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2019-05-22 14:41:40 -04:00
/**
* 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 5.10.3
* @date 2019-05-18
*
* @license
* Copyright (C) 2013-2019 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
*
* https://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(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t():"function"==typeof define&&define.amd?define([],t):"object"==typeof exports?exports.math=t():e.math=t()}(this,function(){return n={},i.m=r=[function(e,t){"use strict";t.name="matrix",t.factory=function(n,e,t,r){var i=r("matrix",{"":function(){return o([])},string:function(e){return o([],e)},"string, string":function(e,t){return o([],e,t)},Array:function(e){return o(e)},Matrix:function(e){return o(e,e.storage())},"Array | Matrix, string":o,"Array | Matrix, string, string":o});return i.toTex={0:"\\begin{bmatrix}\\end{bmatrix}",1:"\\left(${args[0]}\\right)",2:"\\left(${args[0]}\\right)"},i;function o(e,t,r){return new(n.Matrix.storage(t||"default"))(e,r)}}},function(e){"use strict";e.exports=function t(e,r,n){return e&&"function"==typeof e.map?e.map(function(e){return t(e,r,n)}):r(e)}},function(e,t,r){"use strict";r.r(t),r.d(t,"size",function(){return l}),r.d(t,"validate",function(){return p}),r.d(t,"validateIndex",function(){return m}),r.d(t,"resize",function(){return h}),r.d(t,"reshape",function(){return d}),r.d(t,"squeeze",function(){return y}),r.d(t,"unsqueeze",function(){return g}),r.d(t,"flatten",function(){return v}),r.d(t,"map",function(){return x}),r.d(t,"forEach",function(){return b}),r.d(t,"filter",function(){return w}),r.d(t,"filterRegExp",function(){return N}),r.d(t,"join",function(){return M}),r.d(t,"identify",function(){return E}),r.d(t,"generalize",function(){return A});var n=r(3),i=r.n(n),o=r(9),a=r.n(o),s=r(8),u=r.n(s),c=r(48),f=r.n(c);function l(e){for(var t=[];Array.isArray(e);)t.push(e.length),e=e[0];return t}function p(e,t){if(0===t.length){if(Array.isArray(e))throw new u.a(e.length,0)}else!function e(t,r,n){var i,o=t.length;if(o!==r[n])throw new u.a(o,r[n]);if(n<r.length-1){var a=n+1;for(i=0;i<o;i++){var s=t[i];if(!Array.isArray(s))throw new u.a(r.length-1,r.length,"<");e(t[i],r,a)}}else for(i=0;i<o;i++)if(Array.isArray(t[i]))throw new u.a(r.length+1,r.length,">")}(e,t,0)}function m(e,t){if(!i.a.isNumber(e)||!i.a.isInteger(e))throw new TypeError("Index must be an integer (value: "+e+")");if(e<0||"number"==typeof t&&t<=e)throw new f.a(e,t)}function h(e,t,r){if(!Array.isArray(e)||!Array.isArray(t))throw new TypeError("Array expected");if(0===t.length)throw new Error("Resizing to scalar is not supported");return t.forEach(function(e){if(!i.a.isNumber(e)||!i.a.isInteger(e)||e<0)throw new TypeError("Invalid size, must contain positive integers (size: "+a.a.format(t)+")")}),function e(t,r,n,i){var o;var a;var s=t.length;var u=r[n];var c=Math.min(s,u);t.length=u;if(n<r.length-1){var f=n+1;for(o=0;o<c;o++)a=t[o],Array.isArray(a)||(a=[a],t[o]=a),e(a,r,f,i);for(o=c;o<u;o++)a=[],t[o]=a,e(a,r,f,i)}else{for(o=0;o<c;o++)for(;Array.isArray(t[o]);)t[o]=t[o][0];for(o=c;o<u;o++)t[o]=i}}(e,t,0,void 0!