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mathjs.js
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mathjs.js
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/**
* 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 0.25.0
* @date 2014-07-01
*
* @license
* Copyright (C) 2013-2014 Jos de Jong <[email protected]>
*
* 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.
*/
(function webpackUniversalModuleDefinition(root, factory) {
if(typeof exports === 'object' && typeof module === 'object')
module.exports = factory();
else if(typeof define === 'function' && define.amd)
define(factory);
else if(typeof exports === 'object')
exports["math"] = factory();
else
root["math"] = factory();
})(this, function() {
return /******/ (function(modules) { // webpackBootstrap
/******/ // The module cache
/******/ var installedModules = {};
/******/
/******/ // The require function
/******/ function __webpack_require__(moduleId) {
/******/
/******/ // Check if module is in cache
/******/ if(installedModules[moduleId])
/******/ return installedModules[moduleId].exports;
/******/
/******/ // Create a new module (and put it into the cache)
/******/ var module = installedModules[moduleId] = {
/******/ exports: {},
/******/ id: moduleId,
/******/ loaded: false
/******/ };
/******/
/******/ // Execute the module function
/******/ modules[moduleId].call(module.exports, module, module.exports, __webpack_require__);
/******/
/******/ // Flag the module as loaded
/******/ module.loaded = true;
/******/
/******/ // Return the exports of the module
/******/ return module.exports;
/******/ }
/******/
/******/
/******/ // expose the modules object (__webpack_modules__)
/******/ __webpack_require__.m = modules;
/******/
/******/ // expose the module cache
/******/ __webpack_require__.c = installedModules;
/******/
/******/ // __webpack_public_path__
/******/ __webpack_require__.p = "";
/******/
/******/ // Load entry module and return exports
/******/ return __webpack_require__(0);
/******/ })
/************************************************************************/
/******/ ([
/* 0 */
/***/ function(module, exports, __webpack_require__) {
module.exports = __webpack_require__(1);
/***/ },
/* 1 */
/***/ function(module, exports, __webpack_require__) {
var object = __webpack_require__(3);
/**
* math.js factory function.
*
* @param {Object} [config] Available configuration options:
* {String} matrix
* A string 'matrix' (default) or 'array'.
* {String} number
* A string 'number' (default) or 'bignumber'
* {Number} precision
* The number of significant digits for BigNumbers.
* Not applicable for Numbers.
*/
function factory (config) {
// simple test for ES5 support
if (typeof Object.create !== 'function') {
throw new Error('ES5 not supported by this JavaScript engine. ' +
'Please load the es5-shim and es5-sham library for compatibility.');
}
// create namespace (and factory for a new instance)
function math (config) {
return factory(config);
}
// create configuration options. These are private
var _config = {
// type of default matrix output. Choose 'matrix' (default) or 'array'
matrix: 'matrix',
// type of default number output. Choose 'number' (default) or 'bignumber'
number: 'number',
// number of significant digits in BigNumbers
precision: 64,
// minimum relative difference between two compared values,
// used by all comparison functions
epsilon: 1e-14
};
/**
* Set configuration options for math.js, and get current options
* @param {Object} [options] Available options:
* {String} matrix
* A string 'matrix' (default) or 'array'.
* {String} number
* A string 'number' (default) or 'bignumber'
* {Number} precision
* The number of significant digits for BigNumbers.
* Not applicable for Numbers.
* @return {Object} Returns the current configuration
*/
math.config = function config(options) {
if (options) {
// merge options
object.deepExtend(_config, options);
if (options.precision) {
math.type.BigNumber.config({
precision: options.precision
});
}
// TODO: remove deprecated setting some day (deprecated since version 0.17.0)
if (options.number && options.number.defaultType) {
throw new Error('setting `number.defaultType` is deprecated. Use `number` instead.')
}
// TODO: remove deprecated setting some day (deprecated since version 0.17.0)
if (options.number && options.number.precision) {
throw new Error('setting `number.precision` is deprecated. Use `precision` instead.')
}
// TODO: remove deprecated setting some day (deprecated since version 0.17.0)
if (options.matrix && options.matrix.defaultType) {
throw new Error('setting `matrix.defaultType` is deprecated. Use `matrix` instead.')
