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Matrix | 33 | 501 | 190 |
1 | /* | |
2 | * Jalview - A Sequence Alignment Editor and Viewer ($$Version-Rel$$) | |
3 | * Copyright (C) $$Year-Rel$$ The Jalview Authors | |
4 | * | |
5 | * This file is part of Jalview. | |
6 | * | |
7 | * Jalview is free software: you can redistribute it and/or | |
8 | * modify it under the terms of the GNU General Public License | |
9 | * as published by the Free Software Foundation, either version 3 | |
10 | * of the License, or (at your option) any later version. | |
11 | * | |
12 | * Jalview is distributed in the hope that it will be useful, but | |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty | |
14 | * of MERCHANTABILITY or FITNESS FOR A PARTICULAR | |
15 | * PURPOSE. See the GNU General Public License for more details. | |
16 | * | |
17 | * You should have received a copy of the GNU General Public License | |
18 | * along with Jalview. If not, see <http://www.gnu.org/licenses/>. | |
19 | * The Jalview Authors are detailed in the 'AUTHORS' file. | |
20 | */ | |
21 | package jalview.math; | |
22 | ||
23 | import jalview.util.Format; | |
24 | import jalview.util.MessageManager; | |
25 | ||
26 | import java.io.PrintStream; | |
27 | import java.lang.Math; | |
28 | import java.util.Arrays; | |
29 | ||
30 | /** | |
31 | * A class to model rectangular matrices of double values and operations on them | |
32 | */ | |
33 | public class Matrix implements MatrixI | |
34 | { | |
35 | /* | |
36 | * maximum number of iterations for tqli | |
37 | */ | |
38 | private static final int MAX_ITER = 45; | |
39 | // fudge - add 15 iterations, just in case | |
40 | ||
41 | /* | |
42 | * the number of rows | |
43 | */ | |
44 | final protected int rows; | |
45 | ||
46 | /* | |
47 | * the number of columns | |
48 | */ | |
49 | final protected int cols; | |
50 | ||
51 | /* | |
52 | * the cell values in row-major order | |
53 | */ | |
54 | private double[][] value; | |
55 | ||
56 | protected double[] d; // Diagonal | |
57 | ||
58 | protected double[] e; // off diagonal | |
59 | ||
60 | /** | |
61 | * Constructor given number of rows and columns | |
62 | * | |
63 | * @param colCount | |
64 | * @param rowCount | |
65 | */ | |
66 | 22 | protected Matrix(int rowCount, int colCount) |
67 | { | |
68 | 22 | rows = rowCount; |
69 | 22 | cols = colCount; |
70 | } | |
71 | ||
72 | /** | |
73 | * Creates a new Matrix object containing a copy of the supplied array values. | |
74 | * For example | |
75 | * | |
76 | * <pre> | |
77 | * new Matrix(new double[][] {{2, 3, 4}, {5, 6, 7}) | |
78 | * constructs | |
79 | * (2 3 4) | |
80 | * (5 6 7) | |
81 | * </pre> | |
82 | * | |
83 | * Note that ragged arrays (with not all rows, or columns, of the same | |
84 | * length), are not supported by this class. They can be constructed, but | |
85 | * results of operations on them are undefined and may throw exceptions. | |
86 | * | |
87 | * @param values | |
88 | * the matrix values in row-major order | |
89 | */ | |
90 | 82 | public Matrix(double[][] values) |
91 | { | |
92 | 82 | this.rows = values.length; |
93 | 82 | this.cols = this.rows == 0 ? 0 : values[0].length; |
94 | ||
95 | /* | |
96 | * make a copy of the values array, for immutability | |
97 | */ | |
98 | 82 | this.value = new double[rows][]; |
99 | 82 | int i = 0; |
100 | 82 | for (double[] row : values) |
101 | { | |
102 | 1350 | if (row != null) |
103 | { | |
104 | 1350 | value[i] = new double[row.length]; |
105 | 1350 | System.arraycopy(row, 0, value[i], 0, row.length); |
106 | } | |
107 | 1350 | i++; |
108 | } | |
109 | } | |
110 | ||
111 | 0 | public Matrix(float[][] values) |
112 | { | |
113 | 0 | this.rows = values.length; |
114 | 0 | this.cols = this.rows == 0 ? 0 : values[0].length; |
115 | ||
116 | /* | |
117 | * make a copy of the values array, for immutability | |
118 | */ | |
119 | 0 | this.value = new double[rows][]; |
120 | 0 | int i = 0; |
121 | 0 | for (float[] row : values) |
122 | { | |
123 | 0 | if (row != null) |
124 | { | |
125 | 0 | value[i] = new double[row.length]; |
126 | 0 | int j = 0; |
127 | 0 | for (float oldValue : row) |
128 | { | |
129 | 0 | value[i][j] = oldValue; |
130 | 0 | j++; |
131 | } | |
132 | } | |
133 | 0 | i++; |
134 | } | |
135 | } | |
136 | ||
137 | 0 | @Override |
138 | public MatrixI transpose() | |
139 | { | |
140 | 0 | double[][] out = new double[cols][rows]; |
141 | ||
142 | 0 | for (int i = 0; i < cols; i++) |
143 | { | |
144 | 0 | for (int j = 0; j < rows; j++) |
145 | { | |
146 | 0 | out[i][j] = value[j][i]; |
147 | } | |
148 | } | |
149 | ||
150 | 0 | return new Matrix(out); |
151 | } | |
152 | ||
153 | /** | |
154 | * DOCUMENT ME! | |
155 | * | |
