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mathjs

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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.

mathjs.org

josdejong/mathjs

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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 1.5.2 * @date 2015-04-09 * * @license * Copyright (C) 2013-2015 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. */ !function(e,r){"object"==typeof exports&&"object"==typeof module?module.exports=r():"function"==typeof define&&define.amd?define(r):"object"==typeof exports?exports.math=r():e.math=r()}(this,function(){return function(e){function r(n){if(t[n])return t[n].exports;var i=t[n]={exports:{},id:n,loaded:!1};return e[n].call(i.exports,i,i.exports,r),i.loaded=!0,i.exports}var t={};return r.m=e,r.c=t,r.p="",r(0)}([function(e,r,t){e.exports=t(1)},function(e,r,t){"use strict";function n(e){if("function"!=typeof Object.create)throw new Error("ES5 not supported by this JavaScript engine. 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e.type.Matrix,r.prototype.type="CcsMatrix",r.prototype.storage=function(){return"ccs"},r.prototype.subset=function(e,r,t){switch(arguments.length){case 1:return d(this,e);case 2:case 3:return v(this,e,r,t);default:throw new SyntaxError("Wrong number of arguments")}};var d=function(e,r){if(!(r instanceof t))throw new TypeError("Invalid index");var n=r.isScalar();if(n)return e.get(r.min());var o=r.size();if(o.length!=e._size.length)throw new i(o.length,e._size.length);for(var a=r.min(),s=r.max(),u=0,c=e._size.length;c>u;u++)p(a[u],e._size[u]),p(s[u],e._size[u]);var f=function(e){return e};return E(e,a[0],s[0],a[1],s[1],f,!1)},v=function(e,r,n,s){if(!(r instanceof t))throw new TypeError("Invalid index");var u,c=r.size(),f=r.isScalar();if(n instanceof h?(u=n.size(),n=n.toArray()):u=o.size(n),f){if(0!==u.length)throw new TypeError("Scalar expected");e.set(r.min(),n,s)}else{if(1!==c.length&&2!==c.length)throw new i(c.length,e._size.length,"<");if(u.length<c.length){for(var l=0,p=0;1===c[l]&&1===u[l];)l++;for(;1===c[l];)p++,l++;n=o.unsqueeze(n,c.length,p,u)}if(!a.deepEqual(c,u))throw new i(c,u,">");for(var m=r.min()[0],g=r.min()[1],d=u[0],v=u[1],y=0;d>y;y++)for(var x=0;v>x;x++){var w=n[y][x];e.set([y+m,x+g],w,s)}}return e};r.prototype.get=function(e){if(!c(e))throw new TypeError("Array expected");if(e.length!=this._size.length)throw new i(e.length,this._size.length);var r=e[0],t=e[1];p(r,this._size[0]),p(t,this._size[1]);var n=y(r,this._ptr[t],this._ptr[t+1],this._index);return n<this._ptr[t+1]&&this._index[n]===r?a.clone(this._values[n]):0},r.prototype.set=function(r,t,n){if(!c(r))throw new TypeError("Array expected");if(r.length!=this._size.length)throw new i(r.length,this._size.length);var o=r[0],a=r[1],s=this._size[0],u=this._size[1];(o>s-1||a>u-1)&&(b(this,Math.max(o+1,s),Math.max(a+1,u),n),s=this._size[0],u=this._size[1]),p(o,s),p(a,u);var f=y(o,this._ptr[a],this._ptr[a+1],this._index);return f<this._ptr[a+1]&&this._index[f]===o?e.equal(t,0)?x(f,a,this._values,this._index,this._ptr):this._values[f]=t:w(f,o,a,t,this._values,this._index,this._ptr),this};var y=function(e,r,t,n){if(t-r===0||e>n[t-1])return t;for(;t>r;){var i=~~((r+t)/2),o=n[i];if(o>e)t=i;else{if(!