/usr/include/gmm/gmm_condition_number.h is in libgmm-dev 4.0.0-0ubuntu1.
This file is owned by root:root, with mode 0o644.
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//===========================================================================
//
// Copyright (C) 2003-2008 Yves Renard
//
// This file is a part of GETFEM++
//
// Getfem++ is free software; you can redistribute it and/or modify it
// under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation; either version 2.1 of the License, or
// (at your option) any later version.
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
// License for more details.
// You should have received a copy of the GNU Lesser General Public License
// along with this program; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
//
// As a special exception, you may use this file as it is a part of a free
// software library without restriction. Specifically, if other files
// instantiate templates or use macros or inline functions from this file,
// or you compile this file and link it with other files to produce an
// executable, this file does not by itself cause the resulting executable
// to be covered by the GNU Lesser General Public License. This exception
// does not however invalidate any other reasons why the executable file
// might be covered by the GNU Lesser General Public License.
//
//===========================================================================
/**@file gmm_condition_number.h
@author Yves Renard <Yves.Renard@insa-lyon.fr>, Julien Pommier <Julien.Pommier@insa-toulouse.fr>
@date August 27, 2003.
@brief computation of the condition number of dense matrices.
*/
#ifndef GMM_CONDITION_NUMBER_H__
#define GMM_CONDITION_NUMBER_H__
#include "gmm_dense_qr.h"
namespace gmm {
/** computation of the condition number of dense matrices using SVD.
Uses symmetric_qr_algorithm => dense matrices only.
@param M a matrix.
@param emin smallest (in magnitude) eigenvalue
@param emax largest eigenvalue.
*/
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
condition_number(const MAT& M,
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type& emin,
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type& emax) {
typedef typename linalg_traits<MAT>::value_type T;
typedef typename number_traits<T>::magnitude_type R;
size_type m = mat_nrows(M), n = mat_ncols(M);
emax = emin = R(0);
std::vector<R> eig(m+n);
if (m+n == 0) return R(0);
if (is_hermitian(M)) {
eig.resize(m);
gmm::symmetric_qr_algorithm(M, eig);
}
else {
dense_matrix<T> B(m+n, m+n); // not very efficient ??
gmm::copy(conjugated(M), sub_matrix(B, sub_interval(m, n), sub_interval(0, m)));
gmm::copy(M, sub_matrix(B, sub_interval(0, m),
sub_interval(m, n)));
gmm::symmetric_qr_algorithm(B, eig);
}
emin = emax = gmm::abs(eig[0]);
for (size_type i = 1; i < eig.size(); ++i) {
R e = gmm::abs(eig[i]);
emin = std::min(emin, e);
emax = std::max(emax, e);
}
// cout << "emin = " << emin << " emax = " << emax << endl;
if (emin == R(0)) return gmm::default_max(R());
return emax / emin;
}
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
condition_number(const MAT& M) {
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type emax, emin;
return condition_number(M, emin, emax);
}
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
Frobenius_condition_number_sqr(const MAT& M) {
typedef typename linalg_traits<MAT>::value_type T;
typedef typename number_traits<T>::magnitude_type R;
size_type m = mat_nrows(M), n = mat_ncols(M);
dense_matrix<T> B(std::min(m,n), std::min(m,n));
if (m < n) mult(M,gmm::conjugated(M),B);
else mult(gmm::conjugated(M),M,B);
R trB = abs(mat_trace(B));
lu_inverse(B);
return trB*abs(mat_trace(B));
}
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
Frobenius_condition_number(const MAT& M)
{ return sqrt(Frobenius_condition_number_sqr(M)); }
/** estimation of the condition number (TO BE DONE...)
*/
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
condest(const MAT& M,
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type& emin,
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type& emax) {
return condition_number(M, emin, emax);
}
template <typename MAT>
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type
condest(const MAT& M) {
typename number_traits<typename
linalg_traits<MAT>::value_type>::magnitude_type emax, emin;
return condest(M, emin, emax);
}
}
#endif
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