1 /*
2 * Copyright (c) 2011. Philipp Wagner <bytefish[at]gmx[dot]de>.
3 * Released to public domain under terms of the BSD Simplified license.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions are met:
7 * * Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * * Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 * * Neither the name of the organization nor the names of its contributors
13 * may be used to endorse or promote products derived from this software
14 * without specific prior written permission.
15 *
16 * See <http://www.opensource.org/licenses/bsd-license>
17 */
18
19 #include "precomp.hpp"
20 #include <iostream>
21 #include <map>
22 #include <set>
23
24 namespace cv
25 {
26
27 // Removes duplicate elements in a given vector.
28 template<typename _Tp>
remove_dups(const std::vector<_Tp> & src)29 inline std::vector<_Tp> remove_dups(const std::vector<_Tp>& src) {
30 typedef typename std::set<_Tp>::const_iterator constSetIterator;
31 typedef typename std::vector<_Tp>::const_iterator constVecIterator;
32 std::set<_Tp> set_elems;
33 for (constVecIterator it = src.begin(); it != src.end(); ++it)
34 set_elems.insert(*it);
35 std::vector<_Tp> elems;
36 for (constSetIterator it = set_elems.begin(); it != set_elems.end(); ++it)
37 elems.push_back(*it);
38 return elems;
39 }
40
argsort(InputArray _src,bool ascending=true)41 static Mat argsort(InputArray _src, bool ascending=true)
42 {
43 Mat src = _src.getMat();
44 if (src.rows != 1 && src.cols != 1) {
45 String error_message = "Wrong shape of input matrix! Expected a matrix with one row or column.";
46 CV_Error(Error::StsBadArg, error_message);
47 }
48 int flags = SORT_EVERY_ROW | (ascending ? SORT_ASCENDING : SORT_DESCENDING);
49 Mat sorted_indices;
50 sortIdx(src.reshape(1,1),sorted_indices,flags);
51 return sorted_indices;
52 }
53
asRowMatrix(InputArrayOfArrays src,int rtype,double alpha=1,double beta=0)54 static Mat asRowMatrix(InputArrayOfArrays src, int rtype, double alpha=1, double beta=0) {
55 // make sure the input data is a vector of matrices or vector of vector
56 if(src.kind() != _InputArray::STD_VECTOR_MAT && src.kind() != _InputArray::STD_VECTOR_VECTOR) {
57 String error_message = "The data is expected as InputArray::STD_VECTOR_MAT (a std::vector<Mat>) or _InputArray::STD_VECTOR_VECTOR (a std::vector< std::vector<...> >).";
58 CV_Error(Error::StsBadArg, error_message);
59 }
60 // number of samples
61 size_t n = src.total();
62 // return empty matrix if no matrices given
63 if(n == 0)
64 return Mat();
65 // dimensionality of (reshaped) samples
66 size_t d = src.getMat(0).total();
67 // create data matrix
68 Mat data((int)n, (int)d, rtype);
69 // now copy data
70 for(int i = 0; i < (int)n; i++) {
71 // make sure data can be reshaped, throw exception if not!
72 if(src.getMat(i).total() != d) {
73 String error_message = format("Wrong number of elements in matrix #%d! Expected %d was %d.", i, (int)d, (int)src.getMat(i).total());
74 CV_Error(Error::StsBadArg, error_message);
75 }
76 // get a hold of the current row
77 Mat xi = data.row(i);
78 // make reshape happy by cloning for non-continuous matrices
79 if(src.getMat(i).isContinuous()) {
80 src.getMat(i).reshape(1, 1).convertTo(xi, rtype, alpha, beta);
81 } else {
82 src.getMat(i).clone().reshape(1, 1).convertTo(xi, rtype, alpha, beta);
83 }
84 }
85 return data;
86 }
87
sortMatrixColumnsByIndices(InputArray _src,InputArray _indices,OutputArray _dst)88 static void sortMatrixColumnsByIndices(InputArray _src, InputArray _indices, OutputArray _dst) {
89 if(_indices.getMat().type() != CV_32SC1) {
90 CV_Error(Error::StsUnsupportedFormat, "cv::sortColumnsByIndices only works on integer indices!");
91 }
92 Mat src = _src.getMat();
93 std::vector<int> indices = _indices.getMat();
94 _dst.create(src.rows, src.cols, src.type());
95 Mat dst = _dst.getMat();
96 for(size_t idx = 0; idx < indices.size(); idx++) {
97 Mat originalCol = src.col(indices[idx]);
98 Mat sortedCol = dst.col((int)idx);
99 originalCol.copyTo(sortedCol);
100 }
101 }
102
sortMatrixColumnsByIndices(InputArray src,InputArray indices)103 static Mat sortMatrixColumnsByIndices(InputArray src, InputArray indices) {
104 Mat dst;
105 sortMatrixColumnsByIndices(src, indices, dst);
106 return dst;
107 }
108
109
110 template<typename _Tp> static bool
isSymmetric_(InputArray src)111 isSymmetric_(InputArray src) {
112 Mat _src = src.getMat();
113 if(_src.cols != _src.rows)
114 return false;
115 for (int i = 0; i < _src.rows; i++) {
