Visual Servoing Platform  version 3.4.1 under development (2021-10-17)
testMatrixPseudoInverse.cpp
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29  * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
30  *
31  * Description:
32  * Test various svd decompositions.
33  *
34  * Authors:
35  * Fabien Spindler
36  *
37  *****************************************************************************/
38 
44 #include <algorithm>
45 #include <stdio.h>
46 #include <stdlib.h>
47 #include <vector>
48 
49 #include <visp3/core/vpColVector.h>
50 #include <visp3/core/vpMatrix.h>
51 #include <visp3/core/vpTime.h>
52 #include <visp3/io/vpParseArgv.h>
53 
54 // List of allowed command line options
55 #define GETOPTARGS "cdn:i:pf:R:C:vh"
56 
65 void usage(const char *name, const char *badparam)
66 {
67  fprintf(stdout, "\n\
68 Test matrix pseudo-inverse.\n\
69 Outputs a comparison of the results obtained by supported 3rd parties.\n\
70 \n\
71 SYNOPSIS\n\
72  %s [-n <number of matrices>] [-f <plot filename>]\n\
73  [-R <number of rows>] [-C <number of columns>]\n\
74  [-i <number of iterations>] [-p] [-h]\n", name);
75 
76  fprintf(stdout, "\n\
77 OPTIONS: Default\n\
78  -n <number of matrices> \n\
79  Number of matrices inverted during each test loop.\n\
80 \n\
81  -i <number of iterations> \n\
82  Number of iterations of the test.\n\
83 \n\
84  -f <plot filename> \n\
85  Set output path for plot output.\n\
86  The plot logs the times of \n\
87  the different inversion methods: \n\
88  QR,LU,Cholesky and Pseudo-inverse.\n\
89 \n\
90  -R <number of rows>\n\
91  Number of rows of the automatically generated matrices \n\
92  we test on.\n\
93 \n\
94  -C <number of columns>\n\
95  Number of colums of the automatically generated matrices \n\
96  we test on.\n\
97 \n\
98  -p \n\
99  Plot into filename in the gnuplot format. \n\
100  If this option is used, tests results will be logged \n\
101  into a filename specified with -f.\n\
102 \n\
103  -h\n\
104  Print the help.\n\n");
105 
106  if (badparam) {
107  fprintf(stderr, "ERROR: \n");
108  fprintf(stderr, "\nBad parameter [%s]\n", badparam);
109  }
110 }
111 
119 bool getOptions(int argc, const char **argv, unsigned int &nb_matrices, unsigned int &nb_iterations,
120  bool &use_plot_file, std::string &plotfile, unsigned int &nbrows, unsigned int &nbcols, bool &verbose)
121 {
122  const char *optarg_;
123  int c;
124  while ((c = vpParseArgv::parse(argc, argv, GETOPTARGS, &optarg_)) > 1) {
125 
126  switch (c) {
127  case 'h':
128  usage(argv[0], NULL);
129  return false;
130  break;
131  case 'n':
132  nb_matrices = (unsigned int)atoi(optarg_);
133  break;
134  case 'i':
135  nb_iterations = (unsigned int)atoi(optarg_);
136  break;
137  case 'f':
138  plotfile = optarg_;
139  use_plot_file = true;
140  break;
141  case 'p':
142  use_plot_file = true;
143  break;
144  case 'R':
145  nbrows = (unsigned int)atoi(optarg_);
146  break;
147  case 'C':
148  nbcols = (unsigned int)atoi(optarg_);
149  break;
150  case 'v':
151  verbose = true;
152  break;
153  // add default options -c -d
154  case 'c':
155  break;
156  case 'd':
157  break;
158  default:
159  usage(argv[0], optarg_);
160  return false;
161  break;
162  }
163  }
164 
165  if ((c == 1) || (c == -1)) {
166  // standalone param or error
167  usage(argv[0], NULL);
168  std::cerr << "ERROR: " << std::endl;
169  std::cerr << " Bad argument " << optarg_ << std::endl << std::endl;
170  return false;
171  }
172 
173  return true;
174 }
175 
176 vpMatrix make_random_matrix(unsigned int nbrows, unsigned int nbcols)
177 {
178  vpMatrix A;
179  A.resize(nbrows, nbcols);
180 
181  for (unsigned int i = 0; i < A.getRows(); i++) {
182  for (unsigned int j = 0; j < A.getCols(); j++) {
183  A[i][j] = (double)rand() / (double)RAND_MAX;
184  }
185  }
186 
187  return A;
188 }
189 
