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mathjs/math.min.js
josdejong 8a6548027f Implemented array support for all methods
2013-03-13 21:45:05 +01:00

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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.
*
* Features:
* - Supports real and complex numbers, units, strings, arrays*, and matrices*.
* - Contains a large set of built-in functions and constants.
* - Contains a flexible expression parser.
* - Easily extensible.
* - Compatible with JavaScript's built-in Math library.
* - Powerful and easy to use.
*
* * Note: arrays and matrices are to be implemented.
*
* @version 2013-03-13
* @date 0.4.0-SNAPSHOT
*
* @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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Returns 1 if the values are unequal, and 0 if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallereq","largereq"]},yt.log10=D,D.doc={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(1000)","10 ^ 3","log10(0.01)","log(1000) / log(10)","log(1000, 10)"],seealso:["exp","log"]},yt.fix=Y,Y.doc={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero.If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]},yt.add=V,V.doc={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["2.1 + 3.6","ans - 3.6","3 + 2i",'"hello" + " world"',"3 cm + 2 inch"],seealso:["subtract"]},yt.mod=z,z.doc={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","function isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:[]},yt.exp=F,F.doc={name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x)) # Euler's formula"],seealso:["square","multiply","log"]},yt.largereq=H,H.doc={name:"largereq",category:"Operators",syntax:["x >= y","largereq(x, y)"],description:"Check if value x is larger or equal to y. Returns 1 if x is larger or equal to y, and 0 if not.",examples:["2 > 1+1","2 >= 1+1","a = 3.2","b = 6-2.8","(a > b)"],seealso:["equal","unequal","smallereq","smaller","largereq"]},yt.sqrt=j,j.doc={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","multiply"]},yt.square=K,K.doc={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]},yt.larger=W,W.doc={name:"larger",category:"Operators",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns 1 if x is larger than y, and 0 if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallereq","largereq"]},yt.sign=X,X.doc={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]},yt.unaryminus=Z,Z.doc={name:"unaryminus",category:"Operators",syntax:["-x","unaryminus(x)"],description:"Inverse the sign of a value.",examples:["-4.5","-(-5.6)"],seealso:["add","subtract"]},yt.smaller=Q,Q.doc={name:"smaller",category:"Operators",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns 1 if x is smaller than y, and 0 if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallereq","largereq"]},yt.abs=J,J.doc={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]},yt.log=$,$.doc={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 3","log(1000, 10)","log(1000) / log(10)","b = logb(1024, 2)","2 ^ b"],seealso:["exp","log10"]},yt.pow=et,et.doc={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3 = 8","2*2*2","1 + e ^ (pi * i)"],seealso:["unequal","smaller","larger","smallereq","largereq"]},yt.floor=nt,nt.doc={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]},yt.ceil=rt,rt.doc={name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity.If x is complex, both real and imaginary part are rounded towards plus 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t=this.parse_function_assignment(e);if(!(t instanceof pt)){var n="ans",r=void 0,i=e.createDef(n);return new pt(n,r,t,i)}return t},gt.prototype.parse_block=function(e){var t,n,r;for("\n"!=this.token&&";"!=this.token&&""!=this.token&&(t=this.parse_ans(e));"\n"==this.token||";"==this.token;)n||(n=new lt,t&&(r=";"!=this.token,n.add(t,r))),this.getToken(),"\n"!=this.token&&";"!=this.token&&""!=this.token&&(t=this.parse_ans(e),r=";"!=this.token,n.add(t,r));return n?n:(t||(t=this.parse_ans(e)),t)},gt.prototype.parse_function_assignment=function(e){if(this.token_type==this.TOKENTYPE.SYMBOL&&"function"==this.token){if(this.getToken(),this.token_type!=this.TOKENTYPE.SYMBOL)throw this.createSyntaxError("Function name expected");var t=this.token;if(this.getToken(),"("!=this.token)throw this.createSyntaxError("Opening parenthesis ( expected");for(var n=e.createNestedScope(),r=[],i=[];;){if(this.getToken(),this.token_type!=this.TOKENTYPE.SYMBOL)throw this.createSyntaxError("Variable name 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t=[];if("("==this.token){if(this.getToken(),")"!=this.token)for(t.push(this.parse_range(e));","==this.token;)this.getToken(),t.push(this.parse_range(e));if(")"!=this.token)throw this.createSyntaxError("Parenthesis ) missing");this.getToken()}return t},gt.prototype.parse_string=function(e){if('"'==this.token){for(var t="",n="";""!=this.c&&('"'!=this.c||"\\"==n);)t+=this.c,n=this.c,this.getChar();if(this.getToken(),'"'!=this.token)throw this.createSyntaxError('End of string " missing');this.getToken();var r=new ct(t);return r}return this.parse_matrix(e)},gt.prototype.parse_matrix=function(e){return this.parse_number(e)},gt.prototype.parse_number=function(t){if(this.token_type==this.TOKENTYPE.NUMBER){var n;n="."