116 for (int j = 0; j < _src.cols; j++) {
117 _Tp a = _src.at<_Tp> (i, j);
118 _Tp b = _src.at<_Tp> (j, i);
119 if (a != b) {
120 return false;
121 }
122 }
123 }
124 return true;
125 }
126
127 template<typename _Tp> static bool
isSymmetric_(InputArray src,double eps)128 isSymmetric_(InputArray src, double eps) {
129 Mat _src = src.getMat();
130 if(_src.cols != _src.rows)
131 return false;
132 for (int i = 0; i < _src.rows; i++) {
133 for (int j = 0; j < _src.cols; j++) {
134 _Tp a = _src.at<_Tp> (i, j);
135 _Tp b = _src.at<_Tp> (j, i);
136 if (std::abs(a - b) > eps) {
137 return false;
138 }
139 }
140 }
141 return true;
142 }
143
isSymmetric(InputArray src,double eps=1e-16)144 static bool isSymmetric(InputArray src, double eps=1e-16)
145 {
146 Mat m = src.getMat();
147 switch (m.type()) {
148 case CV_8SC1: return isSymmetric_<char>(m); break;
149 case CV_8UC1:
150 return isSymmetric_<unsigned char>(m); break;
151 case CV_16SC1:
152 return isSymmetric_<short>(m); break;
153 case CV_16UC1:
154 return isSymmetric_<unsigned short>(m); break;
155 case CV_32SC1:
156 return isSymmetric_<int>(m); break;
157 case CV_32FC1:
158 return isSymmetric_<float>(m, eps); break;
159 case CV_64FC1:
160 return isSymmetric_<double>(m, eps); break;
161 default:
162 break;
163 }
164 return false;
165 }
166
167
168 //------------------------------------------------------------------------------
169 // cv::subspaceProject
170 //------------------------------------------------------------------------------
subspaceProject(InputArray _W,InputArray _mean,InputArray _src)171 Mat LDA::subspaceProject(InputArray _W, InputArray _mean, InputArray _src) {
172 // get data matrices
173 Mat W = _W.getMat();
174 Mat mean = _mean.getMat();
175 Mat src = _src.getMat();
176 // get number of samples and dimension
177 int n = src.rows;
178 int d = src.cols;
179 // make sure the data has the correct shape
180 if(W.rows != d) {
181 String error_message = format("Wrong shapes for given matrices. Was size(src) = (%d,%d), size(W) = (%d,%d).", src.rows, src.cols, W.rows, W.cols);
182 CV_Error(Error::StsBadArg, error_message);
183 }
184 // make sure mean is correct if not empty
185 if(!mean.empty() && (mean.total() != (size_t) d)) {
186 String error_message = format("Wrong mean shape for the given data matrix. Expected %d, but was %d.", d, mean.total());
187 CV_Error(Error::StsBadArg, error_message);
188 }
189 // create temporary matrices
190 Mat X, Y;
191 // make sure you operate on correct type
192 src.convertTo(X, W.type());
193 // safe to do, because of above assertion
194 if(!mean.empty()) {
195 for(int i=0; i<n; i++) {
196 Mat r_i = X.row(i);
197 subtract(r_i, mean.reshape(1,1), r_i);
198 }
199 }
200 // finally calculate projection as Y = (X-mean)*W
201 gemm(X, W, 1.0, Mat(), 0.0, Y);
202 return Y;
203 }
204
205 //------------------------------------------------------------------------------
206 // cv::subspaceReconstruct
207 //------------------------------------------------------------------------------
subspaceReconstruct(InputArray _W,InputArray _mean,InputArray _src)208 Mat LDA::subspaceReconstruct(InputArray _W, InputArray _mean, InputArray _src)
209 {
210 // get data matrices
211 Mat W = _W.getMat();
212 Mat mean = _mean.getMat();
213 Mat src = _src.getMat();
214 // get number of samples and dimension
215 int n = src.rows;
216 int d = src.cols;
217 // make sure the data has the correct shape
218 if(W.cols != d) {
219 String error_message = format("Wrong shapes for given matrices. Was size(src) = (%d,%d), size(W) = (%d,%d).", src.rows, src.cols, W.rows, W.cols);
220 CV_Error(Error::StsBadArg, error_message);
221 }
222 // make sure mean is correct if not empty
223 if(!mean.empty() && (mean.total() != (size_t) W.rows)) {
224 String error_message = format("Wrong mean shape for the given eigenvector matrix. Expected %d, but was %d.", W.cols, mean.total());
225 CV_Error(Error::StsBadArg, error_message);
226 }
227 // initialize temporary matrices
228 Mat X, Y;
229 // copy data & make sure we are using the correct type
230 src.convertTo(Y, W.type());
231 // calculate the reconstruction
232 gemm(Y, W, 1.0, Mat(), 0.0, X, GEMM_2_T);
233 // safe to do because of above assertion
234 if(!mean.empty()) {
235 for(int i=0; i<n; i++) {
236 Mat r_i = X.row(i);
237 add(r_i, mean.reshape(1,1), r_i);
238 }
239 }
240 return X;
241 }
242
243
244 class EigenvalueDecomposition {
245 private:
246
247 // Holds the data dimension.