}
// TODO: remove deprecated setting some day (deprecated since version 0.15.0)
if (options.matrix && options.matrix['default']) {
throw new Error('setting `matrix.default` is deprecated. Use `matrix` instead.')
}
// TODO: remove deprecated setting some day (deprecated since version 0.20.0)
if (options.decimals) {
throw new Error('setting `decimals` is deprecated. Use `precision` instead.')
}
}
// return a clone of the settings
return object.clone(_config);
};
// create a new BigNumber factory for this instance of math.js
var BigNumber = __webpack_require__(123).constructor();
// extend BigNumber with a function clone
if (typeof BigNumber.prototype.clone !== 'function') {
/**
* Clone a bignumber
* @return {BigNumber} clone
*/
BigNumber.prototype.clone = function clone() {
return new BigNumber(this);
};
}
// extend BigNumber with a function convert
if (typeof BigNumber.convert !== 'function') {
/**
* Try to convert a Number in to a BigNumber.
* If the number has 15 or mor significant digits, the Number cannot be
* converted to BigNumber and will return the original number.
* @param {Number} number
* @return {BigNumber | Number} bignumber
*/
BigNumber.convert = function convert(number) {
if (digits(number) > 15) {
return number;
}
else {
return new BigNumber(number);
}
};
}
else {
throw new Error('Cannot add function convert to BigNumber: function already exists');
}
// errors
math.error = __webpack_require__(4);
// types (Matrix, Complex, Unit, ...)
math.type = {};
math.type.Complex = __webpack_require__(5);
math.type.Range = __webpack_require__(6);
math.type.Index = __webpack_require__(7);
math.type.Matrix = __webpack_require__(8);
math.type.Unit = __webpack_require__(9);
math.type.Help = __webpack_require__(10);
math.type.BigNumber = BigNumber;
math.collection = __webpack_require__(11);
// expression (parse, Parser, nodes, docs)
math.expression = {};
math.expression.node = __webpack_require__(14);
math.expression.parse = __webpack_require__(12);
math.expression.Parser = __webpack_require__(13);
math.expression.docs = __webpack_require__(15);
// expression parser
__webpack_require__(17)(math, _config);
__webpack_require__(18)(math, _config);
__webpack_require__(19)(math, _config);
__webpack_require__(20)(math, _config);
// functions - arithmetic
__webpack_require__(21)(math, _config);
__webpack_require__(22)(math, _config);
__webpack_require__(23)(math, _config);
__webpack_require__(24)(math, _config);
__webpack_require__(25)(math, _config);
__webpack_require__(26)(math, _config);
__webpack_require__(27)(math, _config);
__webpack_require__(28)(math, _config);
__webpack_require__(29)(math, _config);
__webpack_require__(30)(math, _config);
__webpack_require__(31)(math, _config);
__webpack_require__(32)(math, _config);
__webpack_require__(33)(math, _config);
__webpack_require__(34)(math, _config);
__webpack_require__(35)(math, _config);
__webpack_require__(36)(math, _config);
__webpack_require__(37)(math, _config);
__webpack_require__(38)(math, _config);
__webpack_require__(39)(math, _config);
__webpack_require__(40)(math, _config);
__webpack_require__(41)(math, _config);
__webpack_require__(42)(math, _config);
__webpack_require__(43)(math, _config);
__webpack_require__(44)(math, _config);
__webpack_require__(45)(math, _config);
__webpack_require__(46)(math, _config);
__webpack_require__(47)(math, _config);
// functions - comparison
__webpack_require__(48)(math, _config);
__webpack_require__(49)(math, _config);
__webpack_require__(50)(math, _config);
__webpack_require__(51)(math, _config);
__webpack_require__(52)(math, _config);
__webpack_require__(53)(math, _config);
__webpack_require__(54)(math, _config);
__webpack_require__(55)(math, _config);
// functions - complex
__webpack_require__(56)(math, _config);
__webpack_require__(57)(math, _config);
__webpack_require__(58)(math, _config);
__webpack_require__(59)(math, _config);
// functions - construction
__webpack_require__(60)(math, _config);
__webpack_require__(61)(math, _config);
__webpack_require__(62)(math, _config);
__webpack_require__(63)(math, _config);
__webpack_require__(64)(math, _config);
__webpack_require__(65)(math, _config);
__webpack_require__(66)(math, _config);
__webpack_require__(67)(math, _config);
__webpack_require__(68)(math, _config);
__webpack_require__(69)(math, _config);
// functions - matrix
