mirror of
https://github.com/josdejong/mathjs.git
synced 2026-02-01 16:07:46 +00:00
Merge branch 'develop' into karma
This commit is contained in:
Jos de Jong
GitHub
commit
ec463c4705
16
HISTORY.md
16
HISTORY.md
@ -1,6 +1,22 @@
|
||||
# History
|
||||
|
||||
|
||||
## not yet released, version 4.3.0
|
||||
|
||||
- Implemented matrix exponential `math.expm`. Thanks @ericman314.
|
||||
- Upgraded dependencies
|
||||
- `complex.js` from `v2.0.2` to `v2.0.10`.
|
||||
- `fraction.js` from `v4.0.4` to `v4.0.8`.
|
||||
|
||||
|
||||
## 2018-05-05, version 4.2.2
|
||||
|
||||
- Fixed calculating the Frobenius norm of complex matrices correctly,
|
||||
see #1098. Thanks @jackschmidt.
|
||||
- Fixed #1076: cannot use mathjs in React VR by updating to
|
||||
`escape-latex@1.0.3`.
|
||||
|
||||
|
||||
## 2018-05-02, version 4.2.1
|
||||
|
||||
- Fixed `dist/math.js` being minified.
|
||||
|
||||
350
dist/math.js
vendored
350
dist/math.js
vendored
@ -7,8 +7,8 @@
|
||||
* It features real and complex numbers, units, matrices, a large set of
|
||||
* mathematical functions, and a flexible expression parser.
|
||||
*
|
||||
* @version 4.2.1
|
||||
* @date 2018-05-02
|
||||
* @version 4.2.2
|
||||
* @date 2018-05-05
|
||||
*
|
||||
* @license
|
||||
* Copyright (C) 2013-2018 Jos de Jong <wjosdejong@gmail.com>
|
||||
@ -1425,7 +1425,7 @@ exports.toSymbol = function (name, isUnit) {
|
||||
"use strict";
|
||||
|
||||
|
||||
var isBigNumber = __webpack_require__(89);
|
||||
var isBigNumber = __webpack_require__(90);
|
||||
|
||||
/**
|
||||
* Clone an object
|
||||
@ -2893,7 +2893,7 @@ exports.factory = factory;
|
||||
|
||||
var formatNumber = __webpack_require__(3).format;
|
||||
var formatBigNumber = __webpack_require__(541).format;
|
||||
var isBigNumber = __webpack_require__(89);
|
||||
var isBigNumber = __webpack_require__(90);
|
||||
|
||||
/**
|
||||
* Test whether value is a string
|
||||
@ -3984,7 +3984,7 @@ function factory (type, config, load, typed) {
|
||||
var latex = __webpack_require__(4);
|
||||
|
||||
var algorithm01 = load(__webpack_require__(34));
|
||||
var algorithm04 = load(__webpack_require__(87));
|
||||
var algorithm04 = load(__webpack_require__(88));
|
||||
var algorithm10 = load(__webpack_require__(43));
|
||||
var algorithm13 = load(__webpack_require__(7));
|
||||
var algorithm14 = load(__webpack_require__(6));
|
||||
@ -5814,7 +5814,7 @@ function factory (type, config, load, typed) {
|
||||
|
||||
var divideScalar = load(__webpack_require__(12));
|
||||
var multiply = load(__webpack_require__(8));
|
||||
var inv = load(__webpack_require__(81));
|
||||
var inv = load(__webpack_require__(82));
|
||||
var matrix = load(__webpack_require__(1));
|
||||
|
||||
var algorithm11 = load(__webpack_require__(17));
|
||||
@ -6519,7 +6519,7 @@ function factory (type, config, load, typed) {
|
||||
var ConditionalNode = load(__webpack_require__(129));
|
||||
var ConstantNode = load(__webpack_require__(57));
|
||||
var FunctionAssignmentNode = load(__webpack_require__(128));
|
||||
var IndexNode = load(__webpack_require__(85));
|
||||
var IndexNode = load(__webpack_require__(86));
|
||||
var ObjectNode = load(__webpack_require__(127));
|
||||
var OperatorNode = load(__webpack_require__(56));
|
||||
var ParenthesisNode = load(__webpack_require__(69));
|
||||
@ -8355,7 +8355,7 @@ function factory (type, config, load, typed) {
|
||||
var multiply = load(__webpack_require__(8));
|
||||
var matrix = load(__webpack_require__(1));
|
||||
var fraction = load(__webpack_require__(146));
|
||||
var number = load(__webpack_require__(86));
|
||||
var number = load(__webpack_require__(87));
|
||||
|
||||
/**
|
||||
* Calculates the power of x to y, `x ^ y`.
|
||||
@ -9600,7 +9600,7 @@ var isString = string.isString;
|
||||
var validateIndex = array.validateIndex;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var Matrix = load(__webpack_require__(88)); // force loading Matrix (do not use via type.Matrix)
|
||||
var Matrix = load(__webpack_require__(89)); // force loading Matrix (do not use via type.Matrix)
|
||||
|
||||
/**
|
||||
* Dense Matrix implementation. A regular, dense matrix, supporting multi-dimensional matrices. This is the default matrix type.
|
||||
@ -12242,7 +12242,7 @@ exports.factory = factory;
|
||||
var deepMap = __webpack_require__(0);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var gamma = load(__webpack_require__(99));
|
||||
var gamma = load(__webpack_require__(100));
|
||||
var latex = __webpack_require__(4);
|
||||
|
||||
/**
|
||||
@ -14715,6 +14715,68 @@ exports.factory = factory;
|
||||
"use strict";
|
||||
|
||||
|
||||
var deepMap = __webpack_require__(0);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
/**
|
||||
* Compute the complex conjugate of a complex value.
|
||||
* If `x = a+bi`, the complex conjugate of `x` is `a - bi`.
|
||||
*
|
||||
* For matrices, the function is evaluated element wise.