248 int n;
249
250 // Stores real/imag part of a complex division.
251 double cdivr, cdivi;
252
253 // Pointer to internal memory.
254 double *d, *e, *ort;
255 double **V, **H;
256
257 // Holds the computed eigenvalues.
258 Mat _eigenvalues;
259
260 // Holds the computed eigenvectors.
261 Mat _eigenvectors;
262
263 // Allocates memory.
264 template<typename _Tp>
alloc_1d(int m)265 _Tp *alloc_1d(int m) {
266 return new _Tp[m];
267 }
268
269 // Allocates memory.
270 template<typename _Tp>
alloc_1d(int m,_Tp val)271 _Tp *alloc_1d(int m, _Tp val) {
272 _Tp *arr = alloc_1d<_Tp> (m);
273 for (int i = 0; i < m; i++)
274 arr[i] = val;
275 return arr;
276 }
277
278 // Allocates memory.
279 template<typename _Tp>
alloc_2d(int m,int _n)280 _Tp **alloc_2d(int m, int _n) {
281 _Tp **arr = new _Tp*[m];
282 for (int i = 0; i < m; i++)
283 arr[i] = new _Tp[_n];
284 return arr;
285 }
286
287 // Allocates memory.
288 template<typename _Tp>
alloc_2d(int m,int _n,_Tp val)289 _Tp **alloc_2d(int m, int _n, _Tp val) {
290 _Tp **arr = alloc_2d<_Tp> (m, _n);
291 for (int i = 0; i < m; i++) {
292 for (int j = 0; j < _n; j++) {
293 arr[i][j] = val;
294 }
295 }
296 return arr;
297 }
298
cdiv(double xr,double xi,double yr,double yi)299 void cdiv(double xr, double xi, double yr, double yi) {
300 double r, dv;
301 if (std::abs(yr) > std::abs(yi)) {
302 r = yi / yr;
303 dv = yr + r * yi;
304 cdivr = (xr + r * xi) / dv;
305 cdivi = (xi - r * xr) / dv;
306 } else {
307 r = yr / yi;
308 dv = yi + r * yr;
309 cdivr = (r * xr + xi) / dv;
310 cdivi = (r * xi - xr) / dv;
311 }
312 }
313
314 // Nonsymmetric reduction from Hessenberg to real Schur form.
315
hqr2()316 void hqr2() {
317
318 // This is derived from the Algol procedure hqr2,
319 // by Martin and Wilkinson, Handbook for Auto. Comp.,
320 // Vol.ii-Linear Algebra, and the corresponding
321 // Fortran subroutine in EISPACK.
322
323 // Initialize
324 int nn = this->n;
325 int n1 = nn - 1;
326 int low = 0;
327 int high = nn - 1;
328 double eps = std::pow(2.0, -52.0);
329 double exshift = 0.0;
330 double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
331
332 // Store roots isolated by balanc and compute matrix norm
333
334 double norm = 0.0;
335 for (int i = 0; i < nn; i++) {
336 if (i < low || i > high) {
337 d[i] = H[i][i];
338 e[i] = 0.0;
339 }
340 for (int j = std::max(i - 1, 0); j < nn; j++) {
341 norm = norm + std::abs(H[i][j]);
342 }
343 }
344
345 // Outer loop over eigenvalue index
346 int iter = 0;
347 while (n1 >= low) {
348
349 // Look for single small sub-diagonal element
350 int l = n1;
351 while (l > low) {
352 s = std::abs(H[l - 1][l - 1]) + std::abs(H[l][l]);
353 if (s == 0.0) {
354 s = norm;
355 }
356 if (std::abs(H[l][l - 1]) < eps * s) {
357 break;
358 }
359 l--;
360 }
361
362 // Check for convergence
363 // One root found
364
365 if (l == n1) {
366 H[n1][n1] = H[n1][n1] + exshift;
367 d[n1] = H[n1][n1];
368 e[n1] = 0.0;
369 n1--;
370 iter = 0;
371
372 // Two roots found
373
374 } else if (l == n1 - 1) {
375 w = H[n1][n1 - 1] * H[n1 - 1][n1];
376 p = (H[n1 - 1][n1 - 1] - H[n1][n1]) / 2.0;
377 q = p * p + w;
378 z = std::sqrt(std::abs(q));
379 H[n1][n1] = H[n1][n1] + exshift;
380 H[n1 - 1][n1 - 1] = H[n1 - 1][n1 - 1] + exshift;
381 x = H[n1][n1];
382
383 // Real pair
384
385 if (q >= 0) {
386 if (p >= 0) {
387 z = p + z;
388 } else {
389 z = p - z;
390 }
391 d[n1 - 1] = x + z;
392 d[n1] = d[n1 - 1];
393 if (z != 0.0) {
394 d[n1] = x - w / z;
395 }
396 e[n1 - 1] = 0.0;
397 e[n1] = 0.0;
398 x = H[n1][n1 - 1];
399 s = std::abs(x) + std::abs(z);
400 p = x / s;
401 q = z / s;
402 r = std::sqrt(p * p + q * q);
403 p = p / r;
404 q = q / r;
405
406 // Row modification
407
408 for (int j = n1 - 1; j < nn; j++) {
