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mathjs/dist/math.min.js
jos 9f3674380d Release v4.4.2
2018-06-02 11:48:11 +02:00

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"use strict";
/**
* math.js
* https://github.com/josdejong/mathjs
*
* Math.js is an extensive math library for JavaScript and Node.js,
* It features real and complex numbers, units, matrices, a large set of
* mathematical functions, and a flexible expression parser.
*
* @version 4.4.2
* @date 2018-06-02
*
* @license
* Copyright (C) 2013-2018 Jos de Jong <wjosdejong@gmail.com>
*
* 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
* of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*/
/**
* math.js
* https://github.com/josdejong/mathjs
*
* Math.js is an extensive math library for JavaScript and Node.js,
* It features real and complex numbers, units, matrices, a large set of
* mathematical functions, and a flexible expression parser.
*
* @version 4.4.2
* @date 2018-06-02
*
* @license
* Copyright (C) 2013-2018 Jos de Jong <wjosdejong@gmail.com>
*
* 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
* of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*/
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n).type="OperatorNode",a.prototype.isOperatorNode=!0,a.prototype._compile=function(t,r){if("string"!=typeof this.fn||!u(t,this.fn))throw t[this.fn]?new Error('No access to function "'+this.fn+'"'):new Error("Function "+this.fn+' missing in provided namespace "math"');var i=c(t,this.fn),e=s(this.args,function(e){return e._compile(t,r)});if(1===e.length){var n=e[0];return function(e,t,r){return i(n(e,t,r))}}if(2===e.length){n=e[0];var a=e[1];return function(e,t,r){return i(n(e,t,r),a(e,t,r))}}return function(t,r,n){return i.apply(null,s(e,function(e){return e(t,r,n)}))}},a.prototype.forEach=function(e){for(var t=0;t<this.args.length;t++)e(this.args[t],"args["+t+"]",this)},a.prototype.map=function(e){for(var t=[],r=0;r<this.args.length;r++)t[r]=this._ifNode(e(this.args[r],"args["+r+"]",this));return new a(this.op,this.fn,t,this.implicit)},a.prototype.clone=function(){return new a(this.op,this.fn,this.args.slice(0),this.implicit)},a.prototype.isUnary=function(){return 1===this.args.length},a.prototype.isBinary=function(){return 2===this.args.length},a.prototype._toString=function(r){var e=r&&r.parenthesis?r.parenthesis:"keep",t=r&&r.implicit?r.implicit:"hide",n=this.args,i=m(this,e,t,n,!1);if(1===n.length){var a=x.getAssociativity(this,e),o=n[0].toString(r);return i[0]&&(o="("+o+")"),"right"===a?this.op+o:o+this.op}if(2==n.length){var s=n[0].toString(r),u=n[1].toString(r);return i[0]&&(s="("+s+")"),i[1]&&(u="("+u+")"),this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"==t?s+" "+u:s+" "+this.op+" "+u}if(2<n.length&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var c=n.map(function(e,t){return e=e.toString(r),i[t]&&(e="("+e+")"),e});return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===t?c.join(" "):c.join(" "+this.op+" ")}return this.fn+"("+this.args.join(", ")+")"},a.prototype.toJSON=function(){return{mathjs:"OperatorNode",op:this.op,fn:this.fn,args:this.args,implicit:this.implicit}},a.fromJSON=function(e){return new a(e.op,e.fn,e.args,e.implicit)},a.prototype.toHTML=function(r){var e=r&&r.parenthesis?r.parenthesis:"keep",t=r&&r.implicit?r.implicit:"hide",n=this.args,i=m(this,e,t,n,!1);if(1===n.length){var a=x.getAssociativity(this,e),o=n[0].toHTML(r);return i[0]&&(o='<span class="math-parenthesis math-round-parenthesis">(</span>'+o+'<span class="math-parenthesis math-round-parenthesis">)</span>'),"right"===a?'