform or weighted distribution.\n *\n * Syntax:\n *\n * math.pickRandom(array)\n * math.pickRandom(array, number)\n * math.pickRandom(array, weights)\n * math.pickRandom(array, number, weights)\n * math.pickRandom(array, weights, number)\n * math.pickRandom(array, { weights, number, elementWise })\n *\n * Examples:\n *\n * math.pickRandom([3, 6, 12, 2]) // returns one of the values in the array\n * math.pickRandom([3, 6, 12, 2], 2) // returns an array of two of the values in the array\n * math.pickRandom([3, 6, 12, 2], { number: 2 }) // returns an array of two of the values in the array\n * math.pickRandom([3, 6, 12, 2], [1, 3, 2, 1]) // returns one of the values in the array with weighted distribution\n * math.pickRandom([3, 6, 12, 2], 2, [1, 3, 2, 1]) // returns an array of two of the values in the array with weighted distribution\n * math.pickRandom([3, 6, 12, 2], [1, 3, 2, 1], 2) // returns an array of two of the values in the array with weighted distribution\n *\n * math.pickRandom([{x: 1.0, y: 2.0}, {x: 1.1, y: 2.0}], { elementWise: false })\n * // returns one of the items in the array\n *\n * See also:\n *\n * random, randomInt\n *\n * @param {Array | Matrix} array A one dimensional array\n * @param {Int} number An int or float\n * @param {Array | Matrix} weights An array of ints or floats\n * @return {number | Array} Returns a single random value from array when number is 1 or undefined.\n * Returns an array with the configured number of elements when number is > 1.\n */\n return typed({\n 'Array | Matrix': function (possibles) {\n return _pickRandom(possibles, {})\n },\n\n 'Array | Matrix, Object': function (possibles, options) {\n return _pickRandom(possibles, options)\n },\n\n 'Array | Matrix, number': function (possibles, number) {\n return _pickRandom(possibles, { number })\n },\n\n 'Array | Matrix, Array | Matrix': function (possibles, weights) {\n return _pickRandom(possibles, { weights })\n },\n\n 'Array | Matrix, Array | Matrix, number': function (possibles, weights, number) {\n return _pickRandom(possibles, { number, weights })\n },\n\n 'Array | Matrix, number, Array | Matrix': function (possibles, number, weights) {\n return _pickRandom(possibles, { number, weights })\n }\n })\n\n /**\n * @param {Array | Matrix} possibles\n * @param {{\n * number?: number,\n * weights?: Array | Matrix,\n * elementWise: boolean\n * }} options\n * @returns {number | Array}\n * @private\n */\n function _pickRandom (possibles, { number, weights, elementWise = true }) {\n const single = (typeof number === 'undefined')\n if (single) {\n number = 1\n }\n\n const createMatrix = isMatrix(possibles)\n ? possibles.create\n : isMatrix(weights)\n ? weights.create\n : null\n\n possibles = possibles.valueOf() // get Array\n if (weights) {\n weights = weights.valueOf() // get Array\n }\n\n if (elementWise === true) {\n possibles = flatten(possibles)\n weights = flatten(weights)\n }\n\n let totalWeights = 0\n\n if (typeof weights !== 'undefined') {\n if (weights.length !== possibles.length) {\n throw new Error('Weights must have the same length as possibles')\n }\n\n for (let i = 0, len = weights.length; i < len; i++) {\n if (!isNumber(weights[i]) || weights[i] < 0) {\n throw new Error('Weights must be an array of positive numbers')\n }\n\n totalWeights += weights[i]\n }\n }\n\n const length = possibles.length\n\n const result = []\n let pick\n\n while (result.length < number) {\n if (typeof weights === 'undefined') {\n pick = possibles[Math.floor(rng() * length)]\n } else {\n let randKey = rng() * totalWeights\n\n for (let i = 0, len = possibles.length; i < len; i++) {\n randKey -= weights[i]\n\n if (randKey < 0) {\n pick = possibles[i]\n break\n }\n }\n }\n\n result.push(pick)\n }\n\n return single\n ? result[0]\n : createMatrix\n ? createMatrix(result)\n : result\n }\n})\n","/**\n * This is a util function for generating a random matrix recursively.\n * @param {number[]} size\n * @param {function} random\n * @returns {Array}\n */\nexport function randomMatrix (size, random) {\n const data = []\n size = size.slice(0)\n\n if (size.length > 1) {\n for (let i = 0, length = size.shift(); i < length; i++) {\n data.push(randomMatrix(size, random))\n }\n } else {\n for (let i = 0, length = size.shift(); i < length; i++) {\n data.push(random())\n }\n }\n\n return data\n}\n","import { factory } from '../../utils/factory.js'\nimport { isMatrix } from '../../utils/is.js'\nimport { createRng } from './util/seededRNG.js'\nimport { randomMatrix } from './util/randomMatrix.js'\n\nconst name = 'random'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createRandom = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Return a random number larger or equal to `min` and smaller than `max`\n * using a uniform distribution.\n *\n * Syntax:\n *\n * math.random() // generate a random number between 0 and 1\n * math.random(max) // generate a random number between 0 and max\n * math.random(min, max) // generate a random number between min and max\n * math.random(size) // generate a matrix with random numbers between 0 and 1\n * math.random(size, max) // generate a matrix with random numbers between 0 and max\n * math.random(size, min, max) // generate a matrix with random numbers between min and max\n *\n * Examples:\n *\n * math.random() // returns a random number between 0 and 1\n * math.random(100) // returns a random number between 0 and 100\n * math.random(30, 40) // returns a random number between 30 and 40\n * math.random([2, 3]) // returns a 2x3 matrix with random numbers between 0 and 1\n *\n * See also:\n *\n * randomInt, pickRandom\n *\n * @param {Array | Matrix} [size] If provided, an array or matrix with given\n * size and filled with random values is returned\n * @param {number} [min] Minimum boundary for the random value, included\n * @param {number} [max] Maximum boundary for the random value, excluded\n * @return {number | Array | Matrix} A random number\n */\n return typed(name, {\n '': () => _random(0, 1),\n number: (max) => _random(0, max),\n 'number, number': (min, max) => _random(min, max),\n 'Array | Matrix': (size) => _randomMatrix(size, 0, 1),\n 'Array | Matrix, number': (size, max) => _randomMatrix(size, 0, max),\n 'Array | Matrix, number, number': (size, min, max) => _randomMatrix(size, min, max)\n })\n\n function _randomMatrix (size, min, max) {\n const res = randomMatrix(size.valueOf(), () => _random(min, max))\n return isMatrix(size) ? size.create(res) : res\n }\n\n function _random (min, max) {\n return min + rng() * (max - min)\n }\n})\n\n// number only implementation of random, no matrix support\n// TODO: there is quite some duplicate code in both createRandom and createRandomNumber, can we improve that?\nexport const createRandomNumber = /* #__PURE__ */ factory(name, ['typed', 'config', '?on'], ({ typed, config, on, matrix }) => {\n // seeded pseudo random number generator1\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n return typed(name, {\n '': () => _random(0, 1),\n number: (max) => _random(0, max),\n 'number, number': (min, max) => _random(min, max)\n })\n\n function _random (min, max) {\n return min + rng() * (max - min)\n }\n})\n","import { factory } from '../../utils/factory.js'\nimport { randomMatrix } from './util/randomMatrix.js'\nimport { createRng } from './util/seededRNG.js'\nimport { isMatrix } from '../../utils/is.js'\n\nconst name = 'randomInt'\nconst dependencies = ['typed', 'config', '?on']\n\nexport const createRandomInt = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, on }) => {\n // seeded pseudo random number generator\n let rng = createRng(config.randomSeed)\n\n if (on) {\n on('config', function (curr, prev) {\n if (curr.randomSeed !== prev.randomSeed) {\n rng = createRng(curr.randomSeed)\n }\n })\n }\n\n /**\n * Return a random integer number larger or equal to `min` and smaller than `max`\n * using a uniform distribution.\n *\n * Syntax:\n *\n * math.randomInt() // generate a random integer between 0 and 1\n * math.randomInt(max) // generate a random integer between 0 and max\n * math.randomInt(min, max) // generate a random integer between min and max\n * math.randomInt(size) // generate a matrix with random integer between 0 and 1\n * math.randomInt(size, max) // generate a matrix with random integer between 0 and max\n * math.randomInt(size, min, max) // generate a matrix with random integer between min and max\n *\n * Examples:\n *\n * math.randomInt(100) // returns a random integer between 0 and 100\n * math.randomInt(30, 40) // returns a random integer between 30 and 40\n * math.randomInt([2, 3]) // returns a 2x3 matrix with random integers between 0 and 1\n *\n * See also:\n *\n * random, pickRandom\n *\n * @param {Array | Matrix} [size] If provided, an array or matrix with given\n * size and filled with random values is returned\n * @param {number} [min] Minimum boundary for the random value, included\n * @param {number} [max] Maximum boundary for the random value, excluded\n * @return {number | Array | Matrix} A random integer value\n */\n return typed(name, {\n '': () => _randomInt(0, 1),\n number: (max) => _randomInt(0, max),\n 'number, number': (min, max) => _randomInt(min, max),\n 'Array | Matrix': (size) => _randomIntMatrix(size, 0, 1),\n 'Array | Matrix, number': (size, max) => _randomIntMatrix(size, 0, max),\n 'Array | Matrix, number, number': (size, min, max) => _randomIntMatrix(size, min, max)\n })\n\n function _randomIntMatrix (size, min, max) {\n const res = randomMatrix(size.valueOf(), () => _randomInt(min, max))\n return isMatrix(size) ? size.create(res) : res\n }\n\n function _randomInt (min, max) {\n return Math.floor(min + rng() * (max - min))\n }\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'stirlingS2'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'subtract',\n 'multiplyScalar',\n 'divideScalar',\n 'pow',\n 'factorial',\n 'combinations',\n 'isNegative',\n 'isInteger',\n 'larger'\n]\n\nexport const createStirlingS2 = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n subtract,\n multiplyScalar,\n divideScalar,\n pow,\n factorial,\n combinations,\n isNegative,\n isInteger,\n larger\n }\n) => {\n /**\n * The Stirling numbers of the second kind, counts the number of ways to partition\n * a set of n labelled objects into k nonempty unlabelled subsets.\n * stirlingS2 only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * If n = k or k = 1, then s(n,k) = 1\n *\n * Syntax:\n *\n * math.stirlingS2(n, k)\n *\n * Examples:\n *\n * math.stirlingS2(5, 3) //returns 25\n *\n * See also:\n *\n * bellNumbers\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @param {Number | BigNumber} k Number of objects in the subset\n * @return {Number | BigNumber} S(n,k)\n */\n return typed(name, {\n 'number | BigNumber, number | BigNumber': function (n, k) {\n if (!isInteger(n) || isNegative(n) || !isInteger(k) || isNegative(k)) {\n throw new TypeError('Non-negative integer value expected in function stirlingS2')\n } else if (larger(k, n)) {\n throw new TypeError('k must be less than or equal to n in function stirlingS2')\n }\n\n // 1/k! Sum(i=0 -> k) [(-1)^(k-i)*C(k,j)* i^n]\n const kFactorial = factorial(k)\n let result = 0\n for (let i = 0; i <= k; i++) {\n const negativeOne = pow(-1, subtract(k, i))\n const kChooseI = combinations(k, i)\n const iPower = pow(i, n)\n\n result = addScalar(result, multiplyScalar(multiplyScalar(kChooseI, iPower), negativeOne))\n }\n\n return divideScalar(result, kFactorial)\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'bellNumbers'\nconst dependencies = ['typed', 'addScalar', 'isNegative', 'isInteger', 'stirlingS2']\n\nexport const createBellNumbers = /* #__PURE__ */ factory(name, dependencies, ({ typed, addScalar, isNegative, isInteger, stirlingS2 }) => {\n /**\n * The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S.\n * bellNumbers only takes integer arguments.\n * The following condition must be enforced: n >= 0\n *\n * Syntax:\n *\n * math.bellNumbers(n)\n *\n * Examples:\n *\n * math.bellNumbers(3) // returns 5\n * math.bellNumbers(8) // returns 4140\n *\n * See also:\n *\n * stirlingS2\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @return {Number | BigNumber} B(n)\n */\n return typed(name, {\n 'number | BigNumber': function (n) {\n if (!isInteger(n) || isNegative(n)) {\n throw new TypeError('Non-negative integer value expected in function bellNumbers')\n }\n\n // Sum (k=0, n) S(n,k).\n let result = 0\n for (let i = 0; i <= n; i++) {\n result = addScalar(result, stirlingS2(n, i))\n }\n\n return result\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'catalan'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'divideScalar',\n 'multiplyScalar',\n 'combinations',\n 'isNegative',\n 'isInteger'\n]\n\nexport const createCatalan = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n divideScalar,\n multiplyScalar,\n combinations,\n isNegative,\n isInteger\n }\n) => {\n /**\n * The Catalan Numbers enumerate combinatorial structures of many different types.\n * catalan only takes integer arguments.\n * The following condition must be enforced: n >= 0\n *\n * Syntax:\n *\n * math.catalan(n)\n *\n * Examples:\n *\n * math.catalan(3) // returns 5\n * math.catalan(8) // returns 1430\n *\n * See also:\n *\n * bellNumbers\n *\n * @param {Number | BigNumber} n nth Catalan number\n * @return {Number | BigNumber} Cn(n)\n */\n return typed(name, {\n 'number | BigNumber': function (n) {\n if (!isInteger(n) || isNegative(n)) {\n throw new TypeError('Non-negative integer value expected in function catalan')\n }\n\n return divideScalar(combinations(multiplyScalar(n, 2), n), addScalar(n, 1))\n }\n })\n})\n","import { factory } from '../../utils/factory.js'\n\nconst name = 'composition'\nconst dependencies = [\n 'typed',\n 'addScalar',\n 'combinations',\n 'isNegative',\n 'isPositive',\n 'isInteger',\n 'larger'\n]\n\nexport const createComposition = /* #__PURE__ */ factory(name, dependencies, (\n {\n typed,\n addScalar,\n combinations,\n isPositive,\n isNegative,\n isInteger,\n larger\n }\n) => {\n /**\n * The composition counts of n into k parts.\n *\n * composition only takes integer arguments.\n * The following condition must be enforced: k <= n.\n *\n * Syntax:\n *\n * math.composition(n, k)\n *\n * Examples:\n *\n * math.composition(5, 3) // returns 6\n *\n * See also:\n *\n * combinations\n *\n * @param {Number | BigNumber} n Total number of objects in the set\n * @param {Number | BigNumber} k Number of objects in the subset\n * @return {Number | BigNumber} Returns the composition counts of n into k parts.\n */\n return typed(name, {\n 'number | BigNumber, number | BigNumber': function (n, k) {\n if (!isInteger(n) || !isPositive(n) || !isInteger(k) || !isPositive(k)) {\n throw new TypeError('Positive integer value expected in function composition')\n } else if (larger(k, n)) {\n throw new TypeError('k must be less than or equal to n in function composition')\n }\n\n return combinations(addScalar(n, -1), addScalar(k, -1))\n }\n })\n})\n","import { isOperatorNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { hasOwnProperty } from '../../../utils/object.js'\n\nconst name = 'simplifyUtil'\nconst dependencies = [\n 'FunctionNode',\n 'OperatorNode',\n 'SymbolNode'\n]\n\nexport const createUtil = /* #__PURE__ */ factory(name, dependencies, ({ FunctionNode, OperatorNode, SymbolNode }) => {\n // TODO commutative/associative properties rely on the arguments\n // e.g. multiply is not commutative for matrices\n // The properties should be calculated from an argument to simplify, or possibly something in math.config\n // the other option is for typed() to specify a return type so that we can evaluate the type of arguments\n const commutative = {\n add: true,\n multiply: true\n }\n const associative = {\n add: true,\n multiply: true\n }\n\n function isCommutative (node, context) {\n if (!isOperatorNode(node)) {\n return true\n }\n const name = node.fn.toString()\n if (context && hasOwnProperty(context, name) && hasOwnProperty(context[name], 'commutative')) {\n return context[name].commutative\n }\n return commutative[name] || false\n }\n\n function isAssociative (node, context) {\n if (!isOperatorNode(node)) {\n return false\n }\n const name = node.fn.toString()\n if (context && hasOwnProperty(context, name) && hasOwnProperty(context[name], 'associative')) {\n return context[name].associative\n }\n return associative[name] || false\n }\n\n /**\n * Flatten all associative operators in an expression tree.\n * Assumes parentheses have already been removed.\n */\n function flatten (node) {\n if (!node.args || node.args.length === 0) {\n return node\n }\n node.args = allChildren(node)\n for (let i = 0; i < node.args.length; i++) {\n flatten(node.args[i])\n }\n }\n\n /**\n * Get the children of a node as if it has been flattened.\n * TODO implement for FunctionNodes\n */\n function allChildren (node) {\n let op\n const children = []\n const findChildren = function (node) {\n for (let i = 0; i < node.args.length; i++) {\n const child = node.args[i]\n if (isOperatorNode(child) && op === child.op) {\n findChildren(child)\n } else {\n children.push(child)\n }\n }\n }\n\n if (isAssociative(node)) {\n op = node.op\n findChildren(node)\n return children\n } else {\n return node.args\n }\n }\n\n /**\n * Unflatten all flattened operators to a right-heavy binary tree.\n */\n function unflattenr (node) {\n if (!node.args || node.args.length === 0) {\n return\n }\n const makeNode = createMakeNodeFunction(node)\n const l = node.args.length\n for (let i = 0; i < l; i++) {\n unflattenr(node.args[i])\n }\n if (l > 2 && isAssociative(node)) {\n let curnode = node.args.pop()\n while (node.args.length > 0) {\n curnode = makeNode([node.args.pop(), curnode])\n }\n node.args = curnode.args\n }\n }\n\n /**\n * Unflatten all flattened operators to a left-heavy binary tree.\n */\n function unflattenl (node) {\n if (!node.args || node.args.length === 0) {\n return\n }\n const makeNode = createMakeNodeFunction(node)\n const l = node.args.length\n for (let i = 0; i < l; i++) {\n unflattenl(node.args[i])\n }\n if (l > 2 && isAssociative(node)) {\n let curnode = node.args.shift()\n while (node.args.length > 0) {\n curnode = makeNode([curnode, node.args.shift()])\n }\n node.args = curnode.args\n }\n }\n\n function createMakeNodeFunction (node) {\n if (isOperatorNode(node)) {\n return function (args) {\n try {\n return new OperatorNode(node.op, node.fn, args, node.implicit)\n } catch (err) {\n console.error(err)\n return []\n }\n }\n } else {\n return function (args) {\n return new FunctionNode(new SymbolNode(node.name), args)\n }\n }\n }\n\n return {\n createMakeNodeFunction,\n isCommutative,\n isAssociative,\n flatten,\n allChildren,\n unflattenr,\n unflattenl\n }\n})\n","import { isConstantNode, isFunctionNode, isOperatorNode, isParenthesisNode, isSymbolNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'simplifyCore'\nconst dependencies = [\n 'equal',\n 'isZero',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'ParenthesisNode'\n]\n\nexport const createSimplifyCore = /* #__PURE__ */ factory(name, dependencies, ({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n}) => {\n const node0 = new ConstantNode(0)\n const node1 = new ConstantNode(1)\n\n /**\n * simplifyCore() performs single pass simplification suitable for\n * applications requiring ultimate performance. In contrast, simplify()\n * extends simplifyCore() with additional passes to provide deeper\n * simplification.