|
||||
*
|
||||
* Syntax:
|
||||
*
|
||||
* math.conj(x)
|
||||
*
|
||||
* Examples:
|
||||
*
|
||||
* math.conj(math.complex('2 + 3i')); // returns Complex 2 - 3i
|
||||
* math.conj(math.complex('2 - 3i')); // returns Complex 2 + 3i
|
||||
* math.conj(math.complex('-5.2i')); // returns Complex 5.2i
|
||||
*
|
||||
* See also:
|
||||
*
|
||||
* re, im, arg, abs
|
||||
*
|
||||
* @param {number | BigNumber | Complex | Array | Matrix} x
|
||||
* A complex number or array with complex numbers
|
||||
* @return {number | BigNumber | Complex | Array | Matrix}
|
||||
* The complex conjugate of x
|
||||
*/
|
||||
var conj = typed('conj', {
|
||||
'number': function (x) {
|
||||
return x;
|
||||
},
|
||||
|
||||
'BigNumber': function (x) {
|
||||
return x;
|
||||
},
|
||||
|
||||
'Complex': function (x) {
|
||||
return x.conjugate();
|
||||
},
|
||||
|
||||
'Array | Matrix': function (x) {
|
||||
return deepMap(x, conj);
|
||||
}
|
||||
});
|
||||
|
||||
conj.toTex = {1: '\\left(${args[0]}\\right)^*'};
|
||||
|
||||
return conj;
|
||||
}
|
||||
|
||||
exports.name = 'conj';
|
||||
exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 81 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
|
||||
|
||||
|
||||
function factory (type, config, load, typed, math) {
|
||||
var parse = load(__webpack_require__(39));
|
||||
@ -15388,7 +15450,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 81 */
|
||||
/* 82 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -15602,7 +15664,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 82 */
|
||||
/* 83 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -15693,14 +15755,14 @@ function _switch(mat){
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 83 */
|
||||
/* 84 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
|
||||
|
||||
var deepForEach = __webpack_require__(37);
|
||||
var reduce = __webpack_require__(82);
|
||||
var reduce = __webpack_require__(83);
|
||||
var containsCollections = __webpack_require__(66);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
@ -15811,7 +15873,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 84 */
|
||||
/* 85 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -15852,7 +15914,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 85 */
|
||||
/* 86 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16143,7 +16205,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 86 */
|
||||
/* 87 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16233,7 +16295,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 87 */
|
||||
/* 88 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16427,7 +16489,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 88 */
|
||||
/* 89 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16700,7 +16762,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 89 */
|
||||
/* 90 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16716,7 +16778,7 @@ module.exports = function isBigNumber(x) {
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 90 */
|
||||
/* 91 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16791,7 +16853,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 91 */
|
||||
/* 92 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -16932,7 +16994,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 92 */
|
||||
/* 93 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17062,7 +17124,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 93 */
|
||||
/* 94 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17075,7 +17137,7 @@ function factory (type, config, load, typed) {
|
||||
var concat = load(__webpack_require__(67));
|
||||
var size = load(__webpack_require__(23));
|
||||
var subset = load(__webpack_require__(22));
|
||||
var setDifference = load(__webpack_require__(95));
|
||||
var setDifference = load(__webpack_require__(96));
|
||||
|
||||
/**
|
||||
* Create the symmetric difference of two (multi)sets.
|
||||
@ -17120,7 +17182,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 94 */
|
||||
/* 95 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17193,7 +17255,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 95 */
|
||||
/* 96 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17274,7 +17336,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 96 */
|
||||
/* 97 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17371,7 +17433,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 97 */
|
||||
/* 98 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17457,7 +17519,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 98 */
|
||||
/* 99 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17527,7 +17589,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 99 */
|
||||
/* 100 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17736,7 +17798,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 100 */
|
||||
/* 101 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17812,7 +17874,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 101 */
|
||||
/* 102 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -17955,7 +18017,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 102 */
|
||||
/* 103 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18111,7 +18173,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 103 */
|
||||
/* 104 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18231,7 +18293,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 104 */
|
||||
/* 105 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18426,7 +18488,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 105 */
|
||||
/* 106 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18620,7 +18682,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 106 */
|
||||
/* 107 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18652,7 +18714,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 107 */
|
||||
/* 108 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18682,7 +18744,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 108 */
|
||||
/* 109 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18829,7 +18891,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 109 */
|
||||
/* 110 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18888,7 +18950,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 110 */
|
||||
/* 111 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -18979,7 +19041,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 111 */
|
||||
/* 112 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
@ -19372,68 +19434,6 @@ exports.name = 'lup';
|
||||
exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 112 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
|
||||
"use strict";
|
||||
|
||||
|
||||
var deepMap = __webpack_require__(0);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
/**
|
||||
* Compute the complex conjugate of a complex value.
|
||||
* If `x = a+bi`, the complex conjugate of `x` is `a - bi`.
|
||||
*
|
||||
* For matrices, the function is evaluated element wise.
|
||||
*
|
||||
* Syntax:
|
||||
*
|
||||
* math.conj(x)
|
||||
*
|
||||
* Examples:
|
||||
*
|
||||
* math.conj(math.complex('2 + 3i')); // returns Complex 2 - 3i
|
||||
* math.conj(math.complex('2 - 3i')); // returns Complex 2 + 3i
|
||||
* math.conj(math.complex('-5.2i')); // returns Complex 5.2i
|
||||
*
|
||||
* See also:
|
||||
*
|
||||
* re, im, arg, abs
|
||||
*
|
||||
* @param {number | BigNumber | Complex | Array | Matrix} x
|
||||
* A complex number or array with complex numbers
|
||||
* @return {number | BigNumber | Complex | Array | Matrix}
|
||||
* The complex conjugate of x
|
||||
*/
|
||||
var conj = typed('conj', {
|
||||
'number': function (x) {
|
||||
return x;
|
||||
},
|
||||
|
||||
'BigNumber': function (x) {
|
||||
return x;
|
||||
},
|
||||
|
||||
'Complex': function (x) {
|
||||
return x.conjugate();
|
||||
},
|
||||
|
||||
'Array | Matrix': function (x) {
|
||||
return deepMap(x, conj);
|
||||
}
|
||||
});
|
||||
|
||||
conj.toTex = {1: '\\left(${args[0]}\\right)^*'};
|
||||
|
||||
return conj;
|
||||
}
|
||||
|
||||
exports.name = 'conj';
|
||||
exports.factory = factory;
|
||||
|
||||
|
||||
/***/ }),
|
||||
/* 113 */
|
||||
/***/ (function(module, exports, __webpack_require__) {
|
||||
@ -20656,7 +20656,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
var deepForEach = __webpack_require__(37);
|
||||
var reduce = __webpack_require__(82);
|
||||
var reduce = __webpack_require__(83);
|
||||
var containsCollections = __webpack_require__(66);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
@ -20949,7 +20949,7 @@ exports.factory = factory;
|
||||
|
||||
var size = __webpack_require__(2).size;
|
||||
var deepForEach = __webpack_require__(37);
|
||||
var reduce = __webpack_require__(82);
|
||||
var reduce = __webpack_require__(83);
|
||||
var containsCollections = __webpack_require__(66);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
@ -23113,7 +23113,7 @@ var getSafeProperty = __webpack_require__(14).getSafeProperty;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var Node = load(__webpack_require__(13));
|
||||
var IndexNode = load(__webpack_require__(85));
|
||||
var IndexNode = load(__webpack_require__(86));
|
||||
var access = load(__webpack_require__(133));
|
||||
|
||||
/**
|
||||
@ -26180,7 +26180,7 @@ function factory (type, config, load, typed) {
|
||||
|
||||
var algorithm02 = load(__webpack_require__(24));
|
||||
var algorithm03 = load(__webpack_require__(19));
|
||||
var algorithm09 = load(__webpack_require__(102));
|
||||
var algorithm09 = load(__webpack_require__(103));
|
||||
var algorithm11 = load(__webpack_require__(17));
|
||||
var algorithm12 = load(__webpack_require__(18));
|
||||
var algorithm13 = load(__webpack_require__(7));
|
||||
@ -26491,7 +26491,7 @@ exports.factory = factory;
|
||||
var deepMap = __webpack_require__(0);
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var acosh = typed.find(load(__webpack_require__(90)), ['Complex']);
|
||||
var acosh = typed.find(load(__webpack_require__(91)), ['Complex']);
|
||||
|
||||
/**
|
||||
* Calculate the hyperbolic arcsecant of a value,
|
||||
@ -26938,7 +26938,7 @@ exports.factory = factory;
|
||||
|
||||
module.exports = [
|
||||
__webpack_require__(180),
|
||||
__webpack_require__(90),
|
||||
__webpack_require__(91),
|
||||
__webpack_require__(179),
|
||||
__webpack_require__(178),
|
||||
__webpack_require__(177),
|
||||
@ -27087,7 +27087,7 @@ module.exports = [
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var sqrt = load(__webpack_require__(36));
|
||||
var variance = load(__webpack_require__(91));
|
||||
var variance = load(__webpack_require__(92));
|
||||
|
||||
/**
|
||||
* Compute the standard deviation of a matrix or a list with values.