<span class="math-operator math-unary-operator math-lefthand-unary-operator">'+f(this.op)+"</span>"+o:'<span class="math-operator math-unary-operator math-righthand-unary-operator">'+f(this.op)+"</span>"+o}if(2==n.length){var s=n[0].toHTML(r),u=n[1].toHTML(r);return i[0]&&(s='<span class="math-parenthesis math-round-parenthesis">(</span>'+s+'<span class="math-parenthesis math-round-parenthesis">)</span>'),i[1]&&(u='<span class="math-parenthesis math-round-parenthesis">(</span>'+u+'<span class="math-parenthesis math-round-parenthesis">)</span>'),this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"==t?s+'<span class="math-operator math-binary-operator math-implicit-binary-operator"></span>'+u:s+'<span class="math-operator math-binary-operator math-explicit-binary-operator">'+f(this.op)+"</span>"+u}if(2<n.length&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var c=n.map(function(e,t){return e=e.toHTML(r),i[t]&&(e='<span class="math-parenthesis math-round-parenthesis">(</span>'+e+'<span class="math-parenthesis math-round-parenthesis">)</span>'),e});return this.implicit&&"OperatorNode:multiply"===this.getIdentifier()&&"hide"===t?c.join('<span class="math-operator math-binary-operator math-implicit-binary-operator"></span>'):c.join('<span class="math-operator math-binary-operator math-explicit-binary-operator">'+f(this.op)+"</span>")}return'<span class="math-function">'+f(this.fn)+'</span><span class="math-paranthesis math-round-parenthesis">(</span>'+c.join('<span class="math-separator">,</span>')+'<span class="math-paranthesis math-round-parenthesis">)</span>'},a.prototype._toTex=function(r){var e=r&&r.parenthesis?r.parenthesis:"keep",t=r&&r.implicit?r.implicit:"hide",n=this.args,i=m(this,e,t,n,!0),a=h.operators[this.fn];if(a=void 0===a?this.op:a,1===n.length){var o=x.getAssociativity(this,e),s=n[0].toTex(r);return i[0]&&(s="\\left("+s+"\\right)"),"right"===o?a+s:s+a}if(2===n.length){var u=n[0],c=u.toTex(r);i[0]&&(c="\\left("+c+"\\right)");var f,l=n[1].toTex(r);switch(i[1]&&(l="\\left("+l+"\\right)"),f="keep"===e?u.getIdentifier():u.getContent().getIdentifier(),this.getIdentifier()){case"OperatorNode:divide":return a+"{"+c+"}{"+l+"}";case"OperatorNode:pow":switch(c="{"+c+"}",l="{"+l+"}",f){case"ConditionalNode":case"OperatorNode:divide":c="\\left("+c+"\\right)"}case"OperatorNode:multiply":if(this.implicit&&"hide"===t)return c+"~"+l}return c+a+l}if(2<n.length&&("OperatorNode:add"===this.getIdentifier()||"OperatorNode:multiply"===this.getIdentifier())){var p=n.map(function(e,t){return e=e.toTex(r),i[t]&&(e="\\left("+e+"\\right)"),e});return"OperatorNode:multiply"===this.getIdentifier()&&this.implicit?p.join("~"):p.join(a)}return"\\mathrm{"+this.fn+"}\\left("+n.map(function(e){return e.toTex(r)}).join(",")+"\\right)"},a.prototype.getIdentifier=function(){return this.type+":"+this.fn},a}},function(e,t,s){var u=s(9).format,c=s(4).escape;t.name="ConstantNode",t.path="expression.node",t.factory=function(e,t,r,n){var i=r(s(14)),a=r(s(40));function o(e){if(!(this instanceof o))throw new SyntaxError("Constructor must be called with the new operator");if(2===arguments.length)throw new SyntaxError("new 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class="math-symbol">'+t+"</span>"}},o.prototype.toJSON=function(){return{mathjs:"ConstantNode",value:this.value}},o.fromJSON=function(e){return new o(e.value)},o.prototype._toTex=function(e){var t=this._toString(e);switch(a(this.value)){case"string":return"\\mathtt{"+c(t)+"}";case"number":case"BigNumber":var r=t.toLowerCase().indexOf("e");return-1!==r?t.substring(0,r)+"\\cdot10^{"+t.substring(r+1)+"}":t;case"Fraction":return this.value.toLatex();default:return t}},o}},function(e,t,r){var f=[{AssignmentNode:{},FunctionAssignmentNode:{}},{ConditionalNode:{latexLeftParens:!1,latexRightParens:!1,latexParens:!1}},{"OperatorNode:or":{associativity:"left",associativeWith:[]}},{"OperatorNode:xor":{associativity:"left",associativeWith:[]}},{"OperatorNode:and":{associativity:"left",associativeWith:[]}},{"OperatorNode:bitOr":{associativity:"left",associativeWith:[]}},{"OperatorNode:bitXor":{associativity:"left",associativeWith:[]}},{"OperatorNode:bitAnd":{associativity:"left",associativeWith:[]}},{"OperatorNode:equal":{associativity:"left",associativeWith:[]},"OperatorNode:unequal":{associativity:"left",associativeWith:[]},"OperatorNode:smaller":{associativity:"left",associativeWith:[]},"OperatorNode:larger":{associativity:"left",associativeWith:[]},"OperatorNode:smallerEq":{associativity:"left",associativeWith:[]},"OperatorNode:largerEq":{associativity:"left",associativeWith:[]}},{"OperatorNode:leftShift":{associativity:"left",associativeWith:[]},"OperatorNode:rightArithShift":{associativity:"left",associativeWith:[]},"OperatorNode:rightLogShift":{associativity:"left",