==r?r:0),e}function d(t,r){var e,n=v(t);function i(e){return e.reduce(function(e,t){return e*t})}if(!Array.isArray(t)||!Array.isArray(r))throw new TypeError("Array expected");if(0===r.length)throw new u.a(0,i(l(t)),"!=");for(var o=1,a=0;a<r.length;a++)o*=r[a];if(n.length!==o)throw new u.a(i(r),i(l(t)),"!=");try{e=function(e,t){for(var r,n=e,i=t.length-1;0<i;i--){var o=t[i];r=[];for(var a=n.length/o,s=0;s<a;s++)r.push(n.slice(s*o,(s+1)*o));n=r}return n}(n,r)}catch(e){if(e instanceof u.a)throw new u.a(i(r),i(l(t)),"!=");throw e}return e}function y(e,t){for(var r=t||l(e);Array.isArray(e)&&1===e.length;)e=e[0],r.shift();for(var n=r.length;1===r[n-1];)n--;return n<r.length&&(e=function e(t,r,n){var i,o;if(n<r){var a=n+1;for(i=0,o=t.length;i<o;i++)t[i]=e(t[i],r,a)}else for(;Array.isArray(t);)t=t[0];return t}(e,n,0),r.length=n),e}function g(e,t,r,n){var i=n||l(e);if(r)for(var o=0;o<r;o++)e=[e],i.unshift(1);for(e=function e(t,r,n){var i,o;if(Array.isArray(t)){var a=n+1;for(i=0,o=t.length;i<o;i++)t[i]=e(t[i],r,a)}else for(var s=n;s<r;s++)t=[t];return t}(e,t,0);i.length<t;)i.push(1);return e}function v(e){if(!Array.isArray(e))return e;var r=[];return e.forEach(function e(t){Array.isArray(t)?t.forEach(e):r.push(t)}),r}function x(e,t){return Array.prot
/**
* @license Complex.js v2.0.11 11/02/2016
*
* Copyright (c) 2016, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
/**
* @license Complex.js v2.0.11 11/02/2016
*
* Copyright (c) 2016, Robert Eisele (robert@xarg.org)
* Dual licensed under the MIT or GPL Version 2 licenses.
**/
!function(){"use strict";function n(e){return.5*(Math.exp(e)+Math.exp(-e))}function i(e){return.5*(Math.exp(e)-Math.exp(-e))}function u(){throw SyntaxError("Invalid Param")}function c(e,t){var r=Math.abs(e),n=Math.abs(t);return 0===e?Math.log(n):0===t?Math.log(r):r<3e3&&n<3e3?.5*Math.log(e*e+t*t):Math.log(e/Math.cos(Math.atan2(t,e)))}var o=function(e,t){var r={re:0,im:0};if(null==e)r.re=r.im=0;else if(void 0!==t)r.re=e,r.im=t;else switch(typeof e){case"object":if("im"in e&&"re"in e)r.re=e.re,r.im=e.im;else if("abs"in e&&"arg"in e){if(!Number.isFinite(e.abs)&&Number.isFinite(e.arg))return f.INFINITY;r.re=e.abs*Math.cos(e.arg),r.im=e.abs*Math.sin(e.arg)}else if("r"in e&&"phi"in e){if(!Number.isFinite(e.r)&&Number.isFinite(e.phi))return f.INFINITY;r.re=e.r*Math.cos(e.phi),r.im=e.r*Math.sin(e.phi)}else 2===e.length?(r.re=e[0],r.im=e[1]):u();break;case"string":r.im=r.re=0;var n=e.match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g),i=1,o=0;null===n&&u();for(var a=0;a<n.length;a++){var s=n[a];" "===s||"\t"===s||"\n"===s||("+"===s?i++:"-"===s?o++:i=o=("i"===s||"I"===s?(i+o===0&&u()," "===n[a+1]||isNaN(n[a+1])?r.im+=parseFloat((o%2?"-":"")+"1"):(r.im+=parseFloat((o%2?"-":"")+n[a+1]),a++)):(i+o!==0&&!isNaN(s)||u(),"i"===n[a+1]||"I"===n[a+1]?(r.im+=parseFloat((o%2?"-":"")+s),a++):r.re+=parseFloat((o%2?"