156 | * @param ps | |
157 | * DOCUMENT ME! | |
158 | * @param format | |
159 | */ | |
160 | 0 | @Override |
161 | public void print(PrintStream ps, String format) | |
162 | { | |
163 | 0 | for (int i = 0; i < rows; i++) |
164 | { | |
165 | 0 | for (int j = 0; j < cols; j++) |
166 | { | |
167 | 0 | Format.print(ps, format, getValue(i, j)); |
168 | } | |
169 | ||
170 | 0 | ps.println(); |
171 | } | |
172 | } | |
173 | ||
174 | 10 | @Override |
175 | public MatrixI preMultiply(MatrixI in) | |
176 | { | |
177 | 10 | if (in.width() != rows) |
178 | { | |
179 | 2 | throw new IllegalArgumentException("Can't pre-multiply " + this.rows |
180 | + " rows by " + in.width() + " columns"); | |
181 | } | |
182 | 8 | double[][] tmp = new double[in.height()][this.cols]; |
183 | ||
184 | 22 | for (int i = 0; i < in.height(); i++) |
185 | { | |
186 | 48 | for (int j = 0; j < this.cols; j++) |
187 | { | |
188 | /* | |
189 | * result[i][j] is the vector product of | |
190 | * in.row[i] and this.column[j] | |
191 | */ | |
192 | 86 | for (int k = 0; k < in.width(); k++) |
193 | { | |
194 | 52 | if (!Double.isNaN(in.getValue(i, k)) |
195 | && !Double.isNaN(this.value[k][j])) | |
196 | { | |
197 | 52 | tmp[i][j] += (in.getValue(i, k) * this.value[k][j]); |
198 | } | |
199 | } | |
200 | } | |
201 | } | |
202 | ||
203 | 8 | return new Matrix(tmp); |
204 | } | |
205 | ||
206 | /** | |
207 | * | |
208 | * @param in | |
209 | * | |
210 | * @return | |
211 | */ | |
212 | 0 | public double[] vectorPostMultiply(double[] in) |
213 | { | |
214 | 0 | double[] out = new double[in.length]; |
215 | ||
216 | 0 | for (int i = 0; i < in.length; i++) |
217 | { | |
218 | 0 | out[i] = 0.0; |
219 | ||
220 | 0 | for (int k = 0; k < in.length; k++) |
221 | { | |
222 | 0 | out[i] += (value[i][k] * in[k]); |
223 | } | |
224 | } | |
225 | ||
226 | 0 | return out; |
227 | } | |
228 | ||
229 | 6 | @Override |
230 | public MatrixI postMultiply(MatrixI in) | |
231 | { | |
232 | 6 | if (in.height() != this.cols) |
233 | { | |
234 | 0 | throw new IllegalArgumentException("Can't post-multiply " + this.cols |
235 | + " columns by " + in.height() + " rows"); | |
236 | } | |
237 | 6 | return in.preMultiply(this); |
238 | } | |
239 | ||
240 | 10 | @Override |
241 | public MatrixI copy() | |
242 | { | |
243 | 10 | double[][] newmat = new double[rows][cols]; |
244 | ||
245 | 62 | for (int i = 0; i < rows; i++) |
246 | { | |
247 | 52 | System.arraycopy(value[i], 0, newmat[i], 0, value[i].length); |
248 | } | |
249 | ||
250 | 10 | Matrix m = new Matrix(newmat); |
251 | 10 | if (this.d != null) |
252 | { | |
253 | 2 | m.d = Arrays.copyOf(this.d, this.d.length); |
254 | } | |
255 | 10 | if (this.e != null) |
256 | { | |
257 | 2 | m.e = Arrays.copyOf(this.e, this.e.length); |
258 | } | |
259 | ||
260 | 10 | return m; |
261 | } | |
262 | ||
263 | /** | |
264 | * DOCUMENT ME! | |
265 | */ | |
266 | 9 | @Override |
267 | public void tred() | |
268 | { | |
269 | 9 | int n = rows; |
270 | 9 | int k; |
271 | 9 | int j; |
272 | 9 | int i; |
273 | ||
274 | 9 | double scale; |
275 | 9 | double hh; |
276 | 9 | double h; |
277 | 9 | double g; |
278 | 9 | double f; |
279 | ||
280 | 9 | this.d = new double[rows]; |
281 | 9 | this.e = new double[rows]; |
282 | ||
283 | 87 | for (i = n; i >= 2; i--) |
284 | { | |
285 | 78 | final int l = i - 1; |
286 | 78 | h = 0.0; |
287 | 78 | scale = 0.0; |
288 | ||
289 | 78 | if (l > 1) |
290 | { | |
291 | 465 | for (k = 1; k <= l; k++) |
292 | { | |
293 | 396 | double v = Math.abs(getValue(i - 1, k - 1)); |
294 | 396 | scale += v; |
295 | } | |
296 | ||
297 | 69 | if (scale == 0.0) |
298 | { | |
299 | 0 | e[i - 1] = getValue(i - 1, l - 1); |
300 | } | |
301 | else | |
302 | { | |
303 | 465 | for (k = 1; k <= l; k++) |
304 | { | |
305 | 396 | double v = divideValue(i - 1, k - 1, scale); |
306 | 396 | h += v * v; |
307 | } | |
308 | ||
309 | 69 | f = getValue(i - 1, l - 1); |
310 | ||
311 | 69 | if (f > 0) |
312 | { | |
313 | 26 | g = -1.0 * Math.sqrt(h); |
314 | } | |
315 | else | |
316 | { | |
317 | 43 | g = Math.sqrt(h); |
318 | } | |
319 | ||
320 | 69 | e[i - 1] = scale * g; |
321 | 69 | h -= (f * g); |
322 | 69 | setValue(i - 1, l - 1, f - g); |
323 | 69 | f = 0.0; |
324 | ||
325 | 465 | for (j = 1; j <= l; j++) |
326 | { | |
327 | 396 | double val = getValue(i - 1, j - 1) / h; |
328 | 396 | setValue(j - 1, i - 1, val); |
329 | 396 | g = 0.0; |
330 | ||
331 | 2007 | for (k = 1; k <= j; k++) |
332 | { | |
333 | 1611 | g += (getValue(j - 1, k - 1) * getValue(i - 1, k - 1)); |
334 | } | |
335 | ||
336 | 1611 | for (k = j + 1; k <= l; k++) |
337 | { | |
338 | 1215 | g += (getValue(k - 1, j - 1) * getValue(i - 1, k - 1)); |
339 | } | |
340 | ||
341 | 396 | e[j - 1] = g / h; |