190 void create_bench_random_matrix(unsigned int nb_matrices, unsigned int nb_rows, unsigned int nb_cols, bool verbose,
191  std::vector<vpMatrix> &bench)
192 {
193  if (verbose)
194  std::cout << "Create a bench of " << nb_matrices << " " << nb_rows << " by " << nb_cols << " matrices" << std::endl;
195  bench.clear();
196  for (unsigned int i = 0; i < nb_matrices; i++) {
197  vpMatrix M = make_random_matrix(nb_rows, nb_cols);
198  bench.push_back(M);
199  }
200 }
201 
202 int test_pseudo_inverse(const std::vector<vpMatrix> &A, const std::vector<vpMatrix> &Api)
203 {
204  double allowed_error = 1e-3;
205 
206  for (unsigned int i = 0; i < A.size(); i++) {
207  double error = (A[i] * Api[i] * A[i] - A[i]).frobeniusNorm();
208  if (error > allowed_error) {
209  std::cout << "Bad pseudo-inverse [" << i << "]: euclidean norm: " << error << std::endl;
210  return EXIT_FAILURE;
211  }
212  }
213  return EXIT_SUCCESS;
214 }
215 
216 int test_pseudo_inverse(const std::vector<vpMatrix> &A, const std::vector<vpMatrix> &Api,
217  const std::vector<vpColVector> &sv, const std::vector<vpMatrix> &imA,
218  const std::vector<vpMatrix> &imAt, const std::vector<vpMatrix> &kerAt)
219 {
220  double allowed_error = 1e-3;
221  // test Api
222  for (unsigned int i = 0; i < A.size(); i++) {
223  double error = (A[i] * Api[i] * A[i] - A[i]).frobeniusNorm();
224  if (error > allowed_error) {
225  std::cout << "Bad pseudo-inverse [" << i << "]: euclidean norm: " << error << std::endl;
226  return EXIT_FAILURE;
227  }
228  }
229 
230  // test kerA
231  for (unsigned int i = 0; i < kerAt.size(); i++) {
232  if (kerAt[i].size()) {
233  vpMatrix nullspace = A[i] * kerAt[i].t();
234  double error = nullspace.frobeniusNorm();
235 
236  if (error > allowed_error) {
237  std::cout << "Bad kernel [" << i << "]: euclidean norm: " << error << std::endl;
238  return EXIT_FAILURE;
239  }
240  }
241  }
242 
243  // test sv, imA, imAt, kerA
244  for (unsigned int i = 0; i < kerAt.size(); i++) {
245  unsigned int rank = imA[i].getCols();
246  vpMatrix U, S(rank, A[i].getCols()), Vt(A[i].getCols(), A[i].getCols());
247  U = imA[i];
248 
249  for (unsigned int j = 0; j < rank; j++)
250  S[j][j] = sv[i][j];
251 
252  Vt.insert(imAt[i].t(), 0, 0);
253  Vt.insert(kerAt[i], imAt[i].getCols(), 0);
254 
255  double error = (U * S * Vt - A[i]).frobeniusNorm();
256 
257  if (error > allowed_error) {
258  std::cout << "Bad imA, imAt, sv, kerAt [" << i << "]: euclidean norm: " << error << std::endl;
259  return EXIT_FAILURE;
260  }
261  }
262 
263  return EXIT_SUCCESS;
264 }
265 
266 int test_pseudo_inverse_default(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
267 {
268  if (verbose)
269  std::cout << "Test pseudo-inverse using default 3rd party" << std::endl;
270  if (verbose)
271  std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
272 
273  size_t size = bench.size();
274  std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
275  std::vector<vpColVector> sv(size);
276  int ret = EXIT_SUCCESS;
277 
278  // test 0
279  unsigned int test = 0;
280  double t = vpTime::measureTimeMs();
281  for (unsigned int i = 0; i < bench.size(); i++) {
282  PI[i] = bench[i].pseudoInverse();
283  }
284  time[test] = vpTime::measureTimeMs() - t;
285  for (unsigned int i = 0; i < time.size(); i++) {
286  ret += test_pseudo_inverse(bench, PI);
287  }
288 
289  // test 1
290  test++;
291  t = vpTime::measureTimeMs();
292  for (unsigned int i = 0; i < bench.size(); i++) {
293  bench[i].pseudoInverse(PI[i]);
294  }
295  time[test] = vpTime::measureTimeMs() - t;
296  for (unsigned int i = 0; i < time.size(); i++) {
297  ret += test_pseudo_inverse(bench, PI);
298  }
299 
300  // test 2
301  test++;
302  t = vpTime::measureTimeMs();
303  for (unsigned int i = 0; i < bench.size(); i++) {
304  bench[i].pseudoInverse(PI[i], sv[i]);
305  }
306  time[test] = vpTime::measureTimeMs() - t;
307  for (unsigned int i = 0; i < time.size(); i++) {