|
||||
@ -27617,8 +27617,8 @@ var flatten = __webpack_require__(2).flatten;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var abs = load(__webpack_require__(25));
|
||||
var map = load(__webpack_require__(97));
|
||||
var median = load(__webpack_require__(92));
|
||||
var map = load(__webpack_require__(98));
|
||||
var median = load(__webpack_require__(93));
|
||||
var subtract = load(__webpack_require__(15));
|
||||
var improveErrorMessage = load(__webpack_require__(31));
|
||||
|
||||
@ -27696,16 +27696,16 @@ exports.factory = factory;
|
||||
|
||||
module.exports = [
|
||||
__webpack_require__(188),
|
||||
__webpack_require__(83),
|
||||
__webpack_require__(84),
|
||||
__webpack_require__(122),
|
||||
__webpack_require__(92),
|
||||
__webpack_require__(93),
|
||||
__webpack_require__(120),
|
||||
__webpack_require__(187),
|
||||
__webpack_require__(186),
|
||||
__webpack_require__(185),
|
||||
__webpack_require__(184),
|
||||
__webpack_require__(96),
|
||||
__webpack_require__(91)
|
||||
__webpack_require__(97),
|
||||
__webpack_require__(92)
|
||||
];
|
||||
|
||||
|
||||
@ -27938,8 +27938,8 @@ function factory (type, config, load, typed) {
|
||||
var concat = load(__webpack_require__(67));
|
||||
var size = load(__webpack_require__(23));
|
||||
var subset = load(__webpack_require__(22));
|
||||
var setIntersect = load(__webpack_require__(94));
|
||||
var setSymDifference = load(__webpack_require__(93));
|
||||
var setIntersect = load(__webpack_require__(95));
|
||||
var setSymDifference = load(__webpack_require__(94));
|
||||
|
||||
/**
|
||||
* Create the union of two (multi)sets.
|
||||
@ -28399,14 +28399,14 @@ exports.factory = factory;
|
||||
|
||||
module.exports = [
|
||||
__webpack_require__(198),
|
||||
__webpack_require__(95),
|
||||
__webpack_require__(96),
|
||||
__webpack_require__(197),
|
||||
__webpack_require__(94),
|
||||
__webpack_require__(95),
|
||||
__webpack_require__(196),
|
||||
__webpack_require__(195),
|
||||
__webpack_require__(194),
|
||||
__webpack_require__(193),
|
||||
__webpack_require__(93),
|
||||
__webpack_require__(94),
|
||||
__webpack_require__(192)
|
||||
];
|
||||
|
||||
@ -28660,7 +28660,7 @@ module.exports = [
|
||||
__webpack_require__(201),
|
||||
__webpack_require__(50),
|
||||
__webpack_require__(33),
|
||||
__webpack_require__(108),
|
||||
__webpack_require__(109),
|
||||
__webpack_require__(42),
|
||||
__webpack_require__(200),
|
||||
__webpack_require__(114)
|
||||
@ -29249,9 +29249,9 @@ exports.factory = factory;
|
||||
function factory(type, config, load, typed) {
|
||||
var matrix = load(__webpack_require__(1));
|
||||
var divide = load(__webpack_require__(30));
|
||||
var sum = load(__webpack_require__(96));
|
||||
var sum = load(__webpack_require__(97));
|
||||
var multiply = load(__webpack_require__(8));
|
||||
var dotDivide = load(__webpack_require__(103));
|
||||
var dotDivide = load(__webpack_require__(104));
|
||||
var log = load(__webpack_require__(77));
|
||||
var isNumeric = load(__webpack_require__(59));
|
||||
|
||||
@ -29346,7 +29346,7 @@ module.exports = [
|
||||
//require('./distribution'), // TODO: rethink math.distribution
|
||||
__webpack_require__(62),
|
||||
__webpack_require__(63),
|
||||
__webpack_require__(99),
|
||||
__webpack_require__(100),
|
||||
__webpack_require__(211),
|
||||
__webpack_require__(210),
|
||||
__webpack_require__(209),
|
||||
@ -29443,9 +29443,9 @@ function factory(type, config, load, typed) {
|
||||
var multiply = load(__webpack_require__(8));
|
||||
var sqrt = load(__webpack_require__(36));
|
||||
var subtract = load(__webpack_require__(15));
|
||||
var inv = load(__webpack_require__(81));
|
||||
var inv = load(__webpack_require__(82));
|
||||
var size = load(__webpack_require__(23));
|
||||
var max = load(__webpack_require__(83));
|
||||
var max = load(__webpack_require__(84));
|
||||
var eye = load(__webpack_require__(60));
|
||||
|
||||
/**
|
||||
@ -30803,9 +30803,9 @@ module.exports = [
|
||||
__webpack_require__(223),
|
||||
__webpack_require__(222),
|
||||
__webpack_require__(221),
|
||||
__webpack_require__(81),
|
||||
__webpack_require__(82),
|
||||
__webpack_require__(220),
|
||||
__webpack_require__(97),
|
||||
__webpack_require__(98),
|
||||
__webpack_require__(219),
|
||||
__webpack_require__(73),
|
||||
__webpack_require__(119),
|
||||
@ -30816,7 +30816,7 @@ module.exports = [
|
||||
__webpack_require__(214),
|
||||
__webpack_require__(213),
|
||||
__webpack_require__(22),
|
||||
__webpack_require__(101),
|
||||
__webpack_require__(102),
|
||||
__webpack_require__(65),
|
||||
__webpack_require__(40)
|
||||
];
|
||||
@ -31100,7 +31100,7 @@ function factory (type, config, load, typed) {
|
||||
|
||||
var matrix = load(__webpack_require__(1));
|
||||
var zeros = load(__webpack_require__(40));
|
||||
var not = load(__webpack_require__(98));
|
||||
var not = load(__webpack_require__(99));
|
||||
var isZero = load(__webpack_require__(55));
|
||||
|
||||
var algorithm02 = load(__webpack_require__(24));
|
||||
@ -31252,7 +31252,7 @@ exports.factory = factory;
|
||||
|
||||
module.exports = [
|
||||
__webpack_require__(230),
|
||||
__webpack_require__(98),
|
||||
__webpack_require__(99),
|
||||
__webpack_require__(229),
|
||||
__webpack_require__(228)
|
||||
];
|
||||
@ -31975,7 +31975,7 @@ exports.factory = factory;
|
||||
|
||||
module.exports = [
|
||||
__webpack_require__(237),
|
||||
__webpack_require__(112),
|
||||
__webpack_require__(80),
|
||||
__webpack_require__(236),
|
||||
__webpack_require__(235)
|
||||
];
|
||||
@ -32106,7 +32106,7 @@ exports.factory = factory;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var add = load(__webpack_require__(16));
|
||||
var stirlingS2 = load(__webpack_require__(100));
|
||||
var stirlingS2 = load(__webpack_require__(101));
|
||||
var isNegative = load(__webpack_require__(53));
|
||||
var isInteger = load(__webpack_require__(46));
|
||||
|
||||
@ -32166,7 +32166,7 @@ exports.factory = factory;
|
||||
module.exports = [
|
||||
__webpack_require__(241),
|
||||
__webpack_require__(240),
|
||||
__webpack_require__(100),
|
||||
__webpack_require__(101),
|
||||
__webpack_require__(239)
|
||||
];
|
||||
|
||||