==this.token?0:Number(this.token),this.getToken();var r;if(this.token_type==this.TOKENTYPE.SYMBOL){if("i"==this.token||"I"==this.token)return r=new i(0,n),this.getToken(),new ct(r);if(e.isUnit(this.token))return r=new e(n,this.token),this.getToken(),new ct(r);throw this.createTypeError('Unknown unit "'+this.token+'"')}var a=new ct(n);return a}return this.parse_parentheses(t)},gt.prototype.parse_parentheses=function(e){if("("==this.token){this.getToken();var t=this.parse_range(e);if(")"!=this.token)throw this.createSyntaxError("Parenthesis ) expected");return this.getToken(),t}return this.parse_end(e)},gt.prototype.parse_end=function(){throw""==this.token?this.createSyntaxError("Unexpected end of expression"):this.createSyntaxError("Value expected")},gt.prototype.row=function(){return void 0},gt.prototype.col=function(){return this.index-this.token.length+1},gt.prototype.createErrorMessage=function(e){var t=this.row(),n=this.col();return void 0===t?void 0===n?e:e+" (col "+n+")":e+" (ln "+t+", col "+n+")"},gt.prototype.createSyntaxError=function(e){return new SyntaxError(this.createErrorMessage(e))},gt.prototype.createTypeError=function(e){return new TypeError(this.createErrorMessage(e))},gt.prototype.createError=function(e){return Error(this.createErrorMessage(e))},yt.parser.Workspace=vt,vt.prototype.clear=function(){this.nodes={},this.firstNode=void 0,this.lastNode=void 0},vt.prototype.append=function(e){var t=this._getNewId(),n=this.lastNode?this.lastNode.scope:this.scope,r=new dt(n),i=new vt.Node({id:t,expression:e,parser:this.parser,scope:r,nextNode:void 0,previousNode:this.lastNode});return this.nodes[t]=i,this.firstNode||(this.firstNode=i),this.lastNode&&(this.lastNode.nextNode=i),this.lastNode=i,this._update([t]),t},vt.prototype.insertBefore=function(e,t){var n=this.nodes[t];if(!n)throw'Node with id "'+t+'" not found';var r=n.previousNode,i=this._getNewId(),a=r?r.scope:this.scope,s=new dt(a),o=new vt.Node({id:i,expression:e,parser:this.parser,scope:s,nextNode:n,previousNode:r});this.nodes[i]=o,r?r.nextNode=o:this.firstNode=o,n.previousNode=o,n.scope.parentScope=o.scope;var f=this.getDependencies(i);return-1==f.indexOf(i)&&f.unshift(i),this._update(f),i},vt.prototype.insertAfter=function(e,t){var n=this.nodes[t];if(!n)throw'Node with id "'+t+'" not found';return n==this.lastNode?this.append(e):this.insertBefore(t+1,e)},vt.prototype.remove=function(e){var t=this.nodes[e];if(!t)throw'Node with id "'+e+'" not found';var n=this.getDependencies(e),r=t.previousNode,i=t.nextNode;r?r.nextNode=i:this.firstNode=i,i?i.previousNode=r:this.lastNode=r;var a=r?r.scope:this.scope;i&&(i.scope.parentScope=a),delete this.nodes[e],this._update(n)},vt.prototype.replace=function(e,t){var n=this.nodes[t];if(!n)throw'Node with id "'+t+'" not found';var r=[t];vt._merge(r,this.getDependencies(t));var i=n.previousNode;n.nextNode,i?i.scope:this.scope,n.setExpr(e),vt._merge(r,this.getDependencies(t)),this._update(r)},vt.Node=function(e){this.id=e.id,this.parser=e.parser,this.scope=e.scope,this.nextNode=e.nextNode,this.previousNode=e.previousNode,this.updateSeq=0,this.result=void 0,this.setExpr(e.expression)},vt.Node.prototype.setExpr=function(e){this.expression=e||"",this.scope.clear(),this._parse()},vt.Node.prototype.getExpr=function(){return this.expression},vt.Node.prototype.getResult=function(){return this.result},vt.Node.prototype._parse=function(){try{this.fn=this.parser.parse(this.expression,this.scope)}catch(e){var t="Error: "+((e.message||e)+"");this.fn=new ct(t)}},vt.Node.prototype.eval=function(){try{this.scope.init(),this.result=this.fn.eval()}catch(e){this.scope.init(),this.result="Error: "+((e.message||e)+"")}return this.result},vt._merge=function(e,t){for(var n=0,r=t.length;r>n;n++){var i=t[n];-1==e.indexOf(i)&&e.push(i)}},vt.prototype.getDependencies=function(e){var t,n=[],r=this.nodes[e];if(r){var i=r.scope.defs,a=r.scope.updates,s=[];for(t in i)i.hasOwnProperty(t)&&s.push(t);for(t in a)a.hasOwnProperty(t)&&-1==s.indexOf(t)&&s.push(t);for(var o=r.nextNode;o&&s.length;){for(var f=o.scope,u=0;s.length>u;){if(t=s[u],(f.hasLink(t)||f.hasUpdate(t))&&-1==n.indexOf(o.id)){n.push(o.id);var h=this.getDependencies(o.id);vt._merge(n,h)}f.hasDef(t)&&(s.splice(u,1),u--),u++}o=o.nextNode}}return n},vt.prototype.getExpr=function(e){var t=this.nodes[e];if(!t)throw'Node with id "'+e+'" not found';return t.getExpr()},vt.prototype.getResult=function(e){var t=this.nodes[e];if(!t)throw'Node with id "'+e+'" not found';return t.getResult()},vt.prototype._update=function(e){this.updateSeq++;for(var t=this.updateSeq,n=this.nodes,r=0,i=e.length;i>r;r++){var a=e[r],s=n[a];s&&(s.eval(),s.updateSeq=t)}},vt.prototype.getChanges=function(e){var t=[],n=this.firstNode;for(e=e||0;n;)n.updateSeq>e&&t.push(n.id),n=n.nextNode;return{ids:t,updateSeq:this.updateSeq}},vt.prototype._getNewId=function(){return this.idMax++,this.idMax},vt.prototype.toString=function(){return JSON.stringify(this.toJSON())},vt.prototype.toJSON=function(){for(var e=[],t=this.firstNode;t;){var n={id:t.id,expression:t.expression,dependencies:this.getDependencies(t.id)};try{n.result=t.getResult()}catch(r){n.result="Error: "+((r.message||r)+"")}e.push(n),t=t.nextNode}return e}})();
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