Opened 16 years ago

Closed 15 years ago

# [patch][cla] math.matrix bug fixes and enhancements

Reported by: Owned by: erelsgl AT cs.technion.ac.il Tom Trenka high Core 0.3 matrix

### Description

```/*
Copyright (c) 2004-2006, The Dojo Foundation

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!)
//
// 2006-06-25: Some enhancements submitted by Erel Segal:
// * addition: a tolerance constant for determinant calculations.
// * performance fix: removed unnecessary argument copying.
// * addition: function "product" for multiplying more than 2 matrices
// * bug fix: inversion of a 1x1 matrix without using the adjoint
// * performance fixes: upperTriangle
// * addition: argument "value" to function create, to initialize the matrix with a custom val
// * addition: functions "ones" and "zeros" - like Matlab[TM] functions with the same name.
// * addition: function "identity" for creating an identity matrix of a given size.
// * addition: argument "decimal_points" to function format
// * bug fix: adjoint of a 0-size matrix
//

dojo.math.matrix.iDF = 0;

// Erel: values lower than this value are considered zero (in detereminant calculations).
// It is analogous to Maltab[TM]'s "eps".
dojo.math.matrix.ALMOST_ZERO = 1e-10;

dojo.math.matrix.multiply = function(a, b){

// Erel: why copy the input matrices? they don't change.
//a = dojo.math.matrix.copy(a);
//b = dojo.math.matrix.copy(b);

var ay = a.length;
var ax = a[0].length;
var by = b.length;
var bx = b[0].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;
}

// Erel: added a "product" function to calculate product of more than 2 matrices:
dojo.math.matrix.product = function() {
if (arguments.length==0) {
dojo.debug ("can't multiply 0 matrices!");
return 1;
}
var result = arguments[0];
for (var i=1; i<arguments.length; ++i)
result = matrix.multiply(result,arguments[i]);
return result;
}

// Erel: added a "sum" function to calculate sum of more than 2 matrices:
dojo.math.matrix.sum = function() {
if (arguments.length==0) {
dojo.debug ("can't sum 0 matrices!");
return 0;
}
var result = matrix.copy(arguments[0]);
var rows = result.length;
if (rows==0) {
dojo.debug ("can't deal with matrices of 0 rows!");
return 0;
}
var cols = result[0].length;
if (cols==0) {
dojo.debug ("can't deal with matrices of 0 cols!");
return 0;
}
for (var i=1; i<arguments.length; ++i) {
var arg = arguments[i];
if (arg.length!=rows || arg[0].length!=cols) {
dojo.debug ("can't add matrices of different dimensions: first dimensions were " + rows + "x" + cols + ", current dimensions are "+arg.length + "x" + arg[0].length);
return 0;
}

for (var r=0; r<rows; ++r)
for (var c=0; c<cols; ++c)
result[r][c] += arg[r][c];
}
return result;
}

dojo.math.matrix.inverse = function(a){

// Erel: why copy a? it is not changed!
//a = dojo.math.matrix.copy(a);

// Erel: added special case: inverse of a 1x1 matrix can't be calculated by adjoint
if (a.length==1 && a[0].length==1)
return [[ 1 / a[0][0] ]];

// 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 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){
// Erel: why copy? it is not changed.
//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++){
var bii = b[i][i];
if (Math.abs(bii) < dojo.math.matrix.ALMOST_ZERO)
return 0;
det *= bii;
}

det = det * dojo.math.matrix.iDF;

return det;
}

dojo.math.matrix.upperTriangle = function(m){

m = dojo.math.matrix.copy(m);     // Copy m, because m is changed!

var f1 = 0;
var temp = 0;
var tms = m.length;
var v = 1;

//Erel: why use a global variable and not a local variable?
dojo.math.matrix.iDF = 1;

for (var col = 0; col < tms - 1; col++) {

if (typeof m[col][col] != 'number')
dojo.debug("non-numeric entry found in a numeric matrix: m["+col+"]["+col+"]="+m[col][col]);

// Erel: moved out of row loop, because it does not depend on row.
//	Inner loop does not change m[col][col]; only m[row][i] (row>col)
v = 1;

var stop_loop = 0;