308  ret += test_pseudo_inverse(bench, PI);
309  }
310 
311  // test 3
312  test++;
313  t = vpTime::measureTimeMs();
314  for (unsigned int i = 0; i < bench.size(); i++) {
315  bench[i].pseudoInverse(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
316  }
317  time[test] = vpTime::measureTimeMs() - t;
318 
319  for (unsigned int i = 0; i < time.size(); i++) {
320  ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
321  }
322 
323  return ret;
324 }
325 
326 #if defined(VISP_HAVE_EIGEN3)
327 int test_pseudo_inverse_eigen3(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
328 {
329  if (verbose)
330  std::cout << "Test pseudo-inverse using Eigen3 3rd party" << std::endl;
331  if (verbose)
332  std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
333 
334  size_t size = bench.size();
335  std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
336  std::vector<vpColVector> sv(size);
337  int ret = EXIT_SUCCESS;
338 
339  // test 0
340  unsigned int test = 0;
341  double t = vpTime::measureTimeMs();
342  for (unsigned int i = 0; i < bench.size(); i++) {
343  PI[i] = bench[i].pseudoInverseEigen3();
344  }
345  time[test] = vpTime::measureTimeMs() - t;
346  for (unsigned int i = 0; i < time.size(); i++) {
347  ret += test_pseudo_inverse(bench, PI);
348  }
349 
350  // test 1
351  test++;
352  t = vpTime::measureTimeMs();
353  for (unsigned int i = 0; i < bench.size(); i++) {
354  bench[i].pseudoInverseEigen3(PI[i]);
355  }
356  time[test] = vpTime::measureTimeMs() - t;
357  for (unsigned int i = 0; i < time.size(); i++) {
358  ret += test_pseudo_inverse(bench, PI);
359  }
360 
361  // test 2
362  test++;
363  t = vpTime::measureTimeMs();
364  for (unsigned int i = 0; i < bench.size(); i++) {
365  bench[i].pseudoInverseEigen3(PI[i], sv[i]);
366  }
367  time[test] = vpTime::measureTimeMs() - t;
368  for (unsigned int i = 0; i < time.size(); i++) {
369  ret += test_pseudo_inverse(bench, PI);
370  }
371 
372  // test 3
373  test++;
374  t = vpTime::measureTimeMs();
375  for (unsigned int i = 0; i < bench.size(); i++) {
376  bench[i].pseudoInverseEigen3(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
377  }
378  time[test] = vpTime::measureTimeMs() - t;
379 
380  for (unsigned int i = 0; i < time.size(); i++) {
381  ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
382  }
383 
384  return ret;
385 }
386 #endif
387 
388 #if defined(VISP_HAVE_LAPACK)
389 int test_pseudo_inverse_lapack(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
390 {
391  if (verbose)
392  std::cout << "Test pseudo-inverse using Lapack 3rd party" << std::endl;
393  if (verbose)
394  std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
395 
396  size_t size = bench.size();
397  std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
398  std::vector<vpColVector> sv(size);
399  int ret = EXIT_SUCCESS;
400 
401  // test 0
402  unsigned int test = 0;
403  double t = vpTime::measureTimeMs();
404  for (unsigned int i = 0; i < bench.size(); i++) {
405  PI[i] = bench[i].pseudoInverseLapack();
406  }
407  time[test] = vpTime::measureTimeMs() - t;
408  for (unsigned int i = 0; i < time.size(); i++) {
409  ret += test_pseudo_inverse(bench, PI);
410  }
411 
412  // test 1
413  test++;
414  t = vpTime::measureTimeMs();
415  for (unsigned int i = 0; i < bench.size(); i++) {
416  bench[i].pseudoInverseLapack(PI[i]);
417  }
418  time[test] = vpTime::measureTimeMs() - t;
419  for (unsigned int i = 0; i < time.size(); i++) {
420  ret += test_pseudo_inverse(bench, PI);
421  }
422 
423  // test 2
424  test++;
425  t = vpTime::measureTimeMs();
426  for (unsigned int i = 0; i < bench.size(); i++) {
427  bench[i].pseudoInverseLapack(PI[i], sv[i]);
428  }
429  time[test] = vpTime::measureTimeMs() - t;
430  for (unsigned int i = 0; i < time.size(); i++) {
431  ret += test_pseudo_inverse(bench, PI);
432  }
433 
434  // test 3
435  test++;
