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Copyright (c) 2004-2006, The Dojo Foundation
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Licensed under the Academic Free License version 2.1 or above OR the
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modified BSD license. For more information on Dojo licensing, see:
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http://dojotoolkit.org/community/licensing.shtml
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dojo.provide("dojo.math");
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dojo.math.degToRad = function(/* float */x) {
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// Converts degrees to radians.
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return (x*Math.PI) / 180; // float
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dojo.math.radToDeg = function(/* float */x) {
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// Converts radians to degrees.
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return (x*180) / Math.PI; // float
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dojo.math.factorial = function(/* integer */n){
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for(var i=1;i<=n;i++){ retVal *= i; }
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return retVal; // integer
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dojo.math.permutations = function(/* integer */n, /* integer */k) {
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// The number of ways of obtaining an ordered subset of k elements from a set of n elements
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if(n==0 || k==0) return 1;
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return (dojo.math.factorial(n) / dojo.math.factorial(n-k)); // float
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dojo.math.combinations = function (/* integer */n, /* integer */r) {
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// The number of ways of picking n unordered outcomes from r possibilities
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if(n==0 || r==0) return 1;
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return (dojo.math.factorial(n) / (dojo.math.factorial(n-r) * dojo.math.factorial(r))); // float
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dojo.math.bernstein = function(/* float */t, /* float */n, /* float */i) {
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// Calculates a weighted average based on the Bernstein theorem.
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return (dojo.math.combinations(n,i) * Math.pow(t,i) * Math.pow(1-t,n-i)); // float
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dojo.math.gaussianRandom = function(){
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// Returns random numbers with a Gaussian distribution, with the mean set at 0 and the variance set at 1.
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var i = 2 * Math.random() - 1;
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var j = 2 * Math.random() - 1;
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k = Math.sqrt((-2 * Math.log(k)) / k);
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return i * k; // float
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dojo.math.mean = function() {
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// Calculates the mean of an Array of numbers.
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var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
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for (var i = 0; i < array.length; i++) { mean += array[i]; }
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return mean / array.length; // float
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dojo.math.round = function(/* float */number, /* integer */places) {
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// Extends Math.round by adding a second argument specifying the number of decimal places to round to.
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// TODO: add support for significant figures
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if (!places) { var shift = 1; }
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else { var shift = Math.pow(10, places); }
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return Math.round(number * shift) / shift; // float
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dojo.math.sd = dojo.math.standardDeviation = function(/* array */){
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// Calculates the standard deviation of an Array of numbers
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var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
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return Math.sqrt(dojo.math.variance(array)); // float
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dojo.math.variance = function(/* array */) {
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// Calculates the variance of an Array of numbers
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var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
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var mean = 0, squares = 0;
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for (var i = 0; i < array.length; i++) {
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squares += Math.pow(array[i], 2);
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return (squares / array.length) - Math.pow(mean / array.length, 2); // float
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dojo.math.range = function(/* integer */a, /* integer */b, /* integer */step) {
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// implementation of Python's range()
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if(arguments.length < 2) {
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if(arguments.length < 3) {
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for(var i = a; i < b; i += step) {
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} else if(step < 0) {
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for(var i = a; i > b; i += step) {
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throw new Error("dojo.math.range: step must be non-zero");
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return range; // array