\n *\n * Syntax:\n *\n * simplify.simplifyCore(expr)\n *\n * Examples:\n *\n * const f = math.parse('2 * 1 * x ^ (2 - 1)')\n * math.simplify.simpifyCore(f) // Node {2 * x}\n * math.simplify('2 * 1 * x ^ (2 - 1)', [math.simplify.simpifyCore]) // Node {2 * x}\n *\n * See also:\n *\n * derivative\n *\n * @param {Node} node\n * The expression to be simplified\n */\n function simplifyCore (node) {\n if (isOperatorNode(node) && node.isUnary()) {\n const a0 = simplifyCore(node.args[0])\n\n if (node.op === '+') { // unary plus\n return a0\n }\n\n if (node.op === '-') { // unary minus\n if (isOperatorNode(a0)) {\n if (a0.isUnary() && a0.op === '-') {\n return a0.args[0]\n } else if (a0.isBinary() && a0.fn === 'subtract') {\n return new OperatorNode('-', 'subtract', [a0.args[1], a0.args[0]])\n }\n }\n return new OperatorNode(node.op, node.fn, [a0])\n }\n } else if (isOperatorNode(node) && node.isBinary()) {\n const a0 = simplifyCore(node.args[0])\n const a1 = simplifyCore(node.args[1])\n\n if (node.op === '+') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return a1\n } else if (isConstantNode(a1)) {\n return new ConstantNode(add(a0.value, a1.value))\n }\n }\n if (isConstantNode(a1) && isZero(a1.value)) {\n return a0\n }\n if (isOperatorNode(a1) && a1.isUnary() && a1.op === '-') {\n return new OperatorNode('-', 'subtract', [a0, a1.args[0]])\n }\n return new OperatorNode(node.op, node.fn, a1 ? [a0, a1] : [a0])\n } else if (node.op === '-') {\n if (isConstantNode(a0) && a1) {\n if (isConstantNode(a1)) {\n return new ConstantNode(subtract(a0.value, a1.value))\n } else if (isZero(a0.value)) {\n return new OperatorNode('-', 'unaryMinus', [a1])\n }\n }\n // if (node.fn === \"subtract\" && node.args.length === 2) {\n if (node.fn === 'subtract') {\n if (isConstantNode(a1) && isZero(a1.value)) {\n return a0\n }\n if (isOperatorNode(a1) && a1.isUnary() && a1.op === '-') {\n return simplifyCore(new OperatorNode('+', 'add', [a0, a1.args[0]]))\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n }\n } else if (node.op === '*') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return node0\n } else if (equal(a0.value, 1)) {\n return a1\n } else if (isConstantNode(a1)) {\n return new ConstantNode(multiply(a0.value, a1.value))\n }\n }\n if (isConstantNode(a1)) {\n if (isZero(a1.value)) {\n return node0\n } else if (equal(a1.value, 1)) {\n return a0\n } else if (isOperatorNode(a0) && a0.isBinary() && a0.op === node.op) {\n const a00 = a0.args[0]\n if (isConstantNode(a00)) {\n const a00a1 = new ConstantNode(multiply(a00.value, a1.value))\n return new OperatorNode(node.op, node.fn, [a00a1, a0.args[1]], node.implicit) // constants on left\n }\n }\n return new OperatorNode(node.op, node.fn, [a1, a0], node.implicit) // constants on left\n }\n return new OperatorNode(node.op, node.fn, [a0, a1], node.implicit)\n } else if (node.op === '/') {\n if (isConstantNode(a0)) {\n if (isZero(a0.value)) {\n return node0\n } else if (isConstantNode(a1) &&\n (equal(a1.value, 1) || equal(a1.value, 2) || equal(a1.value, 4))) {\n return new ConstantNode(divide(a0.value, a1.value))\n }\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n } else if (node.op === '^') {\n if (isConstantNode(a1)) {\n if (isZero(a1.value)) {\n return node1\n } else if (equal(a1.value, 1)) {\n return a0\n } else {\n if (isConstantNode(a0)) {\n // fold constant\n return new ConstantNode(pow(a0.value, a1.value))\n } else if (isOperatorNode(a0) && a0.isBinary() && a0.op === '^') {\n const a01 = a0.args[1]\n if (isConstantNode(a01)) {\n return new OperatorNode(node.op, node.fn, [\n a0.args[0],\n new ConstantNode(multiply(a01.value, a1.value))\n ])\n }\n }\n }\n }\n return new OperatorNode(node.op, node.fn, [a0, a1])\n }\n } else if (isParenthesisNode(node)) {\n const c = simplifyCore(node.content)\n if (isParenthesisNode(c) || isSymbolNode(c) || isConstantNode(c)) {\n return c\n }\n return new ParenthesisNode(c)\n } else if (isFunctionNode(node)) {\n const args = node.args\n .map(simplifyCore)\n .map(function (arg) {\n return isParenthesisNode(arg) ? arg.content : arg\n })\n return new FunctionNode(simplifyCore(node.fn), args)\n } else {\n // cannot simplify\n }\n return node\n }\n\n return simplifyCore\n})\n","// TODO this could be improved by simplifying seperated constants under associative and commutative operators\nimport { isFraction, isNode, isOperatorNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\nimport { createUtil } from './util.js'\nimport { noBignumber, noFraction } from '../../../utils/noop.js'\n\nconst name = 'simplifyConstant'\nconst dependencies = [\n 'typed',\n 'config',\n 'mathWithTransform',\n '?fraction',\n '?bignumber',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'SymbolNode'\n]\n\nexport const createSimplifyConstant = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n}) => {\n const { isCommutative, isAssociative, allChildren, createMakeNodeFunction } =\n createUtil({ FunctionNode, OperatorNode, SymbolNode })\n\n function simplifyConstant (expr, options) {\n const res = foldFraction(expr, options)\n return isNode(res) ? res : _toNode(res)\n }\n\n function _eval (fnname, args, options) {\n try {\n return _toNumber(mathWithTransform[fnname].apply(null, args), options)\n } catch (ignore) {\n // sometimes the implicit type conversion causes the evaluation to fail, so we'll try again after removing Fractions\n args = args.map(function (x) {\n if (isFraction(x)) {\n return x.valueOf()\n }\n return x\n })\n return _toNumber(mathWithTransform[fnname].apply(null, args), options)\n }\n }\n\n const _toNode = typed({\n Fraction: _fractionToNode,\n number: function (n) {\n if (n < 0) {\n return unaryMinusNode(new ConstantNode(-n))\n }\n return new ConstantNode(n)\n },\n BigNumber: function (n) {\n if (n < 0) {\n return unaryMinusNode(new ConstantNode(-n))\n }\n return new ConstantNode(n) // old parameters: (n.toString(), 'number')\n },\n Complex: function (s) {\n throw new Error('Cannot convert Complex number to Node')\n }\n })\n\n // convert a number to a fraction only if it can be expressed exactly,\n // and when both numerator and denominator are small enough\n function _exactFraction (n, options) {\n const exactFractions = (options && options.exactFractions !== false)\n if (exactFractions && isFinite(n) && fraction) {\n const f = fraction(n)\n const fractionsLimit = (options && typeof options.fractionsLimit === 'number')\n ? options.fractionsLimit\n : Infinity // no limit by default\n\n if (f.valueOf() === n && f.n < fractionsLimit && f.d < fractionsLimit) {\n return f\n }\n }\n return n\n }\n\n // Convert numbers to a preferred number type in preference order: Fraction, number, Complex\n // BigNumbers are left alone\n const _toNumber = typed({\n 'string, Object': function (s, options) {\n if (config.number === 'BigNumber') {\n if (bignumber === undefined) {\n noBignumber()\n }\n return bignumber(s)\n } else if (config.number === 'Fraction') {\n if (fraction === undefined) {\n noFraction()\n }\n return fraction(s)\n } else {\n const n = parseFloat(s)\n return _exactFraction(n, options)\n }\n },\n\n 'Fraction, Object': function (s, options) { return s }, // we don't need options here\n\n 'BigNumber, Object': function (s, options) { return s }, // we don't need options here\n\n 'number, Object': function (s, options) {\n return _exactFraction(s, options)\n },\n\n 'Complex, Object': function (s, options) {\n if (s.im !== 0) {\n return s\n }\n return _exactFraction(s.re, options)\n }\n })\n\n function unaryMinusNode (n) {\n return new OperatorNode('-', 'unaryMinus', [n])\n }\n\n function _fractionToNode (f) {\n let n\n const vn = f.s * f.n\n if (vn < 0) {\n n = new OperatorNode('-', 'unaryMinus', [new ConstantNode(-vn)])\n } else {\n n = new ConstantNode(vn)\n }\n\n if (f.d === 1) {\n return n\n }\n return new OperatorNode('/', 'divide', [n, new ConstantNode(f.d)])\n }\n\n /*\n * Create a binary tree from a list of Fractions and Nodes.\n * Tries to fold Fractions by evaluating them until the first Node in the list is hit, so\n * `args` should be sorted to have the Fractions at the start (if the operator is commutative).\n * @param args - list of Fractions and Nodes\n * @param fn - evaluator for the binary operation evaluator that accepts two Fractions\n * @param makeNode - creates a binary OperatorNode/FunctionNode from a list of child Nodes\n * if args.length is 1, returns args[0]\n * @return - Either a Node representing a binary expression or Fraction\n */\n function foldOp (fn, args, makeNode, options) {\n return args.reduce(function (a, b) {\n if (!isNode(a) && !isNode(b)) {\n try {\n return _eval(fn, [a, b], options)\n } catch (ignoreandcontinue) {}\n a = _toNode(a)\n b = _toNode(b)\n } else if (!isNode(a)) {\n a = _toNode(a)\n } else if (!isNode(b)) {\n b = _toNode(b)\n }\n\n return makeNode([a, b])\n })\n }\n\n // destroys the original node and returns a folded one\n function foldFraction (node, options) {\n switch (node.type) {\n case 'SymbolNode':\n return node\n case 'ConstantNode':\n if (typeof node.value === 'number' || !isNaN(node.value)) {\n return _toNumber(node.value, options)\n }\n return node\n case 'FunctionNode':\n if (mathWithTransform[node.name] && mathWithTransform[node.name].rawArgs) {\n return node\n }\n {\n // Process operators as OperatorNode\n const operatorFunctions = ['add', 'multiply']\n if (operatorFunctions.indexOf(node.name) === -1) {\n let args = node.args.map(arg => foldFraction(arg, options))\n\n // If all args are numbers\n if (!args.some(isNode)) {\n try {\n return _eval(node.name, args, options)\n } catch (ignoreandcontine) {}\n }\n\n // Convert all args to nodes and construct a symbolic function call\n args = args.map(function (arg) {\n return isNode(arg) ? arg : _toNode(arg)\n })\n return new FunctionNode(node.name, args)\n } else {\n // treat as operator\n }\n }\n /* falls through */\n case 'OperatorNode':\n {\n const fn = node.fn.toString()\n let args\n let res\n const makeNode = createMakeNodeFunction(node)\n if (isOperatorNode(node) && node.isUnary()) {\n args = [foldFraction(node.args[0], options)]\n if (!isNode(args[0])) {\n res = _eval(fn, args, options)\n } else {\n res = makeNode(args)\n }\n } else if (isAssociative(node)) {\n args = allChildren(node)\n args = args.map(arg => foldFraction(arg, options))\n\n if (isCommutative(fn)) {\n // commutative binary operator\n const consts = []\n const vars = []\n\n for (let i = 0; i < args.length; i++) {\n if (!isNode(args[i])) {\n consts.push(args[i])\n } else {\n vars.push(args[i])\n }\n }\n\n if (consts.length > 1) {\n res = foldOp(fn, consts, makeNode, options)\n vars.unshift(res)\n res = foldOp(fn, vars, makeNode, options)\n } else {\n // we won't change the children order since it's not neccessary\n res = foldOp(fn, args, makeNode, options)\n }\n } else {\n // non-commutative binary operator\n res = foldOp(fn, args, makeNode, options)\n }\n } else {\n // non-associative binary operator\n args = node.args.map(arg => foldFraction(arg, options))\n res = foldOp(fn, args, makeNode, options)\n }\n return res\n }\n case 'ParenthesisNode':\n // remove the uneccessary parenthesis\n return foldFraction(node.content, options)\n case 'AccessorNode':\n /* falls through */\n case 'ArrayNode':\n /* falls through */\n case 'AssignmentNode':\n /* falls through */\n case 'BlockNode':\n /* falls through */\n case 'FunctionAssignmentNode':\n /* falls through */\n case 'IndexNode':\n /* falls through */\n case 'ObjectNode':\n /* falls through */\n case 'RangeNode':\n /* falls through */\n case 'ConditionalNode':\n /* falls through */\n default:\n throw new Error(`Unimplemented node type in simplifyConstant: ${node.type}`)\n }\n }\n\n return simplifyConstant\n})\n","import { isFunctionNode, isNode, isOperatorNode, isParenthesisNode, isSymbolNode } from '../../../utils/is.js'\nimport { factory } from '../../../utils/factory.js'\n\nconst name = 'resolve'\nconst dependencies = [\n 'parse',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode'\n]\n\nexport const createResolve = /* #__PURE__ */ factory(name, dependencies, ({\n parse,\n FunctionNode,\n OperatorNode,\n ParenthesisNode\n}) => {\n /**\n * resolve(expr, scope) replaces variable nodes with their scoped values\n *\n * Syntax:\n *\n * simplify.resolve(expr, scope)\n *\n * Examples:\n *\n * math.simplify.resolve('x + y', {x:1, y:2}) // Node {1 + 2}\n * math.simplify.resolve(math.parse('x+y'), {x:1, y:2}) // Node {1 + 2}\n * math.simplify('x+y', {x:2, y:'x+x'}).toString() // \"6\"\n *\n * @param {Node} node\n * The expression tree to be simplified\n * @param {Object} scope with variables to be resolved\n */\n function resolve (node, scope) {\n if (!scope) {\n return node\n }\n if (isSymbolNode(node)) {\n const value = scope[node.name]\n if (isNode(value)) {\n return resolve(value, scope)\n } else if (typeof value === 'number') {\n return parse(String(value))\n }\n } else if (isOperatorNode(node)) {\n const args = node.args.map(function (arg) {\n return resolve(arg, scope)\n })\n return new OperatorNode(node.op, node.fn, args, node.implicit)\n } else if (isParenthesisNode(node)) {\n return new ParenthesisNode(resolve(node.content, scope))\n } else if (isFunctionNode(node)) {\n const args = node.args.map(function (arg) {\n return resolve(arg, scope)\n })\n return new FunctionNode(node.name, args)\n }\n return node\n }\n\n return resolve\n})\n","import { isConstantNode, isParenthesisNode } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { createUtil } from './simplify/util.js'\nimport { createSimplifyCore } from './simplify/simplifyCore.js'\nimport { createSimplifyConstant } from './simplify/simplifyConstant.js'\nimport { createResolve } from './simplify/resolve.js'\nimport { hasOwnProperty } from '../../utils/object.js'\n\nconst name = 'simplify'\nconst dependencies = [\n 'config',\n 'typed',\n 'parse',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'isZero',\n 'equal',\n '?fraction',\n '?bignumber',\n 'mathWithTransform',\n 'ConstantNode',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'SymbolNode'\n]\n\nexport const createSimplify = /* #__PURE__ */ factory(name, dependencies, (\n {\n config,\n typed,\n parse,\n add,\n subtract,\n multiply,\n divide,\n pow,\n isZero,\n equal,\n fraction,\n bignumber,\n mathWithTransform,\n ConstantNode,\n FunctionNode,\n OperatorNode,\n ParenthesisNode,\n SymbolNode\n }\n) => {\n const simplifyConstant = createSimplifyConstant({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n })\n const simplifyCore = createSimplifyCore({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n })\n const resolve = createResolve({\n parse,\n FunctionNode,\n OperatorNode,\n ParenthesisNode\n })\n\n const { isCommutative, isAssociative, flatten, unflattenr, unflattenl, createMakeNodeFunction } =\n createUtil({ FunctionNode, OperatorNode, SymbolNode })\n\n /**\n * Simplify an expression tree.\n *\n * A list of rules are applied to an expression, repeating over the list until\n * no further changes are made.\n * It's possible to pass a custom set of rules to the function as second\n * argument. A rule can be specified as an object, string, or function:\n *\n * const rules = [\n * { l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },\n * 'n1*n3 + n2*n3 -> (n1+n2)*n3',\n * function (node) {\n * // ... return a new node or return the node unchanged\n * return node\n * }\n * ]\n *\n * String and object rules consist of a left and right pattern. The left is\n * used to match against the expression and the right determines what matches\n * are replaced with. The main difference between a pattern and a normal\n * expression is that variables starting with the following characters are\n * interpreted as wildcards:\n *\n * - 'n' - matches any Node\n * - 'c' - matches any ConstantNode\n * - 'v' - matches any Node that is not a ConstantNode\n *\n * The default list of rules is exposed on the function as `simplify.rules`\n * and can be used as a basis to built a set of custom rules.\n *\n * For more details on the theory, see:\n *\n * - [Strategies for simplifying math expressions (Stackoverflow)](https://stackoverflow.com/questions/7540227/strategies-for-simplifying-math-expressions)\n * - [Symbolic computation - Simplification (Wikipedia)](https://en.wikipedia.org/wiki/Symbolic_computation#Simplification)\n *\n * An optional `options` argument can be passed as last argument of `simplify`.\n * There is currently one option available:\n * - `exactFractions`: a boolean which is `true` by default.\n * - `fractionsLimit`: when `exactFractions` is true, a fraction will be returned\n * only when both numerator and denominator are smaller than `fractionsLimit`.\n * Default value is 10000.