associativeWith:[]}},{"OperatorNode:to":{associativity:"left",associativeWith:[]}},{RangeNode:{}},{"OperatorNode:add":{associativity:"left",associativeWith:["OperatorNode:add","OperatorNode:subtract"]},"OperatorNode:subtract":{associativity:"left",associativeWith:[]}},{"OperatorNode:multiply":{associativity:"left",associativeWith:["OperatorNode:multiply","OperatorNode:divide","Operator:dotMultiply","Operator:dotDivide"]},"OperatorNode:divide":{associativity:"left",associativeWith:[],latexLeftParens:!1,latexRightParens:!1,latexParens:!1},"OperatorNode:dotMultiply":{associativity:"left",associativeWith:["OperatorNode:multiply","OperatorNode:divide","OperatorNode:dotMultiply","OperatorNode:doDivide"]},"OperatorNode:dotDivide":{associativity:"left",associativeWith:[]},"OperatorNode:mod":{associativity:"left",associativeWith:[]}},{"OperatorNode:unaryPlus":{associativity:"right"},"OperatorNode:unaryMinus":{associativity:"right"},"OperatorNode:bitNot":{associativity:"right"},"OperatorNode:not":{associativity:"right"}},{"OperatorNode:pow":{associativity:"right",associativeWith:[],latexRightParens:!1},"OperatorNode:dotPow":{associativity:"right",associativeWith:[]}},{"OperatorNode:factorial":{associativity:"left"}},{"OperatorNode:transpose":{associativity:"left"}}];function l(e,t){var r=e;"keep"!==t&&(r=e.getContent());for(var n=r.getIdentifier(),i=0;i<f.length;i++)if(n in f[i])return i;return null}e.exports.properties=f,e.exports.getPrecedence=l,e.exports.getAssociativity=function(e,t){var r=e;"keep"!==t&&(r=e.getContent());var n=r.getIdentifier(),i=l(r,t);if(null===i)return null;var a=f[i][n];if(a.hasOwnProperty("associativity")){if("left"===a.associativity)return"left";if("right"===a.associativity)return"right";throw Error("'"+n+"' has the invalid associativity '"+a.associativity+"'.")}return null},e.exports.isAssociativeWith=function(e,t,r){var n=e,i=t;"keep"!==r&&(n=e.getContent(),i=t.getContent());var a=n.getIdentifier(),o=i.getIdentifier(),s=l(n,r);if(null===s)return null;var u=f[s][a];if(u.hasOwnProperty("associativeWith")&&u.associativeWith instanceof Array){for(var c=0;c<u.associativeWith.length;c++)if(u.associativeWith[c]===o)return!0;return!1}return null}},function(e,t,r){var a=r(0);r(3);t.name="isNumeric",t.factory=function(e,t,r,n){var 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a=t(s(1)),y=t(s(12)),x=t(s(20)),w=t(s(8)),b=t(s(32)),N=t(s(122)),M=t(s(52)),E=t(s(23)),n=r("inv",{"Array | Matrix":function(e){var t=i.isMatrix(e)?e.size():u.array.size(e);switch(t.length){case 1:if(1==t[0])return i.isMatrix(e)?a([y(1,e.valueOf()[0])]):[y(1,e[0])];throw new RangeError("Matrix must be square (size: "+u.string.format(t)+")");case 2:var r=t[0],n=t[1];if(r==n)return i.isMatrix(e)?a(o(e.valueOf(),r,n),e.storage()):o(e,r,n);throw new RangeError("Matrix must be square (size: "+u.string.format(t)+")");default:throw new RangeError("Matrix must be two dimensional (size: "+u.string.format(t)+")")}},any:function(e){return y(1,e)}});function o(e,t,r){var n,i,a,o,s;if(1==t){if(0==(o=e[0][0]))throw Error("Cannot calculate inverse, determinant is zero");return[[y(1,o)]]}if(2==t){var u=N(e);if(0==u)throw Error("Cannot calculate inverse, determinant is zero");return[[y(e[1][1],u),y(b(e[0][1]),u)],[y(b(e[1][0]),u),y(e[0][0],u)]]}var c=e.concat();for(n=0;n<t;n++)c[n]=c[n].concat();for(var 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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","min","prod","sum","var"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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","var","quantileSeq"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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","var"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","factorial"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","permutations","gamma"]}},function(e,t){e.exports={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:["permutations","factorial"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","trace","transpose"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","trace","zeros"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","trace","transpose","zeros"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","inv","ones","range","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","inv","ones","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","inv","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={name:"eye",category:"Matrix",syntax:["eye(n)","eye(m, n)","eye([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["eye(3)","eye(3, 