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mathjs/math.min.js
josdejong fc07e50ca3 Updated version number to 0.7.2-SNAPSHOT
2013-04-27 21:13:39 +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 0.7.2-SNAPSHOT
* @date 2013-04-27
*
* @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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n;throw new SyntaxError('String "'+e+'" is no valid complex number');case 2:return new t(arguments[0],arguments[1]);default:throw x("complex",arguments.length,0,2)}},K.matrix=function(e){if(arguments.length>1)throw x("matrix",arguments.length,0,1);return new n(e)},K.parser=function(){return new K.expr.Parser},K.range=function(e){switch(arguments.length){case 1:if(!y(e))throw new TypeError("Two or three numbers or a single string expected in function range");var t=d.parse(e);if(t)return t;throw new SyntaxError('String "'+t+'" is no valid range');case 2:return new d(arguments[0],null,arguments[1]);case 3:return new d(arguments[0],arguments[1],arguments[2]);default:throw 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 t=E.parse(e);if(t)return t;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,t,r=arguments.length,i=-1,a=!1,o=[];for(e=0;r>e;e++){var f=arguments[e];if(f instanceof n&&(a=!0),e==r-1&&v(f)){if(t=i,i=f,!g(i)||1>i)throw new TypeError("Dimension number must be a positive integer (dim = "+i+")");if(e>0&&i>t)throw new RangeError("Dimension out of range ("+i+" > "+t+")")}else{if(!(f instanceof Array||f instanceof n))throw O("concat",f);var s=K.clone(f.valueOf()),u=K.size(f);if(o[e]=s,t=i,i=u.length,e>0&&i!=t)throw new RangeError("Dimension mismatch ("+t+" != "+i+")")}}if(0==o.length)throw new SyntaxError("At least one matrix expected");for(var c=o.shift();o.length;)c=B(c,o.shift(),i-1,0);return a?new n(c):c},K.det=function(e){if(1!=arguments.length)throw x("det",arguments.length,1);var t=K.size(e);switch(t.length){case 0:return K.clone(e);case 1:if(1==t[0])return K.clone(e.valueOf()[0]);throw new RangeError("Matrix must be square (size: "+K.format(t)+")");case 2:var n=t[0],r=t[1];if(n==r)return C(e.valueOf(),n,r);throw new RangeError("Matrix must be square (size: "+K.format(t)+")");default:throw new RangeError("Matrix must be two dimensional (size: "+K.format(t)+")")}},K.diag=function(e,t){var r,i,a,o;if(1!=arguments.length&&2!=arguments.length)throw x("diag",arguments.length,1,2);if(t){if(!v(t)||!g(t))throw new TypeError("Second parameter in function diag must be an integer")}else t=0;var f=t>0?t:0,s=0>t?-t:0;e instanceof n||e instanceof d||(e=new n(e));var u;switch(e.isVector()?(e=e.toVector(),u=[e.length]):u=e.size(),u.length){case 1:i=e.valueOf();var c=new n;for(c.resize([i.length+s,i.length+f]),r=c.valueOf(),o=i.length,a=0;o>a;a++)r[a+s][a+f]=K.clone(i[a]);return c;case 2:for(i=[],r=e.valueOf(),o=Math.min(u[0]-s,u[1]-f),a=0;o>a;a++)i[a]=K.clone(r[a+s][a+f]);return new n(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 t=e[0],r=e[1];if(!v(t)||!g(t)||1>t)throw Error("Parameters in function eye must be positive integers");if(r&&(!v(r)||!g(r)||1>r))throw Error("Parameters in function eye must be positive integers");var i=new n;i.resize(e);for(var a=K.min(e),o=i.valueOf(),f=0;a>f;f++)o[f][f]=1;return i},K.inv=function(e){if(1!=arguments.length)throw x("inv",arguments.length,1);var t=K.size(e);switch(t.length){case 0:return K.divide(1,e);case 1:if(1==t[0])return e instanceof n?new n([K.divide(1,e.valueOf()[0])]):[K.divide(1,e[0])];throw new RangeError("Matrix must be square (size: "+K.format(t)+")");case 2:var r=t[0],i=t[1];if(r==i)return e instanceof n?new n(D(e.valueOf(),r,i)):D(e,r,i);throw new RangeError("Matrix must be square (size: "+K.format(t)+")");default:throw new RangeError("Matrix must be two dimensional (size: "+K.format(t)+")")}},K.ones=function(){var e=Z.argsToArray(arguments);0==e.length?e=[1,1]:1==e.length&&(e[1]=e[0]);var t=new n,r=1;return t.resize(e,r),t},K.size=function(e){if(1!=arguments.length)throw x("size",arguments.length,1);if(v(e)||e instanceof t||e instanceof E||null==e)return[];if(y(e))return[e.length];if(e instanceof Array)return Z.size(e);if(e instanceof n)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?V(K.clone(e)):e instanceof n?V(e.toArray()):e.valueOf()instanceof Array?V(K.clone(e.valueOf())):K.clone(e)},K.transpose=function(e){if(1!