409 z = H[n1 - 1][j];
410 H[n1 - 1][j] = q * z + p * H[n1][j];
411 H[n1][j] = q * H[n1][j] - p * z;
412 }
413
414 // Column modification
415
416 for (int i = 0; i <= n1; i++) {
417 z = H[i][n1 - 1];
418 H[i][n1 - 1] = q * z + p * H[i][n1];
419 H[i][n1] = q * H[i][n1] - p * z;
420 }
421
422 // Accumulate transformations
423
424 for (int i = low; i <= high; i++) {
425 z = V[i][n1 - 1];
426 V[i][n1 - 1] = q * z + p * V[i][n1];
427 V[i][n1] = q * V[i][n1] - p * z;
428 }
429
430 // Complex pair
431
432 } else {
433 d[n1 - 1] = x + p;
434 d[n1] = x + p;
435 e[n1 - 1] = z;
436 e[n1] = -z;
437 }
438 n1 = n1 - 2;
439 iter = 0;
440
441 // No convergence yet
442
443 } else {
444
445 // Form shift
446
447 x = H[n1][n1];
448 y = 0.0;
449 w = 0.0;
450 if (l < n1) {
451 y = H[n1 - 1][n1 - 1];
452 w = H[n1][n1 - 1] * H[n1 - 1][n1];
453 }
454
455 // Wilkinson's original ad hoc shift
456
457 if (iter == 10) {
458 exshift += x;
459 for (int i = low; i <= n1; i++) {
460 H[i][i] -= x;
461 }
462 s = std::abs(H[n1][n1 - 1]) + std::abs(H[n1 - 1][n1 - 2]);
463 x = y = 0.75 * s;
464 w = -0.4375 * s * s;
465 }
466
467 // MATLAB's new ad hoc shift
468
469 if (iter == 30) {
470 s = (y - x) / 2.0;
471 s = s * s + w;
472 if (s > 0) {
473 s = std::sqrt(s);
474 if (y < x) {
475 s = -s;
476 }
477 s = x - w / ((y - x) / 2.0 + s);
478 for (int i = low; i <= n1; i++) {
479 H[i][i] -= s;
480 }
481 exshift += s;
482 x = y = w = 0.964;
483 }
484 }
485
486 iter = iter + 1; // (Could check iteration count here.)
487
488 // Look for two consecutive small sub-diagonal elements
489 int m = n1 - 2;
490 while (m >= l) {
491 z = H[m][m];
492 r = x - z;
493 s = y - z;
494 p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
495 q = H[m + 1][m + 1] - z - r - s;
496 r = H[m + 2][m + 1];
497 s = std::abs(p) + std::abs(q) + std::abs(r);
498 p = p / s;
499 q = q / s;
500 r = r / s;
501 if (m == l) {
502 break;
503 }
504 if (std::abs(H[m][m - 1]) * (std::abs(q) + std::abs(r)) < eps * (std::abs(p)
505 * (std::abs(H[m - 1][m - 1]) + std::abs(z) + std::abs(
506 H[m + 1][m + 1])))) {
507 break;
508 }
509 m--;
510 }
511
512 for (int i = m + 2; i <= n1; i++) {
513 H[i][i - 2] = 0.0;
514 if (i > m + 2) {
515 H[i][i - 3] = 0.0;
516 }
517 }
518
519 // Double QR step involving rows l:n and columns m:n
520
521 for (int k = m; k <= n1 - 1; k++) {
522 bool notlast = (k != n1 - 1);
523 if (k != m) {
524 p = H[k][k - 1];
525 q = H[k + 1][k - 1];
526 r = (notlast ? H[k + 2][k - 1] : 0.0);
527 x = std::abs(p) + std::abs(q) + std::abs(r);
528 if (x != 0.0) {
529 p = p / x;
530 q = q / x;
531 r = r / x;
532 }
533 }
534 if (x == 0.0) {
535 break;
536 }
537 s = std::sqrt(p * p + q * q + r * r);
538 if (p < 0) {
539 s = -s;
540 }
541 if (s != 0) {
542 if (k != m) {
543 H[k][k - 1] = -s * x;
544 } else if (l != m) {
545 H[k][k - 1] = -H[k][k - 1];
546 }
547 p = p + s;
548 x = p / s;
549 y = q / s;
550 z = r / s;
551 q = q / p;
552 r = r / p;
553
554 // Row modification
555
556 for (int j = k; j < nn; j++) {
557 p = H[k][j] + q * H[k + 1][j];
558 if (notlast) {
559 p = p + r * H[k + 2][j];
560 H[k + 2][j] = H[k + 2][j] - p * z;
561 }
562 H[k][j] = H[k][j] - p * x;
563 H[k + 1][j] = H[k + 1][j] - p * y;
564 }
565
566 // Column modification
567
568 for (int i = 0; i <= std::min(n1, k + 3); i++) {
569 p = x * H[i][k] + y * H[i][k + 1];
570 if (notlast) {
571 p = p + z * H[i][k + 2];
572 H[i][k + 2] = H[i][k + 2] - p * r;
573 }
574 H[i][k] = H[i][k] - p;
575 H[i][k + 1] = H[i][k + 1] - p * q;
576 }
577
578 // Accumulate transformations
579
580 for (int i = low; i <= high; i++) {
581 p = x * V[i][k] + y * V[i][k + 1];
582 if (notlast) {
583 p = p + z * V[i][k + 2];
584 V[i][k + 2] = V[i][k + 2] - p * r;
585 }
586 V[i][k] = V[i][k] - p;
