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1318 alexandre_ 1 
/*
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	Copyright (c) 2004-2006, The Dojo Foundation
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	All Rights Reserved.
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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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*/
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1422 alexandre_ 11 
 
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1318 alexandre_ 13 
dojo.provide("dojo.math.matrix");
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dojo.math.matrix.iDF = 0;
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dojo.math.matrix.ALMOST_ZERO = 1e-10;
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dojo.math.matrix.multiply = function (a, b) {
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	var ay = a.length;
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	var ax = a[0].length;
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	var by = b.length;
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	var bx = b[0].length;
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	if (ax != by) {
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		dojo.debug("Can't multiply matricies of sizes " + ax + "," + ay + " and " + bx + "," + by);
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		return [[0]];
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	}
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	var c = [];
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	for (var k = 0; k < ay; k++) {
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		c[k] = [];
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		for (var i = 0; i < bx; i++) {
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			c[k][i] = 0;
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			for (var m = 0; m < ax; m++) {
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				c[k][i] += a[k][m] * b[m][i];
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			}
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		}
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	}
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	return c;
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};
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dojo.math.matrix.product = function () {
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	if (arguments.length == 0) {
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		dojo.debug("can't multiply 0 matrices!");
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		return 1;
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	}
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	var result = arguments[0];
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	for (var i = 1; i < arguments.length; i++) {
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		result = dojo.math.matrix.multiply(result, arguments[i]);
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	}
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	return result;
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};
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dojo.math.matrix.sum = function () {
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	if (arguments.length == 0) {
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		dojo.debug("can't sum 0 matrices!");
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		return 0;
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	}
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	var result = dojo.math.matrix.copy(arguments[0]);
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	var rows = result.length;
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	if (rows == 0) {
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		dojo.debug("can't deal with matrices of 0 rows!");
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		return 0;
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	}
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	var cols = result[0].length;
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	if (cols == 0) {
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		dojo.debug("can't deal with matrices of 0 cols!");
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		return 0;
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	}
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	for (var i = 1; i < arguments.length; ++i) {
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		var arg = arguments[i];
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		if (arg.length != rows || arg[0].length != cols) {
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			dojo.debug("can't add matrices of different dimensions: first dimensions were " + rows + "x" + cols + ", current dimensions are " + arg.length + "x" + arg[0].length);
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			return 0;
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		}
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		for (var r = 0; r < rows; r++) {
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			for (var c = 0; c < cols; c++) {
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				result[r][c] += arg[r][c];
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			}
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		}
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	}
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	return result;
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};
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dojo.math.matrix.inverse = function (a) {
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	if (a.length == 1 && a[0].length == 1) {
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		return [[1 / a[0][0]]];
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	}
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	var tms = a.length;
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	var m = dojo.math.matrix.create(tms, tms);
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	var mm = dojo.math.matrix.adjoint(a);
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	var det = dojo.math.matrix.determinant(a);
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	var dd = 0;
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	if (det == 0) {
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		dojo.debug("Determinant Equals 0, Not Invertible.");
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		return [[0]];
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	} else {
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		dd = 1 / det;
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	}
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	for (var i = 0; i < tms; i++) {
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		for (var j = 0; j < tms; j++) {
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			m[i][j] = dd * mm[i][j];
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		}
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	}
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	return m;
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};
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dojo.math.matrix.determinant = function (a) {
101 
	if (a.length != a[0].length) {
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		dojo.debug("Can't calculate the determiant of a non-squre matrix!");
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		return 0;
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	}
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	var tms = a.length;
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	var det = 1;
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	var b = dojo.math.matrix.upperTriangle(a);
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	for (var i = 0; i < tms; i++) {
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		var bii = b[i][i];
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		if (Math.abs(bii) < dojo.math.matrix.ALMOST_ZERO) {
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			return 0;
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		}
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		det *= bii;
114 
	}
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	det = det * dojo.math.matrix.iDF;
116 
	return det;
117 
};
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dojo.math.matrix.upperTriangle = function (m) {
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	m = dojo.math.matrix.copy(m);
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	var f1 = 0;
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	var temp = 0;
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	var tms = m.length;
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	var v = 1;
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	dojo.math.matrix.iDF = 1;
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	for (var col = 0; col < tms - 1; col++) {
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		if (typeof m[col][col] != "number") {
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			dojo.debug("non-numeric entry found in a numeric matrix: m[" + col + "][" + col + "]=" + m[col][col]);
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		}
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		v = 1;
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		var stop_loop = 0;
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		while ((m[col][col] == 0) && !stop_loop) {
132 
			if (col + v >= tms) {
133 
				dojo.math.matrix.iDF = 0;
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				stop_loop = 1;
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			} else {
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				for (var r = 0; r < tms; r++) {
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					temp = m[col][r];