@ -32979,7 +32979,7 @@ function factory (type, config, load, typed) {
|
||||
var matrix = load(__webpack_require__(1));
|
||||
|
||||
var algorithm01 = load(__webpack_require__(34));
|
||||
var algorithm04 = load(__webpack_require__(87));
|
||||
var algorithm04 = load(__webpack_require__(88));
|
||||
var algorithm10 = load(__webpack_require__(43));
|
||||
var algorithm13 = load(__webpack_require__(7));
|
||||
var algorithm14 = load(__webpack_require__(6));
|
||||
@ -33951,13 +33951,14 @@ function factory (type, config, load, typed) {
|
||||
var abs = load(__webpack_require__(25));
|
||||
var add = load(__webpack_require__(16));
|
||||
var pow = load(__webpack_require__(41));
|
||||
var conj = load(__webpack_require__(80));
|
||||
var sqrt = load(__webpack_require__(36));
|
||||
var multiply = load(__webpack_require__(8));
|
||||
var equalScalar = load(__webpack_require__(9));
|
||||
var larger = load(__webpack_require__(33));
|
||||
var smaller = load(__webpack_require__(42));
|
||||
var matrix = load(__webpack_require__(1));
|
||||
var trace = load(__webpack_require__(101));
|
||||
var trace = load(__webpack_require__(102));
|
||||
var transpose = load(__webpack_require__(65));
|
||||
|
||||
|
||||
@ -34138,7 +34139,12 @@ function factory (type, config, load, typed) {
|
||||
}
|
||||
if (p === 'fro') {
|
||||
// norm(x) = sqrt(sum(diag(x'x)))
|
||||
return sqrt(trace(multiply(transpose(x), x)));
|
||||
var fro = 0;
|
||||
x.forEach(
|
||||
function (value, index) {
|
||||
fro = add( fro, multiply( value, conj(value) ) );
|
||||
});
|
||||
return sqrt(fro);
|
||||
}
|
||||
if (p === 2) {
|
||||
// not implemented
|
||||
@ -34974,7 +34980,7 @@ function factory (type, config, load, typed) {
|
||||
var matrix = load(__webpack_require__(1));
|
||||
|
||||
var algorithm01 = load(__webpack_require__(34));
|
||||
var algorithm04 = load(__webpack_require__(87));
|
||||
var algorithm04 = load(__webpack_require__(88));
|
||||
var algorithm10 = load(__webpack_require__(43));
|
||||
var algorithm13 = load(__webpack_require__(7));
|
||||
var algorithm14 = load(__webpack_require__(6));
|
||||
@ -35476,7 +35482,7 @@ function factory (type, config, load, typed) {
|
||||
var latex = __webpack_require__(4);
|
||||
|
||||
var algorithm02 = load(__webpack_require__(24));
|
||||
var algorithm09 = load(__webpack_require__(102));
|
||||
var algorithm09 = load(__webpack_require__(103));
|
||||
var algorithm11 = load(__webpack_require__(17));
|
||||
var algorithm13 = load(__webpack_require__(7));
|
||||
var algorithm14 = load(__webpack_require__(6));
|
||||
@ -35925,7 +35931,7 @@ module.exports = [
|
||||
__webpack_require__(275),
|
||||
__webpack_require__(274),
|
||||
__webpack_require__(30),
|
||||
__webpack_require__(103),
|
||||
__webpack_require__(104),
|
||||
__webpack_require__(273),
|
||||
__webpack_require__(272),
|
||||
__webpack_require__(271),
|
||||
@ -36015,14 +36021,14 @@ var isArray = Array.isArray;
|
||||
function factory (type, config, load, typed) {
|
||||
|
||||
var matrix = load(__webpack_require__(1));
|
||||
var lup = load(__webpack_require__(111));
|
||||
var slu = load(__webpack_require__(110));
|
||||
var lup = load(__webpack_require__(112));
|
||||
var slu = load(__webpack_require__(111));
|
||||
var cs_ipvec = load(__webpack_require__(278));
|
||||
|
||||
var solveValidation = load(__webpack_require__(78));
|
||||
|
||||
var usolve = load(__webpack_require__(104));
|
||||
var lsolve = load(__webpack_require__(105));
|
||||
var usolve = load(__webpack_require__(105));
|
||||
var lsolve = load(__webpack_require__(106));
|
||||
|
||||
/**
|
||||
* Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.
|
||||
@ -36175,8 +36181,8 @@ exports.factory = factory;
|
||||
|
||||
function factory (type, config, load) {
|
||||
|
||||
var cs_marked = load(__webpack_require__(107));
|
||||
var cs_mark = load(__webpack_require__(106));
|
||||
var cs_marked = load(__webpack_require__(108));
|
||||
var cs_mark = load(__webpack_require__(107));
|
||||
var cs_unflip = load(__webpack_require__(280));
|
||||
|
||||
/**
|
||||
@ -36268,8 +36274,8 @@ exports.factory = factory;
|
||||
function factory (type, config, load) {
|
||||
|
||||
var cs_dfs = load(__webpack_require__(281));
|
||||
var cs_marked = load(__webpack_require__(107));
|
||||
var cs_mark = load(__webpack_require__(106));
|
||||
var cs_marked = load(__webpack_require__(108));
|
||||
var cs_mark = load(__webpack_require__(107));
|
||||
|
||||
/**
|
||||
* The cs_reach function computes X = Reach(B), where B is the nonzero pattern of the n-by-1
|
||||
@ -36433,7 +36439,7 @@ function factory (type, config, load) {
|
||||
var multiply = load(__webpack_require__(8));
|
||||
|
||||
var larger = load(__webpack_require__(33));
|
||||
var largerEq = load(__webpack_require__(108));
|
||||
var largerEq = load(__webpack_require__(109));
|
||||
|
||||
var cs_spsolve = load(__webpack_require__(283));
|
||||
|
||||
@ -36814,7 +36820,7 @@ exports.factory = factory;
|
||||
|
||||
function factory (type, config, load) {
|
||||
|
||||
var cs_tdfs = load(__webpack_require__(109));
|
||||
var cs_tdfs = load(__webpack_require__(110));
|
||||
|
||||
/**
|
||||
* Post order a tree of forest
|
||||
@ -37115,7 +37121,7 @@ function factory (type, config, load) {
|
||||
|
||||
var cs_flip = load(__webpack_require__(79));
|
||||
var cs_fkeep = load(__webpack_require__(290));
|
||||
var cs_tdfs = load(__webpack_require__(109));
|
||||
var cs_tdfs = load(__webpack_require__(110));
|
||||
|
||||
var add = load(__webpack_require__(16));
|
||||
var multiply = load(__webpack_require__(8));
|
||||
@ -37875,7 +37881,7 @@ function factory (type, config, load, typed) {
|
||||
var abs = load(__webpack_require__(25));
|
||||
var sign = load(__webpack_require__(113));
|
||||
var sqrt = load(__webpack_require__(36));
|
||||
var conj = load(__webpack_require__(112));
|
||||
var conj = load(__webpack_require__(80));
|
||||
|
||||
var unaryMinus = load(__webpack_require__(32));
|
||||
var addScalar = load(__webpack_require__(20));
|
||||
@ -38128,7 +38134,7 @@ exports.factory = factory;
|
||||
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var simplify = load(__webpack_require__(80));
|
||||
