Visual Servoing Platform  version 3.2.0 under development (2018-10-20)
testMatrixPseudoInverse.cpp

Test various pseudo inverse implementations.

/****************************************************************************
*
* This file is part of the ViSP software.
* Copyright (C) 2005 - 2017 by Inria. All rights reserved.
*
* This software is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
* See the file LICENSE.txt at the root directory of this source
* distribution for additional information about the GNU GPL.
*
* For using ViSP with software that can not be combined with the GNU
* GPL, please contact Inria about acquiring a ViSP Professional
* Edition License.
*
* See http://visp.inria.fr for more information.
*
* This software was developed at:
* Inria Rennes - Bretagne Atlantique
* Campus Universitaire de Beaulieu
* 35042 Rennes Cedex
* France
*
* If you have questions regarding the use of this file, please contact
* Inria at visp@inria.fr
*
* This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* Description:
* Test various svd decompositions.
*
* Authors:
* Fabien Spindler
*
*****************************************************************************/
#include <algorithm>
#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpTime.h>
#include <visp3/io/vpParseArgv.h>
// List of allowed command line options
#define GETOPTARGS "cdn:i:pf:R:C:vh"
void usage(const char *name, const char *badparam)
{
fprintf(stdout, "\n\
Test matrix pseudo-inverse.\n\
Outputs a comparison of the results obtained by supported 3rd parties.\n\
\n\
SYNOPSIS\n\
%s [-n <number of matrices>] [-f <plot filename>]\n\
[-R <number of rows>] [-C <number of columns>]\n\
[-i <number of iterations>] [-p] [-h]\n", name);
fprintf(stdout, "\n\
OPTIONS: Default\n\
-n <number of matrices> \n\
Number of matrices inverted during each test loop.\n\
\n\
-i <number of iterations> \n\
Number of iterations of the test.\n\
\n\
-f <plot filename> \n\
Set output path for plot output.\n\
The plot logs the times of \n\
the different inversion methods: \n\
QR,LU,Cholesky and Pseudo-inverse.\n\
\n\
-R <number of rows>\n\
Number of rows of the automatically generated matrices \n\
we test on.\n\
\n\
-C <number of columns>\n\
Number of colums of the automatically generated matrices \n\
we test on.\n\
\n\
-p \n\
Plot into filename in the gnuplot format. \n\
If this option is used, tests results will be logged \n\
into a filename specified with -f.\n\
\n\
-h\n\
Print the help.\n\n");
if (badparam) {
fprintf(stderr, "ERROR: \n");
fprintf(stderr, "\nBad parameter [%s]\n", badparam);
}
}
bool getOptions(int argc, const char **argv, unsigned int &nb_matrices, unsigned int &nb_iterations,
bool &use_plot_file, std::string &plotfile, unsigned int &nbrows, unsigned int &nbcols, bool &verbose)
{
const char *optarg_;
int c;
while ((c = vpParseArgv::parse(argc, argv, GETOPTARGS, &optarg_)) > 1) {
switch (c) {
case 'h':
usage(argv[0], NULL);
return false;
break;
case 'n':
nb_matrices = (unsigned int)atoi(optarg_);
break;
case 'i':
nb_iterations = (unsigned int)atoi(optarg_);
break;
case 'f':
plotfile = optarg_;
use_plot_file = true;
break;
case 'p':
use_plot_file = true;
break;
case 'R':
nbrows = (unsigned int)atoi(optarg_);
break;
case 'C':
nbcols = (unsigned int)atoi(optarg_);
break;
case 'v':
verbose = true;
break;
// add default options -c -d
case 'c':
break;
case 'd':
break;
default:
usage(argv[0], optarg_);
return false;
break;
}
}
if ((c == 1) || (c == -1)) {
// standalone param or error
usage(argv[0], NULL);
std::cerr << "ERROR: " << std::endl;
std::cerr << " Bad argument " << optarg_ << std::endl << std::endl;
return false;
}
return true;
}
vpMatrix make_random_matrix(unsigned int nbrows, unsigned int nbcols)
{
A.resize(nbrows, nbcols);
for (unsigned int i = 0; i < A.getRows(); i++) {
for (unsigned int j = 0; j < A.getCols(); j++) {
A[i][j] = (double)rand() / (double)RAND_MAX;
}
}
return A;
}
void create_bench_random_matrix(unsigned int nb_matrices, unsigned int nb_rows, unsigned int nb_cols, bool verbose,
std::vector<vpMatrix> &bench)
{
if (verbose)
std::cout << "Create a bench of " << nb_matrices << " " << nb_rows << " by " << nb_cols << " matrices" << std::endl;
bench.clear();
for (unsigned int i = 0; i < nb_matrices; i++) {
vpMatrix M = make_random_matrix(nb_rows, nb_cols);
bench.push_back(M);
}
}
int test_pseudo_inverse(const std::vector<vpMatrix> &A, const std::vector<vpMatrix> &Api)
{
double allowed_error = 1e-3;
for (unsigned int i = 0; i < A.size(); i++) {
double error = (A[i] * Api[i] * A[i] - A[i]).euclideanNorm();
if (error > allowed_error) {
std::cout << "Bad pseudo-inverse [" << i << "]: euclidean norm: " << error << std::endl;
return EXIT_FAILURE;
}
}
return EXIT_SUCCESS;
}
int test_pseudo_inverse(const std::vector<vpMatrix> &A, const std::vector<vpMatrix> &Api,
const std::vector<vpColVector> &sv, const std::vector<vpMatrix> &imA,
const std::vector<vpMatrix> &imAt, const std::vector<vpMatrix> &kerAt)
{
double allowed_error = 1e-3;
// test Api
for (unsigned int i = 0; i < A.size(); i++) {
double error = (A[i] * Api[i] * A[i] - A[i]).euclideanNorm();
if (error > allowed_error) {