5)","a = [1, 2, 3; 4, 5, 6]","eye(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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","eye","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]}},function(e,t){e.exports={name:"eval",category:"Expression",syntax:["eval(expression)","eval([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['eval("2 + 3")','eval("sqrt(" + 4 + ")")'],seealso:[]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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:[]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={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"]}},function(e,t){e.exports={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","sqrtm","multiply"]}},function(e,t){e.exports={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"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.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]}},function(e,t){e.exports={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"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.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]}},function(e,t){e.exports={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)"],seealso:["multiply"]}},function(e,t){e.exports={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["sqrt","pow"]}},function(e,t){e.exports={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']}},function(e,t){e.exports={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]}},function(e,t){e.exports={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]}},function(e,t){e.exports={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]}},function(e,t){e.exports={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]}},function(e,t){e.exports={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]}},function(e,t){e.exports={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],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).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]}},function(e,t){e.exports={name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]}},function(e,t){e.exports={name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]}},function(e,t){e.exports={name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]}},function(e,t){e.exports={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]}},function(e,t){e.exports={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]}},function(e,t){e.exports={name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]}},function(e,t){e.exports={name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]}},function(e,t){e.exports={name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x)) # Euler's formula"],seealso:["expm","expm1","pow","log"]}},function(e,t){e.exports={name:"dotpow",category:"Operators",syntax:["x .^ y","dotpow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]}},function(e,t){e.exports={name:"dotMultiply",category:"Operators",syntax:["x .* y","dotMultiply(x, y)"],description:"Multiply two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a .* b"],seealso:["multiply","divide","dotDivide"]}},function(e,t){e.exports={name:"dotDivide",category:"Operators",syntax:["x ./ y","dotDivide(x, y)"],description:"Divide two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a ./ b"],seealso:["multiply","dotMultiply","divide"]}},function(e,t){e.exports={name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["a = 2 / 3","a * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]}},function(e,t){e.exports={name:"cube",category:"Arithmetic",syntax:["cube(x)"],description:"Compute the cube of a value. The cube of x is x * x * x.",examples:["cube(2)","2^3","2 * 2 * 