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mathjs/math.min.js
josdejong 65b5d08f51 Released version 0.8.1
2013-05-10 23:15:52 +02:00

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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 0.8.1
* @date 2013-05-10
*
* @license
* Copyright (C) 2013 Jos de Jong <wjosdejong@gmail.com>
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may not
* use this file except in compliance with the License. You may obtain a copy
* of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*/
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x("range",arguments.length,2,3)}},K.unit=function(){switch(arguments.length){case 1:var e=arguments[0];if(!y(e))throw new TypeError("A string or a number and string expected in function unit");if(E.isPlainUnit(e))return new E(null,e);var n=E.parse(e);if(n)return n;throw new SyntaxError('String "'+e+'" is no valid unit');case 2:return new E(arguments[0],arguments[1]);default:throw x("unit",arguments.length,1,2)}},K.workspace=function(){return new K.expr.Workspace},K.concat=function(){var e,n,r=arguments.length,i=-1,a=!1,o=[];for(e=0;r>e;e++){var s=arguments[e];if(s instanceof t&&(a=!0),e==r-1&&v(s)){if(n=i,i=s,!g(i)||1>i)throw new TypeError("Dimension number must be a positive integer (dim = "+i+")");if(e>0&&i>n)throw new RangeError("Dimension out of range ("+i+" > "+n+")")}else{if(!(s instanceof Array||s instanceof t))throw O("concat",s);var f=K.clone(s.valueOf()),u=K.size(s);if(o[e]=f,n=i,i=u.length,e>0&&i!=n)throw new RangeError("Dimension mismatch ("+n+" != 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1:i=e.valueOf();var c=new t;for(c.resize([i.length+f,i.length+s]),r=c.valueOf(),o=i.length,a=0;o>a;a++)r[a+f][a+s]=K.clone(i[a]);return c;case 2:for(i=[],r=e.valueOf(),o=Math.min(u[0]-f,u[1]-s),a=0;o>a;a++)i[a]=K.clone(r[a+f][a+s]);return new t(i);default:throw new RangeError("Matrix for function diag must be 2 dimensional")}},K.eye=function(){var e=Z.argsToArray(arguments);if(0==e.length)e=[1,1];else if(1==e.length)e[1]=e[0];else if(e.length>2)throw x("eye",e.length,0,2);var n=e[0],r=e[1];if(!v(n)||!g(n)||1>n)throw new Error("Parameters in function eye must be positive integers");if(r&&(!v(r)||!g(r)||1>r))throw new Error("Parameters in function eye must be positive integers");var i=new t;i.resize(e);for(var a=K.min(e),o=i.valueOf(),s=0;a>s;s++)o[s][s]=1;return i},K.inv=function(e){if(1!=arguments.length)throw x("inv",arguments.length,1);var n=K.size(e);switch(n.length){case 0:return K.divide(1,e);case 1:if(1==n[0])return e instanceof t?new t([K.divide(1,e.valueOf()[0])]):[K.divide(1,e[0])];throw new RangeError("Matrix must be square (size: "+K.format(n)+")");case 2:var r=n[0],i=n[1];if(r==i)return e instanceof t?new t(D(e.valueOf(),r,i)):D(e,r,i);throw new RangeError("Matrix must be square (size: "+K.format(n)+")");default:throw new RangeError("Matrix must be two dimensional (size: "+K.format(n)+")")}},K.ones=function(){var e=Z.argsToArray(arguments);0==e.length?e=[1,1]:1==e.length&&(e[1]=e[0]);var n=new t,r=1;return n.resize(e,r),n},K.size=function(e){if(1!=arguments.length)throw x("size",arguments.length,1);if(v(e)||e instanceof n||e instanceof E||null==e)return[];if(y(e))return[e.length];if(e instanceof Array)return Z.size(e);if(e instanceof t)return e.size();if(e.valueOf()!