var simplify = load(__webpack_require__(81));
|
||||
var simplifyCore = load(__webpack_require__(116));
|
||||
var simplifyConstant = load(__webpack_require__(118));
|
||||
var ArgumentsError = __webpack_require__(52);
|
||||
@ -38809,7 +38815,7 @@ exports.factory = factory;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var parse = load(__webpack_require__(39));
|
||||
var simplify = load(__webpack_require__(80));
|
||||
var simplify = load(__webpack_require__(81));
|
||||
var equal = load(__webpack_require__(50));
|
||||
var isZero = load(__webpack_require__(55));
|
||||
var numeric = load(__webpack_require__(136));
|
||||
@ -39582,7 +39588,7 @@ module.exports = [
|
||||
__webpack_require__(296),
|
||||
|
||||
// simplify
|
||||
__webpack_require__(80),
|
||||
__webpack_require__(81),
|
||||
|
||||
// polynomial
|
||||
__webpack_require__(294),
|
||||
@ -39590,13 +39596,13 @@ module.exports = [
|
||||
|
||||
// decomposition
|
||||
__webpack_require__(293),
|
||||
__webpack_require__(112),
|
||||
__webpack_require__(111),
|
||||
__webpack_require__(110),
|
||||
|
||||
// solver
|
||||
__webpack_require__(105),
|
||||
__webpack_require__(106),
|
||||
__webpack_require__(279),
|
||||
__webpack_require__(104)
|
||||
__webpack_require__(105)
|
||||
];
|
||||
|
||||
|
||||
@ -39936,7 +39942,7 @@ var isCollection = __webpack_require__(47);
|
||||
* from one-based to zero based
|
||||
*/
|
||||
function factory (type, config, load, typed) {
|
||||
var max = load(__webpack_require__(83));
|
||||
var max = load(__webpack_require__(84));
|
||||
|
||||
return typed('max', {
|
||||
'...any': function (args) {
|
||||
@ -39983,7 +39989,7 @@ var map = __webpack_require__(2).map;
|
||||
* This transform creates a one-based index instead of a zero-based index
|
||||
*/
|
||||
function factory (type, config, load, typed) {
|
||||
var compileInlineExpression = load(__webpack_require__(84));
|
||||
var compileInlineExpression = load(__webpack_require__(85));
|
||||
var matrix = load(__webpack_require__(1));
|
||||
|
||||
function mapTransform(args, math, scope) {
|
||||
@ -40138,7 +40144,7 @@ var forEach = __webpack_require__(2).forEach;
|
||||
* This transform creates a one-based index instead of a zero-based index
|
||||
*/
|
||||
function factory (type, config, load, typed) {
|
||||
var compileInlineExpression = load(__webpack_require__(84));
|
||||
var compileInlineExpression = load(__webpack_require__(85));
|
||||
|
||||
function forEachTransform(args, math, scope) {
|
||||
var x, callback;
|
||||
@ -40219,7 +40225,7 @@ var maxArgumentCount = __webpack_require__(35).maxArgumentCount;
|
||||
* so you can do something like 'filter([3, -2, 5], x > 0)'.
|
||||
*/
|
||||
function factory (type, config, load, typed) {
|
||||
var compileInlineExpression = load(__webpack_require__(84));
|
||||
var compileInlineExpression = load(__webpack_require__(85));
|
||||
var matrix = load(__webpack_require__(1));
|
||||
|
||||
function filterTransform(args, math, scope) {
|
||||
@ -40401,7 +40407,7 @@ module.exports = [
|
||||
__webpack_require__(130),
|
||||
__webpack_require__(129),
|
||||
__webpack_require__(57),
|
||||
__webpack_require__(85),
|
||||
__webpack_require__(86),
|
||||
__webpack_require__(128),
|
||||
__webpack_require__(68),
|
||||
__webpack_require__(13),
|
||||
@ -45298,7 +45304,7 @@ module.exports = [
|
||||
/* 515 */
|
||||
/***/ (function(module, exports) {
|
||||
|
||||
module.exports = '4.2.1';
|
||||
module.exports = '4.2.2';
|
||||
// Note: This file is automatically generated when building math.js.
|
||||
// Changes made in this file will be overwritten.
|
||||
|
||||
@ -45716,7 +45722,7 @@ function factory (type, config, load, typed, math) {
|
||||
var isNumeric = load(__webpack_require__(59));
|
||||
var format = load(__webpack_require__(140));
|
||||
var getTypeOf = load(__webpack_require__(49));
|
||||
var toNumber = load(__webpack_require__(86));
|
||||
var toNumber = load(__webpack_require__(87));
|
||||
var Complex = load(__webpack_require__(147));
|
||||
|
||||
/**
|
||||
@ -50040,7 +50046,7 @@ var isString = string.isString;
|
||||
var validateIndex = array.validateIndex;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
var Matrix = load(__webpack_require__(88)); // force loading Matrix (do not use via type.Matrix)
|
||||
var Matrix = load(__webpack_require__(89)); // force loading Matrix (do not use via type.Matrix)
|
||||
var equalScalar = load(__webpack_require__(9));
|
||||
|
||||
/**
|
||||
@ -51483,7 +51489,7 @@ exports.isBoolean = function(value) {
|
||||
|
||||
module.exports = [
|
||||
// types
|
||||
__webpack_require__(88),
|
||||
__webpack_require__(89),
|
||||
__webpack_require__(51),
|
||||
__webpack_require__(530),
|
||||
__webpack_require__(529),
|
||||
@ -59348,7 +59354,7 @@ module.exports = [
|
||||
__webpack_require__(539),
|
||||
__webpack_require__(535),
|
||||
__webpack_require__(532),
|
||||
__webpack_require__(86),
|
||||
__webpack_require__(87),
|
||||
__webpack_require__(524),
|
||||
__webpack_require__(523),
|
||||
__webpack_require__(522)
|
||||
@ -61260,7 +61266,7 @@ var __WEBPACK_AMD_DEFINE_FACTORY__, __WEBPACK_AMD_DEFINE_ARRAY__, __WEBPACK_AMD_
|
||||
|
||||
var typedFunction = __webpack_require__(554);
|
||||
var digits = __webpack_require__(3).digits;
|
||||
var isBigNumber = __webpack_require__(89);
|
||||
var isBigNumber = __webpack_require__(90);
|
||||
var isMatrix = __webpack_require__(71);
|
||||
|
||||
// returns a new instance of typed-function
|
||||
|
||||
12
dist/math.min.js
vendored
12
dist/math.min.js
vendored
File diff suppressed because one or more lines are too long
2
dist/math.min.map
vendored
2
dist/math.min.map
vendored
File diff suppressed because one or more lines are too long
@ -142,6 +142,7 @@ Function | Description
|
||||
[math.det(x)](functions/det.md) | Calculate the determinant of a matrix.
|
||||
[math.diag(X)](functions/diag.md) | Create a diagonal matrix or retrieve the diagonal of a matrix When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.
|
||||
[math.dot(x, y)](functions/dot.md) | Calculate the dot product of two vectors.
|
||||
[math.expm(x)](functions/expm.md) | Calculate the exponential of a matrix.