2"],seealso:["multiply","square","pow"]}},function(e,t){e.exports={name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.",examples:["ceil(3.2)","ceil(3.8)","ceil(-4.2)"],seealso:["floor","fix","round"]}},function(e,t){e.exports={name:"cbrt",category:"Arithmetic",syntax:["cbrt(x)","cbrt(x, allRoots)"],description:"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",examples:["cbrt(64)","cube(4)","cbrt(-8)","cbrt(2 + 3i)","cbrt(8i)","cbrt(8i, true)","cbrt(27 m^3)"],seealso:["square","sqrt","cube","multiply"]}},function(e,t){e.exports={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["a = 2.1 + 3.6","a - 3.6","3 + 2i","3 cm + 2 inch",'"2.3" + "4"'],seealso:["subtract"]}},function(e,t){e.exports={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]}},function(e,t){e.exports={name:"qr",category:"Algebra",syntax:["qr(A)"],description:"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.",examples:["qr([[1, -1, 4], [1, 4, -2], [1, 4, 2], [1, -1, 0]])"],seealso:["lup","slu","matrix"]}},function(e,t){e.exports={name:"usolve",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Solves the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["lup","lusolve","lsolve","matrix","sparse"]}},function(e,t){e.exports={name:"slu",category:"Algebra",syntax:["slu(A, order, threshold)"],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",examples:["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)"],seealso:["lusolve","lsolve","usolve","matrix","sparse","lup","qr"]}},function(e,t){e.exports={name:"rationalize",category:"Algebra",syntax:["rationalize(expr)","rationalize(expr, scope)","rationalize(expr, scope, detailed)"],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.",examples:['rationalize("2x/y - y/(x+1)")','rationalize("2x/y - y/(x+1)", true)'],seealso:["simplify"]}},function(e,t){e.exports={name:"simplify",category:"Algebra",syntax:["simplify(expr)","simplify(expr, rules)"],description:"Simplify an expression tree.",examples:['simplify("3 + 2 / 4")','simplify("2x + x")','f = parse("x * (x + 2 + x)")',"simplified = simplify(f)","simplified.eval({x: 2})"],seealso:["derivative","parse","eval"]}},function(e,t){e.exports={name:"lusolve",category:"Algebra",syntax:["x=lusolve(A, b)","x=lusolve(lu, b)"],description:"Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lusolve(a, b)"],seealso:["lup","slu","lsolve","usolve","matrix","sparse"]}},function(e,t){e.exports={name:"lup",category:"Algebra",syntax:["lup(m)"],description:"Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U",examples:["lup([[2, 1], [1, 4]])","lup(matrix([[2, 1], [1, 4]]))","lup(sparse([[2, 1], [1, 4]]))"],seealso:["lusolve","lsolve","usolve","matrix","sparse","slu","qr"]}},function(e,t){e.exports={name:"lsolve",category:"Algebra",syntax:["x=lsolve(L, b)"],description:"Solves the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lup","lusolve","usolve","matrix","sparse"]}},function(e,t){e.exports={name:"derivative",category:"Algebra",syntax:["derivative(expr, variable)","derivative(expr, variable, {simplify: boolean})"],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.",examples:['derivative("2x^3", "x")','derivative("2x^3", "x", {simplify: false})','derivative("2x^2 + 3x + 4", "x")','derivative("sin(2x)", "x")','f = parse("x^2 + x")','x = parse("x")',"df = derivative(f, x)","df.eval({x: 3})"],seealso:["simplify","parse","eval"]}},function(e,t){e.exports={name:"version",category:"Constants",syntax:["version"],description:"A string with the version number of math.js",examples:["version"],seealso:[]}},function(e,t){e.exports={name:"true",category:"Constants",syntax:["true"],description:"Boolean value true",examples:["true"],seealso:["false"]}},function(e,t){e.exports={name:"tau",category:"Constants",syntax:["tau"],description:"Tau is the ratio constant of a circle's circumference to radius, equal to 2 * pi, approximately 6.2832.",examples:["tau","2 * pi"],seealso:["pi"]}},function(e,t){e.exports={name:"SQRT2",category:"Constants",syntax:["SQRT2"],description:"Returns the square root of 2, approximately equal to 1.414",examples:["SQRT2","sqrt(2)"],seealso:[]}},function(e,t){e.exports={name:"SQRT1_2",category:"Constants",syntax:["SQRT1_2"],description:"Returns the square root of 1/2, approximately equal to 