=arguments.length)throw x("transpose",arguments.length,1);var t=K.size(e);switch(t.length){case 0:return K.clone(e);case 1:return K.clone(e);case 2:for(var r,i=t[1],a=t[0],o=e instanceof n,f=e.valueOf(),s=[],u=K.clone,c=0;i>c;c++){r=s[c]=[];for(var l=0;a>l;l++)r[l]=u(f[l][c])}return 0==a&&(s[0]=[]),o?new n(s):s;default:throw new RangeError("Matrix must be two dimensional (size: "+K.format(t)+")")}},K.zeros=function(){var e=Z.argsToArray(arguments);0==e.length?e=[1,1]:1==e.length&&(e[1]=e[0]);var t=new n;return t.resize(e),t},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 t=e,r=t;for(t--;t>1;)r*=t,t--;return 0==r&&(r=1),r}if(e instanceof Array||e instanceof n)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 Error("Function max requires one or more parameters (0 provided)");if(e instanceof Array||e instanceof n||e instanceof d){if(arguments.length>1)throw Error("Wrong number of parameters (1 matrix or multiple scalars expected)");var t=K.size(e);if(1==t.length){if(0==e.length)throw Error("Cannot calculate max of an empty vector");return k(e.valueOf())}if(2==t.length){if(0==t[0]||0==t[1])throw Error("Cannot calculate max of an empty matrix");if(e instanceof Array)return F(e,t[0],t[1]);if(e instanceof n||e instanceof d)return new n(F(e.valueOf(),t[0],t[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 Error("Function min requires one or more parameters (0 provided)");if(e instanceof Array||e instanceof n||e instanceof d){if(arguments.length>1)throw Error("Wrong number of parameters (1 matrix or multiple scalars expected)");var t=K.size(e);if(1==t.length){if(0==e.length)throw Error("Cannot calculate min of an empty vector");return j(e.valueOf())}if(2==t.length){if(0==t[0]||0==t[1])throw Error("Cannot calculate min of an empty matrix");if(e instanceof Array)return H(e,t[0],t[1]);if(e instanceof n||e instanceof d)return new n(H(e.valueOf(),t[0],t[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 t(e,0));if(e instanceof t){var r=new t(e.im*e.im-e.re*e.re+1,-2*e.re*e.im),i=K.sqrt(r),a=new t(i.re-e.im,i.im+e.re),o=K.log(a);return new t(1.5707963267948966-o.im,o.re)}if(e instanceof Array||e instanceof n)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 t(e,0));if(e instanceof t){var r=e.re,i=e.im,a=new t(i*i-r*r+1,-2*r*i),o=K.sqrt(a),f=new t(o.re-i,o.im+r),s=K.log(f);return new t(s.im,-s.re)}if(e instanceof Array||e instanceof n)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 t){var r=e.re,i=e.im,a=r*r+(1-i)*(1-i),o=new t((1-i*i-r*r)/a,-2*r/a),f=K.log(o);return new t(-.5*f.im,.5*f.re)}if(e instanceof Array||e instanceof n)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 t&&v(r))return Math.atan2(e.re,r);if(e instanceof Array||e instanceof n||r instanceof Array||r instanceof n)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 t)return new t(.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 n)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 t){var r=Math.exp(-4*e.im)-2*Math.exp(-2*e.im)*Math.cos(2*e.re)+1;return new t(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 n)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 t){var r=.25*(Math.exp(-2*e.im)+Math.exp(2*e.im))-.5*Math.cos(2*e.re);return new t(.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 n)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 t){var r=.25*(Math.exp(-2*e.im)+Math.exp(2*e.im))+.5*Math.cos(2*e.re);return new t(.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 n)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 t)return new t(.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 n)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 t){var r=Math.exp(-4*e.im)+2*Math.exp(-2*e.im)*Math.cos(2*e.re)+1;return new t(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 n)return Z.map(e,K.tan);if(e.valueOf()!==e)return K.tan(e.valueOf());throw O("tan",e)},K["in"]=function(e,t){if(2!=arguments.length)throw x("in",arguments.length,2);if(e instanceof E&&(t instanceof E||y(t)))return e["in"](t);if(e instanceof Array||e instanceof n||t instanceof Array||t instanceof n)return Z.map2(e,t,K["in"]);if(e.valueOf()!==e||t.valueOf()!==t)return K["in"](e.valueOf(),t.valueOf());throw O("in",e,t)},K.clone=function et(t){if(1!=arguments.length)throw x("clone",arguments.length,1);if(null==t)return t;if("function"==typeof t.clone)return t.clone();if(v(t)||y(t)||e(t))return t;if(t instanceof Array){var n=K.clone;return t.map(function(e){return n(e)})}if(t instanceof Object)return Z.mapObject(t,K.clone);throw O("clone",t)},K.eval=function(e){if(1!=arguments.length)throw x("eval",arguments.length,1);if(y(e))return tt.eval(e);if(e instanceof Array||e instanceof n)return Z.map(e,K.eval);throw new TypeError("String or matrix expected")};var tt=new K.expr.Parser({readonly:!0});K.format=function(e,t){var n=arguments.length;if(1!=n&&2!=n)throw x("format",n,1,2);if(1==n){var r=arguments[0];return v(r)?Z.formatNumber(r):r instanceof Array?Z.formatArray(r):y(r)?'"'+r+'"':r instanceof Object?""+r:r+""}if(!y(e))throw new TypeError("String expected as first parameter in function format");if(!(t instanceof Object))throw new TypeError("Object expected as first parameter in function format");return e.replace(/\$([\w\.]+)/g,function(e,n){for(var r=n.split("."),i=t[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,t){var n,r={override:!1};if(t&&t instanceof Object&&Z.extend(r,t),y(e)){if("undefined"==typeof require)throw Error("Cannot load file: require not available.");var i=require(e);K["import"](i)}else if(W(e)){if(n=e.name,!n)throw Error("Cannot import an unnamed function or object");(r.override||void 0===K[n])&&Y(n,e)}else if(e instanceof Object)for(n in e)if(e.hasOwnProperty(n)){var a=e[n];W(a)?(r.override||void 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