342 | 396 | f += (e[j - 1] * getValue(i - 1, j - 1)); |
343 | } | |
344 | ||
345 | 69 | hh = f / (h + h); |
346 | ||
347 | 465 | for (j = 1; j <= l; j++) |
348 | { | |
349 | 396 | f = getValue(i - 1, j - 1); |
350 | 396 | g = e[j - 1] - (hh * f); |
351 | 396 | e[j - 1] = g; |
352 | ||
353 | 2007 | for (k = 1; k <= j; k++) |
354 | { | |
355 | 1611 | double val = (f * e[k - 1]) + (g * getValue(i - 1, k - 1)); |
356 | 1611 | addValue(j - 1, k - 1, -val); |
357 | } | |
358 | } | |
359 | } | |
360 | } | |
361 | else | |
362 | { | |
363 | 9 | e[i - 1] = getValue(i - 1, l - 1); |
364 | } | |
365 | ||
366 | 78 | d[i - 1] = h; |
367 | } | |
368 | ||
369 | 9 | d[0] = 0.0; |
370 | 9 | e[0] = 0.0; |
371 | ||
372 | 96 | for (i = 1; i <= n; i++) |
373 | { | |
374 | 87 | final int l = i - 1; |
375 | ||
376 | 87 | if (d[i - 1] != 0.0) |
377 | { | |
378 | 465 | for (j = 1; j <= l; j++) |
379 | { | |
380 | 396 | g = 0.0; |
381 | ||
382 | 3222 | for (k = 1; k <= l; k++) |
383 | { | |
384 | 2826 | g += (getValue(i - 1, k - 1) * getValue(k - 1, j - 1)); |
385 | } | |
386 | ||
387 | 3222 | for (k = 1; k <= l; k++) |
388 | { | |
389 | 2826 | addValue(k - 1, j - 1, -(g * getValue(k - 1, i - 1))); |
390 | } | |
391 | } | |
392 | } | |
393 | ||
394 | 87 | d[i - 1] = getValue(i - 1, i - 1); |
395 | 87 | setValue(i - 1, i - 1, 1.0); |
396 | ||
397 | 492 | for (j = 1; j <= l; j++) |
398 | { | |
399 | 405 | setValue(j - 1, i - 1, 0.0); |
400 | 405 | setValue(i - 1, j - 1, 0.0); |
401 | } | |
402 | } | |
403 | } | |
404 | ||
405 | /** | |
406 | * Adds f to the value at [i, j] and returns the new value | |
407 | * | |
408 | * @param i | |
409 | * @param j | |
410 | * @param f | |
411 | */ | |
412 | 3005 | protected double addValue(int i, int j, double f) |
413 | { | |
414 | 3005 | double v = value[i][j] + f; |
415 | 3005 | value[i][j] = v; |
416 | 3005 | return v; |
417 | } | |
418 | ||
419 | /** | |
420 | * Divides the value at [i, j] by divisor and returns the new value. If d is | |
421 | * zero, returns the unchanged value. | |
422 | * | |
423 | * @param i | |
424 | * @param j | |
425 | * @param divisor | |
426 | * @return | |
427 | */ | |
428 | 250 | protected double divideValue(int i, int j, double divisor) |
429 | { | |
430 | 250 | if (divisor == 0d) |
431 | { | |
432 | 0 | return getValue(i, j); |
433 | } | |
434 | 250 | double v = value[i][j]; |
435 | 250 | v = v / divisor; |
436 | 250 | value[i][j] = v; |
437 | 250 | return v; |
438 | } | |
439 | ||
440 | /** | |
441 | * DOCUMENT ME! | |
442 | */ | |
443 | 3 | @Override |
444 | public void tqli() throws Exception | |
445 | { | |
446 | 3 | int n = rows; |
447 | ||
448 | 3 | int m; |
449 | 3 | int l; |
450 | 3 | int iter; |
451 | 3 | int i; |
452 | 3 | int k; |
453 | 3 | double s; |
454 | 3 | double r; |
455 | 3 | double p; |
456 | ||
457 | 3 | double g; |
458 | 3 | double f; |
459 | 3 | double dd; |
460 | 3 | double c; |
461 | 3 | double b; |
462 | ||
463 | 27 | for (i = 2; i <= n; i++) |
464 | { | |
465 | 24 | e[i - 2] = e[i - 1]; |
466 | } | |
467 | ||
468 | 3 | e[n - 1] = 0.0; |
469 | ||
470 | 30 | for (l = 1; l <= n; l++) |
471 | { | |
472 | 27 | iter = 0; |
473 | ||
474 | 27 | do |
475 | { | |
476 | 371 | for (m = l; m <= (n - 1); m++) |
477 | { | |
478 | 325 | dd = Math.abs(d[m - 1]) + Math.abs(d[m]); |
479 | ||
480 | 325 | if ((Math.abs(e[m - 1]) + dd) == dd) |
481 | { | |
482 | 27 | break; |
483 | } | |
484 | } | |
485 | ||
486 | 73 | if (m != l) |
487 | { | |
488 | 46 | iter++; |
489 | ||
490 | 46 | if (iter == MAX_ITER) |
491 | { | |
492 | 0 | throw new Exception(MessageManager.formatMessage( |
493 | "exception.matrix_too_many_iteration", new String[] | |
494 | { "tqli", Integer.valueOf(MAX_ITER).toString() })); | |
495 | } | |
496 | else | |
497 | { | |
498 | // jalview.bin.Console.outPrintln("Iteration " + iter); | |
499 | } | |
500 | ||
501 | 46 | g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); |
502 | 46 | r = Math.sqrt((g * g) + 1.0); |
503 | 46 | g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); |
504 | 46 | c = 1.0; |
505 | 46 | s = c; |
506 | 46 | p = 0.0; |
507 | ||
508 | 344 | for (i = m - 1; i >= l; i--) |
509 | { | |
510 | 298 | f = s * e[i - 1]; |
511 | 298 | b = c * e[i - 1]; |
512 | ||
513 | 298 | if (Math.abs(f) >= Math.abs(g)) |
514 | { | |
515 | 34 | c = g / f; |
516 | 34 | r = Math.sqrt((c * c) + 1.0); |
517 | 34 | e[i] = f * r; |
518 | 34 | s = 1.0 / r; |
519 | 34 | c *= s; |
520 | } | |
521 | else | |
522 | { | |
523 | 264 | s = f / g; |
524 | 264 | r = Math.sqrt((s * s) + 1.0); |
525 | 264 | e[i] = g * r; |
526 | 264 | c = 1.0 / r; |
527 | 264 | s *= c; |
528 | } | |
529 | ||
530 | 298 | g = d[i] - p; |
531 | 298 | r = ((d[i - 1] - g) * s) + (2.0 * c * b); |