(e>o))return i;r=i+1}}return r},x=function(e,r,t,n,i){t.splice(e,1),n.splice(e,1);for(var o=r+1;o<i.length;o++)i[o]--},w=function(e,r,t,n,i,o,a){i.splice(e,0,n),o.splice(e,0,r);for(var s=t+1;s<a.length;s++)a[s]++};r.prototype.resize=function(e,r,t){if(!c(e))throw new TypeError("Array expected");if(2!==e.length)throw new Error("Only two dimensions matrix are supported");e.forEach(function(r){if(!u.isNumber(r)||!u.isInteger(r)||0>r)throw new TypeError("Invalid size, must contain positive integers (size: "+s.format(e)+")")});var n=t?this.clone():this;return b(n,e[0],e[1],r)};var b=function(r,t,n,i){var o,a,s,u=i||0,c=!e.equal(u,0),f=r._size[0],l=r._size[1];if(n>l){for(a=l;n>a;a++)if(r._ptr[a]=r._values.length,c)for(o=0;f>o;o++)r._values.push(u),r._index.push(o);r._ptr[n]=r._values.length}else l>n&&(r._ptr.splice(n+1,l-n),r._values.splice(r._ptr[n],r._values.length),r._index.splice(r._ptr[n],r._index.length));if(l=n,t>f){if(c){var p=0;for(a=0;l>a;a++){r._ptr[a]=r._ptr[a]+p,s=r._ptr[a+1]+p;var m=0;for(o=f;t>o;o++,m++)r._values.splice(s+m,0,u),r._index.splice(s+m,0,o),p++}r._ptr[l]=r._values.length}}else if(f>t){var h=0;for(a=0;l>a;a++){r._ptr[a]=r._ptr[a]-h;var g=r._ptr[a],d=r._ptr[a+1]-h;for(s=g;d>s;s++)o=r._index[s],o>t-1&&(r._values.splice(s,1),r._index.splice(s,1),h++)}r._ptr[a]=r._values.length}return r._size[0]=t,r._size[1]=n,r};r.prototype.clone=function(){var e=new r({values:a.clone(this._values),index:a.clone(this._index),ptr:a.clone(this._ptr),size:a.clone(this._size)});return e},r.prototype.size=function(){return a.clone(this._size)},r.prototype.map=function(e,r){var t=this,n=this._size[0],i=this._size[1],o=function(r,n,i){return e(r,[n,i],t)};return E(this,0,n-1,0,i-1,o,r)};var E=function(t,n,i,o,a,s,u){for(var c=[],f=[],l=[],p=function(r,t,n){r=s(r,t,n),e.equal(r,0)||(c.push(r),f.push(t))},m=o;a>=m;m++){l.push(c.length);for(var h=t._ptr[m],g=t._ptr[m+1],d=n,v=h;g>v;v++){var y=t._index[v];if(y>=n&&i>=y){if(!u)for(var x=d;y>x;x++)p(0,x-n,m-o);p(t._values[v],y-n,m-o)}d=y+1}if(!u)for(var w=d;i>=w;w++)p(0,w-n,m-o)}return l.push(c.length),new r({values:c,index:f,ptr:l,size:[i-n+1,a-o+1]})};r.prototype.forEach=function(e,r){for(var t=this,n=this._size[0],i=this._size[1],o=0;i>o;o++){for(var a=this._ptr[o],s=this._ptr[o+1],u=0,c=a;s>c;c++){var f=this._index[c];if(!r)for(var l=u;f>l;l++)e(0,[l,o],t);e(this._values[c],[f,o],t),u=f+1}if(!r)for(var p=u;n>p;p++)e(0,[p,o],t)}},r.prototype.toArray=function(){return N(this,!0)},r.prototype.valueOf=function(){return N(this,!1)};var N=function(e,r){for(var t=[],n=e._size[0],i=e._size[1],o=0;i>o;o++){for(var s=e._ptr[o],u=e._ptr[o+1],c=0,f=s;u>f;f++){for(var l=e._index[f],p=c;l>p;p++)(t[p]=t[p]||[])[o]=0;(t[l]=t[l]||[])[o]=r?a.clone(e._values[f]):e._values[f],c=l+1}for(var m=c;n>m;m++)(t[m]=t[m]||[])[o]=0}return t};r.prototype.format=function(e){for(var r=this._size[0],t=this._size[1],n="CCS ["+s.format(r,e)+" x "+s.format(t,e)+"] density: "+s.format(this._values.length/(r*t),e)+"\n",i=0;t>i;i++)for(var