587 V[i][k + 1] = V[i][k + 1] - p * q;
588 }
589 } // (s != 0)
590 } // k loop
591 } // check convergence
592 } // while (n1 >= low)
593
594 // Backsubstitute to find vectors of upper triangular form
595
596 if (norm == 0.0) {
597 return;
598 }
599
600 for (n1 = nn - 1; n1 >= 0; n1--) {
601 p = d[n1];
602 q = e[n1];
603
604 // Real vector
605
606 if (q == 0) {
607 int l = n1;
608 H[n1][n1] = 1.0;
609 for (int i = n1 - 1; i >= 0; i--) {
610 w = H[i][i] - p;
611 r = 0.0;
612 for (int j = l; j <= n1; j++) {
613 r = r + H[i][j] * H[j][n1];
614 }
615 if (e[i] < 0.0) {
616 z = w;
617 s = r;
618 } else {
619 l = i;
620 if (e[i] == 0.0) {
621 if (w != 0.0) {
622 H[i][n1] = -r / w;
623 } else {
624 H[i][n1] = -r / (eps * norm);
625 }
626
627 // Solve real equations
628
629 } else {
630 x = H[i][i + 1];
631 y = H[i + 1][i];
632 q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
633 t = (x * s - z * r) / q;
634 H[i][n1] = t;
635 if (std::abs(x) > std::abs(z)) {
636 H[i + 1][n1] = (-r - w * t) / x;
637 } else {
638 H[i + 1][n1] = (-s - y * t) / z;
639 }
640 }
641
642 // Overflow control
643
644 t = std::abs(H[i][n1]);
645 if ((eps * t) * t > 1) {
646 for (int j = i; j <= n1; j++) {
647 H[j][n1] = H[j][n1] / t;
648 }
649 }
650 }
651 }
652 // Complex vector
653 } else if (q < 0) {
654 int l = n1 - 1;
655
656 // Last vector component imaginary so matrix is triangular
657
658 if (std::abs(H[n1][n1 - 1]) > std::abs(H[n1 - 1][n1])) {
659 H[n1 - 1][n1 - 1] = q / H[n1][n1 - 1];
660 H[n1 - 1][n1] = -(H[n1][n1] - p) / H[n1][n1 - 1];
661 } else {
662 cdiv(0.0, -H[n1 - 1][n1], H[n1 - 1][n1 - 1] - p, q);
663 H[n1 - 1][n1 - 1] = cdivr;
664 H[n1 - 1][n1] = cdivi;
665 }
666 H[n1][n1 - 1] = 0.0;
667 H[n1][n1] = 1.0;
668 for (int i = n1 - 2; i >= 0; i--) {
669 double ra, sa, vr, vi;
670 ra = 0.0;
671 sa = 0.0;
672 for (int j = l; j <= n1; j++) {
673 ra = ra + H[i][j] * H[j][n1 - 1];
674 sa = sa + H[i][j] * H[j][n1];
675 }
676 w = H[i][i] - p;
677
678 if (e[i] < 0.0) {
679 z = w;
680 r = ra;
681 s = sa;
682 } else {
683 l = i;
684 if (e[i] == 0) {
685 cdiv(-ra, -sa, w, q);
686 H[i][n1 - 1] = cdivr;
687 H[i][n1] = cdivi;
688 } else {
689
690 // Solve complex equations
691
692 x = H[i][i + 1];
693 y = H[i + 1][i];
694 vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
695 vi = (d[i] - p) * 2.0 * q;
696 if (vr == 0.0 && vi == 0.0) {
697 vr = eps * norm * (std::abs(w) + std::abs(q) + std::abs(x)
698 + std::abs(y) + std::abs(z));
699 }
700 cdiv(x * r - z * ra + q * sa,
701 x * s - z * sa - q * ra, vr, vi);
702 H[i][n1 - 1] = cdivr;
703 H[i][n1] = cdivi;
704 if (std::abs(x) > (std::abs(z) + std::abs(q))) {
705 H[i + 1][n1 - 1] = (-ra - w * H[i][n1 - 1] + q
706 * H[i][n1]) / x;
707 H[i + 1][n1] = (-sa - w * H[i][n1] - q * H[i][n1
708 - 1]) / x;
709 } else {
710 cdiv(-r - y * H[i][n1 - 1], -s - y * H[i][n1], z,
711 q);
712 H[i + 1][n1 - 1] = cdivr;
713 H[i + 1][n1] = cdivi;
714 }
715 }
716
717 // Overflow control
718
719 t = std::max(std::abs(H[i][n1 - 1]), std::abs(H[i][n1]));
720 if ((eps * t) * t > 1) {
721 for (int j = i; j <= n1; j++) {
722 H[j][n1 - 1] = H[j][n1 - 1] / t;
723 H[j][n1] = H[j][n1] / t;
724 }
725 }
726 }
727 }
728 }
729 }
730
731 // Vectors of isolated roots
732
733 for (int i = 0; i < nn; i++) {
734 if (i < low || i > high) {
735 for (int j = i; j < nn; j++) {
736 V[i][j] = H[i][j];
737 }
738 }
739 }
740
741 // Back transformation to get eigenvectors of original matrix
742
743 for (int j = nn - 1; j >= low; j--) {
744 for (int i = low; i <= high; i++) {
745 z = 0.0;
746 for (int k = low; k <= std::min(j, high); k++) {
747 z = z + V[i][k] * H[k][j];
748 }
749 V[i][j] = z;
750 }
751 }
752 }
753
754 // Nonsymmetric reduction to Hessenberg form.