==e)return K.size(e.valueOf());throw O("size",e)},K.squeeze=function(e){if(1!=arguments.length)throw x("squeeze",arguments.length,1);return e instanceof Array?F(K.clone(e)):e instanceof t?F(e.toArray()):e.valueOf()instanceof Array?F(K.clone(e.valueOf())):K.clone(e)},K.transpose=function(e){if(1!=arguments.length)throw x("transpose",arguments.length,1);var n=K.size(e);switch(n.length){case 0:return K.clone(e);case 1:return K.clone(e);case 2:for(var r,i=n[1],a=n[0],o=e instanceof t,s=e.valueOf(),f=[],u=K.clone,c=0;i>c;c++){r=f[c]=[];for(var l=0;a>l;l++)r[l]=u(s[l][c])}return 0==a&&(f[0]=[]),o?new t(f):f;default:throw new RangeError("Matrix must be two dimensional (size: "+K.format(n)+")")}},K.zeros=function(){var e=Z.argsToArray(arguments);0==e.length?e=[1,1]:1==e.length&&(e[1]=e[0]);var n=new t;return n.resize(e),n},K.factorial=function(e){if(1!=arguments.length)throw x("factorial",arguments.length,1);if(v(e)){if(!g(e)||0>e)throw new TypeError("Positive integer value expected in function factorial");var n=e,r=n;for(n--;n>1;)r*=n,n--;return 0==r&&(r=1),r}if(e instanceof Array||e instanceof t)return Z.map(e,K.factorial);if(e.valueOf()!==e)return K.factorial(e.valueOf());throw O("factorial",e)},K.random=function(){if(0!=arguments.length)throw x("random",arguments.length,0);return Math.random()},K.max=function(e){if(0==arguments.length)throw new Error("Function max requires one or more parameters (0 provided)");if(e instanceof Array||e instanceof t||e instanceof w){if(arguments.length>1)throw Error("Wrong number of parameters (1 matrix or multiple scalars expected)");var n=K.size(e);if(1==n.length){if(0==e.length)throw new Error("Cannot calculate max of an empty vector");return k(e.valueOf())}if(2==n.length){if(0==n[0]||0==n[1])throw new Error("Cannot calculate max of an empty matrix");if(e instanceof Array)return V(e,n[0],n[1]);if(e instanceof t||e instanceof w)return new t(V(e.valueOf(),n[0],n[1]));throw O("max",e)}throw new RangeError("Cannot calculate max for multi dimensional matrix")}return k(arguments)},K.min=function(e){if(0==arguments.length)throw new Error("Function min requires one or more parameters (0 provided)");if(e instanceof Array||e instanceof t||e instanceof w){if(arguments.length>1)throw Error("Wrong number of parameters (1 matrix or multiple scalars expected)");var n=K.size(e);if(1==n.length){if(0==e.length)throw new Error("Cannot calculate min of an empty vector");return j(e.valueOf())}if(2==n.length){if(0==n[0]||0==n[1])throw new Error("Cannot calculate min of an empty matrix");if(e instanceof Array)return H(e,n[0],n[1]);if(e instanceof t||e instanceof w)return new t(H(e.valueOf(),n[0],n[1]));throw O("min",e)}throw new RangeError("Cannot calculate min for multi dimensional matrix")}return j(arguments)},K.acos=function(e){if(1!=arguments.length)throw x("acos",arguments.length,1);if(v(e))return e>=-1&&1>=e?Math.acos(e):K.acos(new n(e,0));if(e instanceof n){var r=new n(e.im*e.im-e.re*e.re+1,-2*e.re*e.im),i=K.sqrt(r),a=new n(i.re-e.im,i.im+e.re),o=K.log(a);return new n(1.5707963267948966-o.im,o.re)}if(e instanceof Array||e instanceof t)return Z.map(e,K.acos);if(e.valueOf()!==e)return K.acos(e.valueOf());throw O("acos",e)},K.asin=function(e){if(1!