532 | 298 | p = s * r; |
533 | 298 | d[i] = g + p; |
534 | 298 | g = (c * r) - b; |
535 | ||
536 | 4228 | for (k = 1; k <= n; k++) |
537 | { | |
538 | 3930 | f = getValue(k - 1, i); |
539 | 3930 | setValue(k - 1, i, (s * getValue(k - 1, i - 1)) + (c * f)); |
540 | 3930 | setValue(k - 1, i - 1, |
541 | (c * getValue(k - 1, i - 1)) - (s * f)); | |
542 | } | |
543 | } | |
544 | ||
545 | 46 | d[l - 1] = d[l - 1] - p; |
546 | 46 | e[l - 1] = g; |
547 | 46 | e[m - 1] = 0.0; |
548 | } | |
549 | 73 | } while (m != l); |
550 | } | |
551 | } | |
552 | ||
553 | 71178 | @Override |
554 | public double getValue(int i, int j) | |
555 | { | |
556 | 71178 | return value[i][j]; |
557 | } | |
558 | ||
559 | 19083 | @Override |
560 | public void setValue(int i, int j, double val) | |
561 | { | |
562 | 19083 | value[i][j] = val; |
563 | } | |
564 | ||
565 | /** | |
566 | * DOCUMENT ME! | |
567 | */ | |
568 | 0 | public void tred2() |
569 | { | |
570 | 0 | int n = rows; |
571 | 0 | int l; |
572 | 0 | int k; |
573 | 0 | int j; |
574 | 0 | int i; |
575 | ||
576 | 0 | double scale; |
577 | 0 | double hh; |
578 | 0 | double h; |
579 | 0 | double g; |
580 | 0 | double f; |
581 | ||
582 | 0 | this.d = new double[rows]; |
583 | 0 | this.e = new double[rows]; |
584 | ||
585 | 0 | for (i = n - 1; i >= 1; i--) |
586 | { | |
587 | 0 | l = i - 1; |
588 | 0 | h = 0.0; |
589 | 0 | scale = 0.0; |
590 | ||
591 | 0 | if (l > 0) |
592 | { | |
593 | 0 | for (k = 0; k < l; k++) |
594 | { | |
595 | 0 | scale += Math.abs(value[i][k]); |
596 | } | |
597 | ||
598 | 0 | if (scale == 0.0) |
599 | { | |
600 | 0 | e[i] = value[i][l]; |
601 | } | |
602 | else | |
603 | { | |
604 | 0 | for (k = 0; k < l; k++) |
605 | { | |
606 | 0 | value[i][k] /= scale; |
607 | 0 | h += (value[i][k] * value[i][k]); |
608 | } | |
609 | ||
610 | 0 | f = value[i][l]; |
611 | ||
612 | 0 | if (f > 0) |
613 | { | |
614 | 0 | g = -1.0 * Math.sqrt(h); |
615 | } | |
616 | else | |
617 | { | |
618 | 0 | g = Math.sqrt(h); |
619 | } | |
620 | ||
621 | 0 | e[i] = scale * g; |
622 | 0 | h -= (f * g); |
623 | 0 | value[i][l] = f - g; |
624 | 0 | f = 0.0; |
625 | ||
626 | 0 | for (j = 0; j < l; j++) |
627 | { | |
628 | 0 | value[j][i] = value[i][j] / h; |
629 | 0 | g = 0.0; |
630 | ||
631 | 0 | for (k = 0; k < j; k++) |
632 | { | |
633 | 0 | g += (value[j][k] * value[i][k]); |
634 | } | |
635 | ||
636 | 0 | for (k = j; k < l; k++) |
637 | { | |
638 | 0 | g += (value[k][j] * value[i][k]); |
639 | } | |
640 | ||
641 | 0 | e[j] = g / h; |
642 | 0 | f += (e[j] * value[i][j]); |
643 | } | |
644 | ||
645 | 0 | hh = f / (h + h); |
646 | ||
647 | 0 | for (j = 0; j < l; j++) |
648 | { | |
649 | 0 | f = value[i][j]; |
650 | 0 | g = e[j] - (hh * f); |
651 | 0 | e[j] = g; |
652 | ||
653 | 0 | for (k = 0; k < j; k++) |
654 | { | |
655 | 0 | value[j][k] -= ((f * e[k]) + (g * value[i][k])); |
656 | } | |
657 | } | |
658 | } | |
659 | } | |
660 | else | |
661 | { | |
662 | 0 | e[i] = value[i][l]; |
663 | } | |
664 | ||
665 | 0 | d[i] = h; |
666 | } | |
667 | ||
668 | 0 | d[0] = 0.0; |
669 | 0 | e[0] = 0.0; |
670 | ||
671 | 0 | for (i = 0; i < n; i++) |
672 | { | |
673 | 0 | l = i - 1; |
674 | ||
675 | 0 | if (d[i] != 0.0) |
676 | { | |
677 | 0 | for (j = 0; j < l; j++) |
678 | { | |
679 | 0 | g = 0.0; |
680 | ||
681 | 0 | for (k = 0; k < l; k++) |
682 | { | |
683 | 0 | g += (value[i][k] * value[k][j]); |
684 | } | |
685 | ||
686 | 0 | for (k = 0; k < l; k++) |
687 | { | |
688 | 0 | value[k][j] -= (g * value[k][i]); |
689 | } | |
690 | } | |
691 | } | |
692 | ||
693 | 0 | d[i] = value[i][i]; |
694 | 0 | value[i][i] = 1.0; |
695 | ||
696 | 0 | for (j = 0; j < l; j++) |
697 | { | |
698 | 0 | value[j][i] = 0.0; |
699 | 0 | value[i][j] = 0.0; |
700 | } | |
701 | } | |
702 | } | |
703 | ||
704 | /** | |
705 | * DOCUMENT ME! | |
706 | */ | |
707 | 0 | public void tqli2() throws Exception |
708 | { | |
709 | 0 | int n = rows; |
710 | ||
711 | 0 | int m; |
712 | 0 | int l; |
713 | 0 | int iter; |
714 | 0 | int i; |
715 | 0 | int k; |
716 | 0 | double s; |
717 | 0 | double r; |
718 | 0 | double p; |
719 | 0 | ; |
720 | ||
721 | 0 | double g; |
722 | 0 | double f; |
723 | 0 | double dd; |
724 | 0 | double c; |
725 | 0 | double b; |
726 | ||
727 | 0 | for (i = 2; i <= n; i++) |
728 | { | |
729 | 0 | e[i - 2] = e[i - 1]; |
730 | } | |
731 | ||
732 | 0 | e[n - 1] = 0.0; |
733 | ||
734 | 0 | for (l = 1; l <= n; l++) |
735 | { | |
736 | 0 | iter = 0; |
737 | ||
738 | 0 | do |
739 | { | |
740 | 0 | for (m = l; m <= (n - 1); m++) |
741 | { | |
742 | 0 | dd = Math.abs(d[m - 1]) + Math.abs(d[m]); |
743 | ||
744 | 0 | if ((Math.abs(e[m - 1]) + dd) == dd) |
745 | { | |
746 | 0 | break; |
747 | } | |
748 | } | |
749 | ||