std::cout << "Bad pseudo-inverse [" << i << "]: euclidean norm: " << error << std::endl;
return EXIT_FAILURE;
}
}
// test kerA
for (unsigned int i = 0; i < kerAt.size(); i++) {
if (kerAt[i].size()) {
vpMatrix nullspace = A[i] * kerAt[i].t();
double error = nullspace.euclideanNorm();
if (error > allowed_error) {
std::cout << "Bad kernel [" << i << "]: euclidean norm: " << error << std::endl;
return EXIT_FAILURE;
}
}
}
// test sv, imA, imAt, kerA
for (unsigned int i = 0; i < kerAt.size(); i++) {
unsigned int rank = imA[i].getCols();
vpMatrix U, S(rank, A[i].getCols()), Vt(A[i].getCols(), A[i].getCols());
U = imA[i];
for (unsigned int j = 0; j < rank; j++)
S[j][j] = sv[i][j];
Vt.insert(imAt[i].t(), 0, 0);
Vt.insert(kerAt[i], imAt[i].getCols(), 0);
double error = (U * S * Vt - A[i]).euclideanNorm();
if (error > allowed_error) {
std::cout << "Bad imA, imAt, sv, kerAt [" << i << "]: euclidean norm: " << error << std::endl;
return EXIT_FAILURE;
}
}
return EXIT_SUCCESS;
}
int test_pseudo_inverse_default(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
{
if (verbose)
std::cout << "Test pseudo-inverse using default 3rd party" << std::endl;
if (verbose)
std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
size_t size = bench.size();
std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
std::vector<vpColVector> sv(size);
int ret = EXIT_SUCCESS;
// test 0
unsigned int test = 0;
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
PI[i] = bench[i].pseudoInverse();
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 1
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverse(PI[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 2
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverse(PI[i], sv[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 3
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverse(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
}
return ret;
}
#if defined(VISP_HAVE_EIGEN3)
int test_pseudo_inverse_eigen3(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
{
if (verbose)
std::cout << "Test pseudo-inverse using Eigen3 3rd party" << std::endl;
if (verbose)
std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
size_t size = bench.size();
std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
std::vector<vpColVector> sv(size);
int ret = EXIT_SUCCESS;
// test 0
unsigned int test = 0;
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
PI[i] = bench[i].pseudoInverseEigen3();
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 1
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseEigen3(PI[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 2
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseEigen3(PI[i], sv[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 3
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseEigen3(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
}
return ret;
}
#endif
#if defined(VISP_HAVE_LAPACK)
int test_pseudo_inverse_lapack(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
{
if (verbose)
std::cout << "Test pseudo-inverse using Lapack 3rd party" << std::endl;
if (verbose)
std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
size_t size = bench.size();
std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
std::vector<vpColVector> sv(size);
int ret = EXIT_SUCCESS;
// test 0
unsigned int test = 0;
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
PI[i] = bench[i].pseudoInverseLapack();
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 1
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseLapack(PI[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 2
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseLapack(PI[i], sv[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 3
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseLapack(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
}
return ret;
}
#endif
#if defined(VISP_HAVE_GSL)
int test_pseudo_inverse_gsl(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
{
if (verbose)
std::cout << "Test pseudo-inverse using Gsl 3rd party" << std::endl;
if (verbose)
std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
size_t size = bench.size();
std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
std::vector<vpColVector> sv(size);
int ret = EXIT_SUCCESS;
// test 0
unsigned int test = 0;
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
PI[i] = bench[i].pseudoInverseGsl();
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 1
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseGsl(PI[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 2
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseGsl(PI[i], sv[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 3
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseGsl(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
}
return ret;
}
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
int test_pseudo_inverse_opencv(bool verbose, const std::vector<vpMatrix> &bench, std::vector<double> &time)
{
if (verbose)
std::cout << "Test pseudo-inverse using OpenCV 3rd party" << std::endl;
if (verbose)