\n *\n * Syntax:\n *\n * simplify(expr)\n * simplify(expr, rules)\n * simplify(expr, rules)\n * simplify(expr, rules, scope)\n * simplify(expr, rules, scope, options)\n * simplify(expr, scope)\n * simplify(expr, scope, options)\n *\n * Examples:\n *\n * math.simplify('2 * 1 * x ^ (2 - 1)') // Node \"2 * x\"\n * math.simplify('2 * 3 * x', {x: 4}) // Node \"24\"\n * const f = math.parse('2 * 1 * x ^ (2 - 1)')\n * math.simplify(f) // Node \"2 * x\"\n * math.simplify('0.4 * x', {}, {exactFractions: true}) // Node \"x * 2 / 5\"\n * math.simplify('0.4 * x', {}, {exactFractions: false}) // Node \"0.4 * x\"\n *\n * See also:\n *\n * derivative, parse, evaluate, rationalize\n *\n * @param {Node | string} expr\n * The expression to be simplified\n * @param {Array<{l:string, r: string} | string | function>} [rules]\n * Optional list with custom rules\n * @return {Node} Returns the simplified form of `expr`\n */\n const simplify = typed('simplify', {\n string: function (expr) {\n return this(parse(expr), this.rules, {}, {})\n },\n\n 'string, Object': function (expr, scope) {\n return this(parse(expr), this.rules, scope, {})\n },\n\n 'string, Object, Object': function (expr, scope, options) {\n return this(parse(expr), this.rules, scope, options)\n },\n\n 'string, Array': function (expr, rules) {\n return this(parse(expr), rules, {}, {})\n },\n\n 'string, Array, Object': function (expr, rules, scope) {\n return this(parse(expr), rules, scope, {})\n },\n\n 'string, Array, Object, Object': function (expr, rules, scope, options) {\n return this(parse(expr), rules, scope, options)\n },\n\n 'Node, Object': function (expr, scope) {\n return this(expr, this.rules, scope, {})\n },\n\n 'Node, Object, Object': function (expr, scope, options) {\n return this(expr, this.rules, scope, options)\n },\n\n Node: function (expr) {\n return this(expr, this.rules, {}, {})\n },\n\n 'Node, Array': function (expr, rules) {\n return this(expr, rules, {}, {})\n },\n\n 'Node, Array, Object': function (expr, rules, scope) {\n return this(expr, rules, scope, {})\n },\n\n 'Node, Array, Object, Object': function (expr, rules, scope, options) {\n rules = _buildRules(rules)\n let res = resolve(expr, scope)\n res = removeParens(res)\n const visited = {}\n let str = res.toString({ parenthesis: 'all' })\n while (!visited[str]) {\n visited[str] = true\n _lastsym = 0 // counter for placeholder symbols\n for (let i = 0; i < rules.length; i++) {\n if (typeof rules[i] === 'function') {\n res = rules[i](res, options)\n } else {\n flatten(res)\n res = applyRule(res, rules[i])\n }\n unflattenl(res) // using left-heavy binary tree here since custom rule functions may expect it\n }\n str = res.toString({ parenthesis: 'all' })\n }\n return res\n }\n })\n simplify.simplifyCore = simplifyCore\n simplify.resolve = resolve\n\n function removeParens (node) {\n return node.transform(function (node, path, parent) {\n return isParenthesisNode(node)\n ? removeParens(node.content)\n : node\n })\n }\n\n // All constants that are allowed in rules\n const SUPPORTED_CONSTANTS = {\n true: true,\n false: true,\n e: true,\n i: true,\n Infinity: true,\n LN2: true,\n LN10: true,\n LOG2E: true,\n LOG10E: true,\n NaN: true,\n phi: true,\n pi: true,\n SQRT1_2: true,\n SQRT2: true,\n tau: true\n // null: false,\n // undefined: false,\n // version: false,\n }\n\n // Array of strings, used to build the ruleSet.\n // Each l (left side) and r (right side) are parsed by\n // the expression parser into a node tree.\n // Left hand sides are matched to subtrees within the\n // expression to be parsed and replaced with the right\n // hand side.\n // TODO: Add support for constraints on constants (either in the form of a '=' expression or a callback [callback allows things like comparing symbols alphabetically])\n // To evaluate lhs constants for rhs constants, use: { l: 'c1+c2', r: 'c3', evaluate: 'c3 = c1 + c2' }. Multiple assignments are separated by ';' in block format.\n // It is possible to get into an infinite loop with conflicting rules\n simplify.rules = [\n simplifyCore,\n // { l: 'n+0', r: 'n' }, // simplifyCore\n // { l: 'n^0', r: '1' }, // simplifyCore\n // { l: '0*n', r: '0' }, // simplifyCore\n // { l: 'n/n', r: '1'}, // simplifyCore\n // { l: 'n^1', r: 'n' }, // simplifyCore\n // { l: '+n1', r:'n1' }, // simplifyCore\n // { l: 'n--n1', r:'n+n1' }, // simplifyCore\n { l: 'log(e)', r: '1' },\n\n // temporary rules\n { l: 'n-n1', r: 'n+-n1' }, // temporarily replace 'subtract' so we can further flatten the 'add' operator\n { l: '-(c*v)', r: '(-c) * v' }, // make non-constant terms positive\n { l: '-v', r: '(-1) * v' },\n { l: 'n/n1^n2', r: 'n*n1^-n2' }, // temporarily replace 'divide' so we can further flatten the 'multiply' operator\n { l: 'n/n1', r: 'n*n1^-1' },\n\n // expand nested exponentiation\n { l: '(n ^ n1) ^ n2', r: 'n ^ (n1 * n2)' },\n\n // collect like factors\n { l: 'n*n', r: 'n^2' },\n { l: 'n * n^n1', r: 'n^(n1+1)' },\n { l: 'n^n1 * n^n2', r: 'n^(n1+n2)' },\n\n // collect like terms\n { l: 'n+n', r: '2*n' },\n { l: 'n+-n', r: '0' },\n { l: 'n1*n2 + n2', r: '(n1+1)*n2' },\n { l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },\n\n // remove parenthesis in the case of negating a quantitiy\n { l: 'n1 + -1 * (n2 + n3)', r: 'n1 + -1 * n2 + -1 * n3' },\n\n simplifyConstant,\n\n { l: '(-n)*n1', r: '-(n*n1)' }, // make factors positive (and undo 'make non-constant terms positive')\n\n // ordering of constants\n { l: 'c+v', r: 'v+c', context: { add: { commutative: false } } },\n { l: 'v*c', r: 'c*v', context: { multiply: { commutative: false } } },\n\n // undo temporary rules\n // { l: '(-1) * n', r: '-n' }, // #811 added test which proved this is redundant\n { l: 'n+-n1', r: 'n-n1' }, // undo replace 'subtract'\n { l: 'n*(n1^-1)', r: 'n/n1' }, // undo replace 'divide'\n { l: 'n*n1^-n2', r: 'n/n1^n2' },\n { l: 'n1^-1', r: '1/n1' },\n\n { l: 'n*(n1/n2)', r: '(n*n1)/n2' }, // '*' before '/'\n { l: 'n-(n1+n2)', r: 'n-n1-n2' }, // '-' before '+'\n // { l: '(n1/n2)/n3', r: 'n1/(n2*n3)' },\n // { l: '(n*n1)/(n*n2)', r: 'n1/n2' },\n\n { l: '1*n', r: 'n' }, // this pattern can be produced by simplifyConstant\n\n { l: 'n1/(n2/n3)', r: '(n1*n3)/n2' }\n\n ]\n\n /**\n * Parse the string array of rules into nodes\n *\n * Example syntax for rules:\n *\n * Position constants to the left in a product:\n * { l: 'n1 * c1', r: 'c1 * n1' }\n * n1 is any Node, and c1 is a ConstantNode.\n *\n * Apply difference of squares formula:\n * { l: '(n1 - n2) * (n1 + n2)', r: 'n1^2 - n2^2' }\n * n1, n2 mean any Node.\n *\n * Short hand notation:\n * 'n1 * c1 -> c1 * n1'\n */\n function _buildRules (rules) {\n // Array of rules to be used to simplify expressions\n const ruleSet = []\n for (let i = 0; i < rules.length; i++) {\n let rule = rules[i]\n let newRule\n const ruleType = typeof rule\n switch (ruleType) {\n case 'string':\n {\n const lr = rule.split('->')\n if (lr.length === 2) {\n rule = { l: lr[0], r: lr[1] }\n } else {\n throw SyntaxError('Could not parse rule: ' + rule)\n }\n }\n /* falls through */\n case 'object':\n newRule = {\n l: removeParens(parse(rule.l)),\n r: removeParens(parse(rule.r))\n }\n if (rule.context) {\n newRule.evaluate = rule.context\n }\n if (rule.evaluate) {\n newRule.evaluate = parse(rule.evaluate)\n }\n\n if (isAssociative(newRule.l)) {\n const makeNode = createMakeNodeFunction(newRule.l)\n const expandsym = _getExpandPlaceholderSymbol()\n newRule.expanded = {}\n newRule.expanded.l = makeNode([newRule.l.clone(), expandsym])\n // Push the expandsym into the deepest possible branch.\n // This helps to match the newRule against nodes returned from getSplits() later on.\n flatten(newRule.expanded.l)\n unflattenr(newRule.expanded.l)\n newRule.expanded.r = makeNode([newRule.r, expandsym])\n }\n break\n case 'function':\n newRule = rule\n break\n default:\n throw TypeError('Unsupported type of rule: ' + ruleType)\n }\n // console.log('Adding rule: ' + rules[i])\n // console.log(newRule)\n ruleSet.push(newRule)\n }\n return ruleSet\n }\n\n let _lastsym = 0\n function _getExpandPlaceholderSymbol () {\n return new SymbolNode('_p' + _lastsym++)\n }\n\n /**\n * Returns a simplfied form of node, or the original node if no simplification was possible.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The simplified form of `expr`, or the original node if no simplification was possible.\n */\n const applyRule = typed('applyRule', {\n 'Node, Object': function (node, rule) {\n // console.log('Entering applyRule(' + node.toString() + ')')\n\n // Do not clone node unless we find a match\n let res = node\n\n // First replace our child nodes with their simplified versions\n // If a child could not be simplified, the assignments will have\n // no effect since the node is returned unchanged\n if (res instanceof OperatorNode || res instanceof FunctionNode) {\n if (res.args) {\n for (let i = 0; i < res.args.length; i++) {\n res.args[i] = applyRule(res.args[i], rule)\n }\n }\n } else if (res instanceof ParenthesisNode) {\n if (res.content) {\n res.content = applyRule(res.content, rule)\n }\n }\n\n // Try to match a rule against this node\n let repl = rule.r\n let matches = _ruleMatch(rule.l, res)[0]\n\n // If the rule is associative operator, we can try matching it while allowing additional terms.\n // This allows us to match rules like 'n+n' to the expression '(1+x)+x' or even 'x+1+x' if the operator is commutative.\n if (!matches && rule.expanded) {\n repl = rule.expanded.r\n matches = _ruleMatch(rule.expanded.l, res)[0]\n }\n\n if (matches) {\n // const before = res.toString({parenthesis: 'all'})\n\n // Create a new node by cloning the rhs of the matched rule\n // we keep any implicit multiplication state if relevant\n const implicit = res.implicit\n res = repl.clone()\n if (implicit && 'implicit' in repl) {\n res.implicit = true\n }\n\n // Replace placeholders with their respective nodes without traversing deeper into the replaced nodes\n res = res.transform(function (node) {\n if (node.isSymbolNode && hasOwnProperty(matches.placeholders, node.name)) {\n return matches.placeholders[node.name].clone()\n } else {\n return node\n }\n })\n\n // const after = res.toString({parenthesis: 'all'})\n // console.log('Simplified ' + before + ' to ' + after)\n }\n\n return res\n }\n })\n\n /**\n * Get (binary) combinations of a flattened binary node\n * e.g. +(node1, node2, node3) -> [\n * +(node1, +(node2, node3)),\n * +(node2, +(node1, node3)),\n * +(node3, +(node1, node2))]\n *\n */\n function getSplits (node, context) {\n const res = []\n let right, rightArgs\n const makeNode = createMakeNodeFunction(node)\n if (isCommutative(node, context)) {\n for (let i = 0; i < node.args.length; i++) {\n rightArgs = node.args.slice(0)\n rightArgs.splice(i, 1)\n right = (rightArgs.length === 1) ? rightArgs[0] : makeNode(rightArgs)\n res.push(makeNode([node.args[i], right]))\n }\n } else {\n rightArgs = node.args.slice(1)\n right = (rightArgs.length === 1) ? rightArgs[0] : makeNode(rightArgs)\n res.push(makeNode([node.args[0], right]))\n }\n return res\n }\n\n /**\n * Returns the set union of two match-placeholders or null if there is a conflict.\n */\n function mergeMatch (match1, match2) {\n const res = { placeholders: {} }\n\n // Some matches may not have placeholders; this is OK\n if (!match1.placeholders && !match2.placeholders) {\n return res\n } else if (!match1.placeholders) {\n return match2\n } else if (!match2.placeholders) {\n return match1\n }\n\n // Placeholders with the same key must match exactly\n for (const key in match1.placeholders) {\n if (hasOwnProperty(match1.placeholders, key)) {\n res.placeholders[key] = match1.placeholders[key]\n\n if (hasOwnProperty(match2.placeholders, key)) {\n if (!_exactMatch(match1.placeholders[key], match2.placeholders[key])) {\n return null\n }\n }\n }\n }\n\n for (const key in match2.placeholders) {\n if (hasOwnProperty(match2.placeholders, key)) {\n res.placeholders[key] = match2.placeholders[key]\n }\n }\n\n return res\n }\n\n /**\n * Combine two lists of matches by applying mergeMatch to the cartesian product of two lists of matches.\n * Each list represents matches found in one child of a node.\n */\n function combineChildMatches (list1, list2) {\n const res = []\n\n if (list1.length === 0 || list2.length === 0) {\n return res\n }\n\n let merged\n for (let i1 = 0; i1 < list1.length; i1++) {\n for (let i2 = 0; i2 < list2.length; i2++) {\n merged = mergeMatch(list1[i1], list2[i2])\n if (merged) {\n res.push(merged)\n }\n }\n }\n return res\n }\n\n /**\n * Combine multiple lists of matches by applying mergeMatch to the cartesian product of two lists of matches.\n * Each list represents matches found in one child of a node.\n * Returns a list of unique matches.\n */\n function mergeChildMatches (childMatches) {\n if (childMatches.length === 0) {\n return childMatches\n }\n\n const sets = childMatches.reduce(combineChildMatches)\n const uniqueSets = []\n const unique = {}\n for (let i = 0; i < sets.length; i++) {\n const s = JSON.stringify(sets[i])\n if (!unique[s]) {\n unique[s] = true\n uniqueSets.push(sets[i])\n }\n }\n return uniqueSets\n }\n\n /**\n * Determines whether node matches rule.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} rule\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @return {Object} Information about the match, if it exists.\n */\n function _ruleMatch (rule, node, isSplit) {\n // console.log('Entering _ruleMatch(' + JSON.stringify(rule) + ', ' + JSON.stringify(node) + ')')\n // console.log('rule = ' + rule)\n // console.log('node = ' + node)\n\n // console.log('Entering _ruleMatch(' + rule.toString() + ', ' + node.toString() + ')')\n let res = [{ placeholders: {} }]\n\n if ((rule instanceof OperatorNode && node instanceof OperatorNode) ||\n (rule instanceof FunctionNode && node instanceof FunctionNode)) {\n // If the rule is an OperatorNode or a FunctionNode, then node must match exactly\n if (rule instanceof OperatorNode) {\n if (rule.op !== node.op || rule.fn !== node.fn) {\n return []\n }\n } else if (rule instanceof FunctionNode) {\n if (rule.name !== node.name) {\n return []\n }\n }\n\n // rule and node match. Search the children of rule and node.\n if ((node.args.length === 1 && rule.args.length === 1) || !isAssociative(node) || isSplit) {\n // Expect non-associative operators to match exactly\n const childMatches = []\n for (let i = 0; i < rule.args.length; i++) {\n const childMatch = _ruleMatch(rule.args[i], node.args[i])\n if (childMatch.length === 0) {\n // Child did not match, so stop searching immediately\n return []\n }\n // The child matched, so add the information returned from the child to our result\n childMatches.push(childMatch)\n }\n res = mergeChildMatches(childMatches)\n } else if (node.args.length >= 2 && rule.args.length === 2) { // node is flattened, rule is not\n // Associative operators/functions can be split in different ways so we check if the rule matches each\n // them and return their union.\n const splits = getSplits(node, rule.context)\n let splitMatches = []\n for (let i = 0; i < splits.length; i++) {\n const matchSet = _ruleMatch(rule, splits[i], true) // recursing at the same tree depth here\n splitMatches = splitMatches.concat(matchSet)\n }\n return splitMatches\n } else if (rule.args.length > 2) {\n throw Error('Unexpected non-binary associative function: ' + rule.toString())\n } else {\n // Incorrect number of arguments in rule and node, so no match\n return []\n }\n } else if (rule instanceof SymbolNode) {\n // If the rule is a SymbolNode, then it carries a special meaning\n // according to the first character of the symbol node name.\n // c.* matches a ConstantNode\n // n.* matches any node\n if (rule.name.length === 0) {\n throw new Error('Symbol in rule has 0 length...!?')\n }\n if (SUPPORTED_CONSTANTS[rule.name]) {\n // built-in constant must match exactly\n if (rule.name !== node.name) {\n return []\n }\n } else if (rule.name[0] === 'n' || rule.name.substring(0, 2) === '_p') {\n // rule matches _anything_, so assign this node to the rule.name placeholder\n // Assign node to the rule.name placeholder.\n // Our parent will check for matches among placeholders.\n res[0].placeholders[rule.name] = node\n } else if (rule.name[0] === 'v') {\n // rule matches any variable thing (not a ConstantNode)\n if (!isConstantNode(node)) {\n res[0].placeholders[rule.name] = node\n } else {\n // Mis-match: rule was expecting something other than a ConstantNode\n return []\n }\n } else if (rule.name[0] === 'c') {\n // rule matches any ConstantNode\n if (node instanceof ConstantNode) {\n res[0].placeholders[rule.name] = node\n } else {\n // Mis-match: rule was expecting a ConstantNode\n return []\n }\n } else {\n throw new Error('Invalid symbol in rule: ' + rule.name)\n }\n } else if (rule instanceof ConstantNode) {\n // Literal constant must match exactly\n if (!equal(rule.value, node.value)) {\n return []\n }\n } else {\n // Some other node was encountered which we aren't prepared for, so no match\n return []\n }\n\n // It's a match!\n\n // console.log('_ruleMatch(' + rule.toString() + ', ' + node.toString() + ') found a match')\n return res\n }\n\n /**\n * Determines whether p and q (and all their children nodes) are identical.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} p\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} q\n * @return {Object} Information about the match, if it exists.\n */\n function _exactMatch (p, q) {\n if (p instanceof ConstantNode && q instanceof ConstantNode) {\n if (!equal(p.value, q.value)) {\n return false\n }\n } else if (p instanceof SymbolNode && q instanceof SymbolNode) {\n if (p.name !== q.name) {\n return false\n }\n } else if ((p instanceof OperatorNode && q instanceof OperatorNode) ||\n (p instanceof FunctionNode && q instanceof FunctionNode)) {\n if (p instanceof OperatorNode) {\n if (p.op !== q.op || p.fn !== q.fn) {\n return false\n }\n } else if (p instanceof FunctionNode) {\n if (p.name !== q.name) {\n return false\n }\n }\n\n if (p.args.length !== q.args.length) {\n return false\n }\n\n for (let i = 0; i < p.args.length; i++) {\n if (!_exactMatch(p.args[i], q.args[i])) {\n return false\n }\n }\n } else {\n return false\n }\n\n return true\n }\n\n return simplify\n})\n","import { isConstantNode, typeOf } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'derivative'\nconst dependencies = [\n 'typed',\n 'config',\n 'parse',\n 'simplify',\n 'equal',\n 'isZero',\n 'numeric',\n 'ConstantNode',\n 'FunctionNode',\n 'OperatorNode',\n 'ParenthesisNode',\n 'SymbolNode'\n]\n\nexport const createDerivative = /* #__PURE__ */ factory(name, dependencies, ({\n typed,\n config,\n parse,\n simplify,\n equal,\n isZero,\n numeric,\n ConstantNode,\n FunctionNode,\n OperatorNode,\n ParenthesisNode,\n SymbolNode\n}) => {\n /**\n * Takes the derivative of an expression expressed in parser Nodes.\n * The derivative will be taken over the supplied variable in the\n * second parameter. If there are multiple variables in the expression,\n * it will return a partial derivative.\n *\n * This uses rules of differentiation which can be found here:\n *\n * - [Differentiation rules (Wikipedia)](https://en.wikipedia.org/wiki/Differentiation_rules)\n *\n * Syntax:\n *\n * derivative(expr, variable)\n * derivative(expr, variable, options)\n *\n * Examples:\n *\n * math.derivative('x^2', 'x') // Node {2 * x}\n * math.derivative('x^2', 'x', {simplify: false}) // Node {2 * 1 * x ^ (2 - 1)\n * math.derivative('sin(2x)', 'x')) // Node {2 * cos(2 * x)}\n * math.derivative('2*x', 'x').evaluate() // number 2\n * math.derivative('x^2', 'x').evaluate({x: 4}) // number 8\n * const f = math.parse('x^2')\n * const x = math.parse('x')\n * math.derivative(f, x) // Node {2 * x}\n *\n * See also:\n *\n * simplify, parse, evaluate\n *\n * @param {Node | string} expr The expression to differentiate\n * @param {SymbolNode | string} variable The variable over which to differentiate\n * @param {{simplify: boolean}} [options]\n * There is one option available, `simplify`, which\n * is true by default. When false, output will not\n * be simplified.