/*	Copyright (c) 2004-2006, 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.matrix");//// some of this code is based on// http://www.mkaz.com/math/MatrixCalculator.java// (published under a BSD Open Source License)//// the rest is from my vague memory of matricies in school [cal]//// the copying of arguments is a little excessive, and could be trimmed back in// the case where a function doesn't modify them at all (but some do!)//dojo.math.matrix.iDF = 0;dojo.math.matrix.multiply = function(a, b){	a = dojo.math.matrix.copy(a);	b = dojo.math.matrix.copy(b);	var ax = a[0].length;	var ay = a.length;	var bx = b[0].length;	var by = b.length;	if (ax != by){		dojo.debug("Can't multiply matricies of sizes "+ax+','+ay+' and '+bx+','+by);		return [[0]];	}	var c = [];	for(var k=0; k<ay; k++){		c[k] = [];		for(var i=0; i<bx; i++){			c[k][i] = 0;			for(var m=0; m<ax; m++){				c[k][i] += a[k][m]*b[m][i];			}		}	}	return c;}dojo.math.matrix.inverse = function(a){	a = dojo.math.matrix.copy(a);	// Formula used to Calculate Inverse:	// inv(A) = 1/det(A) * adj(A)	var tms = a.length;	var m = dojo.math.matrix.create(tms, tms);	var mm = dojo.math.matrix.adjoint(a);	var det = dojo.math.matrix.determinant(a);	var dd = 0;	if (det == 0){		dojo.debug("Determinant Equals 0, Not Invertible.");		return [[0]];	}else{		dd = 1 / det;	}	for (var i = 0; i < tms; i++)		for (var j = 0; j < tms; j++) {			m[i][j] = dd * mm[i][j];		}	return m;}dojo.math.matrix.determinant = function(a){	a = dojo.math.matrix.copy(a);	if (a.length != a[0].length){		dojo.debug("Can't calculate the determiant of a non-squre matrix!");		return 0;	}	var tms = a.length;	var det = 1;	var b = dojo.math.matrix.upperTriangle(a);	for (var i=0; i < tms; i++){		det *= b[i][i];	}	det = det * dojo.math.matrix.iDF;	return det;}dojo.math.matrix.upperTriangle = function(m){	m = dojo.math.matrix.copy(m);	var f1 = 0;	var temp = 0;	var tms = m.length;	var v = 1;	dojo.math.matrix.iDF = 1;	for (var col = 0; col < tms - 1; col++) {		for (var row = col + 1; row < tms; row++) {			v = 1;			var stop_loop = 0;			// check if 0 in diagonal 			while ((m[col][col] == 0) && !stop_loop){				// if so switch until not				if (col + v >= tms){					// check if switched all rows					dojo.math.matrix.iDF = 0;					stop_loop = 1;				}else{					for (var c = 0; c < tms; c++) {						temp = m[col][c];						m[col][c] = m[col + v][c]; // switch rows						m[col + v][c] = temp;					}					v++; // count row switchs					dojo.math.matrix.iDF *= -1; // each switch changes determinant factor				}			}			if (m[col][col] != 0) {				f1 = (-1) * m[row][col] / m[col][col];				for (var i = col; i < tms; i++) {					m[row][i] = f1 * m[col][i] + m[row][i];				}			}		}	}	return m;}dojo.math.matrix.create = function(a, b){	var m = [];	for(var i=0; i<b; i++){		m[i] = [];		for(var j=0; j<a; j++){			m[i][j] = 0;		}	}	return m;}dojo.math.matrix.adjoint = function(a){	a = dojo.math.matrix.copy(a);	var tms = a.length;	if (a.length != a[0].length){		dojo.debug("Can't find the adjoint of a non-square matrix");		return [[0]];	}	if (tms == 1){		dojo.debug("Can't find the adjoint of a 1x1 matrix");		return [[0]];	}	var m = dojo.math.matrix.create(tms, tms);	var ii = 0;	var jj = 0;	var ia = 0;	var ja = 0;	var det = 0;	for (var i = 0; i < tms; i++){		for (var j = 0; j < tms; j++){			ia = 0;			ja = 0;			var ap = dojo.math.matrix.create(tms-1, tms-1);			for (ii = 0; ii < tms; ii++) {				for (jj = 0; jj < tms; jj++) {					if ((ii != i) && (jj != j)) {						ap[ia][ja] = a[ii][jj];						ja++;					}				}				if ((ii != i) && (jj != j)) {					ia++;				}				ja = 0;			}			det = dojo.math.matrix.determinant(ap);			m[i][j] = Math.pow(-1 , (i + j)) * det;		}	}	m = dojo.math.matrix.transpose(m);	return m;}dojo.math.matrix.transpose = function(a){	a = dojo.math.matrix.copy(a);	var m = dojo.math.matrix.create(a.length, a[0].length);	for (var i = 0; i < a.length; i++)		for (var j = 0; j < a[i].length; j++)			m[j][i] = a[i][j];	return m;}dojo.math.matrix.format = function(a){	function format_int(x){		var dp = 5;		var fac = Math.pow(10 , dp);		var a = Math.round(x*fac)/fac;		var b = a.toString();		if (b.charAt(0) != '-'){ b = ' ' + b;}		var has_dp = 0;		for(var i=1; i<b.length; i++){			if (b.charAt(i) == '.'){ has_dp = 1; }		}		if (!has_dp){ b += '.'; }		while(b.length < dp+3){ b += '0'; }		return b;	}	var ya = a.length;	var xa = a[0].length;	var buffer = '';	for (var y=0; y<ya; y++){		buffer += '| ';		for (var x=0; x<xa; x++){			buffer += format_int(a[y][x]) + ' ';		}		buffer += '|\n';	}	return buffer;}dojo.math.matrix.copy = function(a){	var ya = a.length;	var xa = a[0].length;	var m = dojo.math.matrix.create(xa, ya);	for (var y=0; y<ya; y++){		for (var x=0; x<xa; x++){			m[y][x] = a[y][x];		}	}	return m;}dojo.math.matrix.scale = function(k, a){	a = dojo.math.matrix.copy(a);	var ya = a.length;	var xa = a[0].length;	for (var y=0; y<ya; y++){		for (var x=0; x<xa; x++){			a[y][x] *= k;		}	}	return a;}