orthes()755 void orthes() {
756 // This is derived from the Algol procedures orthes and ortran,
757 // by Martin and Wilkinson, Handbook for Auto. Comp.,
758 // Vol.ii-Linear Algebra, and the corresponding
759 // Fortran subroutines in EISPACK.
760 int low = 0;
761 int high = n - 1;
762
763 for (int m = low + 1; m <= high - 1; m++) {
764
765 // Scale column.
766
767 double scale = 0.0;
768 for (int i = m; i <= high; i++) {
769 scale = scale + std::abs(H[i][m - 1]);
770 }
771 if (scale != 0.0) {
772
773 // Compute Householder transformation.
774
775 double h = 0.0;
776 for (int i = high; i >= m; i--) {
777 ort[i] = H[i][m - 1] / scale;
778 h += ort[i] * ort[i];
779 }
780 double g = std::sqrt(h);
781 if (ort[m] > 0) {
782 g = -g;
783 }
784 h = h - ort[m] * g;
785 ort[m] = ort[m] - g;
786
787 // Apply Householder similarity transformation
788 // H = (I-u*u'/h)*H*(I-u*u')/h)
789
790 for (int j = m; j < n; j++) {
791 double f = 0.0;
792 for (int i = high; i >= m; i--) {
793 f += ort[i] * H[i][j];
794 }
795 f = f / h;
796 for (int i = m; i <= high; i++) {
797 H[i][j] -= f * ort[i];
798 }
799 }
800
801 for (int i = 0; i <= high; i++) {
802 double f = 0.0;
803 for (int j = high; j >= m; j--) {
804 f += ort[j] * H[i][j];
805 }
806 f = f / h;
807 for (int j = m; j <= high; j++) {
808 H[i][j] -= f * ort[j];
809 }
810 }
811 ort[m] = scale * ort[m];
812 H[m][m - 1] = scale * g;
813 }
814 }
815
816 // Accumulate transformations (Algol's ortran).
817
818 for (int i = 0; i < n; i++) {
819 for (int j = 0; j < n; j++) {
820 V[i][j] = (i == j ? 1.0 : 0.0);
821 }
822 }
823
824 for (int m = high - 1; m >= low + 1; m--) {
825 if (H[m][m - 1] != 0.0) {
826 for (int i = m + 1; i <= high; i++) {
827 ort[i] = H[i][m - 1];
828 }
829 for (int j = m; j <= high; j++) {
830 double g = 0.0;
831 for (int i = m; i <= high; i++) {
832 g += ort[i] * V[i][j];
833 }
834 // Double division avoids possible underflow
835 g = (g / ort[m]) / H[m][m - 1];
836 for (int i = m; i <= high; i++) {
837 V[i][j] += g * ort[i];
838 }
839 }
840 }
841 }
842 }
843
844 // Releases all internal working memory.
release()845 void release() {
846 // releases the working data
847 delete[] d;
848 delete[] e;
849 delete[] ort;
850 for (int i = 0; i < n; i++) {
851 delete[] H[i];
852 delete[] V[i];
853 }
854 delete[] H;
855 delete[] V;
856 }
857
858 // Computes the Eigenvalue Decomposition for a matrix given in H.
compute()859 void compute() {
860 // Allocate memory for the working data.
861 V = alloc_2d<double> (n, n, 0.0);
862 d = alloc_1d<double> (n);
863 e = alloc_1d<double> (n);
864 ort = alloc_1d<double> (n);
865 // Reduce to Hessenberg form.
866 orthes();
867 // Reduce Hessenberg to real Schur form.
868 hqr2();
869 // Copy eigenvalues to OpenCV Matrix.
870 _eigenvalues.create(1, n, CV_64FC1);
871 for (int i = 0; i < n; i++) {
872 _eigenvalues.at<double> (0, i) = d[i];
873 }
874 // Copy eigenvectors to OpenCV Matrix.
875 _eigenvectors.create(n, n, CV_64FC1);
876 for (int i = 0; i < n; i++)
877 for (int j = 0; j < n; j++)
878 _eigenvectors.at<double> (i, j) = V[i][j];
879 // Deallocate the memory by releasing all internal working data.
880 release();
881 }
882
883 public:
EigenvalueDecomposition()884 EigenvalueDecomposition()
885 : n(0) { }
886
887 // Initializes & computes the Eigenvalue Decomposition for a general matrix
888 // given in src. This function is a port of the EigenvalueSolver in JAMA,
889 // which has been released to public domain by The MathWorks and the
890 // National Institute of Standards and Technology (NIST).
