Visual Servoing Platform  version 3.2.0 under development (2018-10-21)
testMatrixInverse.cpp

Test various matrix inversions.

/****************************************************************************
*
* 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 inversions.
*
* Authors:
* Fabien Spindler
*
*****************************************************************************/
#include <cmath>
#include <fstream>
#include <iostream>
#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 inversions\n\
using LU, QR and Cholesky methods as well as Pseudo-inverse.\n\
Outputs a comparison of these methods.\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;
}
vpMatrix make_random_symmetric_positive_matrix(unsigned int n)
{
A.resize(n, n);
I.eye(n);
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;
A = 0.5 * (A + A.t());
A = A + n * I;
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++) {
#if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || \
defined(VISP_HAVE_GSL)
double det = 0.;
// don't put singular matrices in the benchmark
for (M = make_random_matrix(nb_rows, nb_cols); std::fabs(det = M.AtA().det()) < .01;
M = make_random_matrix(nb_rows, nb_cols)) {
if (verbose) {
std::cout << " Generated random matrix AtA=" << std::endl << M.AtA() << std::endl;
std::cout << " Generated random matrix not invertible: det=" << det << ". Retrying..." << std::endl;
}
}
#else
M = make_random_matrix(nb_rows, nb_cols);
#endif
bench.push_back(M);
}
}
void create_bench_symmetric_positive_matrix(unsigned int nb_matrices, unsigned int n, bool verbose,
std::vector<vpMatrix> &bench)
{
if (verbose)
std::cout << "Create a bench of " << nb_matrices << " " << n << " by " << n << " symmetric positive matrices"
<< std::endl;
bench.clear();
for (unsigned int i = 0; i < nb_matrices; i++) {
#if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || \
defined(VISP_HAVE_GSL)
double det = 0.;
// don't put singular matrices in the benchmark
for (M = make_random_symmetric_positive_matrix(n); std::fabs(det = M.det()) < .01;
M = make_random_symmetric_positive_matrix(n)) {
if (verbose) {
std::cout << " Generated random symmetric positive matrix A=" << std::endl << M << std::endl;
std::cout << " Generated random symmetric positive matrix not "
"invertibleL: det="
<< det << ". Retrying..." << std::endl;
}
}
#else
M = make_random_symmetric_positive_matrix(n);
#endif
bench.push_back(M);
}
}
int test_inverse(const std::vector<vpMatrix> &bench, const std::vector<vpMatrix> &result)
{
for (unsigned int i = 0; i < bench.size(); i++) {
vpMatrix I = bench[i] * result[i];
if (std::fabs(I.euclideanNorm() - sqrt((double)bench[0].AtA().getRows())) > 1e-10) {
std::cout << "Bad inverse[" << i << "]: " << I.euclideanNorm() << " " << sqrt((double)bench[0].AtA().getRows())
<< std::endl;
return EXIT_FAILURE;
}
}
return EXIT_SUCCESS;
}
#if defined(VISP_HAVE_EIGEN3)
int test_inverse_lu_eigen3(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by LU using Eigen3 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using LU decomposition (Eigen3)." << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByLUEigen3() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
#endif
#if defined(VISP_HAVE_LAPACK)
int test_inverse_lu_lapack(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by LU using Lapack 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using LU decomposition (Lapack)." << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByLULapack() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
int test_inverse_cholesky_lapack(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by Cholesky using Lapack 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using cholesky decomposition (Lapack)." << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByCholeskyLapack() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
int test_inverse_qr_lapack(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by QR using Lapack 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using QR decomposition (Lapack)" << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByQRLapack() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
#endif
#if defined(VISP_HAVE_GSL)
int test_inverse_lu_gsl(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by LU using GSL 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using LU decomposition (GSL)" << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByLUGsl() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
int test_inverse_lu_opencv(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by LU using OpenCV 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using LU decomposition (OpenCV)" << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByLUOpenCV() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
