- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-17 15:39:51+12:00
- Desc:
- tweak html formatting
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/c47db6b2fedb368422c7f4d5191aeb9f319ad684/dojo-presentation/js/dojo/dojox/math/matrix.js
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;
}
});