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					m[col][r] = m[col + v][r];
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					m[col + v][r] = temp;
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				}
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				v++;
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				dojo.math.matrix.iDF *= -1;
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			}
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		}
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		for (var row = col + 1; row < tms; row++) {
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			if (typeof m[row][col] != "number") {
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				dojo.debug("non-numeric entry found in a numeric matrix: m[" + row + "][" + col + "]=" + m[row][col]);
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			}
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			if (typeof m[col][row] != "number") {
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				dojo.debug("non-numeric entry found in a numeric matrix: m[" + col + "][" + row + "]=" + m[col][row]);
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			}
152 
			if (m[col][col] != 0) {
153 
				var f1 = (-1) * m[row][col] / m[col][col];
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				for (var i = col; i < tms; i++) {
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					m[row][i] = f1 * m[col][i] + m[row][i];
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				}
157 
			}
158 
		}
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	}
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	return m;
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};
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dojo.math.matrix.create = function (a, b, value) {
163 
	if (!value) {
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		value = 0;
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	}
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	var m = [];
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	for (var i = 0; i < b; i++) {
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		m[i] = [];
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		for (var j = 0; j < a; j++) {
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			m[i][j] = value;
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		}
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	}
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	return m;
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};
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dojo.math.matrix.ones = function (a, b) {
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	return dojo.math.matrix.create(a, b, 1);
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};
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dojo.math.matrix.zeros = function (a, b) {
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	return dojo.math.matrix.create(a, b, 0);
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};
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dojo.math.matrix.identity = function (size, scale) {
182 
	if (!scale) {
183 
		scale = 1;
184 
	}
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	var m = [];
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	for (var i = 0; i < size; i++) {
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		m[i] = [];
188 
		for (var j = 0; j < size; j++) {
189 
			m[i][j] = (i == j ? scale : 0);
190 
		}
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	}
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	return m;
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};
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dojo.math.matrix.adjoint = function (a) {
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	var tms = a.length;
196 
	if (tms <= 1) {
197 
		dojo.debug("Can't find the adjoint of a matrix with a dimension less than 2");
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		return [[0]];
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	}
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	if (a.length != a[0].length) {
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		dojo.debug("Can't find the adjoint of a non-square matrix");
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		return [[0]];
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	}
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	var m = dojo.math.matrix.create(tms, tms);
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	var ii = 0;
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	var jj = 0;
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	var ia = 0;
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	var ja = 0;
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	var det = 0;
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	var ap = dojo.math.matrix.create(tms - 1, tms - 1);
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	for (var i = 0; i < tms; i++) {
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		for (var j = 0; j < tms; j++) {
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			ia = 0;
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			for (ii = 0; ii < tms; ii++) {
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				if (ii == i) {
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					continue;
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				}
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				ja = 0;
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				for (jj = 0; jj < tms; jj++) {
220 
					if (jj == j) {
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						continue;
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					}
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					ap[ia][ja] = a[ii][jj];
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					ja++;
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				}
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				ia++;
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			}
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			det = dojo.math.matrix.determinant(ap);
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			m[i][j] = Math.pow(-1, (i + j)) * det;
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		}
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	}
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	m = dojo.math.matrix.transpose(m);
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	return m;
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};
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dojo.math.matrix.transpose = function (a) {
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	var m = dojo.math.matrix.create(a.length, a[0].length);
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	for (var i = 0; i < a.length; i++) {
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		for (var j = 0; j < a[i].length; j++) {
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			m[j][i] = a[i][j];
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		}
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	}
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	return m;
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};
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dojo.math.matrix.format = function (a, decimal_points) {
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	if (arguments.length <= 1) {
246 
		decimal_points = 5;
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	}
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	function format_int(x, dp) {
249 
		var fac = Math.pow(10, dp);
250 
		var a = Math.round(x * fac) / fac;
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		var b = a.toString();
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		if (b.charAt(0) != "-") {
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			b = " " + b;
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		}
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		var has_dp = 0;
256 
		for (var i = 1; i < b.length; i++) {
257 
			if (b.charAt(i) == ".") {
258 
				has_dp = 1;
259 
			}
260 
		}
261 
		if (!has_dp) {
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			b += ".";
263 
		}
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		while (b.length < dp + 3) {
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			b += "0";
266 
		}
267 
		return b;
268 
	}
269 
	var ya = a.length;
270 
	var xa = ya > 0 ? a[0].length : 0;
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	var buffer = "";
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	for (var y = 0; y < ya; y++) {
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		buffer += "| ";
274 
		for (var x = 0; x < xa; x++) {
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			buffer += format_int(a[y][x], decimal_points) + " ";
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		}
277 
		buffer += "|\n";
278 
	}
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	return buffer;
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};
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dojo.math.matrix.copy = function (a) {
282 
	var ya = a.length;
283 
	var xa = a[0].length;
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	var m = dojo.math.matrix.create(xa, ya);
285 
	for (var y = 0; y < ya; y++) {
286 
		for (var x = 0; x < xa; x++) {
287 
			m[y][x] = a[y][x];
288 
		}
289 
	}
290 
	return m;
291 
};
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dojo.math.matrix.scale = function (k, a) {
293 
	a = dojo.math.matrix.copy(a);
294 
	var ya = a.length;
295 
	var xa = a[0].length;
296 
	for (var y = 0; y < ya; y++) {
297 
		for (var x = 0; x < xa; x++) {
298 
			a[y][x] *= k;
299 
		}
300 
	}
301 
	return a;
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};
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