=arguments.length)throw x("asin",arguments.length,1);if(v(e))return e>=-1&&1>=e?Math.asin(e):K.asin(new n(e,0));if(e instanceof n){var r=e.re,i=e.im,a=new n(i*i-r*r+1,-2*r*i),o=K.sqrt(a),s=new n(o.re-i,o.im+r),f=K.log(s);return new n(f.im,-f.re)}if(e instanceof Array||e instanceof t)return Z.map(e,K.asin);if(e.valueOf()!==e)return K.asin(e.valueOf());throw O("asin",e)},K.atan=function(e){if(1!=arguments.length)throw x("atan",arguments.length,1);if(v(e))return Math.atan(e);if(e instanceof n){var r=e.re,i=e.im,a=r*r+(1-i)*(1-i),o=new n((1-i*i-r*r)/a,-2*r/a),s=K.log(o);return new n(-.5*s.im,.5*s.re)}if(e instanceof Array||e instanceof t)return Z.map(e,K.atan);if(e.valueOf()!==e)return K.atan(e.valueOf());throw O("atan",e)},K.atan2=function(e,r){if(2!=arguments.length)throw x("atan2",arguments.length,2);if(v(e)){if(v(r))return Math.atan2(e,r)}else if(e instanceof n&&v(r))return Math.atan2(e.re,r);if(e instanceof Array||e instanceof t||r instanceof Array||r instanceof t)return Z.map2(e,r,K.atan2);if(r.valueOf()!==r||e.valueOf()!==e)return K.atan2(e.valueOf(),r.valueOf());throw O("atan2",e,r)},K.cos=function(e){if(1!=arguments.length)throw x("cos",arguments.length,1);if(v(e))return Math.cos(e);if(e instanceof n)return new n(.5*Math.cos(e.re)*(Math.exp(-e.im)+Math.exp(e.im)),.5*Math.sin(e.re)*(Math.exp(-e.im)-Math.exp(e.im)));if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function cos is no angle");return Math.cos(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.cos);if(e.valueOf()!==e)return K.cos(e.valueOf());throw O("cos",e)},K.cot=function(e){if(1!=arguments.length)throw x("cot",arguments.length,1);if(v(e))return 1/Math.tan(e);if(e instanceof n){var r=Math.exp(-4*e.im)-2*Math.exp(-2*e.im)*Math.cos(2*e.re)+1;return new n(2*Math.exp(-2*e.im)*Math.sin(2*e.re)/r,(Math.exp(-4*e.im)-1)/r)}if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function cot is no angle");return 1/Math.tan(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.cot);if(e.valueOf()!==e)return K.cot(e.valueOf());throw O("cot",e)},K.csc=function(e){if(1!=arguments.length)throw x("csc",arguments.length,1);if(v(e))return 1/Math.sin(e);if(e instanceof n){var r=.25*(Math.exp(-2*e.im)+Math.exp(2*e.im))-.5*Math.cos(2*e.re);return new n(.5*Math.sin(e.re)*(Math.exp(-e.im)+Math.exp(e.im))/r,.5*Math.cos(e.re)*(Math.exp(-e.im)-Math.exp(e.im))/r)}if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function csc is no angle");return 1/Math.sin(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.csc);if(e.valueOf()!==e)return K.csc(e.valueOf());throw O("csc",e)},K.sec=function(e){if(1!=arguments.length)throw x("sec",arguments.length,1);if(v(e))return 1/Math.cos(e);if(e instanceof n){var r=.25*(Math.exp(-2*e.im)+Math.exp(2*e.im))+.5*Math.cos(2*e.re);return new n(.5*Math.cos(e.re)*(Math.exp(-e.im)+Math.exp(e.im))/r,.5*Math.sin(e.re)*(Math.exp(e.im)-Math.exp(-e.im))/r)}if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function sec is no angle");return 1/Math.cos(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.sec);if(e.valueOf()!==e)return K.sec(e.valueOf());throw O("sec",e)},K.sin=function(e){if(1!=arguments.length)throw x("sin",arguments.length,1);if(v(e))return Math.sin(e);if(e instanceof n)return new n(.5*Math.sin(e.re)*(Math.exp(-e.im)+Math.exp(e.im)),.5*Math.cos(e.re)*(Math.exp(e.im)-Math.exp(-e.im)));if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function cos is no angle");return Math.sin(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.sin);if(e.valueOf()!