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/* -*- c++ -*- (enables emacs c++ mode) *//*===========================================================================
Copyright (C) 2002-2015 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 3 of the License, or (at your option) any later version along with the GCC Runtime Library Exception either version 3.1 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 and GCC Runtime Library Exception 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. ===========================================================================*/
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/**@file gmm_modified_gram_schmidt.h
@author Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu> @date October 13, 2002. @brief Modified Gram-Schmidt orthogonalization*/
#ifndef GMM_MODIFIED_GRAM_SCHMIDT_H
#define GMM_MODIFIED_GRAM_SCHMIDT_H
#include "gmm_kernel.h"
namespace gmm {
template <typename T> class modified_gram_schmidt { protected: typedef dense_matrix<T> MAT; MAT M;
public:
modified_gram_schmidt(int restart, size_t s) : M(s, restart+1) {}
typename linalg_traits<MAT>::const_sub_col_type operator[](size_t i) const { return mat_const_col(M, i); }
typename linalg_traits<MAT>::sub_col_type operator[](size_t i) { return mat_col(M, i); }
inline size_type nrows(void) const { return M.nrows(); } inline size_type ncols(void) const { return M.ncols(); } MAT &mat(void) { return M; } const MAT &mat(void) const { return M; } };
template <typename T, typename VecHi> inline void orthogonalize(modified_gram_schmidt<T>& V, const VecHi& Hi_, size_t i) { VecHi& Hi = const_cast<VecHi&>(Hi_); for (size_t k = 0; k <= i; k++) { Hi[k] = gmm::vect_hp(V[i+1], V[k]); gmm::add(gmm::scaled(V[k], -Hi[k]), V[i+1]); } }
template <typename T, typename VecHi> void orthogonalize_with_refinment(modified_gram_schmidt<T>& V, const VecHi& Hi_, size_t i) { VecHi& Hi = const_cast<VecHi&>(Hi_); orthogonalize(V, Hi_, i); sub_interval SUBI(0, V.nrows()), SUBJ(0, i+1); std::vector<T> corr(i+1); gmm::mult(conjugated(sub_matrix(V.mat(), SUBI, SUBJ)), V[i+1], corr); gmm::mult(sub_matrix(V.mat(), SUBI, SUBJ), scaled(corr, T(-1)), V[i+1],V[i+1]); gmm::add(corr, sub_vector(Hi, SUBJ)); } template <typename T, typename VecS, typename VecX> void combine(modified_gram_schmidt<T>& V, const VecS& s, VecX& x, size_t i) { for (size_t j = 0; j < i; ++j) gmm::add(gmm::scaled(V[j], s[j]), x); }}
#endif
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