__webpack_require__(70)(math, _config);
__webpack_require__(71)(math, _config);
__webpack_require__(72)(math, _config);
__webpack_require__(73)(math, _config);
__webpack_require__(74)(math, _config);
__webpack_require__(75)(math, _config);
__webpack_require__(76)(math, _config);
__webpack_require__(77)(math, _config);
__webpack_require__(78)(math, _config);
__webpack_require__(79)(math, _config);
__webpack_require__(80)(math, _config);
__webpack_require__(81)(math, _config);
__webpack_require__(82)(math, _config);
// functions - probability
__webpack_require__(83)(math, _config);
__webpack_require__(84)(math, _config);
__webpack_require__(85)(math, _config);
__webpack_require__(86)(math, _config);
__webpack_require__(87)(math, _config);
__webpack_require__(88)(math, _config);
__webpack_require__(89)(math, _config);
// functions - statistics
__webpack_require__(90)(math, _config);
__webpack_require__(91)(math, _config);
__webpack_require__(92)(math, _config);
__webpack_require__(93)(math, _config);
__webpack_require__(94)(math, _config);
__webpack_require__(95)(math, _config);
__webpack_require__(96)(math, _config);
__webpack_require__(97)(math, _config);
// functions - trigonometry
__webpack_require__(98)(math, _config);
__webpack_require__(99)(math, _config);
__webpack_require__(100)(math, _config);
__webpack_require__(101)(math, _config);
__webpack_require__(102)(math, _config);
__webpack_require__(103)(math, _config);
__webpack_require__(104)(math, _config);
__webpack_require__(105)(math, _config);
__webpack_require__(106)(math, _config);
__webpack_require__(107)(math, _config);
__webpack_require__(108)(math, _config);
__webpack_require__(109)(math, _config);
__webpack_require__(110)(math, _config);
__webpack_require__(111)(math, _config);
__webpack_require__(112)(math, _config);
__webpack_require__(113)(math, _config);
// functions - units
__webpack_require__(114)(math, _config);
// functions - utils
__webpack_require__(115)(math, _config);
__webpack_require__(116)(math, _config);
__webpack_require__(117)(math, _config);
__webpack_require__(118)(math, _config);
__webpack_require__(119)(math, _config);
__webpack_require__(120)(math, _config);
__webpack_require__(121)(math, _config);
// TODO: deprecated since version 0.25.0, remove some day.
math.ifElse = function () {
throw new Error('Function ifElse is deprecated. Use the conditional operator instead.');
};
// constants
__webpack_require__(2)(math, _config);
// selector (we initialize after all functions are loaded)
math.chaining = {};
math.chaining.Selector = __webpack_require__(16)(math, _config);
// apply provided configuration options
math.config(_config); // apply the default options
math.config(config); // apply custom options
// return the new instance
return math;
}
// create a default instance of math.js
var math = factory();
if (typeof window !== 'undefined') {
window.mathjs = math; // TODO: deprecate the mathjs namespace some day (replaced with 'math' since version 0.25.0)
}
// export the default instance
module.exports = factory();
/***/ },
/* 2 */
/***/ function(module, exports, __webpack_require__) {
module.exports = function (math) {
var Complex = __webpack_require__(5);
math.version = __webpack_require__(122);
math.pi = Math.PI;
math.e = Math.E;
math.tau = Math.PI * 2;
math.phi = 1.61803398874989484820458683436563811772030917980576286213545; // golden ratio, (1+sqrt(5))/2
math.i = new Complex(0, 1);
math['Infinity'] = Infinity;
math['NaN'] = NaN;
math['true'] = true;
math['false'] = false;
math['null'] = null;
// uppercase constants (for compatibility with built-in Math)
math.E = Math.E;
math.LN2 = Math.LN2;
math.LN10 = Math.LN10;
math.LOG2E = Math.LOG2E;
math.LOG10E = Math.LOG10E;
math.PI = Math.PI;
math.SQRT1_2 = Math.SQRT1_2;
math.SQRT2 = Math.SQRT2;
};
/***/ },
/* 3 */
/***/ function(module, exports, __webpack_require__) {
/**
* Clone an object
*
* clone(x)
*
* Can clone any primitive type, array, and object.
