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+if(!dojo._hasResource["dojox.math.matrix"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code.
+dojo._hasResource["dojox.math.matrix"] = true;
+dojo.provide("dojox.math.matrix");
+
+dojo.mixin(dojox.math.matrix, {
+ iDF:0,
+ ALMOST_ZERO: 1e-10,
+ multiply: function(/* Array */a, /* Array */b){
+ // summary
+ // Multiply matrix a by matrix b.
+ var ay=a.length, ax=a[0].length, by=b.length, bx=b[0].length;
+ if(ax!=by){
+ console.warn("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; // Array
+ },
+ product: function(/* Array... */){
+ // summary
+ // Return the product of N matrices
+ if (arguments.length==0){
+ console.warn("can't multiply 0 matrices!");
+ return 1;
+ }
+ var m=arguments[0];
+ for(var i=1; i<arguments.length; i++){
+ m=this.multiply(m, arguments[i]);
+ }
+ return m; // Array
+ },
+ sum: function(/* Array... */){
+ // summary
+ // Return the sum of N matrices
+ if(arguments.length==0){
+ console.warn("can't sum 0 matrices!");
+ return 0; // Number
+ }
+ var m=this.copy(arguments[0]);
+ var rows=m.length;
+ if(rows==0){
+ console.warn("can't deal with matrices of 0 rows!");
+ return 0;
+ }
+ var cols=m[0].length;
+ if(cols==0){
+ console.warn("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){
+ console.warn("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++) {
+ m[r][c]+=arg[r][c];
+ }
+ }
+ }
+ return m; // Array
+ },
+ inverse: function(/* Array */a){
+ // summary
+ // Return the inversion of the passed matrix
+ if(a.length==1 && a[0].length==1){
+ return [[1/a[0][0]]]; // Array
+ }
+ var tms=a.length, m=this.create(tms, tms), mm=this.adjoint(a), det=this.determinant(a), dd=0;
+ if(det==0){
+ console.warn("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; // Array
+ },
+ determinant: function(/* Array */a){
+ // summary
+ // Calculate the determinant of the passed square matrix.
+ if(a.length!=a[0].length){
+ console.warn("Can't calculate the determinant of a non-squre matrix!");
+ return 0;
+ }
+ var tms=a.length, det=1, b=this.upperTriangle(a);
+ for (var i=0; i<tms; i++){
+ var bii=b[i][i];
+ if (Math.abs(bii)<this.ALMOST_ZERO) {
+ return 0; // Number
+ }
+ det*=bii;
+ }
+ det*=this.iDF;
+ return det; // Number
+ },
+ upperTriangle: function(/* Array */m){
+ // Summary
+ // Find the upper triangle of the passed matrix and return it.
+ m=this.copy(m);
+ var f1=0, temp=0, tms=m.length, v=1;
+ this.iDF=1;
+ for(var col=0; col<tms-1; col++){
+ if(typeof m[col][col]!="number") {
+ console.warn("non-numeric entry found in a numeric matrix: m[" + col + "][" + col + "]=" + m[col][col]);
+ }
+ v=1;
+ var stop_loop=0;
+ while((m[col][col] == 0) && !stop_loop){
+ if (col+v>=tms){
+ this.iDF=0;
+ stop_loop=1;
+ }else{
+ for(var r=0; r<tms; r++){
+ temp=m[col][r];
+ m[col][r]=m[col+v][r];
+ m[col+v][r]=temp;
+ }
+ v++;
+ this.iDF*=-1;
+ }
+ }
+ for(var row=col+1; row<tms; row++){
+ if(typeof m[row][col]!="number"){
+ console.warn("non-numeric entry found in a numeric matrix: m[" + row + "][" + col + "]=" + m[row][col]);
+ }
+ if(typeof m[col][row]!="number"){
+ console.warn("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];
+ for (var i=col; i<tms; i++){
+ m[row][i]=f1*m[col][i]+m[row][i];
+ }
+ }
+ }
+ }
+ return m; // Array
+ },
+ create: function(/* Number */a, /* Number */b, /* Number? */value){
+ // summary
+ // Create a new matrix with rows a and cols b, and pre-populate with value.
+ 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; // Array
+ },
+ ones: function(/* Number */a, /* Number */b){
+ // summary
+ // Create a matrix pre-populated with ones
+ return this.create(a, b, 1); // Array
+ },
+ zeros: function(/* Number */a, /* Number */b){
+ // summary
+ // Create a matrix pre-populated with zeros
+ return this.create(a, b); // Array
+ },
+ identity: function(/* Number */size, /* Number? */scale){
+ // summary
+ // Create an identity matrix based on the size and scale.
+ scale=scale||1;
+ var m=[];
+ for(var i=0; i<size; i++){
+ m[i]=[];
+ for(var j=0; j<size; j++){
+ m[i][j]=(i==j?scale:0);
+ }
+ }
+ return m; // Array
+ },
+ adjoint: function(/* Array */a){
+ // summary
+ // Find the adjoint of the passed matrix
+ var tms=a.length;
+ if(tms<=1){
+ console.warn("Can't find the adjoint of a matrix with a dimension less than 2");
+ return [[0]];
+ }
+ if(a.length!=a[0].length){
+ console.warn("Can't find the adjoint of a non-square matrix");
+ return [[0]];
+ }
+ var m=this.create(tms, tms), ap=this.create(tms-1, tms-1);
+ var ii=0, jj=0, ia=0, ja=0, det=0;
+ for(var i=0; i<tms; i++){
+ for (var j=0; j<tms; j++){
+ ia=0;
+ for(ii=0; ii<tms; ii++){
+ if(ii==i){
+ continue;
+ }
+ ja = 0;
+ for(jj=0; jj<tms; jj++){
+ if(jj==j){
+ continue;
+ }
+ ap[ia][ja] = a[ii][jj];
+ ja++;
+ }
+ ia++;
+ }
+ det=this.determinant(ap);
+ m[i][j]=Math.pow(-1, (i+j))*det;
+ }
+ }
+ return this.transpose(m); // Array
+ },
+ transpose: function(/* Array */a){
+ // summary
+ // Transpose the passed matrix (i.e. rows to columns)
+ var m=this.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; // Array
+ },
+ format: function(/* Array */a, /* Number? */points){
+ // summary
+ // Return a string representation of the matrix, rounded to points (if needed)
+ points=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;
+ }
+ if(b.indexOf(".")>-1){
+ 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], points)+" ";
+ }
+ buffer+="|\n";
+ }
+ return buffer; // string
+ },
+ copy: function(/* Array */a){
+ // summary
+ // Create a copy of the passed matrix
+ var ya=a.length, xa=a[0].length, m=this.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; // Array
+ },
+ scale: function(/* Array */a, /* Number */factor){
+ // summary
+ // Create a copy of passed matrix and scale each member by factor.
+ a=this.copy(a);
+ var ya=a.length, xa=a[0].length;
+ for(var y=0; y<ya; y++){
+ for(var x=0; x<xa; x++){
+ a[y][x]*=factor;
+ }
+ }
+ return a;
+ }
+});
+
+}