\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The derivative of `expr`\n */\n const derivative = typed('derivative', {\n 'Node, SymbolNode, Object': function (expr, variable, options) {\n const constNodes = {}\n constTag(constNodes, expr, variable.name)\n const res = _derivative(expr, constNodes)\n return options.simplify ? simplify(res) : res\n },\n 'Node, SymbolNode': function (expr, variable) {\n return this(expr, variable, { simplify: true })\n },\n\n 'string, SymbolNode': function (expr, variable) {\n return this(parse(expr), variable)\n },\n 'string, SymbolNode, Object': function (expr, variable, options) {\n return this(parse(expr), variable, options)\n },\n\n 'string, string': function (expr, variable) {\n return this(parse(expr), parse(variable))\n },\n 'string, string, Object': function (expr, variable, options) {\n return this(parse(expr), parse(variable), options)\n },\n\n 'Node, string': function (expr, variable) {\n return this(expr, parse(variable))\n },\n 'Node, string, Object': function (expr, variable, options) {\n return this(expr, parse(variable), options)\n }\n\n // TODO: replace the 8 signatures above with 4 as soon as typed-function supports optional arguments\n\n /* TODO: implement and test syntax with order of derivatives -> implement as an option {order: number}\n 'Node, SymbolNode, ConstantNode': function (expr, variable, {order}) {\n let res = expr\n for (let i = 0; i < order; i++) {\n let constNodes = {}\n constTag(constNodes, expr, variable.name)\n res = _derivative(res, constNodes)\n }\n return res\n }\n */\n })\n\n derivative._simplify = true\n\n derivative.toTex = function (deriv) {\n return _derivTex.apply(null, deriv.args)\n }\n\n // FIXME: move the toTex method of derivative to latex.js. Difficulty is that it relies on parse.\n // NOTE: the optional \"order\" parameter here is currently unused\n const _derivTex = typed('_derivTex', {\n 'Node, SymbolNode': function (expr, x) {\n if (isConstantNode(expr) && typeOf(expr.value) === 'string') {\n return _derivTex(parse(expr.value).toString(), x.toString(), 1)\n } else {\n return _derivTex(expr.toString(), x.toString(), 1)\n }\n },\n 'Node, ConstantNode': function (expr, x) {\n if (typeOf(x.value) === 'string') {\n return _derivTex(expr, parse(x.value))\n } else {\n throw new Error(\"The second parameter to 'derivative' is a non-string constant\")\n }\n },\n 'Node, SymbolNode, ConstantNode': function (expr, x, order) {\n return _derivTex(expr.toString(), x.name, order.value)\n },\n 'string, string, number': function (expr, x, order) {\n let d\n if (order === 1) {\n d = '{d\\\\over d' + x + '}'\n } else {\n d = '{d^{' + order + '}\\\\over d' + x + '^{' + order + '}}'\n }\n return d + `\\\\left[${expr}\\\\right]`\n }\n })\n\n /**\n * Does a depth-first search on the expression tree to identify what Nodes\n * are constants (e.g. 2 + 2), and stores the ones that are constants in\n * constNodes. Classification is done as follows:\n *\n * 1. ConstantNodes are constants.\n * 2. If there exists a SymbolNode, of which we are differentiating over,\n * in the subtree it is not constant.\n *\n * @param {Object} constNodes Holds the nodes that are constant\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @param {string} varName Variable that we are differentiating\n * @return {boolean} if node is constant\n */\n // TODO: can we rewrite constTag into a pure function?\n const constTag = typed('constTag', {\n 'Object, ConstantNode, string': function (constNodes, node) {\n constNodes[node] = true\n return true\n },\n\n 'Object, SymbolNode, string': function (constNodes, node, varName) {\n // Treat other variables like constants. For reasoning, see:\n // https://en.wikipedia.org/wiki/Partial_derivative\n if (node.name !== varName) {\n constNodes[node] = true\n return true\n }\n return false\n },\n\n 'Object, ParenthesisNode, string': function (constNodes, node, varName) {\n return constTag(constNodes, node.content, varName)\n },\n\n 'Object, FunctionAssignmentNode, string': function (constNodes, node, varName) {\n if (node.params.indexOf(varName) === -1) {\n constNodes[node] = true\n return true\n }\n return constTag(constNodes, node.expr, varName)\n },\n\n 'Object, FunctionNode | OperatorNode, string': function (constNodes, node, varName) {\n if (node.args.length > 0) {\n let isConst = constTag(constNodes, node.args[0], varName)\n for (let i = 1; i < node.args.length; ++i) {\n isConst = constTag(constNodes, node.args[i], varName) && isConst\n }\n\n if (isConst) {\n constNodes[node] = true\n return true\n }\n }\n return false\n }\n })\n\n /**\n * Applies differentiation rules.\n *\n * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node\n * @param {Object} constNodes Holds the nodes that are constant\n * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The derivative of `expr`\n */\n const _derivative = typed('_derivative', {\n 'ConstantNode, Object': function (node) {\n return createConstantNode(0)\n },\n\n 'SymbolNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n return createConstantNode(1)\n },\n\n 'ParenthesisNode, Object': function (node, constNodes) {\n return new ParenthesisNode(_derivative(node.content, constNodes))\n },\n\n 'FunctionAssignmentNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n return _derivative(node.expr, constNodes)\n },\n\n 'FunctionNode, Object': function (node, constNodes) {\n if (node.args.length !== 1) {\n funcArgsCheck(node)\n }\n\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n\n const arg0 = node.args[0]\n let arg1\n\n let div = false // is output a fraction?\n let negative = false // is output negative?\n\n let funcDerivative\n switch (node.name) {\n case 'cbrt':\n // d/dx(cbrt(x)) = 1 / (3x^(2/3))\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n createConstantNode(3),\n new OperatorNode('^', 'pow', [\n arg0,\n new OperatorNode('/', 'divide', [\n createConstantNode(2),\n createConstantNode(3)\n ])\n ])\n ])\n break\n case 'sqrt':\n case 'nthRoot':\n // d/dx(sqrt(x)) = 1 / (2*sqrt(x))\n if (node.args.length === 1) {\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n createConstantNode(2),\n new FunctionNode('sqrt', [arg0])\n ])\n } else if (node.args.length === 2) {\n // Rearrange from nthRoot(x, a) -> x^(1/a)\n arg1 = new OperatorNode('/', 'divide', [\n createConstantNode(1),\n node.args[1]\n ])\n\n // Is a variable?\n constNodes[arg1] = constNodes[node.args[1]]\n\n return _derivative(new OperatorNode('^', 'pow', [arg0, arg1]), constNodes)\n }\n break\n case 'log10':\n arg1 = createConstantNode(10)\n /* fall through! */\n case 'log':\n if (!arg1 && node.args.length === 1) {\n // d/dx(log(x)) = 1 / x\n funcDerivative = arg0.clone()\n div = true\n } else if ((node.args.length === 1 && arg1) ||\n (node.args.length === 2 && constNodes[node.args[1]] !== undefined)) {\n // d/dx(log(x, c)) = 1 / (x*ln(c))\n funcDerivative = new OperatorNode('*', 'multiply', [\n arg0.clone(),\n new FunctionNode('log', [arg1 || node.args[1]])\n ])\n div = true\n } else if (node.args.length === 2) {\n // d/dx(log(f(x), g(x))) = d/dx(log(f(x)) / log(g(x)))\n return _derivative(new OperatorNode('/', 'divide', [\n new FunctionNode('log', [arg0]),\n new FunctionNode('log', [node.args[1]])\n ]), constNodes)\n }\n break\n case 'pow':\n constNodes[arg1] = constNodes[node.args[1]]\n // Pass to pow operator node parser\n return _derivative(new OperatorNode('^', 'pow', [arg0, node.args[1]]), constNodes)\n case 'exp':\n // d/dx(e^x) = e^x\n funcDerivative = new FunctionNode('exp', [arg0.clone()])\n break\n case 'sin':\n // d/dx(sin(x)) = cos(x)\n funcDerivative = new FunctionNode('cos', [arg0.clone()])\n break\n case 'cos':\n // d/dx(cos(x)) = -sin(x)\n funcDerivative = new OperatorNode('-', 'unaryMinus', [\n new FunctionNode('sin', [arg0.clone()])\n ])\n break\n case 'tan':\n // d/dx(tan(x)) = sec(x)^2\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('sec', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'sec':\n // d/dx(sec(x)) = sec(x)tan(x)\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('tan', [arg0.clone()])\n ])\n break\n case 'csc':\n // d/dx(csc(x)) = -csc(x)cot(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('cot', [arg0.clone()])\n ])\n break\n case 'cot':\n // d/dx(cot(x)) = -csc(x)^2\n negative = true\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('csc', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'asin':\n // d/dx(asin(x)) = 1 / sqrt(1 - x^2)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n break\n case 'acos':\n // d/dx(acos(x)) = -1 / sqrt(1 - x^2)\n div = true\n negative = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n break\n case 'atan':\n // d/dx(atan(x)) = 1 / (x^2 + 1)\n div = true\n funcDerivative = new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n break\n case 'asec':\n // d/dx(asec(x)) = 1 / (|x|*sqrt(x^2 - 1))\n div = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acsc':\n // d/dx(acsc(x)) = -1 / (|x|*sqrt(x^2 - 1))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acot':\n // d/dx(acot(x)) = -1 / (x^2 + 1)\n div = true\n negative = true\n funcDerivative = new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n break\n case 'sinh':\n // d/dx(sinh(x)) = cosh(x)\n funcDerivative = new FunctionNode('cosh', [arg0.clone()])\n break\n case 'cosh':\n // d/dx(cosh(x)) = sinh(x)\n funcDerivative = new FunctionNode('sinh', [arg0.clone()])\n break\n case 'tanh':\n // d/dx(tanh(x)) = sech(x)^2\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('sech', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'sech':\n // d/dx(sech(x)) = -sech(x)tanh(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('tanh', [arg0.clone()])\n ])\n break\n case 'csch':\n // d/dx(csch(x)) = -csch(x)coth(x)\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n node,\n new FunctionNode('coth', [arg0.clone()])\n ])\n break\n case 'coth':\n // d/dx(coth(x)) = -csch(x)^2\n negative = true\n funcDerivative = new OperatorNode('^', 'pow', [\n new FunctionNode('csch', [arg0.clone()]),\n createConstantNode(2)\n ])\n break\n case 'asinh':\n // d/dx(asinh(x)) = 1 / sqrt(x^2 + 1)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n break\n case 'acosh':\n // d/dx(acosh(x)) = 1 / sqrt(x^2 - 1); XXX potentially only for x >= 1 (the real spectrum)\n div = true\n funcDerivative = new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n break\n case 'atanh':\n // d/dx(atanh(x)) = 1 / (1 - x^2)\n div = true\n funcDerivative = new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n break\n case 'asech':\n // d/dx(asech(x)) = -1 / (x*sqrt(1 - x^2))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n arg0.clone(),\n new FunctionNode('sqrt', [\n new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n ])\n ])\n break\n case 'acsch':\n // d/dx(acsch(x)) = -1 / (|x|*sqrt(x^2 + 1))\n div = true\n negative = true\n funcDerivative = new OperatorNode('*', 'multiply', [\n new FunctionNode('abs', [arg0.clone()]),\n new FunctionNode('sqrt', [\n new OperatorNode('+', 'add', [\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ]),\n createConstantNode(1)\n ])\n ])\n ])\n break\n case 'acoth':\n // d/dx(acoth(x)) = -1 / (1 - x^2)\n div = true\n negative = true\n funcDerivative = new OperatorNode('-', 'subtract', [\n createConstantNode(1),\n new OperatorNode('^', 'pow', [\n arg0.clone(),\n createConstantNode(2)\n ])\n ])\n break\n case 'abs':\n // d/dx(abs(x)) = abs(x)/x\n funcDerivative = new OperatorNode('/', 'divide', [\n new FunctionNode(new SymbolNode('abs'), [arg0.clone()]),\n arg0.clone()\n ])\n break\n case 'gamma': // Needs digamma function, d/dx(gamma(x)) = gamma(x)digamma(x)\n default: throw new Error('Function \"' + node.name + '\" is not supported by derivative, or a wrong number of arguments is passed')\n }\n\n let op, func\n if (div) {\n op = '/'\n func = 'divide'\n } else {\n op = '*'\n func = 'multiply'\n }\n\n /* Apply chain rule to all functions:\n F(x) = f(g(x))\n F'(x) = g'(x)*f'(g(x)) */\n let chainDerivative = _derivative(arg0, constNodes)\n if (negative) {\n chainDerivative = new OperatorNode('-', 'unaryMinus', [chainDerivative])\n }\n return new OperatorNode(op, func, [chainDerivative, funcDerivative])\n },\n\n 'OperatorNode, Object': function (node, constNodes) {\n if (constNodes[node] !== undefined) {\n return createConstantNode(0)\n }\n\n if (node.op === '+') {\n // d/dx(sum(f(x)) = sum(f'(x))\n return new OperatorNode(node.op, node.fn, node.args.map(function (arg) {\n return _derivative(arg, constNodes)\n }))\n }\n\n if (node.op === '-') {\n // d/dx(+/-f(x)) = +/-f'(x)\n if (node.isUnary()) {\n return new OperatorNode(node.op, node.fn, [\n _derivative(node.args[0], constNodes)\n ])\n }\n\n // Linearity of differentiation, d/dx(f(x) +/- g(x)) = f'(x) +/- g'(x)\n if (node.isBinary()) {\n return new OperatorNode(node.op, node.fn, [\n _derivative(node.args[0], constNodes),\n _derivative(node.args[1], constNodes)\n ])\n }\n }\n\n if (node.op === '*') {\n // d/dx(c*f(x)) = c*f'(x)\n const constantTerms = node.args.filter(function (arg) {\n return constNodes[arg] !== undefined\n })\n\n if (constantTerms.length > 0) {\n const nonConstantTerms = node.args.filter(function (arg) {\n return constNodes[arg] === undefined\n })\n\n const nonConstantNode = nonConstantTerms.length === 1\n ? nonConstantTerms[0]\n : new OperatorNode('*', 'multiply', nonConstantTerms)\n\n const newArgs = constantTerms.concat(_derivative(nonConstantNode, constNodes))\n\n return new OperatorNode('*', 'multiply', newArgs)\n }\n\n // Product Rule, d/dx(f(x)*g(x)) = f'(x)*g(x) + f(x)*g'(x)\n return new OperatorNode('+', 'add', node.args.map(function (argOuter) {\n return new OperatorNode('*', 'multiply', node.args.map(function (argInner) {\n return (argInner === argOuter)\n ? _derivative(argInner, constNodes)\n : argInner.clone()\n }))\n }))\n }\n\n if (node.op === '/' && node.isBinary()) {\n const arg0 = node.args[0]\n const arg1 = node.args[1]\n\n // d/dx(f(x) / c) = f'(x) / c\n if (constNodes[arg1] !== undefined) {\n return new OperatorNode('/', 'divide', [_derivative(arg0, constNodes), arg1])\n }\n\n // Reciprocal Rule, d/dx(c / f(x)) = -c(f'(x)/f(x)^2)\n if (constNodes[arg0] !== undefined) {\n return new OperatorNode('*', 'multiply', [\n new OperatorNode('-', 'unaryMinus', [arg0]),\n new OperatorNode('/', 'divide', [\n _derivative(arg1, constNodes),\n new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])\n ])\n ])\n }\n\n // Quotient rule, d/dx(f(x) / g(x)) = (f'(x)g(x) - f(x)g'(x)) / g(x)^2\n return new OperatorNode('/', 'divide', [\n new OperatorNode('-', 'subtract', [\n new OperatorNode('*', 'multiply', [_derivative(arg0, constNodes), arg1.clone()]),\n new OperatorNode('*', 'multiply', [arg0.clone(), _derivative(arg1, constNodes)])\n ]),\n new OperatorNode('^', 'pow', [arg1.clone(), createConstantNode(2)])\n ])\n }\n\n if (node.op === '^' && node.isBinary()) {\n const arg0 = node.args[0]\n const arg1 = node.args[1]\n\n if (constNodes[arg0] !== undefined) {\n // If is secretly constant; 0^f(x) = 1 (in JS), 1^f(x) = 1\n if (isConstantNode(arg0) && (isZero(arg0.value) || equal(arg0.value, 1))) {\n return createConstantNode(0)\n }\n\n // d/dx(c^f(x)) = c^f(x)*ln(c)*f'(x)\n return new OperatorNode('*', 'multiply', [\n node,\n new OperatorNode('*', 'multiply', [\n new FunctionNode('log', [arg0.clone()]),\n _derivative(arg1.clone(), constNodes)\n ])\n ])\n }\n\n if (constNodes[arg1] !== undefined) {\n if (isConstantNode(arg1)) {\n // If is secretly constant; f(x)^0 = 1 -> d/dx(1) = 0\n if (isZero(arg1.value)) {\n return createConstantNode(0)\n }\n // Ignore exponent; f(x)^1 = f(x)\n if (equal(arg1.value, 1)) {\n return _derivative(arg0, constNodes)\n }\n }\n\n // Elementary Power Rule, d/dx(f(x)^c) = c*f'(x)*f(x)^(c-1)\n const powMinusOne = new OperatorNode('^', 'pow', [\n arg0.clone(),\n new OperatorNode('-', 'subtract', [\n arg1,\n createConstantNode(1)\n ])\n ])\n\n return new OperatorNode('*', 'multiply', [\n arg1.clone(),\n new OperatorNode('*', 'multiply', [\n _derivative(arg0, constNodes),\n powMinusOne\n ])\n ])\n }\n\n // Functional Power Rule, d/dx(f^g) = f^g*[f'*(g/f) + g'ln(f)]\n return new OperatorNode('*', 'multiply', [\n new OperatorNode('^', 'pow', [arg0.clone(), arg1.clone()]),\n new OperatorNode('+', 'add', [\n new OperatorNode('*', 'multiply', [\n _derivative(arg0, constNodes),\n new OperatorNode('/', 'divide', [arg1.clone(), arg0.clone()])\n ]),\n new OperatorNode('*', 'multiply', [\n _derivative(arg1, constNodes),\n new FunctionNode('log', [arg0.clone()])\n ])\n ])\n ])\n }\n\n throw new Error('Operator \"' + node.op + '\" is not supported by derivative, or a wrong number of arguments is passed')\n }\n })\n\n /**\n * Ensures the number of arguments for a function are correct,\n * and will throw an error otherwise.\n *\n * @param {FunctionNode} node\n */\n function funcArgsCheck (node) {\n // TODO add min, max etc\n if ((node.name === 'log' || node.name === 'nthRoot' || node.name === 'pow') && node.args.length === 2) {\n return\n }\n\n // There should be an incorrect number of arguments if we reach here\n\n // Change all args to constants to avoid unidentified\n // symbol error when compiling function\n for (let i = 0; i < node.args.length; ++i) {\n node.args[i] = createConstantNode(0)\n }\n\n node.compile().evaluate()\n throw new Error('Expected TypeError, but none found')\n }\n\n /**\n * Helper function to create a constant node with a specific type\n * (number, BigNumber, Fraction)\n * @param {number} value\n * @param {string} [valueType]\n * @return {ConstantNode}\n */\n function createConstantNode (value, valueType) {\n return new ConstantNode(numeric(value, valueType || config.number))\n }\n\n return derivative\n})\n","import { isInteger } from '../../utils/number.js'\nimport { factory } from '../../utils/factory.js'\nimport { createSimplifyConstant } from './simplify/simplifyConstant.js'\nimport { createSimplifyCore } from './simplify/simplifyCore.js'\n\nconst name = 'rationalize'\nconst dependencies = [\n 'config',\n 'typed',\n 'equal',\n 'isZero',\n 'add',\n 'subtract',\n 'multiply',\n 'divide',\n 'pow',\n 'parse',\n 'simplify',\n '?bignumber',\n '?fraction',\n 'mathWithTransform',\n 'ConstantNode',\n 'OperatorNode',\n 'FunctionNode',\n 'SymbolNode',\n 'ParenthesisNode'\n]\n\nexport const createRationalize = /* #__PURE__ */ factory(name, dependencies, ({\n config,\n typed,\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n parse,\n simplify,\n fraction,\n bignumber,\n mathWithTransform,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode,\n ParenthesisNode\n}) => {\n const simplifyConstant = createSimplifyConstant({\n typed,\n config,\n mathWithTransform,\n fraction,\n bignumber,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n SymbolNode\n })\n const simplifyCore = createSimplifyCore({\n equal,\n isZero,\n add,\n subtract,\n multiply,\n divide,\n pow,\n ConstantNode,\n OperatorNode,\n FunctionNode,\n ParenthesisNode\n })\n\n /**\n * Transform a rationalizable expression in a rational fraction.