std::cout << " Pseudo-inverse on a " << bench[0].getRows() << "x" << bench[0].getCols() << " matrix" << std::endl;
size_t size = bench.size();
std::vector<vpMatrix> PI(size), imA(size), imAt(size), kerAt(size);
std::vector<vpColVector> sv(size);
int ret = EXIT_SUCCESS;
// test 0
unsigned int test = 0;
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
PI[i] = bench[i].pseudoInverseOpenCV();
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 1
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseOpenCV(PI[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 2
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseOpenCV(PI[i], sv[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI);
}
// test 3
test++;
for (unsigned int i = 0; i < bench.size(); i++) {
bench[i].pseudoInverseOpenCV(PI[i], sv[i], 1e-6, imA[i], imAt[i], kerAt[i]);
}
time[test] = vpTime::measureTimeMs() - t;
for (unsigned int i = 0; i < time.size(); i++) {
ret += test_pseudo_inverse(bench, PI, sv, imA, imAt, kerAt);
}
return ret;
}
#endif
void save_time(const std::string &method, unsigned int nrows, unsigned int ncols, bool verbose, bool use_plot_file,
std::ofstream &of, const std::vector<double> &time)
{
for (size_t i = 0; i < time.size(); i++) {
if (use_plot_file)
of << time[i] << "\t";
if (verbose) {
std::cout << " " << method << " svd(" << nrows << "x" << ncols << ")"
<< " test " << i << ": " << time[i] << std::endl;
}
}
}
int main(int argc, const char *argv[])
{
try {
#if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || \
defined(VISP_HAVE_GSL)
unsigned int nb_matrices = 10;
unsigned int nb_iterations = 10;
unsigned int nb_rows = 12;
unsigned int nb_cols = 6;
bool verbose = false;
std::string plotfile("plot-pseudo-inv.csv");
bool use_plot_file = false;
std::ofstream of;
unsigned int nb_svd_functions = 4; // 4 tests for each existing vpMatrix::pseudoInverse(...) functions
unsigned int nb_test_matrix_size = 3; // 3 tests: m > n, m = n, m < n
std::vector<double> time(nb_svd_functions);
std::vector<unsigned int> nrows(nb_test_matrix_size), ncols(nb_test_matrix_size);
// Read the command line options
if (getOptions(argc, argv, nb_matrices, nb_iterations, use_plot_file, plotfile, nb_rows, nb_cols, verbose) ==
false) {
exit(-1);
}
for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
// consider m > n, m = n, m < n
if (s == 0) {
nrows[s] = nb_rows;
ncols[s] = nb_cols;
} else if (s == 1) {
nrows[s] = nb_cols;
ncols[s] = nb_cols;
} else {
nrows[s] = nb_cols;
ncols[s] = nb_rows;
}
}
if (use_plot_file) {
of.open(plotfile.c_str());
of << "iter"
<< "\t";
for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
for (unsigned int i = 0; i < nb_svd_functions; i++)
of << "\"default " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
<< "\t";
#if defined(VISP_HAVE_LAPACK)
for (unsigned int i = 0; i < nb_svd_functions; i++)
of << "\"Lapack " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
<< "\t";
#endif
#if defined(VISP_HAVE_EIGEN3)
for (unsigned int i = 0; i < nb_svd_functions; i++)
of << "\"Eigen3 " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
<< "\t";
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
for (unsigned int i = 0; i < nb_svd_functions; i++)
of << "\"OpenCV " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
<< "\t";
#endif
#if defined(VISP_HAVE_GSL)
for (unsigned int i = 0; i < nb_svd_functions; i++)
of << "\"GSL " << nrows[s] << "x" << ncols[s] << " test " << i << "\""
<< "\t";
#endif
}
of << std::endl;
}
int ret = EXIT_SUCCESS;
for (unsigned int iter = 0; iter < nb_iterations; iter++) {
if (use_plot_file)
of << iter << "\t";
for (unsigned int s = 0; s < nb_test_matrix_size; s++) {
std::vector<vpMatrix> bench_random_matrices;
create_bench_random_matrix(nb_matrices, nrows[s], ncols[s], verbose, bench_random_matrices);
ret += test_pseudo_inverse_default(verbose, bench_random_matrices, time);
save_time("default -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
#if defined(VISP_HAVE_LAPACK)
ret += test_pseudo_inverse_lapack(verbose, bench_random_matrices, time);
save_time("Lapack -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
#endif
#if defined(VISP_HAVE_EIGEN3)
ret += test_pseudo_inverse_eigen3(verbose, bench_random_matrices, time);
save_time("Eigen3 -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
ret += test_pseudo_inverse_opencv(verbose, bench_random_matrices, time);
save_time("OpenCV -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
#endif
#if defined(VISP_HAVE_GSL)
ret += test_pseudo_inverse_gsl(verbose, bench_random_matrices, time);
save_time("GSL -", nrows[s], ncols[s], verbose, use_plot_file, of, time);
#endif
}
if (use_plot_file)
of << std::endl;
}
if (use_plot_file) {
of.close();
std::cout << "Result saved in " << plotfile << std::endl;
}
if (ret == EXIT_SUCCESS) {
std::cout << "Test succeed" << std::endl;
} else {
std::cout << "Test failed" << std::endl;
}
return ret;
#else
(void)argc;
(void)argv;
std::cout << "Test does nothing since you dont't have Eigen3, Lapack, "
"OpenCV or GSL 3rd party"
<< std::endl;
return EXIT_SUCCESS;
#endif
} catch (const vpException &e) {
std::cout << "Catch an exception: " << e.getStringMessage() << std::endl;
return EXIT_FAILURE;
}
}