// check if there is a 0 in diagonal
while ((m[col][col] == 0) && !stop_loop) {

// if so,  switch rows until there is no 0 in diagonal:
if (col + v >= tms){

// check if switched all rows
dojo.math.matrix.iDF = 0;
stop_loop = 1;
}
else{
for (var r = 0; r < tms; r++) {
temp = m[col][r];
m[col][r] = m[col + v][r]; // switch rows
m[col + v][r] = temp;
}
v++; // count row switchs
dojo.math.matrix.iDF *= -1; // each switch changes determinant factor
}
}

// loop over lower-right triangle (where row>col):
// for each row, make m[row][col] = 0 by linear operations that don't change the determinant:
for (var row = col + 1; row < tms; row++) {
if (typeof m[row][col] != 'number')
dojo.debug("non-numeric entry found in a numeric matrix: m["+row+"]["+col+"]="+m[row][col]);
if (typeof m[col][row] != 'number')
dojo.debug("non-numeric entry found in a numeric matrix: m["+col+"]["+row+"]="+m[col][row]);
if (m[col][col] != 0) {
var f1 = (-1) * m[row][col] / m[col][col];
// this should make m[row][col] zero:
// 	m[row] += f1 * m[col];
for (var i = col; i < tms; i++) {
m[row][i] = f1 * m[col][i] + m[row][i];
}
}
}
}

return m;
}

// Erel: added parameter "value" - a custom default value to fill the matrix with.
dojo.math.matrix.create = function(a, b, value){
if (!value)
value = 0;
var m = [];
for(var i=0; i<b; i++){
m[i] = [];
for(var j=0; j<a; j++){
m[i][j] = value;
}
}
return m;
}

// Erel implement Matlab[TM] functions "ones" and "zeros"
dojo.math.matrix.ones = function(a,b) { return dojo.math.matrix.create(a,b,1); }
dojo.math.matrix.zeros = function(a,b) { return dojo.math.matrix.create(a,b,0); }

// Erel: added function that returns identity matrix.
//	size = number of rows and cols in the matrix.
//	scale = an optional value to multiply the matrix by (default is 1).
dojo.math.matrix.identity = function(size, scale){
if (!scale)
scale = 1;
var m = [];
for(var i=0; i<n; i++){
m[i] = [];
for(var j=0; j<n; j++)
m[i][j] = (i==j? scale: 0);
}
return m;
}

// Erel: no need to copy - a does not change
//a = dojo.math.matrix.copy(a);

var tms = a.length;

// Erel: added "<=" to catch zero-size matrix
if (tms <= 1){
dojo.debug("Can't find the adjoint of a matrix with a dimension less than 2");
return [[0]];
}

if (a.length != a[0].length){
dojo.debug("Can't find the adjoint of a non-square 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;
// Erel: create temporary matrix outside the loops:
var ap = dojo.math.matrix.create(tms-1, tms-1);

for (var i = 0; i < tms; i++){
for (var j = 0; j < tms; j++){

// Erel: simplified loop structure
ia = 0;
for (ii = 0; ii < tms; ii++) {   // create a temporary matrix for determinant calc
if (ii==i) continue;       // skip current row
ja = 0;
for (jj = 0; jj < tms; jj++) {
if (jj==j) continue;       // skip current col
ap[ia][ja] = a[ii][jj];
ja++;
}
ia++;
}

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){
// Erel: no need to copy - a does not change
//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, decimal_points){

if (arguments.length<=1)
decimal_points = 5;

function format_int(x, dp){
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 = ya>0? a[0].length: 0;

var buffer = '';

for (var y=0; y<ya; y++){
buffer += '| ';
for (var x=0; x<xa; x++){
buffer += format_int(a[y][x], decimal_points) + ' ';
}
buffer += '|
';
}

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);  // Copy a because a is changed!

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;
}

```

### comment:1 Changed 15 years ago by dylan

Owner: changed from alex to Tom Trenka math.matrix bug fixes and enhancements → [patch][cla] math.matrix bug fixes and enhancements 0.4 → 0.3

### comment:2 Changed 15 years ago by Tom Trenka

Resolution: → fixed new → closed

(In [5493]) Fixes #1020.

### comment:3 Changed 15 years ago by (none)

 Milestone: 0.4

Milestone 0.4 deleted

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