int test_inverse_cholesky_opencv(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test inverse by Cholesky using OpenCV 3rd party" << std::endl;
// Compute inverse
if (verbose)
std::cout << " Inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols()
<< " matrix using Cholesky decomposition (OpenCV)" << std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().inverseByCholeskyOpenCV() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
#endif
#if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || \
defined(VISP_HAVE_GSL)
// SVD is only available for these 3rd parties
int test_pseudo_inverse(bool verbose, const std::vector<vpMatrix> &bench, double &time)
{
if (verbose)
std::cout << "Test pseudo inverse using either Eigen3, Lapack, OpenCV or "
"GSL 3rd party"
<< std::endl;
// Compute inverse
if (verbose)
std::cout << " Pseudo inverting " << bench[0].AtA().getRows() << "x" << bench[0].AtA().getCols() << " matrix"
<< std::endl;
std::vector<vpMatrix> result(bench.size());
double t = vpTime::measureTimeMs();
for (unsigned int i = 0; i < bench.size(); i++) {
result[i] = bench[i].AtA().pseudoInverse() * bench[i].transpose();
}
time = vpTime::measureTimeMs() - t;
// Test inverse
return test_inverse(bench, result);
}
#endif
void save_time(const std::string &method, bool verbose, bool use_plot_file, std::ofstream &of, double time)
{
if (use_plot_file)
of << time << "\t";
if (verbose || !use_plot_file) {
std::cout << method << time << 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 = 1000;
unsigned int nb_iterations = 10;
unsigned int nb_rows = 6;
unsigned int nb_cols = 6;
bool verbose = false;
std::string plotfile("plot-inv.csv");
bool use_plot_file = false;
std::ofstream of;
// 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);
}
if (use_plot_file) {
of.open(plotfile.c_str());
of << "iter"
<< "\t";
#if defined(VISP_HAVE_LAPACK)
of << "\"LU Lapack\""
<< "\t";
#endif
#if defined(VISP_HAVE_EIGEN3)
of << "\"LU Eigen3\""
<< "\t";
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
of << "\"LU OpenCV\""
<< "\t";
#endif
#if defined(VISP_HAVE_GSL)
of << "\"LU GSL\""
<< "\t";
#endif
#if defined(VISP_HAVE_LAPACK)
of << "\"Cholesky Lapack\""
<< "\t";
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
of << "\"Cholesky OpenCV\""
<< "\t";
#endif
#if defined(VISP_HAVE_LAPACK)
of << "\"QR Lapack\""
<< "\t";
#endif
#if defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || defined(VISP_HAVE_GSL)
of << "\"Pseudo inverse (Lapack, OpenCV, GSL)\""
<< "\t";
#endif
of << std::endl;
}
int ret = EXIT_SUCCESS;
for (unsigned int iter = 0; iter < nb_iterations; iter++) {
std::vector<vpMatrix> bench_random_matrices;
create_bench_random_matrix(nb_matrices, nb_rows, nb_cols, verbose, bench_random_matrices);
std::vector<vpMatrix> bench_symmetric_positive_matrices;
create_bench_symmetric_positive_matrix(nb_matrices, nb_rows, verbose, bench_symmetric_positive_matrices);
if (use_plot_file)
of << iter << "\t";
double time;
// LU decomposition
#if defined(VISP_HAVE_LAPACK)
ret += test_inverse_lu_lapack(verbose, bench_random_matrices, time);
save_time("Inverse by LU (Lapack): ", verbose, use_plot_file, of, time);
#endif
#if defined(VISP_HAVE_EIGEN3)
ret += test_inverse_lu_eigen3(verbose, bench_random_matrices, time);
save_time("Inverse by LU (Eigen3): ", verbose, use_plot_file, of, time);
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
ret += test_inverse_lu_opencv(verbose, bench_random_matrices, time);
save_time("Inverse by LU (OpenCV): ", verbose, use_plot_file, of, time);
#endif
#if defined(VISP_HAVE_GSL)
ret += test_inverse_lu_gsl(verbose, bench_random_matrices, time);
save_time("Inverse by LU (GSL): ", verbose, use_plot_file, of, time);
#endif
// Cholesky for symmetric positive matrices
#if defined(VISP_HAVE_LAPACK)
ret += test_inverse_cholesky_lapack(verbose, bench_symmetric_positive_matrices, time);
save_time("Inverse by Cholesly (Lapack): ", verbose, use_plot_file, of, time);
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101)
ret += test_inverse_cholesky_opencv(verbose, bench_symmetric_positive_matrices, time);
save_time("Inverse by Cholesky (OpenCV): ", verbose, use_plot_file, of, time);
#endif
// QR decomposition
#if defined(VISP_HAVE_LAPACK)
ret += test_inverse_qr_lapack(verbose, bench_random_matrices, time);
save_time("Inverse by QR (Lapack): ", verbose, use_plot_file, of, time);
#endif
// Pseudo-inverse with SVD
#if defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_LAPACK) || (VISP_HAVE_OPENCV_VERSION >= 0x020101) || \
defined(VISP_HAVE_GSL)
ret += test_pseudo_inverse(verbose, bench_random_matrices, time);
save_time("Pseudo inverse (Lapack, Eigen3, OpenCV or GSL): ", 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;
}
}