0.707",examples:["SQRT1_2","sqrt(1/2)"],seealso:[]}},function(e,t){e.exports={name:"phi",category:"Constants",syntax:["phi"],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...",examples:["phi"],seealso:[]}},function(e,t){e.exports={name:"null",category:"Constants",syntax:["null"],description:"Value null",examples:["null"],seealso:["true","false"]}},function(e,t){e.exports={name:"NaN",category:"Constants",syntax:["NaN"],description:"Not a number",examples:["NaN","0 / 0"],seealso:[]}},function(e,t){e.exports={name:"LOG10E",category:"Constants",syntax:["LOG10E"],description:"Returns the base-10 logarithm of E, approximately equal to 0.434",examples:["LOG10E","log(e, 10)"],seealso:[]}},function(e,t){e.exports={name:"LOG2E",category:"Constants",syntax:["LOG2E"],description:"Returns the base-2 logarithm of E, approximately equal to 1.442",examples:["LOG2E","log(e, 2)"],seealso:[]}},function(e,t){e.exports={name:"LN10",category:"Constants",syntax:["LN10"],description:"Returns the natural logarithm of 10, approximately equal to 2.302",examples:["LN10","log(10)"],seealso:[]}},function(e,t){e.exports={name:"LN2",category:"Constants",syntax:["LN2"],description:"Returns the natural logarithm of 2, approximately equal to 0.693",examples:["LN2","log(2)"],seealso:[]}},function(e,t){e.exports={name:"Infinity",category:"Constants",syntax:["Infinity"],description:"Infinity, a number which is larger than the maximum number that can be handled by a floating point number.",examples:["Infinity","1 / 0"],seealso:[]}},function(e,t){e.exports={name:"i",category:"Constants",syntax:["i"],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.",examples:["i","i * i","sqrt(-1)"],seealso:[]}},function(e,t){e.exports={name:"false",category:"Constants",syntax:["false"],description:"Boolean value false",examples:["false"],seealso:["true"]}},function(e,t){e.exports={name:"unit",category:"Construction",syntax:["value unit","unit(value, unit)","unit(string)"],description:"Create a unit.",examples:["5.5 mm","3 inch",'unit(7.1, "kilogram")','unit("23 deg")'],seealso:["bignumber","boolean","complex","index","matrix","number","string"]}},function(e,t){e.exports={name:"string",category:"Construction",syntax:['"text"',"string(x)"],description:"Create a string or convert a value to a string",examples:['"Hello World!"',"string(4.2)","string(3 + 2i)"],seealso:["bignumber","boolean","complex","index","matrix","number","unit"]}},function(e,t){e.exports={name:"splitUnit",category:"Construction",syntax:["splitUnit(unit: Unit, parts: Unit[])"],description:"Split a unit in an array of units whose sum is equal to the original unit.",examples:['splitUnit(1 m, ["feet", "inch"])'],seealso:["unit","createUnit"]}},function(e,t){e.exports={name:"sparse",category:"Construction",syntax:["sparse()","sparse([a1, b1, ...; a1, b2, ...])",'sparse([a1, b1, ...; a1, b2, ...], "number")'],description:"Create a sparse matrix.",examples:["sparse()","sparse([3, 4; 5, 6])",'sparse([3, 0; 5, 0], "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","matrix"]}},function(e,t){e.exports={name:"number",category:"Construction",syntax:["x","number(x)","number(unit, valuelessUnit)"],description:"Create a number or convert a string or boolean into a number.",examples:["2","2e3","4.05","number(2)",'number("7.2")',"number(true)","number([true, false, true, true])",'number(unit("52cm"), "m")'],seealso:["bignumber","boolean","complex","fraction","index","matrix","string","unit"]}},function(e,t){e.exports={name:"matrix",category:"Construction",syntax:["[]","[a1, b1, ...; a2, b2, ...]","matrix()",'matrix("dense")',"matrix([...])"],description:"Create a matrix.",examples:["[]","[1, 2, 3]","[1, 2, 3; 4, 5, 6]","matrix()","matrix([3, 4])",'matrix([3, 4; 5, 6], "sparse")','matrix([3, 4; 5, 6], "sparse", "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","sparse"]}},function(e,t){e.exports={name:"index",category:"Construction",syntax:["[start]","[start:end]","[start:step:end]","[start1, start 2, ...]","[start1:end1, start2:end2, ...]","[start1:step1:end1, start2:step2:end2, ...]"],description:"Create an index to get or replace a subset of a matrix",examples:["[]","[1, 2, 3]","A = [1, 2, 3; 