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143 lines
5.3 KiB
143 lines
5.3 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2003-2012 Yves Renard, Julien Pommier
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This file is a part of GETFEM++
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Getfem++ is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as published
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by the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version along with the GCC Runtime Library
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Exception either version 3.1 or (at your option) any later version.
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This program is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License and GCC Runtime Library Exception for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program; if not, write to the Free Software Foundation,
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Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
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As a special exception, you may use this file as it is a part of a free
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software library without restriction. Specifically, if other files
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instantiate templates or use macros or inline functions from this file,
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or you compile this file and link it with other files to produce an
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executable, this file does not by itself cause the resulting executable
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to be covered by the GNU Lesser General Public License. This exception
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does not however invalidate any other reasons why the executable file
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might be covered by the GNU Lesser General Public License.
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===========================================================================*/
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/**@file gmm_condition_number.h
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@author Yves Renard <Yves.Renard@insa-lyon.fr>, Julien Pommier <Julien.Pommier@insa-toulouse.fr>
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@date August 27, 2003.
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@brief computation of the condition number of dense matrices.
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*/
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#ifndef GMM_CONDITION_NUMBER_H__
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#define GMM_CONDITION_NUMBER_H__
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#include "gmm_dense_qr.h"
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namespace gmm {
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/** computation of the condition number of dense matrices using SVD.
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Uses symmetric_qr_algorithm => dense matrices only.
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@param M a matrix.
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@param emin smallest (in magnitude) eigenvalue
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@param emax largest eigenvalue.
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*/
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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condition_number(const MAT& M,
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type& emin,
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type& emax) {
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typedef typename linalg_traits<MAT>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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size_type m = mat_nrows(M), n = mat_ncols(M);
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emax = emin = R(0);
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std::vector<R> eig(m+n);
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if (m+n == 0) return R(0);
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if (is_hermitian(M)) {
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eig.resize(m);
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gmm::symmetric_qr_algorithm(M, eig);
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}
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else {
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dense_matrix<T> B(m+n, m+n); // not very efficient ??
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gmm::copy(conjugated(M), sub_matrix(B, sub_interval(m, n), sub_interval(0, m)));
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gmm::copy(M, sub_matrix(B, sub_interval(0, m),
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sub_interval(m, n)));
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gmm::symmetric_qr_algorithm(B, eig);
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}
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emin = emax = gmm::abs(eig[0]);
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for (size_type i = 1; i < eig.size(); ++i) {
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R e = gmm::abs(eig[i]);
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emin = std::min(emin, e);
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emax = std::max(emax, e);
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}
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// cout << "emin = " << emin << " emax = " << emax << endl;
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if (emin == R(0)) return gmm::default_max(R());
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return emax / emin;
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}
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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condition_number(const MAT& M) {
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type emax, emin;
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return condition_number(M, emin, emax);
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}
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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Frobenius_condition_number_sqr(const MAT& M) {
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typedef typename linalg_traits<MAT>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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size_type m = mat_nrows(M), n = mat_ncols(M);
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dense_matrix<T> B(std::min(m,n), std::min(m,n));
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if (m < n) mult(M,gmm::conjugated(M),B);
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else mult(gmm::conjugated(M),M,B);
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R trB = abs(mat_trace(B));
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lu_inverse(B);
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return trB*abs(mat_trace(B));
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}
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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Frobenius_condition_number(const MAT& M)
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{ return sqrt(Frobenius_condition_number_sqr(M)); }
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/** estimation of the condition number (TO BE DONE...)
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*/
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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condest(const MAT& M,
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type& emin,
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type& emax) {
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return condition_number(M, emin, emax);
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}
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template <typename MAT>
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type
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condest(const MAT& M) {
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typename number_traits<typename
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linalg_traits<MAT>::value_type>::magnitude_type emax, emin;
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return condest(M, emin, emax);
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}
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}
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#endif
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