436  t = vpTime::measureTimeMs();
437  for (unsigned int i = 0; i < bench.size(); i++) {
438  bench[i].pseudoInverseLapack(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
439  }
440  time[test] = vpTime::measureTimeMs() - t;
441 
442  for (unsigned int i = 0; i < time.size(); i++) {
443  ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
444  }
445 
446  return ret;
447 }
448 #endif
449 
450 #if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
451 int test_pseudo_inverse_opencv(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
452 {
453  if (verbose)
454  std::cout << "Test pseudo-inverse using OpenCV 3rd party" << std::endl;
455  if (verbose)
456  std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
457 
458  size_t size = bench.size();
459  std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
460  std::vector<vpColVector> sv(size);
461  int ret = EXIT_SUCCESS;
462 
463  // test 0
464  unsigned int test = 0;
465  double t = vpTime::measureTimeMs();
466  for (unsigned int i = 0; i < bench.size(); i++) {
467  PI[i] = bench[i].pseudoInverseOpenCV();
468  }
469  time[test] = vpTime::measureTimeMs() - t;
470  for (unsigned int i = 0; i < time.size(); i++) {
471  ret += test_pseudo_inverse(bench, PI);
472  }
473 
474  // test 1
475  test++;
476  t = vpTime::measureTimeMs();
477  for (unsigned int i = 0; i < bench.size(); i++) {
478  bench[i].pseudoInverseOpenCV(PI[i]);
479  }
480  time[test] = vpTime::measureTimeMs() - t;
481  for (unsigned int i = 0; i < time.size(); i++) {
482  ret += test_pseudo_inverse(bench, PI);
483  }
484 
485  // test 2
486  test++;
487  t = vpTime::measureTimeMs();
488  for (unsigned int i = 0; i < bench.size(); i++) {
489  bench[i].pseudoInverseOpenCV(PI[i], sv[i]);
490  }
491  time[test] = vpTime::measureTimeMs() - t;
492  for (unsigned int i = 0; i < time.size(); i++) {
493  ret += test_pseudo_inverse(bench, PI);
494  }
495 
496  // test 3
497  test++;
498  t = vpTime::measureTimeMs();
499  for (unsigned int i = 0; i < bench.size(); i++) {
500  bench[i].pseudoInverseOpenCV(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
501  }
502  time[test] = vpTime::measureTimeMs() - t;
503 
504  for (unsigned int i = 0; i < time.size(); i++) {
505  ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
506  }
507 
508  return ret;
509 }
510 #endif
511 
512 void save_time(const std::string &method, unsigned int nrows, unsigned int ncols, bool verbose, bool use_plot_file,
513  std::ofstream &of, const std::vector<double> &time)
514 {
515  for (size_t i = 0; i < time.size(); i++) {
516  if (use_plot_file)
517  of << time[i] << "\t";
518  if (verbose) {
519  std::cout << " " << method << " svd(" << nrows << "x" << ncols << ")"
520  << " test " << i << ": " << time[i] << std::endl;
521  }
522  }
523 }
524 
525 int main(int argc, const char *argv[])
526 {
527  try {
528 #if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101)
529  unsigned int nb_matrices = 10;
530  unsigned int nb_iterations = 10;
531  unsigned int nb_rows = 12;
532  unsigned int nb_cols = 6;
533  bool verbose = false;
534  std::string plotfile("plot-pseudo-inv.csv");
535  bool use_plot_file = false;
536  std::ofstream of;
537 
538  unsigned int nb_svd_functions = 4; // 4 tests for each existing vpMatrix::pseudoInverse(...) functions
539  unsigned int nb_test_matrix_size = 3; // 3 tests: m > n, m = n, m < n
540  std::vector<double> time(nb_svd_functions);
541  std::vector<unsigned int> nrows(nb_test_matrix_size), ncols(nb_test_matrix_size);
542 
543  // Read the command line options
544  if (getOptions(argc, argv, nb_matrices, nb_iterations, use_plot_file, plotfile, nb_rows, nb_cols, verbose) ==
545  false) {
546  exit(-1);
547  }
548 
549  for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
550  // consider m > n, m = n, m < n
551  if (s == 0) {
552  nrows[s] = nb_rows;
553  ncols[s] = nb_cols;