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d={dimensions:[]};for(u=0;u<P.length;u++)d.dimensions[u]=0;d.dimensions[P.length-1]=1,d.key=m,R[m]=d,c={name:t,value:1,dimensions:R[m].dimensions.slice(0),prefixes:i,offset:s,base:m},F[m]={unit:c,prefix:B.NONE[""]}}for(M.UNITS[t]=c,u=0;u<o.length;u++){var g=o[u],v={};for(var y in c)c.hasOwnProperty(y)&&(v[y]=c[y]);v.name=g,M.UNITS[g]=v}return new M(null,t)},M.deleteUnit=function(e){delete M.UNITS[e]},M.PREFIXES=B,M.BASE_DIMENSIONS=P,M.BASE_UNITS=R,M.UNIT_SYSTEMS=L,M.UNITS=q,M},t.math=!0},function(e,t,r){e.exports=[r(527),r(526),r(525),r(524),r(523)]},function(e,t,r){var a=r(0),o=r(3);t.name="string",t.factory=function(e,t,r,n){var i=n("string",{"":function(){return""},number:o.format,null:function(e){return"null"},boolean:function(e){return e+""},string:function(e){return e},"Array | Matrix":function(e){return a(e,i)},any:function(e){return String(e)}});return i.toTex={0:'\\mathtt{""}',1:"\\mathrm{string}\\left(${args[0]}\\right)"},i}},function(e,t,r){e.exports=[r(145)]},function(e,t,r){t.name="sparse",t.factory=function(e,t,r,n){var i=e.SparseMatrix,a=n("sparse",{"":function(){return new i([])},string:function(e){return new i([],e)},"Array | Matrix":function(e){return new i(e)},"Array | Matrix, string":function(e,t){return new i(e,t)}});return a.toTex={0:"\\begin{bsparse}\\end{bsparse}",1:"\\left(${args[0]}\\right)"},a}},function(e,t,r){t.name="index",t.factory=function(n,e,t,r){return r("index",{"...number | string | BigNumber | Range | Array | Matrix":function(e){var t=e.map(function(e){return n.isBigNumber(e)?e.toNumber():Array.isArray(e)||n.isMatrix(e)?e.map(function(e){return n.isBigNumber(e)?e.toNumber():e}):e}),r=new n.Index;return n.Index.apply(r,t),r}})}},function(e,t,o){var s=o(29),r=s.string,u=s.object,c=Array.isArray,f=r.isString;t.name="ImmutableDenseMatrix",t.path="type",t.factory=function(n,e,t){var 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t=null;this.forEach(function(e){(null===t||r(t,e))&&(t=e)}),this._max=null!==t?t:void 0}return this._max},a}},function(e,t,c){t.name="FibonacciHeap",t.path="type",t.factory=function(e,t,r,n){var m=r(c(43)),h=r(c(33)),d=1/Math.log((1+Math.sqrt(5))/2);function i(){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");this._minimum=null,this._size=0}i.prototype.type="FibonacciHeap",i.prototype.isFibonacciHeap=!0,i.prototype.insert=function(e,t){var r={key:e,value:t,degree:0};if(this._minimum){var n=this._minimum;r.left=n,r.right=n.right,(n.right=r).right.left=r,m(e,n.key)&&(this._minimum=r)}else(r.left=r).right=r,this._minimum=r;return this._size++,r},i.prototype.size=function(){return this._size},i.prototype.clear=function(){this._minimum=null,this._size=0},i.prototype.isEmpty=function(){return 0===this._size},i.prototype.extractMinimum=function(){var e=this._minimum;if(null===e)return e;for(var t=this._minimum,r=e.degree,n=e.child;0<r;){var 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f=c[s];a(f,o)||(e._values.push(f),e._index.push(u))}}else 0===s&&i<1&&(i=1),a(c,o)||(e._values.push(c),e._index.push(u))}s++}while(s<i)}e._ptr.push(e._index.length),e._size=[n,i]};(M.prototype=new r).type="SparseMatrix",M.prototype.isSparseMatrix=!0,M.prototype.storage=function(){return"sparse"},M.prototype.datatype=function(){return this._datatype},M.prototype.create=function(e,t){return new M(e,t)},M.prototype.density=function(){var e=this._size[0],t=this._size[1];return 0!==e&&0!==t?this._index.length/(e*t):0},M.prototype.subset=function(e,t,r){if(!this._values)throw new Error("Cannot invoke subset on a Pattern only matrix");switch(arguments.length){case 1:return a(this,e);case 2:case 3:return o(this,e,t,r);default:throw new SyntaxError("Wrong number of arguments")}};var a=function(e,t){if(!w.isIndex(t))throw new TypeError("Invalid index");if(t.isScalar())return e.get(t.min());var r,n,i,a,o=t.size();if(o.length!=e._size.length)throw new x(o.length,e._size.length);var s=t.min(),u=t.max();for(r=0,n=e._size.length;r<n;r++)_(s[r],e._size[r]),_(u[r],e._size[r]);var c=e._values,f=e._index,l=e._ptr,p=t.dimension(0),m=t.dimension(1),h=[],d=[];p.forEach(function(e,t){d[e]=t[0],h[e]=!0});var g=c?