o=this._ptr[i],a=this._ptr[i+1],u=o;a>u;u++){var c=this._index[u];n+="\n ("+s.format(c,e)+", "+s.format(i,e)+") ==> "+s.format(this._values[u],e)}return n},r.prototype.toString=function(){return s.format(this.toArray())},r.prototype.toJSON=function(){return{mathjs:"CcsMatrix",values:this._values,index:this._index,ptr:this._ptr,size:this._size}},r.prototype.transpose=function(){var r=this._size[0],t=this._size[1];if(0===t)throw new RangeError("Cannot transpose a 2D matrix with no columns (size: "+s.format(this._size)+")");return new e.type.CrsMatrix({values:a.clone(this._values),index:a.clone(this._index),ptr:a.clone(this._ptr),size:[t,r]})},r.prototype.diagonal=function(e){if(e){if(e instanceof m&&(e=e.toNumber()),!f(e)||!l(e))throw new TypeError("The parameter k must be an integer number")}else e=0;for(var r=e>0?e:0,t=0>e?-e:0,n=this._size[0],i=this._size[1],o=Math.min(n-t,i-r),s=[],u=r;i>u&&s.length<o;u++){for(var c=this._ptr[u],p=this._ptr[u+1],h=!1,g=c;p>g;g++){var d=this._index[g];if(d===u-r+t){h=!0,s.push(a.clone(this._values[g]));break}if(d>u-r+t)break}!h&&s.length<o&&s.push(0)}return s},r.fromJSON=function(e){return new r(e)},r.diagonal=function(t,n,i){if(!c(t))throw new TypeError("Array expected, size parameter");if(2!==t.length)throw new Error("Only two dimensions matrix are supported");if(t=t.map(function(e){if(e instanceof m&&(e=e.toNumber()),!f(e)||!l(e)||1>e)throw new Error("Size values must be positive integers");return e}),i){if(i instanceof m&&(i=i.toNumber()),!f(i)||!l(i))throw new TypeError("The parameter k must be an integer number")}else i=0;var o,a=i>0?i:0,s=0>i?-i:0,u=t[0],p=t[1],h=Math.min(u-s,p-a);if(c(n)){if(n.length!==h)throw new Error("Invalid value array length");o=function(e){return n[e]}}else o=function(){return n};for(var g=[],d=[],v=[],y=0;p>y;y++){v.push(g.length);var x=y-a;if(x>=0&&h>x){var w=o(x);e.equal(w,0)||(d.push(x+s),g.push(w))}}return v.push(g.length),new r({values:g,index:d,ptr:v,size:[u,p]})},r.prototype.trace=function(){var r=this._size,t=r[0],n=r[1];if(t===n){var i=0;if(this._values.length>0)for(var o=0;n>o;o++)for(var a=this._ptr[o],u=this._ptr[o+1],c=a;u>c;c++){var f=this._index[c];if(f===o){i=e.add(i,this._values[c]);break}if(f>o)break}return i}throw new RangeError("Matrix must be square (size: "+s.format(r)+")")},r.prototype.multiply=function(r){var t=this._size[0],n=this._size[1];if(r instanceof h){var i=r.size();if(1===i.length)return M(this,i[0],1,function(e){return r.get([e])});if(2===i.length)return M(this,i[0],i[1],function(e,t){return r.get([e,t])});throw new Error("Can only multiply a 1 or 2 dimensional matrix (value has "+i.length+" dimensions)")}if(c(r)){var a=o.size(r);if(1===a.length)return M(this,a[0],1,function(e){return r[e]});if(2===a.length)return M(this,a[0],a[1],function(e,t){return r[e][t]});throw new Error("Can only multiply a 1 or 2 dimensional matrix (value has "+a.length+" dimensions)")}var s=function(t){return e.multiply(t,r)};return E(this,0,t-1,0,n-1,s,!1)};var M=function(t,n,i,o){var a=t._size[0],s=t._size[1];if(s!==n)throw new RangeError("Dimension mis