291 lines
7 KiB
JavaScript
291 lines
7 KiB
JavaScript
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dojo.provide("dojox.math.matrix");
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dojo.mixin(dojox.math.matrix, {
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iDF:0,
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ALMOST_ZERO: 1e-10,
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multiply: function(/* Array */a, /* Array */b){
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// summary
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// Multiply matrix a by matrix b.
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var ay=a.length, ax=a[0].length, by=b.length, bx=b[0].length;
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if(ax!=by){
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console.warn("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; // Array
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},
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product: function(/* Array... */){
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// summary
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// Return the product of N matrices
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if (arguments.length==0){
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console.warn("can't multiply 0 matrices!");
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return 1;
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}
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var m=arguments[0];
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for(var i=1; i<arguments.length; i++){
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m=this.multiply(m, arguments[i]);
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}
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return m; // Array
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},
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sum: function(/* Array... */){
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// summary
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// Return the sum of N matrices
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if(arguments.length==0){
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console.warn("can't sum 0 matrices!");
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return 0; // Number
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}
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var m=this.copy(arguments[0]);
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var rows=m.length;
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if(rows==0){
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console.warn("can't deal with matrices of 0 rows!");
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return 0;
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}
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var cols=m[0].length;
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if(cols==0){
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console.warn("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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console.warn("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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m[r][c]+=arg[r][c];
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}
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}
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}
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return m; // Array
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},
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inverse: function(/* Array */a){
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// summary
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// Return the inversion of the passed matrix
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if(a.length==1 && a[0].length==1){
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return [[1/a[0][0]]]; // Array
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}
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var tms=a.length, m=this.create(tms, tms), mm=this.adjoint(a), det=this.determinant(a), dd=0;
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if(det==0){
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console.warn("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; // Array
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},
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determinant: function(/* Array */a){
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// summary
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// Calculate the determinant of the passed square matrix.
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if(a.length!=a[0].length){
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console.warn("Can't calculate the determinant of a non-squre matrix!");
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return 0;
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}
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var tms=a.length, det=1, b=this.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)<this.ALMOST_ZERO) {
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return 0; // Number
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}
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det*=bii;
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}
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det*=this.iDF;
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return det; // Number
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},
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upperTriangle: function(/* Array */m){
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// Summary
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// Find the upper triangle of the passed matrix and return it.
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m=this.copy(m);
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var f1=0, temp=0, tms=m.length, v=1;
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this.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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console.warn("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){
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if (col+v>=tms){
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this.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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this.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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console.warn("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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console.warn("non-numeric entry found in a numeric matrix: m[" + col + "][" + row + "]=" + m[col][row]);
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}
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if(m[col][col]!=0){
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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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}
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}
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}
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}
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return m; // Array
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},
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create: function(/* Number */a, /* Number */b, /* Number? */value){
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// summary
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// Create a new matrix with rows a and cols b, and pre-populate with value.
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value=value||0;
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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; // Array
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},
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ones: function(/* Number */a, /* Number */b){
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// summary
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// Create a matrix pre-populated with ones
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return this.create(a, b, 1); // Array
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},
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zeros: function(/* Number */a, /* Number */b){
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// summary
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// Create a matrix pre-populated with zeros
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return this.create(a, b); // Array
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},
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identity: function(/* Number */size, /* Number? */scale){
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// summary
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// Create an identity matrix based on the size and scale.
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scale=scale||1;
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var m=[];
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for(var i=0; i<size; i++){
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m[i]=[];
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for(var j=0; j<size; j++){
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m[i][j]=(i==j?scale:0);
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}
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}
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return m; // Array
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},
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adjoint: function(/* Array */a){
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// summary
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// Find the adjoint of the passed matrix
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var tms=a.length;
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if(tms<=1){
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console.warn("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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console.warn("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=this.create(tms, tms), ap=this.create(tms-1, tms-1);
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var ii=0, jj=0, ia=0, ja=0, det=0;
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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++){
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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=this.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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return this.transpose(m); // Array
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},
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transpose: function(/* Array */a){
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// summary
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// Transpose the passed matrix (i.e. rows to columns)
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var m=this.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; // Array
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},
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format: function(/* Array */a, /* Number? */points){
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// summary
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// Return a string representation of the matrix, rounded to points (if needed)
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points=points||5;
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function format_int(x, dp){
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var fac=Math.pow(10, dp);
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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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if(b.indexOf(".")>-1){
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b+=".";
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}
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while(b.length<dp+3){
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b+="0";
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}
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return b;
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}
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var ya=a.length;
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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+="| ";
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for(var x=0; x<xa; x++){
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buffer+=format_int(a[y][x], points)+" ";
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}
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buffer+="|\n";
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}
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return buffer; // string
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},
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copy: function(/* Array */a){
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// summary
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// Create a copy of the passed matrix
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var ya=a.length, xa=a[0].length, m=this.create(xa, ya);
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for(var y=0; y<ya; y++){
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for(var x=0; x<xa; x++){
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m[y][x]=a[y][x];
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}
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}
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return m; // Array
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},
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scale: function(/* Array */a, /* Number */factor){
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// summary
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// Create a copy of passed matrix and scale each member by factor.
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a=this.copy(a);
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var ya=a.length, xa=a[0].length;
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for(var y=0; y<ya; y++){
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for(var x=0; x<xa; x++){
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a[y][x]*=factor;
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}
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}
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return a;
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}
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});
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