==e)return K.sin(e.valueOf());throw O("sin",e)},K.tan=function(e){if(1!=arguments.length)throw x("tan",arguments.length,1);if(v(e))return Math.tan(e);if(e instanceof n){var r=Math.exp(-4*e.im)+2*Math.exp(-2*e.im)*Math.cos(2*e.re)+1;return new n(2*Math.exp(-2*e.im)*Math.sin(2*e.re)/r,(1-Math.exp(-4*e.im))/r)}if(e instanceof E){if(!e.hasBase(E.BASE_UNITS.ANGLE))throw new TypeError("Unit in function tan is no angle");return Math.tan(e.value)}if(e instanceof Array||e instanceof t)return Z.map(e,K.tan);if(e.valueOf()!==e)return K.tan(e.valueOf());throw O("tan",e)},K["in"]=function(e,n){if(2!=arguments.length)throw x("in",arguments.length,2);if(e instanceof E&&(n instanceof E||y(n)))return e["in"](n);if(e instanceof Array||e instanceof t||n instanceof Array||n instanceof t)return Z.map2(e,n,K["in"]);if(e.valueOf()!==e||n.valueOf()!==n)return K["in"](e.valueOf(),n.valueOf());throw O("in",e,n)},K.clone=function(n){if(1!=arguments.length)throw x("clone",arguments.length,1);if(null==n)return n;if("function"==typeof n.clone)return n.clone();if(v(n)||y(n)||e(n))return n;if(n instanceof Array){var t=K.clone;return n.map(function(e){return t(e)})}if(n instanceof 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r=t.split("."),i=n[r.shift()];r.length&&void 0!=i;){var a=r.shift();i=a?i[a]:i+"."}return void 0!=i?i:e})},K["import"]=function(e,n){var t,r={override:!1};if(n&&n instanceof Object&&Z.extend(r,n),y(e)){if("undefined"==typeof require)throw new Error("Cannot load file: require not available.");var i=require(e);K["import"](i)}else if(W(e)){if(t=e.name,!t)throw new Error("Cannot import an unnamed function or object");(r.override||void 0===K[t])&&Y(t,e)}else if(e instanceof Object)for(t in e)if(e.hasOwnProperty(t)){var a=e[t];W(a)?(r.override||void 0===K[t])&&Y(t,a):K["import"](a)}},K.select=function(e){return new K.type.Selector(e)},K["typeof"]=function(e){if(1!=arguments.length)throw x("typeof",arguments.length,1);var n,t=typeof e;if("object"==t){if(null==e)return"null";if(e instanceof Boolean)return"boolean";if(e instanceof Number)return"number";if(e instanceof String)return"string";if(e instanceof Array)return"array";if(e instanceof Date)return"date";if(e.constructor){for(n in K)if(K.hasOwnProperty(n)&&e.constructor==K[n])return n.toLowerCase();for(n in K.type)if(K.type.hasOwnProperty(n)&&e.constructor==K.type[n])return n.toLowerCase();if(e.constructor.name)return e.constructor.name.toLowerCase()}}return t},Array.prototype.indexOf||(Array.prototype.indexOf=function(e){for(var n=0;n<this.length;n++)if(this[n]==e)return n;return-1}),Array.prototype.forEach||(Array.prototype.forEach=function(e,n){for(var t=0,r=this.length;r>t;++t)e.call(n||this,this[t],t,this)}),Array.prototype.map||(Array.prototype.map=function(e,n){var t,r,i;if(null==this)throw new TypeError(" this is null or not defined");var a=Object(this),o=a.length>>>0;if("function"!=typeof e)throw new TypeError(e+" is not a function");for(n&&(t=n),r=new Array(o),i=0;o>i;){var s,f;i in a&&(s=a[i],f=e.call(t,s,i,a),r[i]=f),i++}return r}),Array.prototype.every||(Array.prototype.every=function(e){"use strict";if(null==this)throw new TypeError;var n=Object(this),t=n.length>>>0;if("function"!=typeof e)throw 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