EigenvalueDecomposition(InputArray src)891 EigenvalueDecomposition(InputArray src) {
892 compute(src);
893 }
894
895 // This function computes the Eigenvalue Decomposition for a general matrix
896 // given in src. This function is a port of the EigenvalueSolver in JAMA,
897 // which has been released to public domain by The MathWorks and the
898 // National Institute of Standards and Technology (NIST).
compute(InputArray src)899 void compute(InputArray src)
900 {
901 if(isSymmetric(src)) {
902 // Fall back to OpenCV for a symmetric matrix!
903 cv::eigen(src, _eigenvalues, _eigenvectors);
904 } else {
905 Mat tmp;
906 // Convert the given input matrix to double. Is there any way to
907 // prevent allocating the temporary memory? Only used for copying
908 // into working memory and deallocated after.
909 src.getMat().convertTo(tmp, CV_64FC1);
910 // Get dimension of the matrix.
911 this->n = tmp.cols;
912 // Allocate the matrix data to work on.
913 this->H = alloc_2d<double> (n, n);
914 // Now safely copy the data.
915 for (int i = 0; i < tmp.rows; i++) {
916 for (int j = 0; j < tmp.cols; j++) {
917 this->H[i][j] = tmp.at<double>(i, j);
918 }
919 }
920 // Deallocates the temporary matrix before computing.
921 tmp.release();
922 // Performs the eigenvalue decomposition of H.
923 compute();
924 }
925 }
926
~EigenvalueDecomposition()927 ~EigenvalueDecomposition() {}
928
929 // Returns the eigenvalues of the Eigenvalue Decomposition.
eigenvalues()930 Mat eigenvalues() { return _eigenvalues; }
931 // Returns the eigenvectors of the Eigenvalue Decomposition.
eigenvectors()932 Mat eigenvectors() { return _eigenvectors; }
933 };
934
935
936 //------------------------------------------------------------------------------
937 // Linear Discriminant Analysis implementation
938 //------------------------------------------------------------------------------
939
LDA(int num_components)940 LDA::LDA(int num_components) : _num_components(num_components) { }
941
LDA(InputArrayOfArrays src,InputArray labels,int num_components)942 LDA::LDA(InputArrayOfArrays src, InputArray labels, int num_components) : _num_components(num_components)
943 {
944 this->compute(src, labels); //! compute eigenvectors and eigenvalues
945 }
946
~LDA()947 LDA::~LDA() {}
948
save(const String & filename) const949 void LDA::save(const String& filename) const
950 {
951 FileStorage fs(filename, FileStorage::WRITE);
952 if (!fs.isOpened()) {
953 CV_Error(Error::StsError, "File can't be opened for writing!");
954 }
955 this->save(fs);
956 fs.release();
957 }
958
959 // Deserializes this object from a given filename.
load(const String & filename)960 void LDA::load(const String& filename) {
961 FileStorage fs(filename, FileStorage::READ);
962 if (!fs.isOpened())
963 CV_Error(Error::StsError, "File can't be opened for writing!");
964 this->load(fs);
965 fs.release();
966 }
967
968 // Serializes this object to a given FileStorage.
save(FileStorage & fs) const969 void LDA::save(FileStorage& fs) const {
970 // write matrices
971 fs << "num_components" << _num_components;
972 fs << "eigenvalues" << _eigenvalues;
973 fs << "eigenvectors" << _eigenvectors;
974 }
975
976 // Deserializes this object from a given FileStorage.
load(const FileStorage & fs)977 void LDA::load(const FileStorage& fs) {
978 //read matrices
979 fs["num_components"] >> _num_components;
980 fs["eigenvalues"] >> _eigenvalues;
981 fs["eigenvectors"] >> _eigenvectors;
982 }
983
lda(InputArrayOfArrays _src,InputArray _lbls)984 void LDA::lda(InputArrayOfArrays _src, InputArray _lbls) {
985 // get data
986 Mat src = _src.getMat();
987 std::vector<int> labels;
988 // safely copy the labels
989 {
990 Mat tmp = _lbls.getMat();
991 for(unsigned int i = 0; i < tmp.total(); i++) {
992 labels.push_back(tmp.at<int>(i));
993 }
994 }
995 // turn into row sampled matrix
996 Mat data;
997 // ensure working matrix is double precision
998 src.convertTo(data, CV_64FC1);
999 // maps the labels, so they're ascending: [0,1,...,C]
1000 std::vector<int> mapped_labels(labels.size());
1001 std::vector<int> num2label = remove_dups(labels);
1002 std::map<int, int> label2num;
1003 for (int i = 0; i < (int)num2label.size(); i++)
1004 label2num[num2label[i]] = i;
1005 for (size_t i = 0; i < labels.size(); i++)
1006 mapped_labels[i] = label2num[labels[i]];
1007 // get sample size, dimension
1008 int N = data.rows;
1009 int D = data.cols;
1010 // number of unique labels
1011 int C = (int)num2label.size();
1012 // we can't do a LDA on one class, what do you
1013 // want to separate from each other then?