* If x has a function clone, this function will be invoked to clone the object.
*
* @param {*} x
* @return {*} clone
*/
exports.clone = function clone(x) {
var type = typeof x;
// immutable primitive types
if (type === 'number' || type === 'string' || type === 'boolean' ||
x === null || x === undefined) {
return x;
}
// use clone function of the object when available
if (typeof x.clone === 'function') {
return x.clone();
}
// array
if (Array.isArray(x)) {
return x.map(function (value) {
return clone(value);
});
}
if (x instanceof Number) return new Number(x.valueOf());
if (x instanceof String) return new String(x.valueOf());
if (x instanceof Boolean) return new Boolean(x.valueOf());
if (x instanceof Date) return new Date(x.valueOf());
if (x instanceof RegExp) throw new TypeError('Cannot clone ' + x); // TODO: clone a RegExp
// object
var m = {};
for (var key in x) {
if (x.hasOwnProperty(key)) {
m[key] = clone(x[key]);
}
}
return m;
};
/**
* Extend object a with the properties of object b
* @param {Object} a
* @param {Object} b
* @return {Object} a
*/
exports.extend = function extend (a, b) {
for (var prop in b) {
if (b.hasOwnProperty(prop)) {
a[prop] = b[prop];
}
}
return a;
};
/**
* Deep extend an object a with the properties of object b
* @param {Object} a
* @param {Object} b
* @returns {Object}
*/
exports.deepExtend = function deepExtend (a, b) {
// TODO: add support for Arrays to deepExtend
if (Array.isArray(b)) {
throw new TypeError('Arrays are not supported by deepExtend');
}
for (var prop in b) {
if (b.hasOwnProperty(prop)) {
if (b[prop] && b[prop].constructor === Object) {
if (a[prop] === undefined) {
a[prop] = {};
}
if (a[prop].constructor === Object) {
deepExtend(a[prop], b[prop]);
}
else {
a[prop] = b[prop];
}
} else if (Array.isArray(b[prop])) {
throw new TypeError('Arrays are not supported by deepExtend');
} else {
a[prop] = b[prop];
}
}
}
return a;
};
/**
* Deep test equality of all fields in two pairs of arrays or objects.
* @param {Array | Object} a
* @param {Array | Object} b
* @returns {boolean}
*/
exports.deepEqual = function deepEqual (a, b) {
var prop, i, len;
if (Array.isArray(a)) {
if (!Array.isArray(b)) {
return false;
}
if (a.length != b.length) {
return false;
}
for (i = 0, len = a.length; i < len; i++) {
if (!exports.deepEqual(a[i], b[i])) {
return false;
}
}
return true;
}
else if (a instanceof Object) {
if (Array.isArray(b) || !(b instanceof Object)) {
return false;
}
for (prop in a) {
//noinspection JSUnfilteredForInLoop
if (!exports.deepEqual(a[prop], b[prop])) {
return false;
}
}
for (prop in b) {
//noinspection JSUnfilteredForInLoop
if (!exports.deepEqual(a[prop], b[prop])) {
return false;
}
}
return true;
}
else {
return (typeof a === typeof b) && (a == b);
}
};
/***/ },
/* 4 */
/***/ function(module, exports, __webpack_require__) {
exports.ArgumentsError = __webpack_require__(124);
exports.DimensionError = __webpack_require__(125);
exports.IndexError = __webpack_require__(126);
exports.UnsupportedTypeError = __webpack_require__(127);
// TODO: implement an InvalidValueError?
