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127 lines
5.4 KiB
127 lines
5.4 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2002-2012 Yves Renard
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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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//===========================================================================
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//
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// Copyright (c) 1998-2001, University of Notre Dame. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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// * Neither the name of the University of Notre Dame nor the
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// names of its contributors may be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND
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// CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
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// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES
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// OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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//===========================================================================
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/**@file gmm_modified_gram_schmidt.h
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@author Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu>
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@date October 13, 2002.
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@brief Modified Gram-Schmidt orthogonalization
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*/
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#ifndef GMM_MODIFIED_GRAM_SCHMIDT_H
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#define GMM_MODIFIED_GRAM_SCHMIDT_H
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#include "gmm_kernel.h"
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namespace gmm {
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template <typename T>
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class modified_gram_schmidt {
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protected:
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typedef dense_matrix<T> MAT;
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MAT M;
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public:
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modified_gram_schmidt(int restart, size_t s) : M(s, restart+1) {}
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typename linalg_traits<MAT>::const_sub_col_type
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operator[](size_t i) const { return mat_const_col(M, i); }
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typename linalg_traits<MAT>::sub_col_type
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operator[](size_t i) { return mat_col(M, i); }
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inline size_type nrows(void) const { return M.nrows(); }
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inline size_type ncols(void) const { return M.ncols(); }
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MAT &mat(void) { return M; }
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const MAT &mat(void) const { return M; }
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};
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template <typename T, typename VecHi> inline
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void orthogonalize(modified_gram_schmidt<T>& V, const VecHi& Hi_, size_t i) {
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VecHi& Hi = const_cast<VecHi&>(Hi_);
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for (size_t k = 0; k <= i; k++) {
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Hi[k] = gmm::vect_hp(V[i+1], V[k]);
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gmm::add(gmm::scaled(V[k], -Hi[k]), V[i+1]);
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}
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}
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template <typename T, typename VecHi>
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void orthogonalize_with_refinment(modified_gram_schmidt<T>& V,
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const VecHi& Hi_, size_t i) {
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VecHi& Hi = const_cast<VecHi&>(Hi_);
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orthogonalize(V, Hi_, i);
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sub_interval SUBI(0, V.nrows()), SUBJ(0, i+1);
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std::vector<T> corr(i+1);
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gmm::mult(conjugated(sub_matrix(V.mat(), SUBI, SUBJ)),
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V[i+1], corr);
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gmm::mult(sub_matrix(V.mat(), SUBI, SUBJ),
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scaled(corr, T(-1)), V[i+1],V[i+1]);
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gmm::add(corr, sub_vector(Hi, SUBJ));
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}
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template <typename T, typename VecS, typename VecX>
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void combine(modified_gram_schmidt<T>& V, const VecS& s, VecX& x, size_t i)
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{ for (size_t j = 0; j < i; ++j) gmm::add(gmm::scaled(V[j], s[j]), x); }
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}
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#endif
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