|
||||
[math.eye(n)](functions/eye.md) | Create a 2-dimensional identity matrix with size m x n or n x n.
|
||||
[math.filter(x, test)](functions/filter.md) | Filter the items in an array or one dimensional matrix.
|
||||
[math.flatten(x)](functions/flatten.md) | Flatten a multi dimensional matrix into a single dimensional matrix.
|
||||
|
||||
@ -13,6 +13,7 @@ module.exports = {
|
||||
'(exp(i*x) == cos(x) + i*sin(x)) # Euler\'s formula'
|
||||
],
|
||||
'seealso': [
|
||||
'expm',
|
||||
'expm1',
|
||||
'pow',
|
||||
'log'
|
||||
|
||||
@ -5,6 +5,7 @@ function factory (type, config, load, typed) {
|
||||
var abs = load(require('../arithmetic/abs'));
|
||||
var add = load(require('../arithmetic/add'));
|
||||
var pow = load(require('../arithmetic/pow'));
|
||||
var conj = load(require('../complex/conj'));
|
||||
var sqrt = load(require('../arithmetic/sqrt'));
|
||||
var multiply = load(require('../arithmetic/multiply'));
|
||||
var equalScalar = load(require('../relational/equalScalar'));
|
||||
@ -192,7 +193,12 @@ function factory (type, config, load, typed) {
|
||||
}
|
||||
if (p === 'fro') {
|
||||
// norm(x) = sqrt(sum(diag(x'x)))
|
||||
return sqrt(trace(multiply(transpose(x), x)));
|
||||
var fro = 0;
|
||||
x.forEach(
|
||||
function (value, index) {
|
||||
fro = add( fro, multiply( value, conj(value) ) );
|
||||
});
|
||||
return sqrt(fro);
|
||||
}
|
||||
if (p === 2) {
|
||||
// not implemented
|
||||
|
||||
175
lib/function/matrix/expm.js
Normal file
175
lib/function/matrix/expm.js
Normal file
@ -0,0 +1,175 @@
|
||||
'use strict';
|
||||
|
||||
var format = require('../../utils/string').format;
|
||||
|
||||
function factory (type, config, load, typed) {
|
||||
|
||||
var abs = load(require('../arithmetic/abs'));
|
||||
var add = load(require('../arithmetic/add'));
|
||||
var eye = load(require('./eye'));
|
||||
var inv = load(require('./inv'));
|
||||
var multiply = load(require('../arithmetic/multiply'));
|
||||
|
||||
var SparseMatrix = type.SparseMatrix;
|
||||
|
||||
/**
|
||||
* 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.
|
||||
*
|
||||
* The exponential is calculated using the Padé approximant with scaling and
|
||||
* squaring; see "Nineteen Dubious Ways to Compute the Exponential of a
|
||||
* Matrix," by Moler and Van Loan.
|
||||
*
|
||||
* Syntax:
|
||||
*
|
||||
* math.expm(x)
|
||||
*
|
||||
* Examples:
|
||||
*
|
||||
* var A = [[0,2],[0,0]]
|
||||
* math.expm(A); // returns [[1,2],[0,1]]
|
||||
*
|
||||
* See also:
|
||||
*
|
||||
* exp
|
||||
*
|
||||
* @param {Matrix} x A square Matrix
|
||||
* @return {Matrix} The exponential of x
|
||||
*/
|
||||
var expm = typed('expm', {
|
||||
|
||||
'Matrix': function (A) {
|
||||
|
||||
// Check matrix size
|
||||
var size = A.size();
|
||||
|
||||
if(size.length !== 2 || size[0] !== size[1]) {
|
||||
throw new RangeError('Matrix must be square ' +
|
||||
'(size: ' + format(size) + ')');
|
||||
}
|
||||
|
||||
var n = size[0];
|
||||
|
||||
// Desired accuracy of the approximant (The actual accuracy
|
||||
// will be affected by round-off error)
|
||||
var eps = 1e-15;
|
||||
|
||||
// The Padé approximant is not so accurate when the values of A
|
||||
// are "large", so scale A by powers of two. Then compute the
|
||||
// exponential, and square the result repeatedly according to
|
||||
// the identity e^A = (e^(A/m))^m
|
||||
|
||||
// Compute infinity-norm of A, ||A||, to see how "big" it is
|
||||
var infNorm = infinityNorm(A);
|
||||
|
||||
// Find the optimal scaling factor and number of terms in the
|
||||
// Padé approximant to reach the desired accuracy
|
||||
var params = findParams(infNorm, eps);
|
||||
var q = params.q;
|
||||
var j = params.j;
|
||||
|
||||
// The Pade approximation to e^A is:
|
||||
// Rqq(A) = Dqq(A) ^ -1 * Nqq(A)
|
||||
// where
|
||||
// Nqq(A) = sum(i=0, q, (2q-i)!p! / [ (2q)!i!(q-i)! ] A^i
|
||||
// Dqq(A) = sum(i=0, q, (2q-i)!q! / [ (2q)!i!(q-i)! ] (-A)^i
|
||||
|
||||
// Scale A by 1 / 2^j
|
||||
var Apos = multiply(A, Math.pow(2, -j));
|
||||
|
||||
// The i=0 term is just the identity matrix
|
||||
var N = eye(n);
|
||||
var D = eye(n);
|
||||
|
||||
// Initialization (i=0)
|
||||
var factor = 1;
|
||||
|
||||
// Initialization (i=1)
|
||||
var Apos_to_i = Apos; // Cloning not necessary
|
||||
var alternate = -1;
|
||||
|
||||
for(var i=1; i<=q; i++) {
|
||||
if(i>1) {
|
||||
Apos_to_i = multiply(Apos_to_i, Apos);
|
||||
alternate = -alternate;
|
||||
}
|
||||
factor = factor*(q-i+1)/((2*q-i+1)*i);
|
||||
|
||||
N = add(N, multiply(factor, Apos_to_i));
|
||||
D = add(D, multiply(factor*alternate, Apos_to_i));
|
||||
}
|
||||
|
||||
var R = multiply(inv(D), N);
|
||||
|
||||
// Square j times
|
||||
for(var i=0; i<j; i++) {
|
||||
R = multiply(R, R);
|
||||
}
|
||||
|
||||
return type.isSparseMatrix(A)
|
||||
? new SparseMatrix(R)
|
||||
: R;
|
||||
}
|
||||
|
||||
});
|
||||
|
||||
function infinityNorm(A) {
|
||||
var n = A.size()[0];
|
||||
var infNorm = 0;
|
||||
for(var i=0; i<n; i++) {
|
||||
var rowSum = 0;
|
||||
for(var j=0; j<n; j++) {
|
||||
rowSum += abs(A.get([i,j]));
|
||||
}
|
||||
infNorm = Math.max(rowSum, infNorm);
|
||||
}
|
||||
return infNorm;
|
||||
}
|
||||
|
||||
/**
|
||||
* Find the best parameters for the Pade approximant given
|
||||
* the matrix norm and desired accuracy. Returns the first acceptable
|
||||
* combination in order of increasing computational load.
|
||||
*/
|
||||
function findParams(infNorm, eps) {
|
||||
var maxSearchSize = 30;
|
||||
for(var k=0; k<maxSearchSize; k++) {
|
||||
for(var q=0; q<=k; q++) {
|
||||
var j = k - q;
|
||||
if(errorEstimate(infNorm, q, j) < eps) {
|
||||
return {q: q, j: j};
|
||||
}
|
||||
}
|
||||
}
|
||||
throw new Error("Could not find acceptable parameters to compute the matrix exponential (try increasing maxSearchSize in expm.js)");
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the estimated error of the Pade approximant for the given
|
||||
* parameters.