/***/ },
/* 5 */
/***/ function(module, exports, __webpack_require__) {
var util = __webpack_require__(128),
Unit = __webpack_require__(9),
number = util.number,
isNumber = util.number.isNumber,
isUnit = Unit.isUnit,
isString = util.string.isString;
/**
* @constructor Complex
*
* A complex value can be constructed in the following ways:
* var a = new Complex();
* var b = new Complex(re, im);
* var c = Complex.parse(str);
*
* Example usage:
* var a = new Complex(3, -4); // 3 - 4i
* a.re = 5; // a = 5 - 4i
* var i = a.im; // -4;
* var b = Complex.parse('2 + 6i'); // 2 + 6i
* var c = new Complex(); // 0 + 0i
* var d = math.add(a, b); // 5 + 2i
*
* @param {Number} re The real part of the complex value
* @param {Number} [im] The imaginary part of the complex value
*/
function Complex(re, im) {
if (!(this instanceof Complex)) {
throw new SyntaxError('Constructor must be called with the new operator');
}
switch (arguments.length) {
case 0:
this.re = 0;
this.im = 0;
break;
case 1:
var arg = arguments[0];
if (typeof arg === 'object') {
if('re' in arg && 'im' in arg) {
var construct = new Complex(arg.re, arg.im); // pass on input validation
this.re = construct.re;
this.im = construct.im;
break;
} else if ('r' in arg && 'phi' in arg) {
var construct = Complex.fromPolar(arg.r, arg.phi);
this.re = construct.re;
this.im = construct.im;
break;
}
}
throw new SyntaxError('Object with the re and im or r and phi properties expected.');
case 2:
if (!isNumber(re) || !isNumber(im)) {
throw new TypeError('Two numbers expected in Complex constructor');
}
this.re = re;
this.im = im;
break;
default:
throw new SyntaxError('One, two or three arguments expected in Complex constructor');
}
}
/**
* Test whether value is a Complex value
* @param {*} value
* @return {Boolean} isComplex
*/
Complex.isComplex = function (value) {
return (value instanceof Complex);
};
// private variables and functions for the parser
var text, index, c;
function skipWhitespace() {
while (c == ' ' || c == '\t') {
next();
}
}
function isDigitDot (c) {
return ((c >= '0' && c <= '9') || c == '.');
}
function isDigit (c) {
return ((c >= '0' && c <= '9'));
}
function next() {
index++;
c = text.charAt(index);
}
function revert(oldIndex) {
index = oldIndex;
c = text.charAt(index);
}
function parseNumber () {
var number = '';
var oldIndex;
oldIndex = index;
if (c == '+') {
next();
}
else if (c == '-') {
number += c;
next();
}
if (!isDigitDot(c)) {
// a + or - must be followed by a digit
revert(oldIndex);
return null;
}
// get number, can have a single dot
if (c == '.') {
number += c;
next();
if (!isDigit(c)) {
// this is no legal number, it is just a dot
revert(oldIndex);
return null;
}
}
else {
while (isDigit(c)) {
number += c;
next();
}
if (c == '.') {
number += c;
next();
}
}
while (isDigit(c)) {
number += c;
next();
}
// check for exponential notation like "2.3e-4" or "1.23e50"
if (c == 'E' || c == 'e') {
number += c;
next();
if (c == '+' || c == '-') {
number += c;
next();
}
// Scientific notation MUST be followed by an exponent
if (!isDigit(c)) {
// this is no legal number, exponent is missing.
revert(oldIndex);
return null;
}
while (isDigit(c)) {
number += c;
next();
}
}
return number;
}
function parseComplex () {
// check for 'i', '-i', '+i'
var cnext = text.charAt(index + 1);
if (c == 'I' || c == 'i') {
next();
return '1';
}
else if ((c == '+' || c == '-') && (cnext == 'I' || cnext == 'i')) {
var number = (c == '+') ? '1' : '-1';
next();
next();
return number;
}
return null;
}
/**
* Parse a complex number from a string. For example Complex.parse("2 + 3i")
* will return a Complex value where re = 2, im = 3.