554  } else if (s == 1) {
555  nrows[s] = nb_cols;
556  ncols[s] = nb_cols;
557  } else {
558  nrows[s] = nb_cols;
559  ncols[s] = nb_rows;
560  }
561  }
562 
563  if (use_plot_file) {
564  of.open(plotfile.c_str());
565  of << "iter"
566  << "\t";
567 
568  for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
569  for (unsigned int i = 0; i < nb_svd_functions; i++)
570  of << "\"default " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
571  << "\t";
572 
573 #if defined(VISP_HAVE_LAPACK)
574  for (unsigned int i = 0; i < nb_svd_functions; i++)
575  of << "\"Lapack " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
576  << "\t";
577 #endif
578 #if defined(VISP_HAVE_EIGEN3)
579  for (unsigned int i = 0; i < nb_svd_functions; i++)
580  of << "\"Eigen3 " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
581  << "\t";
582 #endif
583 #if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
584  for (unsigned int i = 0; i < nb_svd_functions; i++)
585  of << "\"OpenCV " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
586  << "\t";
587 #endif
588  }
589  of << std::endl;
590  }
591 
592  int ret = EXIT_SUCCESS;
593  for (unsigned int iter = 0; iter < nb_iterations; iter++) {
594 
595  if (use_plot_file)
596  of << iter << "\t";
597 
598  for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
599  std::vector<vpMatrix> bench_random_matrices;
600  create_bench_random_matrix(nb_matrices, nrows[s], ncols[s], verbose, bench_random_matrices);
601 
602  ret += test_pseudo_inverse_default(verbose, bench_random_matrices, time);
603  save_time("default -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
604 
605 #if defined(VISP_HAVE_LAPACK)
606  ret += test_pseudo_inverse_lapack(verbose, bench_random_matrices, time);
607  save_time("Lapack -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
608 #endif
609 
610 #if defined(VISP_HAVE_EIGEN3)
611  ret += test_pseudo_inverse_eigen3(verbose, bench_random_matrices, time);
612  save_time("Eigen3 -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
613 #endif
614 
615 #if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
616  ret += test_pseudo_inverse_opencv(verbose, bench_random_matrices, time);
617  save_time("OpenCV -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
618 #endif
619  }
620  if (use_plot_file)
621  of << std::endl;
622  }
623  if (use_plot_file) {
624  of.close();
625  std::cout << "Result saved in " << plotfile << std::endl;
626  }
627 
628  if (ret == EXIT_SUCCESS) {
629  std::cout << "Test succeed" << std::endl;
630  } else {
631  std::cout << "Test failed" << std::endl;
632  }
633 
634  return ret;
635 #else
636  (void)argc;
637  (void)argv;
638  std::cout << "Test does nothing since you dont't have Lapack, Eigen3 or OpenCV 3rd party"
639  << std::endl;
640  return EXIT_SUCCESS;
641 #endif
642  } catch (const vpException &e) {
643  std::cout << "Catch an exception: " << e.getStringMessage() << std::endl;
644  return EXIT_FAILURE;
645  }
646 }
Implementation of a matrix and operations on matrices.
Definition: vpMatrix.h:153
void resize(unsigned int nrows, unsigned int ncols, bool flagNullify=true, bool recopy_=true)
Definition: vpArray2D.h:304
error that can be emited by ViSP classes.
Definition: vpException.h:71
unsigned int getRows() const
Definition: vpArray2D.h:289
VISP_EXPORT double measureTimeMs()
Definition: vpTime.cpp:126
static bool parse(int *argcPtr, const char **argv, vpArgvInfo *argTable, int flags)
Definition: vpParseArgv.cpp:69
unsigned int getCols() const
Definition: vpArray2D.h:279
vpMatrix t() const
Definition: vpMatrix.cpp:464
const std::string & getStringMessage() const
Send a reference (constant) related the error message (can be empty).
Definition: vpException.cpp:92
void insert(const vpMatrix &A, unsigned int r, unsigned int c)
Definition: vpMatrix.cpp:5988
double frobeniusNorm() const
Definition: vpMatrix.cpp:6704