|
||||
*/
|
||||
function errorEstimate(infNorm, q, j) {
|
||||
|
||||
var qfac = 1;
|
||||
for(var i=2; i<=q; i++) {
|
||||
qfac *= i;
|
||||
}
|
||||
var twoqfac = qfac;
|
||||
for(var i=q+1; i<=2*q; i++) {
|
||||
twoqfac *= i;
|
||||
}
|
||||
var twoqp1fac = twoqfac * (2*q+1);
|
||||
|
||||
return 8.0 *
|
||||
Math.pow(infNorm / Math.pow(2, j), 2*q) *
|
||||
qfac*qfac / (twoqfac*twoqp1fac);
|
||||
}
|
||||
|
||||
expm.toTex = {1: '\\exp\\left(${args[0]}\\right)'};
|
||||
|
||||
return expm;
|
||||
}
|
||||
|
||||
exports.name = 'expm';
|
||||
exports.factory = factory;
|
||||
@ -6,6 +6,7 @@ module.exports = [
|
||||
require('./diag'),
|
||||
require('./dot'),
|
||||
require('./eye'),
|
||||
require('./expm'),
|
||||
require('./filter'),
|
||||
require('./flatten'),
|
||||
require('./forEach'),
|
||||
|
||||
@ -1,3 +1,3 @@
|
||||
module.exports = '4.2.1';
|
||||
module.exports = '4.2.2';
|
||||
// Note: This file is automatically generated when building math.js.
|
||||
// Changes made in this file will be overwritten.
|
||||
|
||||
20
package-lock.json
generated
20
package-lock.json
generated
@ -1,6 +1,6 @@
|
||||
{
|
||||
"name": "mathjs",
|
||||
"version": "4.2.1",
|
||||
"version": "4.2.2",
|
||||
"lockfileVersion": 1,
|
||||
"requires": true,
|
||||
"dependencies": {
|
||||
@ -1093,9 +1093,9 @@
|
||||
"dev": true
|
||||
},
|
||||
"complex.js": {
|
||||
"version": "2.0.4",
|
||||
"resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.0.4.tgz",
|
||||
"integrity": "sha512-Syl95HpxUTS0QjwNxencZsKukgh1zdS9uXeXX2Us0pHaqBR6kiZZi0AkZ9VpZFwHJyVIUVzI4EumjWdXP3fy6w=="
|
||||
"version": "2.0.10",
|
||||
"resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.0.10.tgz",
|
||||
"integrity": "sha512-PsT3WqpnTjS2ijoMM8XodCi/BYO04vkS8kBg1YXcqf5KcnKVV6uXUc1eeLHhBksj8i7Vu9iQF2/6ZG9gqI6CPQ=="
|
||||
},
|
||||
"component-bind": {
|
||||
"version": "1.0.0",
|
||||
@ -1856,9 +1856,9 @@
|
||||
"dev": true
|
||||
},
|
||||
"escape-latex": {
|
||||
"version": "1.0.0",
|
||||
"resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.0.0.tgz",
|
||||
"integrity": "sha512-oogO9Cg3n/4nspF34CTfXFymgI79skca66DebIIQgxVy6qRVqczl/ji2YGAqhFCzpD/oAt/fCWF4qlhMAfda+g=="
|
||||
"version": "1.0.3",
|
||||
"resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.0.3.tgz",
|
||||
"integrity": "sha512-GfKaG/7FOKdIdciylIzgaShBTPjdGQ5LJ2EcKLKXPLpcMO1MvCEVotkhydEShwCINRacZr2r3fk5A1PwZ4e5sA=="
|
||||
},
|
||||
"escape-string-regexp": {
|
||||
"version": "1.0.5",
|
||||
@ -2481,9 +2481,9 @@
|
||||
}
|
||||
},
|
||||
"fraction.js": {
|
||||
"version": "4.0.4",
|
||||
"resolved": "https://registry.npmjs.org/fraction.js/-/fraction.js-4.0.4.tgz",
|
||||
"integrity": "sha512-aK/oGatyYLTtXRHjfEsytX5fieeR5H4s8sLorzcT12taFS+dbMZejnvm9gRa8mZAPwci24ucjq9epDyaq5u8Iw=="
|
||||
"version": "4.0.8",
|
||||
"resolved": "https://registry.npmjs.org/fraction.js/-/fraction.js-4.0.8.tgz",
|
||||
"integrity": "sha512-8Jx2AkFIFQtFaF8wP7yUIW+lnCgzPbxsholryMZ+oPK6kKjY/nUrvMKtq1+A8aSAeFau7+G/zfO8aGk2Aw1wCA=="
|
||||
},
|
||||
"fragment-cache": {
|
||||
"version": "0.2.1",
|
||||
|
||||
11
package.json
11
package.json
@ -1,6 +1,6 @@
|
||||
{
|
||||
"name": "mathjs",
|
||||
"version": "4.2.1",
|
||||
"version": "4.2.2",
|
||||
"description": "Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with different data types like numbers, big numbers, complex numbers, fractions, units, and matrices.",
|
||||
"author": "Jos de Jong <wjosdejong@gmail.com> (https://github.com/josdejong)",
|
||||
"contributors": [
|
||||
@ -33,6 +33,7 @@
|
||||
"Huseyn Guliyev (https://github.com/husayt)",
|
||||
"Ivan Vergiliev (IvanVergiliev)",
|
||||
"jean-emmanuel (https://github.com/jean-emmanuel)",
|
||||
"Jack Schmidt (https://github.com/jackschmidt)",
|
||||
"Jim Garrison (https://github.com/garrison)",
|
||||
"Joel Hoover (https://github.com/joelhoover)",
|
||||
"Karl Lew (https://github.com/firepick1)",
|
||||
@ -93,10 +94,10 @@
|
||||
"unit"
|
||||
],
|
||||
"dependencies": {
|
||||
"complex.js": "2.0.4",
|
||||
"complex.js": "2.0.10",
|
||||
"decimal.js": "9.0.1",
|
||||
"escape-latex": "1.0.0",
|
||||
"fraction.js": "4.0.4",
|
||||
"escape-latex": "1.0.3",
|
||||
"fraction.js": "4.0.8",
|
||||
"javascript-natural-sort": "0.7.1",
|
||||
"seed-random": "2.2.0",
|
||||
"tiny-emitter": "2.0.2",
|
||||
@ -138,7 +139,7 @@
|
||||
"build": "gulp",
|
||||
"watch": "gulp watch",
|
||||
"docs": "gulp docs",
|
||||
"test": "mocha test --recursive",
|
||||
"test": "mocha test node-test --recursive",
|
||||
"karma": "karma start",
|
||||
"coverage": "istanbul cover _mocha -- test --recursive; echo \"\nCoverage report is available at ./coverage/lcov-report/index.html\"",
|
||||
"prepublishOnly": "npm run build && npm test"
|
||||
|
||||
@ -60,10 +60,10 @@ describe('divide', function() {
|
||||
approx.deepEqual(divide(complex('2+3i'), complex('4i')), complex('0.75 - 0.5i'));
|
||||
approx.deepEqual(divide(complex('2i'), complex('4i')), complex('0.5'));
|
||||
approx.deepEqual(divide(4, complex('1+2i')), complex('0.8 - 1.6i'));
|
||||
approx.deepEqual(divide(math.i, 0), complex(0, Infinity));
|
||||