[]:void 0,v=[],y=[];return m.forEach(function(e){for(y.push(v.length),i=l[e],a=l[e+1];i<a;i++)r=f[i],!0===h[r]&&(v.push(d[r]),g&&g.push(c[i]))}),y.push(v.length),new M({values:g,index:v,ptr:y,size:o,datatype:e._datatype})},o=function(e,t,r,n){if(!t||!0!==t.isIndex)throw new TypeError("Invalid index");var i,a=t.size(),o=t.isScalar();if(w.isMatrix(r)?(i=r.size(),r=r.toArray()):i=g.size(r),o){if(0!==i.length)throw new TypeError("Scalar expected");e.set(t.min(),r,n)}else{if(1!==a.length&&2!==a.length)throw new x(a.length,e._size.length,"<");if(i.length<a.length){for(var s=0,u=0;1===a[s]&&1===i[s];)s++;for(;1===a[s];)u++,s++;r=g.unsqueeze(r,a.length,u,i)}if(!v.deepEqual(a,i))throw new x(a,i,">");for(var c=t.min()[0],f=t.min()[1],l=i[0],p=i[1],m=0;m<l;m++)for(var h=0;h<p;h++){var d=r[m][h];e.set([m+c,h+f],d,n)}}return e};M.prototype.get=function(e){if(!A(e))throw new TypeError("Array expected");if(e.length!=this._size.length)throw new x(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke get on a Pattern only matrix");var t=e[0],r=e[1];_(t,this._size[0]),_(r,this._size[1]);var n=h(t,this._ptr[r],this._ptr[r+1],this._index);return n<this._ptr[r+1]&&this._index[n]===t?this._values[n]:0},M.prototype.set=function(e,t,r){if(!A(e))throw new TypeError("Array expected");if(e.length!=this._size.length)throw new x(e.length,this._size.length);if(!this._values)throw new Error("Cannot invoke set on a Pattern only matrix");var n=e[0],i=e[1],a=this._size[0],o=this._size[1],s=N,u=0;T(this._datatype)&&(s=b.find(N,[this._datatype,this._datatype])||N,u=b.convert(0,this._datatype)),(a-1<n||o-1<i)&&(l(this,Math.max(n+1,a),Math.max(i+1,o),r),a=this._size[0],o=this._size[1]),_(n,a),_(i,o);var c=h(n,this._ptr[i],this._ptr[i+1],this._index);return c<this._ptr[i+1]&&this._index[c]===n?s(t,u)?f(c,i,this._values,this._index,this._ptr):this._values[c]=t:d(c,n,i,t,this._values,this._index,this._ptr),this};var h=function(e,t,r,n){if(r-t==0)return r;for(var i=t;i<r;i++)if(n[i]===e)return i;return t},f=function(e,t,r,n,i){r.splice(e,1),n.splice(e,1);for(var a=t+1;a<i.length;a++)i[a]--},d=function(e,t,r,n,i,a,o){i.splice(e,0,n),a.splice(e,0,t);for(var s=r+1;s<o.length;s++)o[s]++};M.prototype.resize=function(t,e,r){if(!A(t))throw new TypeError("Array expected");if(2!==t.length)throw new Error("Only two dimensions matrix are supported");t.forEach(function(e){if(!E.isNumber(e)||!E.isInteger(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+y.format(t)+")")});var n=r?this.clone():this;return l(n,t[0],t[1],e)};var l=function(e,t,r,n){var i=n||0,a=N,o=0;T(e._datatype)&&(a=b.find(N,[e._datatype,e._datatype])||N,o=b.convert(0,e._datatype),i=b.convert(i,e._datatype));var s,u,c,f=!a(i,o),l=e._size[0],p=e._size[1];if(p<r){for(u=p;u<r;u++)if(e._ptr[u]=e._values.length,f)for(s=0;s<l;s++)e._values.push(i),e._index.push(s);e._ptr[r]=e._values.length}else r<p&&(e._ptr.splice(r+1,p-r),e._values.splice(e._ptr[r],e._values.length),e._index.splice(e._ptr[r],e._index.length));if(p=r,l<t){if(f){var m=0;for(u=0;u<p;u++){e._ptr[u]=e._ptr[u]+m,c=e._ptr[u+1]+m;var h=0;for(s=l;s<t;s++,h++)e._values.splice(c+h,0,i),e._index.splice(c+h,0,s),m++}e._ptr[p]=e._values.length}}else if(t<l){var d=0;for(u=0;u<p;u++){e._ptr[u]=e._ptr[u]-d;var g=e._ptr[u],v=e._ptr[u+1]-d;for(c=g;c<v;c++)t-1<(s=e._index[c])&&(e._values.splice(c,1),e._index.splice(c,1),d++)}e._ptr[u]=e._values.length}return e._size[0]=t,e._size[1]=r,e};M.prototype.reshape=function(t,e){if(!A(t))throw new TypeError("Array expected");if(2!==t.length)throw new Error("Sparse matrices can 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/**
* @license Fraction.js v4.0.8 09/09/2015
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
*
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
/**
* @license Fraction.js v4.0.8 09/09/2015
* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
*
* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
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/**
* @license Complex.js v2.0.10 11/02/2016
*
* Copyright (c) 2016, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
/**
* @license Complex.js v2.0.10 11/02/2016
*
* Copyright (c) 2016, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
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