\n * If rational fraction is one variable polynomial then converts\n * the numerator and denominator in canonical form, with decreasing\n * exponents, returning the coefficients of numerator.\n *\n * Syntax:\n *\n * rationalize(expr)\n * rationalize(expr, detailed)\n * rationalize(expr, scope)\n * rationalize(expr, scope, detailed)\n *\n * Examples:\n *\n * math.rationalize('sin(x)+y')\n * // Error: There is an unsolved function call\n * math.rationalize('2x/y - y/(x+1)')\n * // (2*x^2-y^2+2*x)/(x*y+y)\n * math.rationalize('(2x+1)^6')\n * // 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1\n * math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3')\n * // -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4)\n * math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') =\n * // (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/\n * // (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72)\n *\n * math.rationalize('x+x+x+y',{y:1}) // 3*x+1\n * math.rationalize('x+x+x+y',{}) // 3*x+y\n *\n * const ret = math.rationalize('x+x+x+y',{},true)\n * // ret.expression=3*x+y, ret.variables = [\"x\",\"y\"]\n * const ret = math.rationalize('-2+5x^2',{},true)\n * // ret.expression=5*x^2-2, ret.variables = [\"x\"], ret.coefficients=[-2,0,5]\n *\n * See also:\n *\n * simplify\n *\n * @param {Node|string} expr The expression to check if is a polynomial expression\n * @param {Object|boolean} optional scope of expression or true for already evaluated rational expression at input\n * @param {Boolean} detailed optional True if return an object, false if return expression node (default)\n *\n * @return {Object | Node} The rational polynomial of `expr` or na object\n * {Object}\n * {Expression Node} expression: node simplified expression\n * {Expression Node} numerator: simplified numerator of expression\n * {Expression Node | boolean} denominator: simplified denominator or false (if there is no denominator)\n * {Array} variables: variable names\n * {Array} coefficients: coefficients of numerator sorted by increased exponent\n * {Expression Node} node simplified expression\n *\n */\n return typed(name, {\n string: function (expr) {\n return this(parse(expr), {}, false)\n },\n\n 'string, boolean': function (expr, detailed) {\n return this(parse(expr), {}, detailed)\n },\n\n 'string, Object': function (expr, scope) {\n return this(parse(expr), scope, false)\n },\n\n 'string, Object, boolean': function (expr, scope, detailed) {\n return this(parse(expr), scope, detailed)\n },\n\n Node: function (expr) {\n return this(expr, {}, false)\n },\n\n 'Node, boolean': function (expr, detailed) {\n return this(expr, {}, detailed)\n },\n\n 'Node, Object': function (expr, scope) {\n return this(expr, scope, false)\n },\n\n 'Node, Object, boolean': function (expr, scope, detailed) {\n const setRules = rulesRationalize() // Rules for change polynomial in near canonical form\n const polyRet = polynomial(expr, scope, true, setRules.firstRules) // Check if expression is a rationalizable polynomial\n const nVars = polyRet.variables.length\n expr = polyRet.expression\n\n if (nVars >= 1) { // If expression in not a constant\n expr = expandPower(expr) // First expand power of polynomials (cannot be made from rules!)\n let sBefore // Previous expression\n let rules\n let eDistrDiv = true\n let redoInic = false\n expr = simplify(expr, setRules.firstRules, {}, { exactFractions: false }) // Apply the initial rules, including succ div rules\n let s\n while (true) { // Apply alternately successive division rules and distr.div.rules\n rules = eDistrDiv ? setRules.distrDivRules : setRules.sucDivRules\n expr = simplify(expr, rules) // until no more changes\n eDistrDiv = !eDistrDiv // Swap between Distr.Div and Succ. Div. Rules\n\n s = expr.toString()\n if (s === sBefore) {\n break // No changes : end of the loop\n }\n\n redoInic = true\n sBefore = s\n }\n\n if (redoInic) { // Apply first rules again without succ div rules (if there are changes)\n expr = simplify(expr, setRules.firstRulesAgain, {}, { exactFractions: false })\n }\n expr = simplify(expr, setRules.finalRules, {}, { exactFractions: false }) // Apply final rules\n } // NVars >= 1\n\n const coefficients = []\n const retRationalize = {}\n\n if (expr.type === 'OperatorNode' && expr.isBinary() && expr.op === '/') { // Separate numerator from denominator\n if (nVars === 1) {\n expr.args[0] = polyToCanonical(expr.args[0], coefficients)\n expr.args[1] = polyToCanonical(expr.args[1])\n }\n if (detailed) {\n retRationalize.numerator = expr.args[0]\n retRationalize.denominator = expr.args[1]\n }\n } else {\n if (nVars === 1) {\n expr = polyToCanonical(expr, coefficients)\n }\n if (detailed) {\n retRationalize.numerator = expr\n retRationalize.denominator = null\n }\n }\n // nVars\n\n if (!detailed) return expr\n retRationalize.coefficients = coefficients\n retRationalize.variables = polyRet.variables\n retRationalize.expression = expr\n return retRationalize\n } // ^^^^^^^ end of rationalize ^^^^^^^^\n }) // end of typed rationalize\n\n /**\n * Function to simplify an expression using an optional scope and\n * return it if the expression is a polynomial expression, i.e.\n * an expression with one or more variables and the operators\n * +, -, *, and ^, where the exponent can only be a positive integer.\n *\n * Syntax:\n *\n * polynomial(expr,scope,extended, rules)\n *\n * @param {Node | string} expr The expression to simplify and check if is polynomial expression\n * @param {object} scope Optional scope for expression simplification\n * @param {boolean} extended Optional. Default is false. When true allows divide operator.\n * @param {array} rules Optional. Default is no rule.\n *\n *\n * @return {Object}\n * {Object} node: node simplified expression\n * {Array} variables: variable names\n */\n function polynomial (expr, scope, extended, rules) {\n const variables = []\n const node = simplify(expr, rules, scope, { exactFractions: false }) // Resolves any variables and functions with all defined parameters\n extended = !!extended\n\n const oper = '+-*' + (extended ? '/' : '')\n recPoly(node)\n const retFunc = {}\n retFunc.expression = node\n retFunc.variables = variables\n return retFunc\n\n // -------------------------------------------------------------------------------------------------------\n\n /**\n * Function to simplify an expression using an optional scope and\n * return it if the expression is a polynomial expression, i.e.\n * an expression with one or more variables and the operators\n * +, -, *, and ^, where the exponent can only be a positive integer.\n *\n * Syntax:\n *\n * recPoly(node)\n *\n *\n * @param {Node} node The current sub tree expression in recursion\n *\n * @return nothing, throw an exception if error\n */\n function recPoly (node) {\n const tp = node.type // node type\n if (tp === 'FunctionNode') {\n // No function call in polynomial expression\n throw new Error('There is an unsolved function call')\n } else if (tp === 'OperatorNode') {\n if (node.op === '^') {\n // TODO: handle negative exponents like in '1/x^(-2)'\n if (node.args[1].type !== 'ConstantNode' || !isInteger(parseFloat(node.args[1].value))) {\n throw new Error('There is a non-integer exponent')\n } else {\n recPoly(node.args[0])\n }\n } else {\n if (oper.indexOf(node.op) === -1) {\n throw new Error('Operator ' + node.op + ' invalid in polynomial expression')\n }\n for (let i = 0; i < node.args.length; i++) {\n recPoly(node.args[i])\n }\n } // type of operator\n } else if (tp === 'SymbolNode') {\n const name = node.name // variable name\n const pos = variables.indexOf(name)\n if (pos === -1) {\n // new variable in expression\n variables.push(name)\n }\n } else if (tp === 'ParenthesisNode') {\n recPoly(node.content)\n } else if (tp !== 'ConstantNode') {\n throw new Error('type ' + tp + ' is not allowed in polynomial expression')\n }\n } // end of recPoly\n } // end of polynomial\n\n // ---------------------------------------------------------------------------------------\n /**\n * Return a rule set to rationalize an polynomial expression in rationalize\n *\n * Syntax:\n *\n * rulesRationalize()\n *\n * @return {array} rule set to rationalize an polynomial expression\n */\n function rulesRationalize () {\n const oldRules = [simplifyCore, // sCore\n { l: 'n+n', r: '2*n' },\n { l: 'n+-n', r: '0' },\n simplifyConstant, // sConstant\n { l: 'n*(n1^-1)', r: 'n/n1' },\n { l: 'n*n1^-n2', r: 'n/n1^n2' },\n { l: 'n1^-1', r: '1/n1' },\n { l: 'n*(n1/n2)', r: '(n*n1)/n2' },\n { l: '1*n', r: 'n' }]\n\n const rulesFirst = [\n { l: '(-n1)/(-n2)', r: 'n1/n2' }, // Unary division\n { l: '(-n1)*(-n2)', r: 'n1*n2' }, // Unary multiplication\n { l: 'n1--n2', r: 'n1+n2' }, // '--' elimination\n { l: 'n1-n2', r: 'n1+(-n2)' }, // Subtraction turn into add with un�ry minus\n { l: '(n1+n2)*n3', r: '(n1*n3 + n2*n3)' }, // Distributive 1\n { l: 'n1*(n2+n3)', r: '(n1*n2+n1*n3)' }, // Distributive 2\n { l: 'c1*n + c2*n', r: '(c1+c2)*n' }, // Joining constants\n { l: 'c1*n + n', r: '(c1+1)*n' }, // Joining constants\n { l: 'c1*n - c2*n', r: '(c1-c2)*n' }, // Joining constants\n { l: 'c1*n - n', r: '(c1-1)*n' }, // Joining constants\n { l: 'v/c', r: '(1/c)*v' }, // variable/constant (new!)\n { l: 'v/-c', r: '-(1/c)*v' }, // variable/constant (new!)\n { l: '-v*-c', r: 'c*v' }, // Inversion constant and variable 1\n { l: '-v*c', r: '-c*v' }, // Inversion constant and variable 2\n { l: 'v*-c', r: '-c*v' }, // Inversion constant and variable 3\n { l: 'v*c', r: 'c*v' }, // Inversion constant and variable 4\n { l: '-(-n1*n2)', r: '(n1*n2)' }, // Unary propagation\n { l: '-(n1*n2)', r: '(-n1*n2)' }, // Unary propagation\n { l: '-(-n1+n2)', r: '(n1-n2)' }, // Unary propagation\n { l: '-(n1+n2)', r: '(-n1-n2)' }, // Unary propagation\n { l: '(n1^n2)^n3', r: '(n1^(n2*n3))' }, // Power to Power\n { l: '-(-n1/n2)', r: '(n1/n2)' }, // Division and Unary\n { l: '-(n1/n2)', r: '(-n1/n2)' }] // Divisao and Unary\n\n const rulesDistrDiv = [\n { l: '(n1/n2 + n3/n4)', r: '((n1*n4 + n3*n2)/(n2*n4))' }, // Sum of fractions\n { l: '(n1/n2 + n3)', r: '((n1 + n3*n2)/n2)' }, // Sum fraction with number 1\n { l: '(n1 + n2/n3)', r: '((n1*n3 + n2)/n3)' }] // Sum fraction with number 1\n\n const rulesSucDiv = [\n { l: '(n1/(n2/n3))', r: '((n1*n3)/n2)' }, // Division simplification\n { l: '(n1/n2/n3)', r: '(n1/(n2*n3))' }]\n\n const setRules = {} // rules set in 4 steps.\n\n // All rules => infinite loop\n // setRules.allRules =oldRules.concat(rulesFirst,rulesDistrDiv,rulesSucDiv)\n\n setRules.firstRules = oldRules.concat(rulesFirst, rulesSucDiv) // First rule set\n setRules.distrDivRules = rulesDistrDiv // Just distr. div. rules\n setRules.sucDivRules = rulesSucDiv // Jus succ. div. rules\n setRules.firstRulesAgain = oldRules.concat(rulesFirst) // Last rules set without succ. div.\n\n // Division simplification\n\n // Second rule set.\n // There is no aggregate expression with parentesis, but the only variable can be scattered.\n setRules.finalRules = [simplifyCore, // simplify.rules[0]\n { l: 'n*-n', r: '-n^2' }, // Joining multiply with power 1\n { l: 'n*n', r: 'n^2' }, // Joining multiply with power 2\n simplifyConstant, // simplify.rules[14] old 3rd index in oldRules\n { l: 'n*-n^n1', r: '-n^(n1+1)' }, // Joining multiply with power 3\n { l: 'n*n^n1', r: 'n^(n1+1)' }, // Joining multiply with power 4\n { l: 'n^n1*-n^n2', r: '-n^(n1+n2)' }, // Joining multiply with power 5\n { l: 'n^n1*n^n2', r: 'n^(n1+n2)' }, // Joining multiply with power 6\n { l: 'n^n1*-n', r: '-n^(n1+1)' }, // Joining multiply with power 7\n { l: 'n^n1*n', r: 'n^(n1+1)' }, // Joining multiply with power 8\n { l: 'n^n1/-n', r: '-n^(n1-1)' }, // Joining multiply with power 8\n { l: 'n^n1/n', r: 'n^(n1-1)' }, // Joining division with power 1\n { l: 'n/-n^n1', r: '-n^(1-n1)' }, // Joining division with power 2\n { l: 'n/n^n1', r: 'n^(1-n1)' }, // Joining division with power 3\n { l: 'n^n1/-n^n2', r: 'n^(n1-n2)' }, // Joining division with power 4\n { l: 'n^n1/n^n2', r: 'n^(n1-n2)' }, // Joining division with power 5\n { l: 'n1+(-n2*n3)', r: 'n1-n2*n3' }, // Solving useless parenthesis 1\n { l: 'v*(-c)', r: '-c*v' }, // Solving useless unary 2\n { l: 'n1+-n2', r: 'n1-n2' }, // Solving +- together (new!)\n { l: 'v*c', r: 'c*v' }, // inversion constant with variable\n { l: '(n1^n2)^n3', r: '(n1^(n2*n3))' } // Power to Power\n\n ]\n return setRules\n } // End rulesRationalize\n\n // ---------------------------------------------------------------------------------------\n /**\n * Expand recursively a tree node for handling with expressions with exponents\n * (it's not for constants, symbols or functions with exponents)\n * PS: The other parameters are internal for recursion\n *\n * Syntax:\n *\n * expandPower(node)\n *\n * @param {Node} node Current expression node\n * @param {node} parent Parent current node inside the recursion\n * @param (int} Parent number of chid inside the rercursion\n *\n * @return {node} node expression with all powers expanded.\n */\n function expandPower (node, parent, indParent) {\n const tp = node.type\n const internal = (arguments.length > 1) // TRUE in internal calls\n\n if (tp === 'OperatorNode' && node.isBinary()) {\n let does = false\n let val\n if (node.op === '^') { // First operator: Parenthesis or UnaryMinus\n if ((node.args[0].type === 'ParenthesisNode' ||\n node.args[0].type === 'OperatorNode') &&\n (node.args[1].type === 'ConstantNode')) { // Second operator: Constant\n val = parseFloat(node.args[1].value)\n does = (val >= 2 && isInteger(val))\n }\n }\n\n if (does) { // Exponent >= 2\n // Before:\n // operator A --> Subtree\n // parent pow\n // constant\n //\n if (val > 2) { // Exponent > 2,\n // AFTER: (exponent > 2)\n // operator A --> Subtree\n // parent *\n // deep clone (operator A --> Subtree\n // pow\n // constant - 1\n //\n const nEsqTopo = node.args[0]\n const nDirTopo = new OperatorNode('^', 'pow', [node.args[0].cloneDeep(), new ConstantNode(val - 1)])\n node = new OperatorNode('*', 'multiply', [nEsqTopo, nDirTopo])\n } else { // Expo = 2 - no power\n // AFTER: (exponent = 2)\n // operator A --> Subtree\n // parent oper\n // deep clone (operator A --> Subtree)\n //\n node = new OperatorNode('*', 'multiply', [node.args[0], node.args[0].cloneDeep()])\n }\n\n if (internal) {\n // Change parent references in internal recursive calls\n if (indParent === 'content') { parent.content = node } else { parent.args[indParent] = node }\n }\n } // does\n } // binary OperatorNode\n\n if (tp === 'ParenthesisNode') {\n // Recursion\n expandPower(node.content, node, 'content')\n } else if (tp !== 'ConstantNode' && tp !== 'SymbolNode') {\n for (let i = 0; i < node.args.length; i++) {\n expandPower(node.args[i], node, i)\n }\n }\n\n if (!internal) {\n // return the root node\n return node\n }\n } // End expandPower\n\n // ---------------------------------------------------------------------------------------\n /**\n * Auxilary function for rationalize\n * Convert near canonical polynomial in one variable in a canonical polynomial\n * with one term for each exponent in decreasing order\n *\n * Syntax:\n *\n * polyToCanonical(node [, coefficients])\n *\n * @param {Node | string} expr The near canonical polynomial expression to convert in a a canonical polynomial expression\n *\n * The string or tree expression needs to be at below syntax, with free spaces:\n * ( (^(-)? | [+-]? )cte (*)? var (^expo)? | cte )+\n * Where 'var' is one variable with any valid name\n * 'cte' are real numeric constants with any value. It can be omitted if equal than 1\n * 'expo' are integers greater than 0. It can be omitted if equal than 1.\n *\n * @param {array} coefficients Optional returns coefficients sorted by increased exponent\n *\n *\n * @return {node} new node tree with one variable polynomial or string error.\n */\n function polyToCanonical (node, coefficients) {\n if (coefficients === undefined) { coefficients = [] } // coefficients.\n\n coefficients[0] = 0 // index is the exponent\n const o = {}\n o.cte = 1\n o.oper = '+'\n\n // fire: mark with * or ^ when finds * or ^ down tree, reset to \"\" with + and -.\n // It is used to deduce the exponent: 1 for *, 0 for \"\".\n o.fire = ''\n\n let maxExpo = 0 // maximum exponent\n let varname = '' // variable name\n\n recurPol(node, null, o)\n maxExpo = coefficients.length - 1\n let first = true\n let no\n\n for (let i = maxExpo; i >= 0; i--) {\n if (coefficients[i] === 0) continue\n let n1 = new ConstantNode(\n first ? coefficients[i] : Math.abs(coefficients[i]))\n const op = coefficients[i] < 0 ? '-' : '+'\n\n if (i > 0) { // Is not a constant without variable\n let n2 = new SymbolNode(varname)\n if (i > 1) {\n const n3 = new ConstantNode(i)\n n2 = new OperatorNode('^', 'pow', [n2, n3])\n }\n if (coefficients[i] === -1 && first) { n1 = new OperatorNode('-', 'unaryMinus', [n2]) } else if (Math.abs(coefficients[i]) === 1) { n1 = n2 } else { n1 = new OperatorNode('*', 'multiply', [n1, n2]) }\n }\n\n if (first) { no = n1 } else if (op === '+') { no = new OperatorNode('+', 'add', [no, n1]) } else { no = new OperatorNode('-', 'subtract', [no, n1]) }\n\n first = false\n } // for\n\n if (first) { return new ConstantNode(0) } else { return no }\n\n /**\n * Recursive auxilary function inside polyToCanonical for\n * converting expression in canonical form\n *\n * Syntax:\n *\n * recurPol(node, noPai, obj)\n *\n * @param {Node} node The current subpolynomial expression\n * @param {Node | Null} noPai The current parent node\n * @param {object} obj Object with many internal flags\n *\n * @return {} No return. If error, throws an exception\n */\n function recurPol (node, noPai, o) {\n const tp = node.type\n if (tp === 'FunctionNode') {\n // ***** FunctionName *****\n // No function call in polynomial expression\n throw new Error('There is an unsolved function call')\n } else if (tp === 'OperatorNode') {\n // ***** OperatorName *****\n if ('+-*^'.indexOf(node.op) === -1) throw new Error('Operator ' + node.op + ' invalid')\n\n if (noPai !== null) {\n // -(unary),^ : children of *,+,-\n if ((node.fn === 'unaryMinus' || node.fn === 'pow') && noPai.fn !== 'add' &&\n noPai.fn !== 'subtract' && noPai.fn !== 'multiply') { throw new Error('Invalid ' + node.op + ' placing') }\n\n // -,+,* : children of +,-\n if ((node.fn === 'subtract' || node.fn === 'add' || node.fn === 'multiply') &&\n noPai.fn !== 'add' && noPai.fn !== 'subtract') { throw new Error('Invalid ' + node.op + ' placing') }\n\n // -,+ : first child\n if ((node.fn === 'subtract' || node.fn === 'add' ||\n node.fn === 'unaryMinus') && o.noFil !