approx.deepEqual(divide(complex(0,1), 0), complex(0, Infinity));
|
||||
approx.deepEqual(divide(complex(1,0), 0), complex(Infinity, 0));
|
||||
approx.deepEqual(divide(complex(0,1), complex(0,0)), complex(0, Infinity));
|
||||
approx.deepEqual(divide(math.i, 0), complex(Infinity, Infinity));
|
||||
approx.deepEqual(divide(complex(0,1), 0), complex(Infinity, Infinity));
|
||||
approx.deepEqual(divide(complex(1,0), 0), complex(Infinity, Infinity));
|
||||
approx.deepEqual(divide(complex(0,1), complex(0,0)), complex(Infinity, Infinity));
|
||||
approx.deepEqual(divide(complex(1,1), complex(0,0)), complex(Infinity, Infinity));
|
||||
approx.deepEqual(divide(complex(1,-1), complex(0,0)), complex(Infinity, -Infinity));
|
||||
approx.deepEqual(divide(complex(-1,1), complex(0,0)), complex(-Infinity, Infinity));
|
||||
|
||||
@ -81,8 +81,8 @@ describe('multiply', function() {
|
||||
approx.deepEqual(multiply(complex(2, 3), 0), complex(0, 0));
|
||||
approx.deepEqual(multiply(complex(0, 3), complex(0, -4)), complex(12, 0));
|
||||
approx.deepEqual(multiply(multiply(3, i), multiply(-4, i)), complex(12, 0));
|
||||
approx.deepEqual(multiply(math.i, Infinity), complex(NaN, Infinity));
|
||||
approx.deepEqual(multiply(Infinity, math.i), complex(NaN, Infinity));
|
||||
approx.deepEqual(multiply(math.i, Infinity), complex(Infinity, Infinity));
|
||||
approx.deepEqual(multiply(Infinity, math.i), complex(Infinity, Infinity));
|
||||
|
||||
approx.deepEqual(multiply(complex(2,0), complex(0,2)), complex(0, 4));
|
||||
approx.deepEqual(multiply(complex(0,2), complex(0,2)), -4);
|
||||
|
||||
@ -29,6 +29,7 @@ describe('norm', function () {
|
||||
assert.equal(math.norm(math.complex(3, -4)), 5);
|
||||
assert.equal(math.norm(math.complex(1e200, -4e200)), 4.12310562561766e+200);
|
||||
assert.equal(math.norm(math.complex(-4e200, 1e200)), 4.12310562561766e+200);
|
||||
assert.equal(math.norm(math.matrix([[math.complex(3, -4)]]),'fro'), 5);
|
||||
});
|
||||
|
||||
it('should return the norm of a vector', function () {
|
||||
|
||||
95
test/function/matrix/expm.test.js
Normal file
95
test/function/matrix/expm.test.js
Normal file
@ -0,0 +1,95 @@
|
||||
// test expm
|
||||
var assert = require('assert'),
|
||||
approx = require('../../../tools/approx');
|
||||
math = require('../../../index'),
|
||||
expm = math.expm;
|
||||
|
||||
describe('expm', function() {
|
||||
|
||||
it('should only accept a square matrix', function() {
|
||||
assert.throws(function() { expm(5); }, /Unexpected type/);
|
||||
assert.throws(function() { expm([1,2]); }, /Matrix must be square/);
|
||||
assert.throws(function() { expm([[1,2]]); }, /Matrix must be square/);
|
||||
assert.throws(function() { expm([[1,2,3],[4,5,6]]); }, /Matrix must be square/);
|
||||
});
|
||||
|
||||
it('should compute the exponential of a matrix', function() {
|
||||
|
||||
// Trivial example
|
||||
approx.deepEqual(expm(
|
||||
[[1,0],
|
||||
[0,1]]
|
||||
),
|
||||
math.matrix(
|
||||
[[2.718281828, 0 ],
|
||||
[0, 2.718281828]]
|
||||
));
|
||||
|
||||
// Example given in the Moler and Van Loan paper
|
||||
approx.deepEqual(expm(
|
||||
[[-49, 24],
|
||||
[-64, 31]]
|
||||
),
|
||||
math.matrix(
|
||||
[[-0.735759,0.551819],
|
||||
[-1.471518,1.103638]]
|
||||
));
|
||||
|
||||
// Another example from the same paper
|
||||
approx.deepEqual(expm(
|
||||
[[0, 6, 0, 0],
|
||||
[0, 0, 6, 0],
|
||||
[0, 0, 0, 6],
|
||||
[0, 0, 0, 0]]
|
||||
),
|
||||
math.matrix(
|
||||
[[1, 6, 18, 36],
|
||||
[0, 1, 6, 18],
|
||||
[0, 0, 1, 6],
|
||||
[0, 0, 0, 1]]
|
||||
));
|
||||
|
||||
// And another
|
||||
approx.deepEqual(expm(
|
||||
[[1,1],
|
||||
[0,1]]
|
||||
),
|
||||
math.matrix(
|
||||
[[2.718282, 2.718282 ],
|
||||
[0, 2.718282]]
|
||||
));
|
||||
|
||||
// And another
|
||||
approx.deepEqual(expm(
|
||||
[[1+1e-5, 1],
|
||||
[0, 1-1e-5]]
|
||||
),
|
||||
math.matrix(
|
||||
[[2.718309, 2.718282 ],
|
||||
[0, 2.718255]]
|
||||
));
|
||||
});
|
||||
|
||||
it('should work on SparseMatrix', function() {
|
||||
approx.deepEqual(expm(
|
||||
math.sparse(
|
||||
[[0, 6, 0, 0],
|
||||
[0, 0, 6, 0],
|
||||
[0, 0, 0, 6],
|
||||
[0, 0, 0, 0]]
|
||||
)
|
||||
),
|
||||
math.sparse(
|
||||
[[1, 6, 18, 36],
|
||||
[0, 1, 6, 18],
|
||||
[0, 0, 1, 6],
|
||||
[0, 0, 0, 1]]
|
||||
));
|
||||
|
||||
});
|
||||
|
||||
it('should LaTeX transpose', function () {
|
||||
var expression = math.parse('expm([[1,2],[3,4]])');
|
||||
assert.equal(expression.toTex(), '\\exp\\left(\\begin{bmatrix}1&2\\\\3&4\\\\\\end{bmatrix}\\right)');
|
||||
});
|
||||
});
|
||||
@ -84,7 +84,7 @@ describe('asech', function() {
|
||||
approx.deepEqual(asech(complex('2')), complex(0, pi / 3));
|
||||
assert.deepEqual(asech(complex('1')), complex(0, 0));
|
||||
approx.deepEqual(asech(complex('0.5')), complex(1.3169578969248, 0));
|
||||
assert.deepEqual(asech(complex('0')), complex(Infinity, 0));
|
||||
assert.deepEqual(asech(complex('0')), complex(Infinity, Infinity));
|
||||
approx.deepEqual(asech(complex('-0.5')), complex(1.3169578969248, pi));
|
||||
approx.deepEqual(asech(complex('-1')), complex(0, pi));
|
||||
});
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user