-":"")+s)),0))}0<i+o&&u();break;case"number":r.im=0,r.re=e;break;default:u()}return isNaN(r.re)||isNaN(r.im),r};function f(e,t){if(!(this instanceof f))return new f(e,t);var r=o(e,t);this.re=r.re,this.im=r.im}f.prototype={re:0,im:0,sign:function(){var e=this.abs();return new f(this.re/e,this.im/e)},add:function(e,t){var r=new f(e,t);return this.isInfinite()&&r.isInfinite()?f.NAN:this.isInfinite()||r.isInfinite()?f.INFINITY:new f(this.re+r.re,this.im+r.im)},sub:function(e,t){var r=new f(e,t);return this.isInfinite()&&r.isInfinite()?f.NAN:this.isInfinite()||r.isInfinite()?f.INFINITY:new f(this.re-r.re,this.im-r.im)},mul:function(e,t){var r=new f(e,t);return this.isInfinite()&&r.isZero()||this.isZero()&&r.isInfinite()?f.NAN:this.isInfinite()||r.isInfinite()?f.INFINITY:0===r.im&&0===this.im?new f(this.re*r.re,0):new f(this.re*r.re-this.im*r.im,this.re*r.im+this.im*r.re)},div:function(e,t){var r=new f(e,t);if(this.isZero()&&r.isZero()||this.isInfinite()&&r.isInfinite())return f.NAN;if(this.isInfinite()||r.isZero())return f.INFINITY;if(this.isZero()||r.isInfinite())return f.ZERO;e=this.re,t=this.im;var n,i,o=r.re,a=r.im;return 0===a?new f(e/o,t/o):Math.abs(o)<Math.abs(a)?new f((e*(i=o/a)+t)/(n=o*i+a),(t*i-e)/n):new f((e+t*(i=a/o))/(n=a*i+o),(t-e*i)/n)},pow:function(e,t){var r=new f(e,t);if(e=this.re,t=this.im,r.isZero())return f.ONE;if(0===r.im){if(0===t&&0<=e)return new f(Math.pow(e,r.re),0);if(0===e)switch((r.re%4+4)%4){case 0:return new f(Math.pow(t,r.re),0);case 1:return new f(0,Math.pow(t,r.re));case 2:return new f(-Math.pow(t,r.re),0);case 3:return new f(0,-Math.pow(t,r.re))}}if(0===e&&0===t&&0<r.re&&0<=r.im)return f.ZERO;var n=Math.atan2(t,e),i=c(e,t);return e=Math.exp(r.re*i-r.im*n),t=r.im*i+r.re*n,new f(e*Math.cos(t),e*Math.sin(t))},sqrt:function(){var e,t,r=this.re,n=this.im,i=this.abs();if(0<=r){if(0===n)return new f(Math.sqrt(r),0);e=.5*Math.sqrt(2*(i+r))}else e=Math.abs(n)/Math.sqrt(2*(i-r));return t=r<=0?.5*Math.sqrt(2*(i-r)):Math.abs(n)/Math.sqrt(2*(i+r)),new f(e,n<0?-t:t)},exp:function(){var e=Math.exp(this.re);return this.im,new f(e*Math.cos(this.im),e*Math.sin(this.im))},expm1:function(){var e=this.re,t=this.im;return new f(Math.expm1(e)*Math.cos(t)+function(e){var t=Math.PI/4;if(e<-t||t<e)return Math.cos(e)-1;var r=e*e;return r*(r*(1/24+r*(-1/720+r*(1/40320+r*(-1/3628800+r*(1/4790014600+r*(-1/87178291200+1/20922789888e3*r))))))-.5)}(t),Math.exp(e)*Math.sin(t))},log:function(){var e=this.re,t=this.im;return new f(c(e,t),Math.atan2(t,e))},abs:function(){return function(e,t){var r=Math.abs(e),n=Math.abs(t);return r<3e3&&n<3e3?Math.sqrt(r*r+n*n):(n=r<n?(r=n,e/t):t/e,r*Math.sqrt(1+n*n))}(this.re,this.im)},arg:function(){return Math.atan2(this.im,this.re)},sin:function(){var e=this.re,t=this.im;return new f(Math.sin(e)*n(t),Math.c
/**
* @license Fraction.js v4.0.12 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 v4.0.12 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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