== 0) { throw new Error('Invalid ' + node.op + ' placing') }\n } // Has parent\n\n // Firers: ^,* Old: ^,&,-(unary): firers\n if (node.op === '^' || node.op === '*') {\n o.fire = node.op\n }\n\n for (let i = 0; i < node.args.length; i++) {\n // +,-: reset fire\n if (node.fn === 'unaryMinus') o.oper = '-'\n if (node.op === '+' || node.fn === 'subtract') {\n o.fire = ''\n o.cte = 1 // default if there is no constant\n o.oper = (i === 0 ? '+' : node.op)\n }\n o.noFil = i // number of son\n recurPol(node.args[i], node, o)\n } // for in children\n } else if (tp === 'SymbolNode') { // ***** SymbolName *****\n if (node.name !== varname && varname !== '') { throw new Error('There is more than one variable') }\n varname = node.name\n if (noPai === null) {\n coefficients[1] = 1\n return\n }\n\n // ^: Symbol is First child\n if (noPai.op === '^' && o.noFil !== 0) { throw new Error('In power the variable should be the first parameter') }\n\n // *: Symbol is Second child\n if (noPai.op === '*' && o.noFil !== 1) { throw new Error('In multiply the variable should be the second parameter') }\n\n // Symbol: firers '',* => it means there is no exponent above, so it's 1 (cte * var)\n if (o.fire === '' || o.fire === '*') {\n if (maxExpo < 1) coefficients[1] = 0\n coefficients[1] += o.cte * (o.oper === '+' ? 1 : -1)\n maxExpo = Math.max(1, maxExpo)\n }\n } else if (tp === 'ConstantNode') {\n const valor = parseFloat(node.value)\n if (noPai === null) {\n coefficients[0] = valor\n return\n }\n if (noPai.op === '^') {\n // cte: second child of power\n if (o.noFil !== 1) throw new Error('Constant cannot be powered')\n\n if (!isInteger(valor) || valor <= 0) { throw new Error('Non-integer exponent is not allowed') }\n\n for (let i = maxExpo + 1; i < valor; i++) coefficients[i] = 0\n if (valor > maxExpo) coefficients[valor] = 0\n coefficients[valor] += o.cte * (o.oper === '+' ? 1 : -1)\n maxExpo = Math.max(valor, maxExpo)\n return\n }\n o.cte = valor\n\n // Cte: firer '' => There is no exponent and no multiplication, so the exponent is 0.\n if (o.fire === '') { coefficients[0] += o.cte * (o.oper === '+' ? 1 : -1) }\n } else { throw new Error('Type ' + tp + ' is not allowed') }\n } // End of recurPol\n } // End of polyToCanonical\n})\n","import { factory } from '../utils/factory.js'\n\nconst name = 'reviver'\nconst dependencies = [\n 'classes'\n]\n\nexport const createReviver = /* #__PURE__ */ factory(name, dependencies, ({ classes }) => {\n /**\n * Instantiate mathjs data types from their JSON representation\n * @param {string} key\n * @param {*} value\n * @returns {*} Returns the revived object\n */\n return function reviver (key, value) {\n const constructor = classes[value && value.mathjs]\n\n if (constructor && typeof constructor.fromJSON === 'function') {\n return constructor.fromJSON(value)\n }\n\n return value\n }\n})\n","import { factory } from '../utils/factory.js'\n\nconst name = 'replacer'\nconst dependencies = []\n\nexport const createReplacer = /* #__PURE__ */ factory(name, dependencies, () => {\n /**\n * Stringify data types into their JSON representation.\n * Most data types can be serialized using their `.toJSON` method,\n * but not all, for example the number `Infinity`. For these cases you have\n * to use the replacer. Example usage:\n *\n * JSON.stringify([2, Infinity], math.replacer)\n *\n * @param {string} key\n * @param {*} value\n * @returns {*} Returns the replaced object\n */\n return function replacer (key, value) {\n // the numeric values Infinitiy, -Infinity, and NaN cannot be serialized to JSON\n if (typeof value === 'number' && (!isFinite(value) || isNaN(value))) {\n return {\n mathjs: 'number',\n value: String(value)\n }\n }\n\n return value\n }\n})\n","\nexport const pi = Math.PI\nexport const tau = 2 * Math.PI\nexport const e = Math.E\nexport const phi = 1.6180339887498948 // eslint-disable-line no-loss-of-precision\n","import { factory } from './utils/factory.js'\nimport { version } from './version.js'\nimport {\n createBigNumberE,\n createBigNumberPhi,\n createBigNumberPi,\n createBigNumberTau\n} from './utils/bignumber/constants.js'\nimport { pi, tau, e, phi } from './plain/number/index.js'\n\nexport const createTrue = /* #__PURE__ */ factory('true', [], () => true)\nexport const createFalse = /* #__PURE__ */ factory('false', [], () => false)\nexport const createNull = /* #__PURE__ */ factory('null', [], () => null)\n\nexport const createInfinity = /* #__PURE__ */ recreateFactory(\n 'Infinity',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(Infinity)\n : Infinity\n)\n\nexport const createNaN = /* #__PURE__ */ recreateFactory(\n 'NaN',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(NaN)\n : NaN\n)\n\nexport const createPi = /* #__PURE__ */ recreateFactory(\n 'pi',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberPi(BigNumber)\n : pi\n)\n\nexport const createTau = /* #__PURE__ */ recreateFactory(\n 'tau',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberTau(BigNumber)\n : tau\n)\n\nexport const createE = /* #__PURE__ */ recreateFactory(\n 'e',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberE(BigNumber)\n : e\n)\n\n// golden ratio, (1+sqrt(5))/2\nexport const createPhi = /* #__PURE__ */ recreateFactory(\n 'phi',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? createBigNumberPhi(BigNumber)\n : phi\n)\n\nexport const createLN2 = /* #__PURE__ */ recreateFactory(\n 'LN2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(2).ln()\n : Math.LN2\n)\n\nexport const createLN10 = /* #__PURE__ */ recreateFactory(\n 'LN10',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(10).ln()\n : Math.LN10\n)\n\nexport const createLOG2E = /* #__PURE__ */ recreateFactory(\n 'LOG2E',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(1).div(new BigNumber(2).ln())\n : Math.LOG2E\n)\n\nexport const createLOG10E = /* #__PURE__ */ recreateFactory(\n 'LOG10E',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(1).div(new BigNumber(10).ln())\n : Math.LOG10E\n)\n\nexport const createSQRT1_2 = /* #__PURE__ */ recreateFactory( // eslint-disable-line camelcase\n 'SQRT1_2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber('0.5').sqrt()\n : Math.SQRT1_2\n)\n\nexport const createSQRT2 = /* #__PURE__ */ recreateFactory(\n 'SQRT2',\n ['config', '?BigNumber'],\n ({ config, BigNumber }) => (config.number === 'BigNumber')\n ? new BigNumber(2).sqrt()\n : Math.SQRT2\n)\n\nexport const createI = /* #__PURE__ */ recreateFactory(\n 'i',\n ['Complex'],\n ({ Complex }) => Complex.I\n)\n\n// for backward compatibility with v5\nexport const createUppercasePi = /* #__PURE__ */ factory('PI', ['pi'], ({ pi }) => pi)\nexport const createUppercaseE = /* #__PURE__ */ factory('E', ['e'], ({ e }) => e)\n\nexport const createVersion = /* #__PURE__ */ factory('version', [], () => version)\n\n// helper function to create a factory with a flag recreateOnConfigChange\n// idea: allow passing optional properties to be attached to the factory function as 4th argument?\nfunction recreateFactory (name, dependencies, create) {\n return factory(name, dependencies, create, {\n recreateOnConfigChange: true\n })\n}\n","export const version = '9.0.0'\n// Note: This file is automatically generated when building math.js.\n// Changes made in this file will be overwritten.\n","import { factory } from '../../utils/factory.js'\n\n// Source: https://en.wikipedia.org/wiki/Physical_constant\n\n// Universal constants\nexport const createSpeedOfLight = /* #__PURE__ */ unitFactory('speedOfLight', '299792458', 'm s^-1')\nexport const createGravitationConstant = /* #__PURE__ */ unitFactory('gravitationConstant', '6.67430e-11', 'm^3 kg^-1 s^-2')\nexport const createPlanckConstant = /* #__PURE__ */ unitFactory('planckConstant', '6.62607015e-34', 'J s')\nexport const createReducedPlanckConstant = /* #__PURE__ */ unitFactory('reducedPlanckConstant', '1.0545718176461565e-34', 'J s')\n\n// Electromagnetic constants\nexport const createMagneticConstant = /* #__PURE__ */ unitFactory('magneticConstant', '1.25663706212e-6', 'N A^-2')\nexport const createElectricConstant = /* #__PURE__ */ unitFactory('electricConstant', '8.8541878128e-12', 'F m^-1')\nexport const createVacuumImpedance = /* #__PURE__ */ unitFactory('vacuumImpedance', '376.730313667', 'ohm')\nexport const createCoulomb = /* #__PURE__ */ unitFactory('coulomb', '8.987551792261171e9', 'N m^2 C^-2')\nexport const createElementaryCharge = /* #__PURE__ */ unitFactory('elementaryCharge', '1.602176634e-19', 'C')\nexport const createBohrMagneton = /* #__PURE__ */ unitFactory('bohrMagneton', '9.2740100783e-24', 'J T^-1')\nexport const createConductanceQuantum = /* #__PURE__ */ unitFactory('conductanceQuantum', '7.748091729863649e-5', 'S')\nexport const createInverseConductanceQuantum = /* #__PURE__ */ unitFactory('inverseConductanceQuantum', '12906.403729652257', 'ohm')\nexport const createMagneticFluxQuantum = /* #__PURE__ */ unitFactory('magneticFluxQuantum', '2.0678338484619295e-15', 'Wb')\nexport const createNuclearMagneton = /* #__PURE__ */ unitFactory('nuclearMagneton', '5.0507837461e-27', 'J T^-1')\nexport const createKlitzing = /* #__PURE__ */ unitFactory('klitzing', '25812.807459304513', 'ohm')\nexport const createJosephson = /* #__PURE__ */ unitFactory('josephson', '4.835978484169836e14 Hz V', 'Hz V^-1') // TODO: support for Hz needed\n\n// Atomic and nuclear constants\nexport const createBohrRadius = /* #__PURE__ */ unitFactory('bohrRadius', '5.29177210903e-11', 'm')\nexport const createClassicalElectronRadius = /* #__PURE__ */ unitFactory('classicalElectronRadius', '2.8179403262e-15', 'm')\nexport const createElectronMass = /* #__PURE__ */ unitFactory('electronMass', '9.1093837015e-31', 'kg')\nexport const createFermiCoupling = /* #__PURE__ */ unitFactory('fermiCoupling', '1.1663787e-5', 'GeV^-2')\nexport const createFineStructure = numberFactory('fineStructure', 7.2973525693e-3)\nexport const createHartreeEnergy = /* #__PURE__ */ unitFactory('hartreeEnergy', '4.3597447222071e-18', 'J')\nexport const createProtonMass = /* #__PURE__ */ unitFactory('protonMass', '1.67262192369e-27', 'kg')\nexport const createDeuteronMass = /* #__PURE__ */ unitFactory('deuteronMass', '3.3435830926e-27', 'kg')\nexport const createNeutronMass = /* #__PURE__ */ unitFactory('neutronMass', '1.6749271613e-27', 'kg')\nexport const createQuantumOfCirculation = /* #__PURE__ */ unitFactory('quantumOfCirculation', '3.6369475516e-4', 'm^2 s^-1')\nexport const createRydberg = /* #__PURE__ */ unitFactory('rydberg', '10973731.568160', 'm^-1')\nexport const createThomsonCrossSection = /* #__PURE__ */ unitFactory('thomsonCrossSection', '6.6524587321e-29', 'm^2')\nexport const createWeakMixingAngle = numberFactory('weakMixingAngle', 0.22290)\nexport const createEfimovFactor = numberFactory('efimovFactor', 22.7)\n\n// Physico-chemical constants\nexport const createAtomicMass = /* #__PURE__ */ unitFactory('atomicMass', '1.66053906660e-27', 'kg')\nexport const createAvogadro = /* #__PURE__ */ unitFactory('avogadro', '6.02214076e23', 'mol^-1')\nexport const createBoltzmann = /* #__PURE__ */ unitFactory('boltzmann', '1.380649e-23', 'J K^-1')\nexport const createFaraday = /* #__PURE__ */ unitFactory('faraday', '96485.33212331001', 'C mol^-1')\nexport const createFirstRadiation = /* #__PURE__ */ unitFactory('firstRadiation', '3.7417718521927573e-16', 'W m^2')\n// export const createSpectralRadiance = /* #__PURE__ */ unitFactory('spectralRadiance', '1.1910429723971881e-16', 'W m^2 sr^-1') // TODO spectralRadiance\nexport const createLoschmidt = /* #__PURE__ */ unitFactory('loschmidt', '2.686780111798444e25', 'm^-3')\nexport const createGasConstant = /* #__PURE__ */ unitFactory('gasConstant', '8.31446261815324', 'J K^-1 mol^-1')\nexport const createMolarPlanckConstant = /* #__PURE__ */ unitFactory('molarPlanckConstant', '3.990312712893431e-10', 'J s mol^-1')\nexport const createMolarVolume = /* #__PURE__ */ unitFactory('molarVolume', '0.022413969545014137', 'm^3 mol^-1')\nexport const createSackurTetrode = numberFactory('sackurTetrode', -1.16487052358)\nexport const createSecondRadiation = /* #__PURE__ */ unitFactory('secondRadiation', '0.014387768775039337', 'm K')\nexport const createStefanBoltzmann = /* #__PURE__ */ unitFactory('stefanBoltzmann', '5.67037441918443e-8', 'W m^-2 K^-4')\nexport const createWienDisplacement = /* #__PURE__ */ unitFactory('wienDisplacement', '2.897771955e-3', 'm K')\n\n// Adopted values\nexport const createMolarMass = /* #__PURE__ */ unitFactory('molarMass', '0.99999999965e-3', 'kg mol^-1')\nexport const createMolarMassC12 = /* #__PURE__ */ unitFactory('molarMassC12', '11.9999999958e-3', 'kg mol^-1')\nexport const createGravity = /* #__PURE__ */ unitFactory('gravity', '9.80665', 'm s^-2')\n// atm is defined in Unit.js\n\n// Natural units\nexport const createPlanckLength = /* #__PURE__ */ unitFactory('planckLength', '1.616255e-35', 'm')\nexport const createPlanckMass = /* #__PURE__ */ unitFactory('planckMass', '2.176435e-8', 'kg')\nexport const createPlanckTime = /* #__PURE__ */ unitFactory('planckTime', '5.391245e-44', 's')\nexport const createPlanckCharge = /* #__PURE__ */ unitFactory('planckCharge', '1.87554603778e-18', 'C')\nexport const createPlanckTemperature = /* #__PURE__ */ unitFactory('planckTemperature', '1.416785e+32', 'K')\n\n// helper function to create a factory function which creates a physical constant,\n// a Unit with either a number value or a BigNumber value depending on the configuration\nfunction unitFactory (name, valueStr, unitStr) {\n const dependencies = ['config', 'Unit', 'BigNumber']\n\n return factory(name, dependencies, ({ config, Unit, BigNumber }) => {\n // Note that we can parse into number or BigNumber.\n // We do not parse into Fractions as that doesn't make sense: we would lose precision of the values\n // Therefore we dont use Unit.parse()\n const value = config.number === 'BigNumber'\n ? new BigNumber(valueStr)\n : parseFloat(valueStr)\n\n const unit = new Unit(value, unitStr)\n unit.fixPrefix = true\n return unit\n })\n}\n\n// helper function to create a factory function which creates a numeric constant,\n// either a number or BigNumber depending on the configuration\nfunction numberFactory (name, value) {\n const dependencies = ['config', 'BigNumber']\n\n return factory(name, dependencies, ({ config, BigNumber }) => {\n return config.number === 'BigNumber'\n ? new BigNumber(value)\n : value\n })\n}\n","import { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createApply } from '../../function/matrix/apply.js'\nimport { isBigNumber, isNumber } from '../../utils/is.js'\n\nconst name = 'apply'\nconst dependencies = ['typed', 'isInteger']\n\n/**\n * Attach a transform function to math.apply\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function apply\n * from one-based to zero based\n */\nexport const createApplyTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, isInteger }) => {\n const apply = createApply({ typed, isInteger })\n\n // @see: comment of concat itself\n return typed('apply', {\n '...any': function (args) {\n // change dim from one-based to zero-based\n const dim = args[1]\n\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n\n try {\n return apply.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createColumn } from '../../function/matrix/column.js'\nimport { isNumber } from '../../utils/is.js'\n\nconst name = 'column'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\n/**\n * Attach a transform function to matrix.column\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `index` parameter of function column\n * from zero-based to one-based\n */\nexport const createColumnTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n const column = createColumn({ typed, Index, matrix, range })\n\n // @see: comment of column itself\n return typed('column', {\n '...any': function (args) {\n // change last argument from zero-based to one-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n }\n\n try {\n return column.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isSymbolNode } from '../../../utils/is.js'\n\n/**\n * Compile an inline expression like \"x > 0\"\n * @param {Node} expression\n * @param {Object} math\n * @param {Object} scope\n * @return {function} Returns a function with one argument which fills in the\n * undefined variable (like \"x\") and evaluates the expression\n */\nexport function compileInlineExpression (expression, math, scope) {\n // find an undefined symbol\n const symbol = expression.filter(function (node) {\n return isSymbolNode(node) &&\n !(node.name in math) &&\n !(node.name in scope)\n })[0]\n\n if (!symbol) {\n throw new Error('No undefined variable found in inline expression \"' + expression + '\"')\n }\n\n // create a test function for this equation\n const name = symbol.name // variable name\n const subScope = Object.create(scope)\n const eq = expression.compile()\n return function inlineExpression (x) {\n subScope[name] = x\n return eq.evaluate(subScope)\n }\n}\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { filter, filterRegExp } from '../../utils/array.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'filter'\nconst dependencies = ['typed']\n\nexport const createFilterTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.filter\n * Adds a property transform containing the transform function.\n *\n * This transform adds support for equations as test function for math.filter,\n * so you can do something like 'filter([3, -2, 5], x > 0)'.\n */\n function filterTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like filter([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like filter([3, -2, 5], x > 0)\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return filter(x, callback)\n }\n filterTransform.rawArgs = true\n\n // one based version of function filter\n const filter = typed('filter', {\n 'Array, function': _filter,\n\n 'Matrix, function': function (x, test) {\n return x.create(_filter(x.toArray(), test))\n },\n\n 'Array, RegExp': filterRegExp,\n\n 'Matrix, RegExp': function (x, test) {\n return x.create(filterRegExp(x.toArray(), test))\n }\n })\n\n return filterTransform\n}, { isTransformFunction: true })\n\n/**\n * Filter values in a callback given a callback function\n *\n * !!! Passes a one-based index !!!