/*
	Copyright (c) 2004-2005, The Dojo Foundation
	All Rights Reserved.

	Licensed under the Academic Free License version 2.1 or above OR the
	modified BSD license. For more information on Dojo licensing, see:

		http://dojotoolkit.org/community/licensing.shtml
*/

dojo.provide("dojo.math");

dojo.math.degToRad = function (x) { return (x*Math.PI) / 180; }
dojo.math.radToDeg = function (x) { return (x*180) / Math.PI; }

dojo.math.factorial = function (n) {
	if(n<1){ return 0; }
	var retVal = 1;
	for(var i=1;i<=n;i++){ retVal *= i; }
	return retVal;
}

//The number of ways of obtaining an ordered subset of k elements from a set of n elements
dojo.math.permutations = function (n,k) {
	if(n==0 || k==0) return 1;
	return (dojo.math.factorial(n) / dojo.math.factorial(n-k));
}

//The number of ways of picking n unordered outcomes from r possibilities
dojo.math.combinations = function (n,r) {
	if(n==0 || r==0) return 1;
	return (dojo.math.factorial(n) / (dojo.math.factorial(n-r) * dojo.math.factorial(r)));
}

dojo.math.bernstein = function (t,n,i) {
	return (dojo.math.combinations(n,i) * Math.pow(t,i) * Math.pow(1-t,n-i));
}

/**
 * Returns random numbers with a Gaussian distribution, with the mean set at
 * 0 and the variance set at 1.
 *
 * @return A random number from a Gaussian distribution
 */
dojo.math.gaussianRandom = function () {
	var k = 2;
	do {
		var i = 2 * Math.random() - 1;
		var j = 2 * Math.random() - 1;
		k = i * i + j * j;
	} while (k >= 1);
	k = Math.sqrt((-2 * Math.log(k)) / k);
	return i * k;
}

/**
 * Calculates the mean of an Array of numbers.
 *
 * @return The mean of the numbers in the Array
 */
dojo.math.mean = function () {
	var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
	var mean = 0;
	for (var i = 0; i < array.length; i++) { mean += array[i]; }
	return mean / array.length;
}

/**
 * Extends Math.round by adding a second argument specifying the number of
 * decimal places to round to.
 *
 * @param number The number to round
 * @param places The number of decimal places to round to
 * @return The rounded number
 */
// TODO: add support for significant figures
dojo.math.round = function (number, places) {
	if (!places) { var shift = 1; }
	else { var shift = Math.pow(10, places); }
	return Math.round(number * shift) / shift;
}

/**
 * Calculates the standard deviation of an Array of numbers
 *
 * @return The standard deviation of the numbers
 */
dojo.math.sd = function () {
	var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
	return Math.sqrt(dojo.math.variance(array));
}

/**
 * Calculates the variance of an Array of numbers
 *
 * @return The variance of the numbers
 */
dojo.math.variance = function () {
	var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments;
	var mean = 0, squares = 0;
	for (var i = 0; i < array.length; i++) {
		mean += array[i];
		squares += Math.pow(array[i], 2);
	}
	return (squares / array.length)
		- Math.pow(mean / array.length, 2);
}