1014 if(C == 1) {
1015 String error_message = "At least two classes are needed to perform a LDA. Reason: Only one class was given!";
1016 CV_Error(Error::StsBadArg, error_message);
1017 }
1018 // throw error if less labels, than samples
1019 if (labels.size() != static_cast<size_t>(N)) {
1020 String error_message = format("The number of samples must equal the number of labels. Given %d labels, %d samples. ", labels.size(), N);
1021 CV_Error(Error::StsBadArg, error_message);
1022 }
1023 // warn if within-classes scatter matrix becomes singular
1024 if (N < D) {
1025 std::cout << "Warning: Less observations than feature dimension given!"
1026 << "Computation will probably fail."
1027 << std::endl;
1028 }
1029 // clip number of components to be a valid number
1030 if ((_num_components <= 0) || (_num_components > (C - 1))) {
1031 _num_components = (C - 1);
1032 }
1033 // holds the mean over all classes
1034 Mat meanTotal = Mat::zeros(1, D, data.type());
1035 // holds the mean for each class
1036 std::vector<Mat> meanClass(C);
1037 std::vector<int> numClass(C);
1038 // initialize
1039 for (int i = 0; i < C; i++) {
1040 numClass[i] = 0;
1041 meanClass[i] = Mat::zeros(1, D, data.type()); //! Dx1 image vector
1042 }
1043 // calculate sums
1044 for (int i = 0; i < N; i++) {
1045 Mat instance = data.row(i);
1046 int classIdx = mapped_labels[i];
1047 add(meanTotal, instance, meanTotal);
1048 add(meanClass[classIdx], instance, meanClass[classIdx]);
1049 numClass[classIdx]++;
1050 }
1051 // calculate total mean
1052 meanTotal.convertTo(meanTotal, meanTotal.type(), 1.0 / static_cast<double> (N));
1053 // calculate class means
1054 for (int i = 0; i < C; i++) {
1055 meanClass[i].convertTo(meanClass[i], meanClass[i].type(), 1.0 / static_cast<double> (numClass[i]));
1056 }
1057 // subtract class means
1058 for (int i = 0; i < N; i++) {
1059 int classIdx = mapped_labels[i];
1060 Mat instance = data.row(i);
1061 subtract(instance, meanClass[classIdx], instance);
1062 }
1063 // calculate within-classes scatter
1064 Mat Sw = Mat::zeros(D, D, data.type());
1065 mulTransposed(data, Sw, true);
1066 // calculate between-classes scatter
1067 Mat Sb = Mat::zeros(D, D, data.type());
1068 for (int i = 0; i < C; i++) {
1069 Mat tmp;
1070 subtract(meanClass[i], meanTotal, tmp);
1071 mulTransposed(tmp, tmp, true);
1072 add(Sb, tmp, Sb);
1073 }
1074 // invert Sw
1075 Mat Swi = Sw.inv();
1076 // M = inv(Sw)*Sb
1077 Mat M;
1078 gemm(Swi, Sb, 1.0, Mat(), 0.0, M);
1079 EigenvalueDecomposition es(M);
1080 _eigenvalues = es.eigenvalues();
1081 _eigenvectors = es.eigenvectors();
1082 // reshape eigenvalues, so they are stored by column
1083 _eigenvalues = _eigenvalues.reshape(1, 1);
1084 // get sorted indices descending by their eigenvalue
1085 std::vector<int> sorted_indices = argsort(_eigenvalues, false);
1086 // now sort eigenvalues and eigenvectors accordingly
1087 _eigenvalues = sortMatrixColumnsByIndices(_eigenvalues, sorted_indices);
1088 _eigenvectors = sortMatrixColumnsByIndices(_eigenvectors, sorted_indices);
1089 // and now take only the num_components and we're out!
1090 _eigenvalues = Mat(_eigenvalues, Range::all(), Range(0, _num_components));
1091 _eigenvectors = Mat(_eigenvectors, Range::all(), Range(0, _num_components));
1092 }
1093
compute(InputArrayOfArrays _src,InputArray _lbls)1094 void LDA::compute(InputArrayOfArrays _src, InputArray _lbls) {
1095 switch(_src.kind()) {
1096 case _InputArray::STD_VECTOR_MAT:
1097 lda(asRowMatrix(_src, CV_64FC1), _lbls);
1098 break;
1099 case _InputArray::MAT:
1100 lda(_src.getMat(), _lbls);
1101 break;
1102 default:
1103 String error_message= format("InputArray Datatype %d is not supported.", _src.kind());
1104 CV_Error(Error::StsBadArg, error_message);
1105 break;
1106 }
1107 }
1108
1109 // Projects samples into the LDA subspace.
project(InputArray src)1110 Mat LDA::project(InputArray src) {
1111 return subspaceProject(_eigenvectors, Mat(), _dataAsRow ? src : src.getMat().t());
1112 }
1113
1114 // Reconstructs projections from the LDA subspace.
reconstruct(InputArray src)1115 Mat LDA::reconstruct(InputArray src) {
1116 return subspaceReconstruct(_eigenvectors, Mat(), _dataAsRow ? src : src.getMat().t());
1117 }
1118
1119 }
1120