\n *\n * @param {Array} x\n * @param {Function} callback\n * @return {Array} Returns the filtered array\n * @private\n */\nfunction _filter (x, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n return filter(x, function (value, index, array) {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n return callback(value)\n } else if (args === 2) {\n return callback(value, [index + 1])\n } else { // 3 or -1\n return callback(value, [index + 1], array)\n }\n })\n}\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { forEach } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\n\nconst name = 'forEach'\nconst dependencies = ['typed']\n\nexport const createForEachTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.forEach\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n function forEachTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like forEach([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like forEach([3, -2, 5], x > 0 ? callback1(x) : callback2(x) )\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return _forEach(x, callback)\n }\n forEachTransform.rawArgs = true\n\n // one-based version of forEach\n const _forEach = typed('forEach', {\n 'Array | Matrix, function': function (array, callback) {\n // figure out what number of arguments the callback function expects\n const args = maxArgumentCount(callback)\n\n const recurse = function (value, index) {\n if (Array.isArray(value)) {\n forEach(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n recurse(child, index.concat(i + 1)) // one based index, hence i+1\n })\n } else {\n // invoke the callback function with the right number of arguments\n if (args === 1) {\n callback(value)\n } else if (args === 2) {\n callback(value, index)\n } else { // 3 or -1\n callback(value, index, array)\n }\n }\n }\n recurse(array.valueOf(), []) // pass Array\n }\n })\n\n return forEachTransform\n}, { isTransformFunction: true })\n","import { isArray, isBigNumber, isMatrix, isNumber, isRange } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\n\nconst name = 'index'\nconst dependencies = ['Index']\n\nexport const createIndexTransform = /* #__PURE__ */ factory(name, dependencies, ({ Index }) => {\n /**\n * Attach a transform function to math.index\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n return function indexTransform () {\n const args = []\n for (let i = 0, ii = arguments.length; i < ii; i++) {\n let arg = arguments[i]\n\n // change from one-based to zero based, and convert BigNumber to number\n if (isRange(arg)) {\n arg.start--\n arg.end -= (arg.step > 0 ? 0 : 2)\n } else if (arg && arg.isSet === true) {\n arg = arg.map(function (v) { return v - 1 })\n } else if (isArray(arg) || isMatrix(arg)) {\n arg = arg.map(function (v) { return v - 1 })\n } else if (isNumber(arg)) {\n arg--\n } else if (isBigNumber(arg)) {\n arg = arg.toNumber() - 1\n } else if (typeof arg === 'string') {\n // leave as is\n } else {\n throw new TypeError('Dimension must be an Array, Matrix, number, string, or Range')\n }\n\n args[i] = arg\n }\n\n const res = new Index()\n Index.apply(res, args)\n return res\n }\n}, { isTransformFunction: true })\n","import { isFunctionAssignmentNode, isSymbolNode } from '../../utils/is.js'\nimport { maxArgumentCount } from '../../utils/function.js'\nimport { map } from '../../utils/array.js'\nimport { factory } from '../../utils/factory.js'\nimport { compileInlineExpression } from './utils/compileInlineExpression.js'\n\nconst name = 'map'\nconst dependencies = ['typed']\n\nexport const createMapTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed }) => {\n /**\n * Attach a transform function to math.map\n * Adds a property transform containing the transform function.\n *\n * This transform creates a one-based index instead of a zero-based index\n */\n function mapTransform (args, math, scope) {\n let x, callback\n\n if (args[0]) {\n x = args[0].compile().evaluate(scope)\n }\n\n if (args[1]) {\n if (isSymbolNode(args[1]) || isFunctionAssignmentNode(args[1])) {\n // a function pointer, like filter([3, -2, 5], myTestFunction)\n callback = args[1].compile().evaluate(scope)\n } else {\n // an expression like filter([3, -2, 5], x > 0)\n callback = compileInlineExpression(args[1], math, scope)\n }\n }\n\n return map(x, callback)\n }\n mapTransform.rawArgs = true\n\n // one-based version of map function\n const map = typed('map', {\n 'Array, function': function (x, callback) {\n return _map(x, callback, x)\n },\n\n 'Matrix, function': function (x, callback) {\n return x.create(_map(x.valueOf(), callback, x))\n }\n })\n\n return mapTransform\n}, { isTransformFunction: true })\n\n/**\n * Map for a multi dimensional array. One-based indexes\n * @param {Array} array\n * @param {function} callback\n * @param {Array} orig\n * @return {Array}\n * @private\n */\nfunction _map (array, callback, orig) {\n // figure out what number of arguments the callback function expects\n const argsCount = maxArgumentCount(callback)\n\n function recurse (value, index) {\n if (Array.isArray(value)) {\n return map(value, function (child, i) {\n // we create a copy of the index array and append the new index value\n return recurse(child, index.concat(i + 1)) // one based index, hence i + 1\n })\n } else {\n // invoke the (typed) callback function with the right number of arguments\n if (argsCount === 1) {\n return callback(value)\n } else if (argsCount === 2) {\n return callback(value, index)\n } else { // 3 or -1\n return callback(value, index, orig)\n }\n }\n }\n\n return recurse(array, [])\n}\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMax } from '../../function/statistics/max.js'\n\nconst name = 'max'\nconst dependencies = ['typed', 'config', 'numeric', 'larger']\n\nexport const createMaxTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, larger }) => {\n const max = createMax({ typed, config, numeric, larger })\n\n /**\n * Attach a transform function to math.max\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function max\n * from one-based to zero based\n */\n return typed('max', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return max.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMean } from '../../function/statistics/mean.js'\n\nconst name = 'mean'\nconst dependencies = ['typed', 'add', 'divide']\n\nexport const createMeanTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide }) => {\n const mean = createMean({ typed, add, divide })\n\n /**\n * Attach a transform function to math.mean\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function mean\n * from one-based to zero based\n */\n return typed('mean', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return mean.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createMin } from '../../function/statistics/min.js'\n\nconst name = 'min'\nconst dependencies = ['typed', 'config', 'numeric', 'smaller']\n\nexport const createMinTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, numeric, smaller }) => {\n const min = createMin({ typed, config, numeric, smaller })\n\n /**\n * Attach a transform function to math.min\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function min\n * from one-based to zero based\n */\n return typed('min', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return min.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createRange } from '../../function/matrix/range.js'\n\nconst name = 'range'\nconst dependencies = ['typed', 'config', '?matrix', '?bignumber', 'smaller', 'smallerEq', 'larger', 'largerEq']\n\nexport const createRangeTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq }) => {\n const range = createRange({ typed, config, matrix, bignumber, smaller, smallerEq, larger, largerEq })\n\n /**\n * Attach a transform function to math.range\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed('range', {\n '...any': function (args) {\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (typeof last !== 'boolean') {\n // append a parameter includeEnd=true\n args.push(true)\n }\n\n return range.apply(null, args)\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createRow } from '../../function/matrix/row.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { isNumber } from '../../utils/is.js'\n\nconst name = 'row'\nconst dependencies = ['typed', 'Index', 'matrix', 'range']\n\n/**\n * Attach a transform function to matrix.column\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `index` parameter of function column\n * from zero-based to one-based\n */\nexport const createRowTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, Index, matrix, range }) => {\n const row = createRow({ typed, Index, matrix, range })\n\n // @see: comment of row itself\n return typed('row', {\n '...any': function (args) {\n // change last argument from zero-based to one-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n }\n\n try {\n return row.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createSubset } from '../../function/matrix/subset.js'\n\nconst name = 'subset'\nconst dependencies = ['typed', 'matrix']\n\nexport const createSubsetTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix }) => {\n const subset = createSubset({ typed, matrix })\n\n /**\n * Attach a transform function to math.subset\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed('subset', {\n '...any': function (args) {\n try {\n return subset.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isNumber } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { factory } from '../../utils/factory.js'\nimport { createConcat } from '../../function/matrix/concat.js'\n\nconst name = 'concat'\nconst dependencies = ['typed', 'matrix', 'isInteger']\n\nexport const createConcatTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, isInteger }) => {\n const concat = createConcat({ typed, matrix, isInteger })\n\n /**\n * Attach a transform function to math.range\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function concat\n * from one-based to zero based\n */\n return typed('concat', {\n '...any': function (args) {\n // change last argument from one-based to zero-based\n const lastIndex = args.length - 1\n const last = args[lastIndex]\n if (isNumber(last)) {\n args[lastIndex] = last - 1\n } else if (isBigNumber(last)) {\n args[lastIndex] = last.minus(1)\n }\n\n try {\n return concat.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createDiff } from '../../function/matrix/diff.js'\n\nconst name = 'diff'\nconst dependencies = ['typed', 'matrix', 'subtract', 'number', 'bignumber']\n\nexport const createDiffTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, subtract, number, bignumber }) => {\n const diff = createDiff({ typed, matrix, subtract, number, bignumber })\n\n /**\n * Attach a transform function to math.diff\n * Adds a property transform containing the transform function.\n *\n * This transform creates a range which includes the end value\n */\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return diff.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { createStd } from '../../function/statistics/std.js'\nimport { isBigNumber, isNumber, isCollection } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\n\nconst name = 'std'\nconst dependencies = ['typed', 'sqrt', 'variance']\n\n/**\n * Attach a transform function to math.std\n * Adds a property transform containing the transform function.\n *\n * This transform changed the `dim` parameter of function std\n * from one-based to zero based\n */\nexport const createStdTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, sqrt, variance }) => {\n const std = createStd({ typed, sqrt, variance })\n\n return typed('std', {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length >= 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return std.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { factory } from '../../utils/factory.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createSum } from '../../function/statistics/sum.js'\n\n/**\n * Attach a transform function to math.sum\n * Adds a property transform containing the transform function.\n *\n * This transform changed the last `dim` parameter of function mean\n * from one-based to zero based\n */\nconst name = 'sum'\nconst dependencies = ['typed', 'config', 'add', 'numeric']\n\nexport const createSumTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, add, numeric }) => {\n const sum = createSum({ typed, config, add, numeric })\n\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length === 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return sum.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { factory } from '../../utils/factory.js'\nimport { isBigNumber, isCollection, isNumber } from '../../utils/is.js'\nimport { errorTransform } from './utils/errorTransform.js'\nimport { createVariance } from '../../function/statistics/variance.js'\n\nconst name = 'variance'\nconst dependencies = ['typed', 'add', 'subtract', 'multiply', 'divide', 'apply', 'isNaN']\n\n/**\n * Attach a transform function to math.var\n * Adds a property transform containing the transform function.\n *\n * This transform changed the `dim` parameter of function var\n * from one-based to zero based\n */\nexport const createVarianceTransform = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, subtract, multiply, divide, apply, isNaN }) => {\n const variance = createVariance({ typed, add, subtract, multiply, divide, apply, isNaN })\n\n return typed(name, {\n '...any': function (args) {\n // change last argument dim from one-based to zero-based\n if (args.length >= 2 && isCollection(args[0])) {\n const dim = args[1]\n if (isNumber(dim)) {\n args[1] = dim - 1\n } else if (isBigNumber(dim)) {\n args[1] = dim.minus(1)\n }\n }\n\n try {\n return variance.apply(null, args)\n } catch (err) {\n throw errorTransform(err)\n }\n }\n })\n}, { isTransformFunction: true })\n","import { isBigNumber, isComplex, isFraction, isMatrix, isUnit } from '../../utils/is.js'\nimport { isFactory, stripOptionalNotation } from '../../utils/factory.js'\nimport { hasOwnProperty, lazy } from '../../utils/object.js'\nimport { contains } from '../../utils/array.js'\nimport { ArgumentsError } from '../../error/ArgumentsError.js'\n\nexport function importFactory (typed, load, math, importedFactories) {\n /**\n * Import functions from an object or a module.\n *\n * This function is only available on a mathjs instance created using `create`.\n *\n * Syntax:\n *\n * math.import(functions)\n * math.import(functions, options)\n *\n * Where:\n *\n * - `functions: Object`\n * An object with functions or factories to be imported.\n * - `options: Object` An object with import options. Available options:\n * - `override: boolean`\n * If true, existing functions will be overwritten. False by default.\n * - `silent: boolean`\n * If true, the function will not throw errors on duplicates or invalid\n * types. False by default.\n * - `wrap: boolean`\n * If true, the functions will be wrapped in a wrapper function\n * which converts data types like Matrix to primitive data types like Array.\n * The wrapper is needed when extending math.js with libraries which do not\n * support these data type. False by default.\n *\n * Examples:\n *\n * import { create, all } from 'mathjs'\n * import * as numbers from 'numbers'\n *\n * // create a mathjs instance\n * const math = create(all)\n *\n * // define new functions and variables\n * math.import({\n * myvalue: 42,\n * hello: function (name) {\n * return 'hello, ' + name + '!'\n * }\n * })\n *\n * // use the imported function and variable\n * math.myvalue * 2 // 84\n * math.hello('user') // 'hello, user!'\n *\n * // import the npm module 'numbers'\n * // (must be installed first with `npm install numbers`)\n * math.import(numbers, {wrap: true})\n *\n * math.fibonacci(7) // returns 13\n *\n * @param {Object | Array} functions Object with functions to be imported.\n * @param {Object} [options] Import options.\n */\n function mathImport (functions, options) {\n const num = arguments.length\n if (num !== 1 && num !== 2) {\n throw new ArgumentsError('import', num, 1, 2)\n }\n\n if (!options) {\n options = {}\n }\n\n function flattenImports (flatValues, value, name) {\n if (Array.isArray(value)) {\n value.forEach(item => flattenImports(flatValues, item))\n } else if (typeof value === 'object') {\n for (const name in value) {\n if (hasOwnProperty(value, name)) {\n flattenImports(flatValues, value[name], name)\n }\n }\n } else if (isFactory(value) || name !== undefined) {\n const flatName = isFactory(value)\n ? isTransformFunctionFactory(value)\n ? (value.fn + '.transform') // TODO: this is ugly\n : value.fn\n : name\n\n // we allow importing the same function twice if it points to the same implementation\n if (hasOwnProperty(flatValues, flatName) && flatValues[flatName] !