750 | 0 | if (m != l) |
751 | { | |
752 | 0 | iter++; |
753 | ||
754 | 0 | if (iter == MAX_ITER) |
755 | { | |
756 | 0 | throw new Exception(MessageManager.formatMessage( |
757 | "exception.matrix_too_many_iteration", new String[] | |
758 | { "tqli2", Integer.valueOf(MAX_ITER).toString() })); | |
759 | } | |
760 | else | |
761 | { | |
762 | // jalview.bin.Console.outPrintln("Iteration " + iter); | |
763 | } | |
764 | ||
765 | 0 | g = (d[l] - d[l - 1]) / (2.0 * e[l - 1]); |
766 | 0 | r = Math.sqrt((g * g) + 1.0); |
767 | 0 | g = d[m - 1] - d[l - 1] + (e[l - 1] / (g + sign(r, g))); |
768 | 0 | c = 1.0; |
769 | 0 | s = c; |
770 | 0 | p = 0.0; |
771 | ||
772 | 0 | for (i = m - 1; i >= l; i--) |
773 | { | |
774 | 0 | f = s * e[i - 1]; |
775 | 0 | b = c * e[i - 1]; |
776 | ||
777 | 0 | if (Math.abs(f) >= Math.abs(g)) |
778 | { | |
779 | 0 | c = g / f; |
780 | 0 | r = Math.sqrt((c * c) + 1.0); |
781 | 0 | e[i] = f * r; |
782 | 0 | s = 1.0 / r; |
783 | 0 | c *= s; |
784 | } | |
785 | else | |
786 | { | |
787 | 0 | s = f / g; |
788 | 0 | r = Math.sqrt((s * s) + 1.0); |
789 | 0 | e[i] = g * r; |
790 | 0 | c = 1.0 / r; |
791 | 0 | s *= c; |
792 | } | |
793 | ||
794 | 0 | g = d[i] - p; |
795 | 0 | r = ((d[i - 1] - g) * s) + (2.0 * c * b); |
796 | 0 | p = s * r; |
797 | 0 | d[i] = g + p; |
798 | 0 | g = (c * r) - b; |
799 | ||
800 | 0 | for (k = 1; k <= n; k++) |
801 | { | |
802 | 0 | f = value[k - 1][i]; |
803 | 0 | value[k - 1][i] = (s * value[k - 1][i - 1]) + (c * f); |
804 | 0 | value[k - 1][i - 1] = (c * value[k - 1][i - 1]) - (s * f); |
805 | } | |
806 | } | |
807 | ||
808 | 0 | d[l - 1] = d[l - 1] - p; |
809 | 0 | e[l - 1] = g; |
810 | 0 | e[m - 1] = 0.0; |
811 | } | |
812 | 0 | } while (m != l); |
813 | } | |
814 | } | |
815 | ||
816 | /** | |
817 | * Answers the first argument with the sign of the second argument | |
818 | * | |
819 | * @param a | |
820 | * @param b | |
821 | * | |
822 | * @return | |
823 | */ | |
824 | 46 | static double sign(double a, double b) |
825 | { | |
826 | 46 | if (b < 0) |
827 | { | |
828 | 12 | return -Math.abs(a); |
829 | } | |
830 | else | |
831 | { | |
832 | 34 | return Math.abs(a); |
833 | } | |
834 | } | |
835 | ||
836 | /** | |
837 | * returns the matrix as a double[][] array | |
838 | * | |
839 | * @return | |
840 | */ | |
841 | 0 | @Override |
842 | public double[][] asArray() | |
843 | { | |
844 | 0 | return value; |
845 | } | |
846 | ||
847 | /** | |
848 | * Returns an array containing the values in the specified column | |
849 | * | |
850 | * @param col | |
851 | * | |
852 | * @return | |
853 | */ | |
854 | 0 | @Override |
855 | public double[] getColumn(int col) | |
856 | { | |
857 | 0 | double[] out = new double[rows]; |
858 | ||
859 | 0 | for (int i = 0; i < rows; i++) |
860 | { | |
861 | 0 | out[i] = value[i][col]; |
862 | } | |
863 | ||
864 | 0 | return out; |
865 | } | |
866 | ||
867 | /** | |
868 | * DOCUMENT ME! | |
869 | * | |
870 | * @param ps | |
871 | * DOCUMENT ME! | |
872 | * @param format | |
873 | */ | |
874 | 0 | @Override |
875 | public void printD(PrintStream ps, String format) | |
876 | { | |
877 | 0 | for (int j = 0; j < d.length; j++) |
878 | { | |
879 | 0 | Format.print(ps, format, d[j]); |
880 | } | |
881 | } | |
882 | ||
883 | /** | |
884 | * DOCUMENT ME! | |
885 | * | |
886 | * @param ps | |
887 | * DOCUMENT ME! | |
888 | * @param format | |
889 | * TODO | |
890 | */ | |
891 | 0 | @Override |
892 | public void printE(PrintStream ps, String format) | |
893 | { | |
894 | 0 | for (int j = 0; j < rows; j++) |
895 | { | |
896 | 0 | Format.print(ps, format, e[j]); |
897 | } | |
898 | } | |
899 | ||
900 | 72 | @Override |
901 | public double[] getD() | |
902 | { | |
903 | 72 | return d; |
904 | } | |
905 | ||
906 | 27 | @Override |
907 | public double[] getE() | |
908 | { | |
909 | 27 | return e; |
910 | } | |
911 | ||
912 | 346 | @Override |
913 | public int height() | |
914 | { | |
915 | 346 | return rows; |
916 | } | |
917 | ||
918 | 2450 | @Override |
919 | public int width() | |
920 | { | |
921 | 2450 | return cols; |
922 | } | |
923 | ||
924 | 26 | @Override |
925 | public double[] getRow(int i) | |
926 | { | |
927 | 26 | double[] row = new double[cols]; |
928 | 26 | System.arraycopy(value[i], 0, row, 0, cols); |
929 | 26 | return row; |
930 | } | |
931 | ||
932 | /** | |
933 | * Returns a length 2 array of {minValue, maxValue} of all values in the | |
934 | * matrix. Returns null if the matrix is null or empty. | |
935 | * | |
936 | * @return | |
937 | */ | |
938 | 13 | double[] findMinMax() |
939 | { | |
940 | 13 | if (value == null) |
941 | { | |
942 | 0 | return null; |
943 | } | |
944 | 13 | double min = Double.MAX_VALUE; |
945 | 13 | double max = -Double.MAX_VALUE; |
