1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
|
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;
}
});
}
|
