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/****************************************************************************
*
* ViSP, open source Visual Servoing Platform software.
* Copyright (C) 2005 - 2023 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 https://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 matrix condition number.
*
*****************************************************************************/
/*!
\example testMatrixConditionNumber.cpp
\brief Test matrix condition number computation.
*/
#include <iostream>
#include <stdlib.h>
#include <visp3/core/vpMatrix.h>
int test_condition_number(const std::string &test_name, const vpMatrix &M)
{
double precision = 1e-6;
bool is_square = (M.getCols() == M.getRows() ? true : false);
double inducedL2_norm_inv = 0, cond_inv = 0;
double inducedL2_norm = M.inducedL2Norm();
double inducedL2_norm_pinv = M.pseudoInverse().inducedL2Norm();
double cond = M.cond();
double cond_pinv = inducedL2_norm * inducedL2_norm_pinv;
vpMatrix kerMt;
double rank = M.kernel(kerMt);
if (is_square) {
inducedL2_norm_inv = M.inverseByLU().inducedL2Norm();
cond_inv = inducedL2_norm * inducedL2_norm_inv;
}
M.print(std::cout, 4, test_name);
std::cout << " Matrix rank: " << rank << std::endl;
std::cout << " Matrix induced L2 norm ||M||_L2: " << inducedL2_norm << std::endl;
if (is_square) {
std::cout << " Inverse induced L2 norm ||M^-1||_L2: " << inducedL2_norm_inv << std::endl;
}
std::cout << " Pseudo inverse induced L2 norm norm ||M^+||_L2: " << inducedL2_norm_pinv << std::endl;
if (is_square) {
std::cout << " Condition number such as cond(M)=||M||_L2 * ||M^-1||_L2: " << cond_inv << std::endl;
}
std::cout << " Condition number such as cond(M)=||M||_L2 * ||M^+||_L2: " << cond_pinv << std::endl;
std::cout << " Condition number cond(M): " << cond << std::endl;
if (!vpMath::equal(cond, cond_pinv, precision)) {
std::cout << " Condition number differ from the one computed with the pseudo inverse" << std::endl;
return EXIT_FAILURE;
}
if (is_square) {
if (!vpMath::equal(cond, cond_inv, precision)) {
std::cout << " Condition number differ from the one computed with the inverse" << std::endl;
return EXIT_FAILURE;
}
}
return EXIT_SUCCESS;
}
int main()
{
#if defined(VISP_HAVE_LAPACK) || defined(VISP_HAVE_EIGEN3) || defined(VISP_HAVE_OPENCV)
vpMatrix M(3, 3);
M.eye();
if (test_condition_number("* Test square matrix M", M)) {
std::cout << " - Condition number computation fails" << std::endl;
return EXIT_FAILURE;
} else {
std::cout << " + Condition number computation succeed" << std::endl;
}
M.resize(2, 3);
M[0][0] = 1;
M[0][1] = 2;
M[0][2] = 3;
M[1][0] = 4;
M[1][1] = 5;
M[1][2] = 6;
if (test_condition_number("* Test rect matrix M", M)) {
std::cout << " - Condition number computation fails" << std::endl;
return EXIT_FAILURE;
} else {
std::cout << " + Condition number computation succeed" << std::endl;
}
M = M.transpose();
if (test_condition_number("* Test rect matrix M", M)) {
std::cout << " - Condition number computation fails" << std::endl;
return EXIT_FAILURE;
} else {
std::cout << " + Condition number computation succeed" << std::endl;
}
M.resize(3, 4);
M[0][0] = 1;
M[0][1] = 2;
M[0][2] = 3;
M[0][3] = 0;
M[1][0] = 4;
M[1][1] = 5;
M[1][2] = 6;
M[1][3] = 0;
M[2][0] = 0;
M[2][1] = 0;
M[2][2] = 0;
M[2][3] = 0;
if (test_condition_number("* Test rect matrix M", M)) {
std::cout << " - Condition number computation fails" << std::endl;
return EXIT_FAILURE;
} else {
std::cout << " + Condition number computation succeed" << std::endl;
}
M = M.transpose();
if (test_condition_number("* Test rect matrix M", M)) {
std::cout << " - Condition number computation fails" << std::endl;
return EXIT_FAILURE;
} else {
std::cout << " + Condition number computation succeed" << std::endl;
}
std::cout << "Test succeed" << std::endl;
#else
std::cout << "Test ignored: install Lapack, Eigen3 or OpenCV" << std::endl;
#endif
return EXIT_SUCCESS;
}
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