946 | 13 | boolean empty = true; |
947 | 13 | for (double[] row : value) |
948 | { | |
949 | 1023 | if (row != null) |
950 | { | |
951 | 1023 | for (double x : row) |
952 | { | |
953 | 1000054 | empty = false; |
954 | 1000054 | if (x > max) |
955 | { | |
956 | 39 | max = x; |
957 | } | |
958 | 1000054 | if (x < min) |
959 | { | |
960 | 35 | min = x; |
961 | } | |
962 | } | |
963 | } | |
964 | } | |
965 | 13 | return empty ? null : new double[] { min, max }; |
966 | } | |
967 | ||
968 | /** | |
969 | * {@inheritDoc} | |
970 | */ | |
971 | 10 | @Override |
972 | public void reverseRange(boolean maxToZero) | |
973 | { | |
974 | 10 | if (value == null) |
975 | { | |
976 | 0 | return; |
977 | } | |
978 | 10 | double[] minMax = findMinMax(); |
979 | 10 | if (minMax == null) |
980 | { | |
981 | 0 | return; // empty matrix |
982 | } | |
983 | 10 | double subtractFrom = maxToZero ? minMax[1] : minMax[0] + minMax[1]; |
984 | ||
985 | 10 | for (double[] row : value) |
986 | { | |
987 | 20 | if (row != null) |
988 | { | |
989 | 20 | int j = 0; |
990 | 20 | for (double x : row) |
991 | { | |
992 | 48 | row[j] = subtractFrom - x; |
993 | 48 | j++; |
994 | } | |
995 | } | |
996 | } | |
997 | } | |
998 | ||
999 | /** | |
1000 | * Multiplies every entry in the matrix by the given value. | |
1001 | * | |
1002 | * @param | |
1003 | */ | |
1004 | 1 | @Override |
1005 | public void multiply(double by) | |
1006 | { | |
1007 | 1 | for (double[] row : value) |
1008 | { | |
1009 | 2 | if (row != null) |
1010 | { | |
1011 | 8 | for (int i = 0; i < row.length; i++) |
1012 | { | |
1013 | 6 | row[i] *= by; |
1014 | } | |
1015 | } | |
1016 | } | |
1017 | } | |
1018 | ||
1019 | /** | |
1020 | * Add d to all entries of this matrix | |
1021 | * | |
1022 | * @param d | |
1023 | * ~ value to add | |
1024 | */ | |
1025 | 0 | @Override |
1026 | public void add(double d) | |
1027 | { | |
1028 | 0 | for (double[] row : value) |
1029 | { | |
1030 | 0 | if (row != null) |
1031 | { | |
1032 | 0 | for (int i = 0; i < row.length; i++) |
1033 | { | |
1034 | 0 | row[i] += d; |
1035 | } | |
1036 | } | |
1037 | } | |
1038 | } | |
1039 | ||
1040 | 2 | @Override |
1041 | public void setD(double[] v) | |
1042 | { | |
1043 | 2 | d = v; |
1044 | } | |
1045 | ||
1046 | 2 | @Override |
1047 | public void setE(double[] v) | |
1048 | { | |
1049 | 2 | e = v; |
1050 | } | |
1051 | ||
1052 | 0 | public double getTotal() |
1053 | { | |
1054 | 0 | double d = 0d; |
1055 | 0 | for (int i = 0; i < this.height(); i++) |
1056 | { | |
1057 | 0 | for (int j = 0; j < this.width(); j++) |
1058 | { | |
1059 | 0 | d += value[i][j]; |
1060 | } | |
1061 | } | |
1062 | 0 | return d; |
1063 | } | |
1064 | ||
1065 | /** | |
1066 | * {@inheritDoc} | |
1067 | */ | |
1068 | 12 | @Override |
1069 | public boolean equals(MatrixI m2, double delta) | |
1070 | { | |
1071 | 12 | if (m2 == null || this.height() != m2.height() |
1072 | || this.width() != m2.width()) | |
1073 | { | |
1074 | 2 | return false; |
1075 | } | |
1076 | 27 | for (int i = 0; i < this.height(); i++) |
1077 | { | |
1078 | 66 | for (int j = 0; j < this.width(); j++) |
1079 | { | |
1080 | 49 | double diff = this.getValue(i, j) - m2.getValue(i, j); |
1081 | 49 | if (Math.abs(diff) > delta) |
1082 | { | |
1083 | 3 | return false; |
1084 | } | |
1085 | } | |
1086 | } | |
1087 | 7 | return true; |
1088 | } | |
1089 | ||
1090 | /** | |
1091 | * Returns a copy in which every value in the matrix is its absolute | |
1092 | * | |
1093 | * @return | |
1094 | */ | |
1095 | 0 | @Override |
1096 | public MatrixI absolute() | |
1097 | { | |
1098 | 0 | MatrixI copy = this.copy(); |
1099 | 0 | for (int i = 0; i < copy.width(); i++) |
1100 | { | |
1101 | 0 | double[] row = copy.getRow(i); |
1102 | 0 | if (row != null) |
1103 | { | |
1104 | 0 | for (int j = 0; j < row.length; j++) |
1105 | { | |
1106 | 0 | row[j] = Math.abs(row[j]); |
1107 | } | |
1108 | } | |
1109 | } | |
1110 | 0 | return copy; |
1111 | } | |
1112 | ||
1113 | /** | |
1114 | * Returns the mean of each row | |
1115 | * | |
1116 | * @return | |
1117 | */ | |
1118 | 0 | @Override |
1119 | public double[] meanRow() | |
1120 | { | |
1121 | 0 | double[] mean = new double[rows]; |
1122 | 0 | int i = 0; |
1123 | 0 | for (double[] row : value) |
1124 | { | |
1125 | 0 | if (row != null) |
1126 | { | |
1127 | 0 | mean[i++] = MiscMath.mean(row); |
1128 | } | |
1129 | } | |
1130 | 0 | return mean; |
1131 | } | |
1132 | ||
1133 | /** | |
1134 | * Returns the mean of each column | |
1135 | * | |
1136 | * @return | |
1137 | */ | |
1138 | 0 | @Override |
1139 | public double[] meanCol() | |
1140 | { | |
1141 | 0 | double[] mean = new double[cols]; |
1142 | 0 | for (int j = 0; j < cols; j++) |