== value && !options.silent) {\n throw new Error('Cannot import \"' + flatName + '\" twice')\n }\n\n flatValues[flatName] = value\n } else {\n if (!options.silent) {\n throw new TypeError('Factory, Object, or Array expected')\n }\n }\n }\n\n const flatValues = {}\n flattenImports(flatValues, functions)\n\n for (const name in flatValues) {\n if (hasOwnProperty(flatValues, name)) {\n // console.log('import', name)\n const value = flatValues[name]\n\n if (isFactory(value)) {\n // we ignore name here and enforce the name of the factory\n // maybe at some point we do want to allow overriding it\n // in that case we can implement an option overrideFactoryNames: true\n _importFactory(value, options)\n } else if (isSupportedType(value)) {\n _import(name, value, options)\n } else {\n if (!options.silent) {\n throw new TypeError('Factory, Object, or Array expected')\n }\n }\n }\n }\n }\n\n /**\n * Add a property to the math namespace\n * @param {string} name\n * @param {*} value\n * @param {Object} options See import for a description of the options\n * @private\n */\n function _import (name, value, options) {\n // TODO: refactor this function, it's to complicated and contains duplicate code\n if (options.wrap && typeof value === 'function') {\n // create a wrapper around the function\n value = _wrap(value)\n }\n\n // turn a plain function with a typed-function signature into a typed-function\n if (hasTypedFunctionSignature(value)) {\n value = typed(name, {\n [value.signature]: value\n })\n }\n\n if (isTypedFunction(math[name]) && isTypedFunction(value)) {\n if (options.override) {\n // give the typed function the right name\n value = typed(name, value.signatures)\n } else {\n // merge the existing and typed function\n value = typed(math[name], value)\n }\n\n math[name] = value\n delete importedFactories[name]\n\n _importTransform(name, value)\n math.emit('import', name, function resolver () {\n return value\n })\n return\n }\n\n if (math[name] === undefined || options.override) {\n math[name] = value\n delete importedFactories[name]\n\n _importTransform(name, value)\n math.emit('import', name, function resolver () {\n return value\n })\n return\n }\n\n if (!options.silent) {\n throw new Error('Cannot import \"' + name + '\": already exists')\n }\n }\n\n function _importTransform (name, value) {\n if (value && typeof value.transform === 'function') {\n math.expression.transform[name] = value.transform\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = value.transform\n }\n } else {\n // remove existing transform\n delete math.expression.transform[name]\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = value\n }\n }\n }\n\n function _deleteTransform (name) {\n delete math.expression.transform[name]\n if (allowedInExpressions(name)) {\n math.expression.mathWithTransform[name] = math[name]\n } else {\n delete math.expression.mathWithTransform[name]\n }\n }\n\n /**\n * Create a wrapper a round an function which converts the arguments\n * to their primitive values (like convert a Matrix to Array)\n * @param {Function} fn\n * @return {Function} Returns the wrapped function\n * @private\n */\n function _wrap (fn) {\n const wrapper = function wrapper () {\n const args = []\n for (let i = 0, len = arguments.length; i < len; i++) {\n const arg = arguments[i]\n args[i] = arg && arg.valueOf()\n }\n return fn.apply(math, args)\n }\n\n if (fn.transform) {\n wrapper.transform = fn.transform\n }\n\n return wrapper\n }\n\n /**\n * Import an instance of a factory into math.js\n * @param {function(scope: object)} factory\n * @param {Object} options See import for a description of the options\n * @param {string} [name=factory.name] Optional custom name\n * @private\n */\n function _importFactory (factory, options, name = factory.fn) {\n if (contains(name, '.')) {\n throw new Error('Factory name should not contain a nested path. ' +\n 'Name: ' + JSON.stringify(name))\n }\n\n const namespace = isTransformFunctionFactory(factory)\n ? math.expression.transform\n : math\n\n const existingTransform = name in math.expression.transform\n const existing = hasOwnProperty(namespace, name) ? namespace[name] : undefined\n\n const resolver = function () {\n // collect all dependencies, handle finding both functions and classes and other special cases\n const dependencies = {}\n factory.dependencies\n .map(stripOptionalNotation)\n .forEach(dependency => {\n if (contains(dependency, '.')) {\n throw new Error('Factory dependency should not contain a nested path. ' +\n 'Name: ' + JSON.stringify(dependency))\n }\n\n if (dependency === 'math') {\n dependencies.math = math\n } else if (dependency === 'mathWithTransform') {\n dependencies.mathWithTransform = math.expression.mathWithTransform\n } else if (dependency === 'classes') { // special case for json reviver\n dependencies.classes = math\n } else {\n dependencies[dependency] = math[dependency]\n }\n })\n\n const instance = /* #__PURE__ */ factory(dependencies)\n\n if (instance && typeof instance.transform === 'function') {\n throw new Error('Transforms cannot be attached to factory functions. ' +\n 'Please create a separate function for it with exports.path=\"expression.transform\"')\n }\n\n if (existing === undefined || options.override) {\n return instance\n }\n\n if (isTypedFunction(existing) && isTypedFunction(instance)) {\n // merge the existing and new typed function\n return typed(existing, instance)\n }\n\n if (options.silent) {\n // keep existing, ignore imported function\n return existing\n } else {\n throw new Error('Cannot import \"' + name + '\": already exists')\n }\n }\n\n // TODO: add unit test with non-lazy factory\n if (!factory.meta || factory.meta.lazy !== false) {\n lazy(namespace, name, resolver)\n\n // FIXME: remove the `if (existing &&` condition again. Can we make sure subset is loaded before subset.transform? (Name collision, and no dependencies between the two)\n if (existing && existingTransform) {\n _deleteTransform(name)\n } else {\n if (isTransformFunctionFactory(factory) || factoryAllowedInExpressions(factory)) {\n lazy(math.expression.mathWithTransform, name, () => namespace[name])\n }\n }\n } else {\n namespace[name] = resolver()\n\n // FIXME: remove the `if (existing &&` condition again. Can we make sure subset is loaded before subset.transform? (Name collision, and no dependencies between the two)\n if (existing && existingTransform) {\n _deleteTransform(name)\n } else {\n if (isTransformFunctionFactory(factory) || factoryAllowedInExpressions(factory)) {\n lazy(math.expression.mathWithTransform, name, () => namespace[name])\n }\n }\n }\n\n // TODO: improve factories, store a list with imports instead which can be re-played\n importedFactories[name] = factory\n\n math.emit('import', name, resolver)\n }\n\n /**\n * Check whether given object is a type which can be imported\n * @param {Function | number | string | boolean | null | Unit | Complex} object\n * @return {boolean}\n * @private\n */\n function isSupportedType (object) {\n return typeof object === 'function' ||\n typeof object === 'number' ||\n typeof object === 'string' ||\n typeof object === 'boolean' ||\n object === null ||\n isUnit(object) ||\n isComplex(object) ||\n isBigNumber(object) ||\n isFraction(object) ||\n isMatrix(object) ||\n Array.isArray(object)\n }\n\n /**\n * Test whether a given thing is a typed-function\n * @param {*} fn\n * @return {boolean} Returns true when `fn` is a typed-function\n */\n function isTypedFunction (fn) {\n return typeof fn === 'function' && typeof fn.signatures === 'object'\n }\n\n function hasTypedFunctionSignature (fn) {\n return typeof fn === 'function' && typeof fn.signature === 'string'\n }\n\n function allowedInExpressions (name) {\n return !hasOwnProperty(unsafe, name)\n }\n\n function factoryAllowedInExpressions (factory) {\n return factory.fn.indexOf('.') === -1 && // FIXME: make checking on path redundant, check on meta data instead\n !hasOwnProperty(unsafe, factory.fn) &&\n (!factory.meta || !factory.meta.isClass)\n }\n\n function isTransformFunctionFactory (factory) {\n return (factory !== undefined &&\n factory.meta !== undefined &&\n factory.meta.isTransformFunction === true) || false\n }\n\n // namespaces and functions not available in the parser for safety reasons\n const unsafe = {\n expression: true,\n type: true,\n docs: true,\n error: true,\n json: true,\n chain: true // chain method not supported. Note that there is a unit chain too.\n }\n\n return mathImport\n}\n","export const DEFAULT_CONFIG = {\n // minimum relative difference between two compared values,\n // used by all comparison functions\n epsilon: 1e-12,\n\n // type of default matrix output. Choose 'matrix' (default) or 'array'\n matrix: 'Matrix',\n\n // type of default number output. Choose 'number' (default) 'BigNumber', or 'Fraction\n number: 'number',\n\n // number of significant digits in BigNumbers\n precision: 64,\n\n // predictable output type of functions. When true, output type depends only\n // on the input types. When false (default), output type can vary depending\n // on input values. For example `math.sqrt(-4)` returns `complex('2i')` when\n // predictable is false, and returns `NaN` when true.\n predictable: false,\n\n // random seed for seeded pseudo random number generation\n // null = randomly seed\n randomSeed: null\n}\n","import { clone, mapObject, deepExtend } from '../../utils/object.js'\nimport { DEFAULT_CONFIG } from '../config.js'\n\nexport const MATRIX_OPTIONS = ['Matrix', 'Array'] // valid values for option matrix\nexport const NUMBER_OPTIONS = ['number', 'BigNumber', 'Fraction'] // valid values for option number\n\nexport function configFactory (config, emit) {\n /**\n * Set configuration options for math.js, and get current options.\n * Will emit a 'config' event, with arguments (curr, prev, changes).\n *\n * This function is only available on a mathjs instance created using `create`.\n *\n * Syntax:\n *\n * math.config(config: Object): Object\n *\n * Examples:\n *\n *\n * import { create, all } from 'mathjs'\n *\n * // create a mathjs instance\n * const math = create(all)\n *\n * math.config().number // outputs 'number'\n * math.evaluate('0.4') // outputs number 0.4\n * math.config({number: 'Fraction'})\n * math.evaluate('0.4') // outputs Fraction 2/5\n *\n * @param {Object} [options] Available options:\n * {number} epsilon\n * Minimum relative difference between two\n * compared values, used by all comparison functions.\n * {string} matrix\n * A string 'Matrix' (default) or 'Array'.\n * {string} number\n * A string 'number' (default), 'BigNumber', or 'Fraction'\n * {number} precision\n * The number of significant digits for BigNumbers.\n * Not applicable for Numbers.\n * {string} parenthesis\n * How to display parentheses in LaTeX and string\n * output.\n * {string} randomSeed\n * Random seed for seeded pseudo random number generator.\n * Set to null to randomly seed.\n * @return {Object} Returns the current configuration\n */\n function _config (options) {\n if (options) {\n const prev = mapObject(config, clone)\n\n // validate some of the options\n validateOption(options, 'matrix', MATRIX_OPTIONS)\n validateOption(options, 'number', NUMBER_OPTIONS)\n\n // merge options\n deepExtend(config, options)\n\n const curr = mapObject(config, clone)\n\n const changes = mapObject(options, clone)\n\n // emit 'config' event\n emit('config', curr, prev, changes)\n\n return curr\n } else {\n return mapObject(config, clone)\n }\n }\n\n // attach the valid options to the function so they can be extended\n _config.MATRIX_OPTIONS = MATRIX_OPTIONS\n _config.NUMBER_OPTIONS = NUMBER_OPTIONS\n\n // attach the config properties as readonly properties to the config function\n Object.keys(DEFAULT_CONFIG).forEach(key => {\n Object.defineProperty(_config, key, {\n get: () => config[key],\n enumerable: true,\n configurable: true\n })\n })\n\n return _config\n}\n\n/**\n * Test whether an Array contains a specific item.\n * @param {Array.} array\n * @param {string} item\n * @return {boolean}\n */\nfunction contains (array, item) {\n return array.indexOf(item) !== -1\n}\n\n/**\n * Validate an option\n * @param {Object} options Object with options\n * @param {string} name Name of the option to validate\n * @param {Array.} values Array with valid values for this option\n */\nfunction validateOption (options, name, values) {\n if (options[name] !== undefined && !contains(values, options[name])) {\n // unknown value\n console.warn('Warning: Unknown value \"' + options[name] + '\" for configuration option \"' + name + '\". ' +\n 'Available options: ' + values.map(value => JSON.stringify(value)).join(', ') + '.')\n }\n}\n","import * as all from './factoriesAny.js'\nimport { create } from './core/create.js'\n\nexport default create(all)\n","import './../utils/polyfills.js'\nimport { deepFlatten, isLegacyFactory, values } from '../utils/object.js'\nimport * as emitter from './../utils/emitter.js'\nimport { importFactory } from './function/import.js'\nimport { configFactory } from './function/config.js'\nimport { factory, isFactory } from '../utils/factory.js'\nimport {\n isAccessorNode,\n isArray,\n isArrayNode,\n isAssignmentNode,\n isBigNumber,\n isBlockNode,\n isBoolean,\n isChain,\n isCollection,\n isComplex,\n isConditionalNode,\n isConstantNode,\n isDate,\n isDenseMatrix,\n isFraction,\n isFunction,\n isFunctionAssignmentNode,\n isFunctionNode,\n isHelp,\n isIndex,\n isIndexNode,\n isMatrix,\n isNode,\n isNull,\n isNumber,\n isObject,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRange,\n isRangeNode,\n isRegExp,\n isResultSet,\n isSparseMatrix,\n isString,\n isSymbolNode,\n isUndefined,\n isUnit\n} from '../utils/is.js'\nimport { ArgumentsError } from '../error/ArgumentsError.js'\nimport { DimensionError } from '../error/DimensionError.js'\nimport { IndexError } from '../error/IndexError.js'\nimport { DEFAULT_CONFIG } from './config.js'\n\n/**\n * Create a mathjs instance from given factory functions and optionally config\n *\n * Usage:\n *\n * const mathjs1 = create({ createAdd, createMultiply, ...})\n * const config = { number: 'BigNumber' }\n * const mathjs2 = create(all, config)\n *\n * @param {Object} [factories] An object with factory functions\n * The object can contain nested objects,\n * all nested objects will be flattened.\n * @param {Object} [config] Available options:\n * {number} epsilon\n * Minimum relative difference between two\n * compared values, used by all comparison functions.\n * {string} matrix\n * A string 'Matrix' (default) or 'Array'.\n * {string} number\n * A string 'number' (default), 'BigNumber', or 'Fraction'\n * {number} precision\n * The number of significant digits for BigNumbers.\n * Not applicable for Numbers.\n * {boolean} predictable\n * Predictable output type of functions. When true,\n * output type depends only on the input types. When\n * false (default), output type can vary depending\n * on input values. For example `math.sqrt(-4)`\n * returns `complex('2i')` when predictable is false, and\n * returns `NaN` when true.\n * {string} randomSeed\n * Random seed for seeded pseudo random number generator.\n * Set to null to randomly seed.\n * @returns {Object} Returns a bare-bone math.js instance containing\n * functions:\n * - `import` to add new functions\n * - `config` to change configuration\n * - `on`, `off`, `once`, `emit` for events\n */\nexport function create (factories, config) {\n const configInternal = Object.assign({}, DEFAULT_CONFIG, config)\n\n // simple test for ES5 support\n if (typeof Object.create !== 'function') {\n throw new Error('ES5 not supported by this JavaScript engine. ' +\n 'Please load the es5-shim and es5-sham library for compatibility.')\n }\n\n // create the mathjs instance\n const math = emitter.mixin({\n // only here for backward compatibility for legacy factory functions\n isNumber,\n isComplex,\n isBigNumber,\n isFraction,\n isUnit,\n isString,\n isArray,\n isMatrix,\n isCollection,\n isDenseMatrix,\n isSparseMatrix,\n isRange,\n isIndex,\n isBoolean,\n isResultSet,\n isHelp,\n isFunction,\n isDate,\n isRegExp,\n isObject,\n isNull,\n isUndefined,\n\n isAccessorNode,\n isArrayNode,\n isAssignmentNode,\n isBlockNode,\n isConditionalNode,\n isConstantNode,\n isFunctionAssignmentNode,\n isFunctionNode,\n isIndexNode,\n isNode,\n isObjectNode,\n isOperatorNode,\n isParenthesisNode,\n isRangeNode,\n isSymbolNode,\n\n isChain\n })\n\n // load config function and apply provided config\n math.config = configFactory(configInternal, math.emit)\n\n math.expression = {\n transform: {},\n mathWithTransform: {\n config: math.config\n }\n }\n\n // cached factories and instances used by function load\n const legacyFactories = []\n const legacyInstances = []\n\n /**\n * Load a function or data type from a factory.\n * If the function or data type already exists, the existing instance is\n * returned.\n * @param {Function} factory\n * @returns {*}\n */\n function load (factory) {\n if (isFactory(factory)) {\n return factory(math)\n }\n\n const firstProperty = factory[Object.keys(factory)[0]]\n if (isFactory(firstProperty)) {\n return firstProperty(math)\n }\n\n if (!isLegacyFactory(factory)) {\n console.warn('Factory object with properties `type`, `name`, and `factory` expected', factory)\n throw new Error('Factory object with properties `type`, `name`, and `factory` expected')\n }\n\n const index = legacyFactories.indexOf(factory)\n let instance\n if (index === -1) {\n // doesn't yet exist\n if (factory.math === true) {\n // pass with math namespace\n instance = factory.factory(math.type, configInternal, load, math.typed, math)\n } else {\n instance = factory.factory(math.type, configInternal, load, math.typed)\n }\n\n // append to the cache\n legacyFactories.push(factory)\n legacyInstances.push(instance)\n } else {\n // already existing function, return the cached instance\n instance = legacyInstances[index]\n }\n\n return instance\n }\n\n const importedFactories = {}\n\n // load the import function\n function lazyTyped (...args) {\n return math.typed.apply(math.typed, args)\n }\n const internalImport = importFactory(lazyTyped, load, math, importedFactories)\n math.import = internalImport\n\n // listen for changes in config, import all functions again when changed\n // TODO: move this listener into the import function?\n math.on('config', () => {\n values(importedFactories).forEach(factory => {\n if (factory && factory.meta && factory.meta.recreateOnConfigChange) {\n // FIXME: only re-create when the current instance is the same as was initially created\n // FIXME: delete the functions/constants before importing them again?\n internalImport(factory, { override: true })\n }\n })\n })\n\n // the create function exposed on the mathjs instance is bound to\n // the factory functions passed before\n math.create = create.bind(null, factories)\n\n // export factory function\n math.factory = factory\n\n // import the factory functions like createAdd as an array instead of object,\n // else they will get a different naming (`createAdd` instead of `add`).\n math.import(values(deepFlatten(factories)))\n\n math.ArgumentsError = ArgumentsError\n math.DimensionError = DimensionError\n math.IndexError = IndexError\n\n return math\n}\n","import Emitter from 'tiny-emitter'\n\n/**\n * Extend given object with emitter functions `on`, `off`, `once`, `emit`\n * @param {Object} obj\n * @return {Object} obj\n */\nexport function mixin (obj) {\n // create event emitter\n const emitter = new Emitter()\n\n // bind methods to obj (we don't want to expose the emitter.e Array...)\n obj.on = emitter.on.bind(emitter)\n obj.off = emitter.off.bind(emitter)\n obj.once = emitter.once.bind(emitter)\n obj.emit = emitter.emit.bind(emitter)\n\n return obj\n}\n"],"sourceRoot":""} \ No newline at end of file diff --git a/package-lock.json b/package-lock.json index 7215b12e6..f9d2b0654 100644 --- a/package-lock.json +++ b/package-lock.json @@ -1902,9 +1902,9 @@ "dev": true }, "ini": { - "version": "1.3.5", - "resolved": "https://registry.npmjs.org/ini/-/ini-1.3.5.tgz", - "integrity": "sha512-RZY5huIKCMRWDUqZlEi72f/lmXKMvuszcMBduliQ3nnWbx9X/ZBQO7DijMEYS9EhHBb2qacRUMtC7svLwe0lcw==", + "version": "1.3.8", + "resolved": "https://registry.npmjs.org/ini/-/ini-1.3.8.tgz", + "integrity": "sha512-JV/yugV2uzW5iMRSiZAyDtQd+nxtUnjeLt0acNdw98kKLrvuRVyB80tsREOE7yvGVgalhZ6RNXCmEHkUKBKxew==", "dev": true }, "interpret": { @@ -2319,9 +2319,9 @@ } }, "mathjs": { - "version": "8.1.1", - "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-8.1.1.tgz", - "integrity": "sha512-b3TX3EgiZObujjwb8lZnTDLUuivC2jar4ZBjmGJ4stFYCDXx/DNwx5yry5t/z65p9mvejyZel1qoeR05KtChcQ==", + "version": "9.0.0", + "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-9.0.0.tgz", + "integrity": "sha512-ZfNz90wyed1MJUQOfL+Jr9IWG6vevVPM+cFf93sV568lbY8w2obEv5Ba7e7+Ylg5Zv0PTPtEY5CbqivHw/AxGQ==", "requires": { "complex.js": "^2.0.11", "decimal.js": "^10.2.1", diff --git a/package.json b/package.json index f375b071a..c19004656 100644 --- a/package.json +++ b/package.json @@ -6,7 +6,7 @@ "url": "https://github.com/josdejong/mathjs.git" }, "dependencies": { - "mathjs": "8.1.1" + "mathjs": "9.0.0" }, "devDependencies": { "fancy-log": "1.3.3",