* Returns null if provided string does not contain a valid complex number.
* @param {String} str
* @returns {Complex | null} complex
*/
Complex.parse = function (str) {
text = str;
index = -1;
c = '';
if (!isString(text)) {
return null;
}
next();
skipWhitespace();
var first = parseNumber();
if (first) {
if (c == 'I' || c == 'i') {
// pure imaginary number
next();
skipWhitespace();
if (c) {
// garbage at the end. not good.
return null;
}
return new Complex(0, Number(first));
}
else {
// complex and real part
skipWhitespace();
var separator = c;
if (separator != '+' && separator != '-') {
// pure real number
skipWhitespace();
if (c) {
// garbage at the end. not good.
return null;
}
return new Complex(Number(first), 0);
}
else {
// complex and real part
next();
skipWhitespace();
var second = parseNumber();
if (second) {
if (c != 'I' && c != 'i') {
// 'i' missing at the end of the complex number
return null;
}
next();
}
else {
second = parseComplex();
if (!second) {
// imaginary number missing after separator
return null;
}
}
if (separator == '-') {
if (second[0] == '-') {
second = '+' + second.substring(1);
}
else {
second = '-' + second;
}
}
next();
skipWhitespace();
if (c) {
// garbage at the end. not good.
return null;
}
return new Complex(Number(first), Number(second));
}
}
}
else {
// check for 'i', '-i', '+i'
first = parseComplex();
if (first) {
skipWhitespace();
if (c) {
// garbage at the end. not good.
return null;
}
return new Complex(0, Number(first));
}
}
return null;
};
/**
* Create a complex number from polar coordinates
*
* Usage:
*
* Complex.fromPolar(r: Number, phi: Number) : Complex
* Complex.fromPolar({r: Number, phi: Number}) : Complex
*
* @param {*} args...
* @return {Complex}
*/
Complex.fromPolar = function (args) {
switch (arguments.length) {
case 1:
var arg = arguments[0];
if(typeof arg === 'object') {
return Complex.fromPolar(arg.r, arg.phi);
}
throw new TypeError('Input has to be an object with r and phi keys.');
case 2:
var r = arguments[0],
phi = arguments[1];
if(isNumber(r)) {
if (isUnit(phi) && phi.hasBase(Unit.BASE_UNITS.ANGLE)) {
// convert unit to a number in radians
phi = phi.toNumber('rad');
}
if(isNumber(phi)) {
return new Complex(r * Math.cos(phi), r * Math.sin(phi));
}
throw new TypeError('Phi is not a number nor an angle unit.');
} else {
throw new TypeError('Radius r is not a number.');
}
default:
throw new SyntaxError('Wrong number of arguments in function fromPolar');
}
};
/*
* Return the value of the complex number in polar notation
* The angle phi will be set in the interval of [-pi, pi].
* @return {{r: number, phi: number}} Returns and object with properties r and phi.
*/
Complex.prototype.toPolar = function() {
return {
r: Math.sqrt(this.re * this.re + this.im * this.im),
phi: Math.atan2(this.im, this.re)
};
};
/**
* Create a copy of the complex value
* @return {Complex} clone
*/
Complex.prototype.clone = function () {
return new Complex(this.re, this.im);
};
/**
* Test whether this complex number equals an other complex value.
* Two complex numbers are equal when both their real and imaginary parts
* are equal.
* @param {Complex} other
* @return {boolean} isEqual
*/
Complex.prototype.equals = function (other) {
return (this.re === other.re) && (this.im === other.im);
};
/**
* Get a string representation of the complex number,
* with optional formatting options.
* @param {Object | Number | Function} [options] Formatting options. See
* lib/util/number:format for a
* description of the available
* options.
* @return {String} str
*/
Complex.prototype.format = function (options) {
var str = '',
strRe = number.format(this.re, options),
strIm = number.format(this.im, options);
if (this.im == 0) {
// real value
str = strRe;
}
else if (this.re == 0) {
// purely complex value
if (this.im == 1) {
str = 'i';
}
else if (this.im == -1) {
str = '-i';
}
else {
str = strIm + 'i';
}
}
else {
// complex value