1143 | { | |
1144 | 0 | double[] column = getColumn(j); |
1145 | 0 | if (column != null) |
1146 | { | |
1147 | 0 | mean[j] = MiscMath.mean(column); |
1148 | } | |
1149 | } | |
1150 | 0 | return mean; |
1151 | } | |
1152 | ||
1153 | /** | |
1154 | * return a flattened matrix containing the sum of each column | |
1155 | * | |
1156 | * @return | |
1157 | */ | |
1158 | 0 | @Override |
1159 | public double[] sumCol() | |
1160 | { | |
1161 | 0 | double[] sum = new double[cols]; |
1162 | 0 | for (int j = 0; j < cols; j++) |
1163 | { | |
1164 | 0 | double[] column = getColumn(j); |
1165 | 0 | if (column != null) |
1166 | { | |
1167 | 0 | sum[j] = MiscMath.sum(column); |
1168 | } | |
1169 | } | |
1170 | 0 | return sum; |
1171 | } | |
1172 | ||
1173 | /** | |
1174 | * returns the mean value of the complete matrix | |
1175 | * | |
1176 | * @return | |
1177 | */ | |
1178 | 0 | @Override |
1179 | public double mean() | |
1180 | { | |
1181 | 0 | double sum = 0; |
1182 | 0 | int nanCount = 0; |
1183 | 0 | for (double[] row : value) |
1184 | { | |
1185 | 0 | for (double col : row) |
1186 | { | |
1187 | 0 | if (!Double.isNaN(col)) |
1188 | { | |
1189 | 0 | sum += col; |
1190 | } | |
1191 | else | |
1192 | { | |
1193 | 0 | nanCount++; |
1194 | } | |
1195 | } | |
1196 | } | |
1197 | 0 | return sum / (double) (this.rows * this.cols - nanCount); |
1198 | } | |
1199 | ||
1200 | /** | |
1201 | * fills up a diagonal matrix with its transposed copy !other side should be | |
1202 | * filled with 0 !keeps Double.NaN found in either side | |
1203 | * | |
1204 | * TODO check on which side it was diagonal and only do calculations for the | |
1205 | * other side | |
1206 | */ | |
1207 | 0 | @Override |
1208 | public void fillDiagonal() | |
1209 | { | |
1210 | 0 | int n = this.rows; |
1211 | 0 | int m = this.cols; |
1212 | 0 | MatrixI copy = this.transpose(); // goes through each element in the matrix |
1213 | // and | |
1214 | 0 | for (int i = 0; i < n; i++) // adds the value in the transposed copy to the |
1215 | // original value | |
1216 | { | |
1217 | 0 | for (int j = 0; j < m; j++) |
1218 | { | |
1219 | 0 | if (i != j) |
1220 | { | |
1221 | 0 | this.addValue(i, j, copy.getValue(i, j)); |
1222 | } | |
1223 | } | |
1224 | } | |
1225 | } | |
1226 | ||
1227 | /** | |
1228 | * counts the number of Double.NaN in the matrix | |
1229 | * | |
1230 | * @return | |
1231 | */ | |
1232 | 0 | @Override |
1233 | public int countNaN() | |
1234 | { | |
1235 | 0 | int NaN = 0; |
1236 | 0 | for (int i = 0; i < this.rows; i++) |
1237 | { | |
1238 | 0 | for (int j = 0; j < this.cols; j++) |
1239 | { | |
1240 | 0 | if (Double.isNaN(this.getValue(i, j))) |
1241 | { | |
1242 | 0 | NaN++; |
1243 | } | |
1244 | } | |
1245 | } | |
1246 | 0 | return NaN; |
1247 | } | |
1248 | ||
1249 | /** | |
1250 | * performs an element-wise addition of this matrix by another matrix ~ this - | |
1251 | * m | |
1252 | * | |
1253 | * @param m | |
1254 | * ~ other matrix | |
1255 | * | |
1256 | * @return | |
1257 | */ | |
1258 | 0 | @Override |
1259 | public MatrixI add(MatrixI m) | |
1260 | { | |
1261 | 0 | if (m.width() != cols || m.height() != rows) |
1262 | { | |
1263 | 0 | throw new IllegalArgumentException( |
1264 | "Can't add a " + m.height() + "x" + m.width() + " to a " | |
1265 | + this.rows + "x" + this.cols + " matrix"); | |
1266 | } | |
1267 | 0 | double[][] tmp = new double[this.rows][this.cols]; |
1268 | 0 | for (int i = 0; i < this.rows; i++) |
1269 | { | |
1270 | 0 | for (int j = 0; j < this.cols; j++) |
1271 | { | |
1272 | 0 | tmp[i][j] = this.getValue(i, j) + m.getValue(i, j); |
1273 | } | |
1274 | } | |
1275 | 0 | return new Matrix(tmp); |
1276 | } | |
1277 | ||
1278 | /** | |
1279 | * performs an element-wise subtraction of this matrix by another matrix ~ | |
1280 | * this - m | |
1281 | * | |
1282 | * @param m | |
1283 | * ~ other matrix | |
1284 | * | |
1285 | * @return | |
1286 | */ | |
1287 | 0 | @Override |
1288 | public MatrixI subtract(MatrixI m) | |
1289 | { | |
1290 | 0 | if (m.width() != cols || m.height() != rows) |
1291 | { | |
1292 | 0 | throw new IllegalArgumentException("Can't subtract a " + m.height() |
1293 | + "x" + m.width() + " from a " + this.rows + "x" + this.cols | |
1294 | + " matrix"); | |
1295 | } | |
1296 | 0 | double[][] tmp = new double[this.rows][this.cols]; |
1297 | 0 | for (int i = 0; i < this.rows; i++) |
1298 | { | |
1299 | 0 | for (int j = 0; j < this.cols; j++) |
1300 | { | |
1301 | 0 | tmp[i][j] = this.getValue(i, j) - m.getValue(i, j); |
1302 | } | |
1303 | } | |
1304 | 0 | return new Matrix(tmp); |
1305 | } | |
1306 | ||
1307 | /** | |
1308 | * performs an element-wise multiplication of this matrix by another matrix ~ | |
1309 | * this * m | |
1310 | * | |
1311 | * @param m | |
1312 | * ~ other matrix | |
1313 | * | |
1314 | * @return | |
1315 | */ | |
1316 | 0 | @Override |
1317 | public MatrixI elementwiseMultiply(MatrixI m) | |
1318 | { | |
1319 | 0 | if (m.width() != cols || m.height() != rows) |
1320 | { | |
1321 | 0 | throw new IllegalArgumentException( |
1322 | "Can't multiply a " + this.rows + "x" + this.cols + " by a " | |
1323 | + m.height() + "x" + m.width() + " matrix"); | |
1324 | } | |
1325 | 0 | double[][] tmp = new double[this.rows][this.cols]; |
1326 | 0 | for (int i = 0; i < this.rows; i++) |
1327 | { | |
1328 | 0 | for (int j = 0; j < this.cols; j++) |
1329 | { | |
1330 | 0 | tmp[i][j] = this.getValue(i, j) * m.getValue(i, j); |
1331 | } | |
1332 | } | |
1333 | 0 | return new Matrix(tmp); |
1334 | } | |
1335 | ||
1336 | /** | |
1337 | * performs an element-wise division of this matrix by another matrix ~ this / | |
1338 | * m | |
1339 | * | |
1340 | * @param m | |
1341 | * ~ other matrix | |
1342 | * | |
1343 | * @return | |
1344 | */ | |
1345 | 0 | @Override |
1346 | public MatrixI elementwiseDivide(MatrixI m) | |
1347 | { | |
1348 | 0 | if (m.width() != cols || m.height() != rows) |
1349 | { | |
1350 | 0 | throw new IllegalArgumentException( |
1351 | "Can't divide a " + this.rows + "x" + this.cols + " by a " | |
1352 | + m.height() + "x" + m.width() + " matrix"); | |
1353 | } | |
1354 | 0 | double[][] tmp = new double[this.rows][this.cols]; |
1355 | 0 | for (int i = 0; i < this.rows; i++) |
1356 | { | |
1357 | 0 | for (int j = 0; j < this.cols; j++) |
1358 | { | |
1359 | 0 | tmp[i][j] = this.getValue(i, j) / m.getValue(i, j); |
1360 | } | |
1361 | } | |
1362 | 0 | return new Matrix(tmp); |
1363 | } | |
1364 | ||
1365 | /** | |
1366 | * calculate the root-mean-square for tow matrices | |
1367 | * | |
1368 | * @param m | |
1369 | * ~ other matrix | |
1370 | * | |
1371 | * @return | |
1372 | */ | |
1373 | 0 | @Override |
1374 | public double rmsd(MatrixI m) | |
1375 | { | |
1376 | 0 | MatrixI squaredDeviates = this.subtract(m); |
1377 | 0 | squaredDeviates = squaredDeviates.preMultiply(squaredDeviates); |
1378 | 0 | return Math.sqrt(squaredDeviates.mean()); |
1379 | } | |
1380 | ||
1381 | /** | |
1382 | * calculates the Frobenius norm of this matrix | |
1383 | * | |
1384 | * @return | |
1385 | */ | |
1386 | 0 | @Override |
1387 | public double norm() | |
1388 | { | |
1389 | 0 | double result = 0; |
1390 | 0 | for (double[] row : value) |
1391 | { | |
1392 | 0 | for (double val : row) |
1393 | { | |
1394 | 0 | result += Math.pow(val, 2); |
1395 | } | |
1396 | } | |
1397 | 0 | return Math.sqrt(result); |
1398 | } | |
1399 | ||
1400 | /** | |
1401 | * returns the sum of all values in this matrix | |
1402 | * | |
1403 | * @return | |
1404 | */ | |
1405 | 0 | @Override |
1406 | public double sum() | |
1407 | { | |
1408 | 0 | double sum = 0; |
1409 | 0 | for (double[] row : value) |
1410 | { | |
1411 | 0 | for (double val : row) |
1412 | { | |
1413 | 0 | sum += (Double.isNaN(val)) ? 0.0 : val; |
1414 | } | |
1415 | } | |
1416 | 0 | return sum; |
1417 | } | |
1418 | ||
1419 | /** | |
1420 | * returns the sum-product of this matrix with vector v | |
1421 | * | |
1422 | * @param v | |
1423 | * ~ vector | |
1424 | * | |
1425 | * @return | |
1426 | */ | |
1427 | 0 | @Override |
1428 | public double[] sumProduct(double[] v) | |
1429 | { | |
1430 | 0 | if (v.length != cols) |
1431 | { | |
1432 | 0 | throw new IllegalArgumentException( |
1433 | "Vector and matrix do not have the same dimension! (" | |
1434 | + v.length + " != " + cols + ")"); | |
1435 | } | |
1436 | 0 | double[] result = new double[rows]; |
1437 | 0 | for (int i = 0; i < rows; i++) |
1438 | { | |
1439 | 0 | double[] row = value[i]; |
1440 | 0 | double sum = 0; |
1441 | 0 | for (int j = 0; j < row.length; j++) |
1442 | { | |
1443 | 0 | sum += row[j] * v[j]; |
1444 | } | |
1445 | 0 | result[i] = sum; |
1446 | } | |
1447 | 0 | return result; |
1448 | } | |
1449 | ||
1450 | /** | |
1451 | * mirrors columns of the matrix | |
1452 | * | |
1453 | * @return | |
1454 | */ | |
1455 | 0 | @Override |
1456 | public MatrixI mirrorCol() | |
1457 | { | |
1458 | 0 | double[][] result = new double[rows][cols]; |
1459 | 0 | for (int i = 0; i < rows; i++) |
1460 | { | |
1461 | 0 | int k = cols - 1; // reverse col |
1462 | 0 | for (int j = 0; j < cols; j++) |
1463 | { | |
1464 | 0 | result[i][k--] = this.getValue(i, j); |
1465 | } | |
1466 | } | |
1467 | 0 | MatrixI resultMatrix = new Matrix(result); |
1468 | 0 | if (d != null) |
1469 | 0 | resultMatrix.setD(d); |
1470 | 0 | if (e != null) |
1471 | 0 | resultMatrix.setE(e); |
1472 | ||
1473 | 0 | return resultMatrix; |
1474 | } | |
1475 | } |