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// -*- c++ -*- (enables emacs c++ mode)
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//===========================================================================
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// Copyright (C) 1997-2008 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 2.1 of the License, or
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// (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 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 part of a free software
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// library without restriction. Specifically, if other files instantiate
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// templates or use macros or inline functions from this file, or you compile
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// this file and link it with other files to produce an executable, this
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// file does not by itself cause the resulting executable to be covered by
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// the GNU General Public License. This exception does not however
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// invalidate any other reasons why the executable file might be covered by
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// the GNU General Public License.
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//===========================================================================
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// This file is a modified version of gmres.h from ITL.
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// See http://osl.iu.edu/research/itl/
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// Following the corresponding Copyright notice.
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//===========================================================================
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// Copyright (c) 1997-2001, The Trustees of Indiana University.
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// 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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// * 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 California, Berkeley 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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// 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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/**@file gmm_solver_gmres.h
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@author Andrew Lumsdaine <lums@osl.iu.edu>
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@author Lie-Quan Lee <llee@osl.iu.edu>
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@author Yves Renard <Yves.Renard@insa-lyon.fr>
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@date October 13, 2002.
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@brief GMRES (Generalized Minimum Residual) iterative solver.
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#ifndef GMM_KRYLOV_GMRES_H
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#define GMM_KRYLOV_GMRES_H
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#include "gmm_kernel.h"
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#include "gmm_modified_gram_schmidt.h"
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/** Generalized Minimum Residual
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This solve the unsymmetric linear system Ax = b using restarted GMRES.
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See: Y. Saad and M. Schulter. GMRES: A generalized minimum residual
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algorithm for solving nonsysmmetric linear systems, SIAM
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J. Sci. Statist. Comp. 7(1986), pp, 856-869
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template <typename Mat, typename Vec, typename VecB, typename Precond,
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void gmres(const Mat &A, Vec &x, const VecB &b, const Precond &M,
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int restart, iteration &outer, Basis& KS) {
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typedef typename linalg_traits<Vec>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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std::vector<T> w(vect_size(x)), r(vect_size(x)), u(vect_size(x));
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std::vector<T> c_rot(restart+1), s_rot(restart+1), s(restart+1);
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gmm::dense_matrix<T> H(restart+1, restart);
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double t_ref, t_prec = MPI_Wtime(), t_tot = 0;
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static double tmult_tot = 0.0;
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cout << "GMRES " << endl;
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outer.set_rhsnorm(gmm::vect_norm2(r));
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if (outer.get_rhsnorm() == 0.0) { clear(x); return; }
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mult(A, scaled(x, -1), b, w);
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R beta = gmm::vect_norm2(r), beta_old = beta;
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iteration inner = outer;
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inner.reduce_noisy();
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inner.set_maxiter(restart);
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inner.set_name("GMRes inner");
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while (! outer.finished(beta)) {
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gmm::copy(gmm::scaled(r, R(1)/beta), KS[0]);
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size_type i = 0; inner.init();
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orthogonalize(KS, mat_col(H, i), i);
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R a = gmm::vect_norm2(KS[i+1]);
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gmm::scale(KS[i+1], T(1) / a);
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for (size_type k = 0; k < i; ++k)
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Apply_Givens_rotation_left(H(k,i), H(k+1,i), c_rot[k], s_rot[k]);
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Givens_rotation(H(i,i), H(i+1,i), c_rot[i], s_rot[i]);
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Apply_Givens_rotation_left(H(i,i), H(i+1,i), c_rot[i], s_rot[i]);
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Apply_Givens_rotation_left(s[i], s[i+1], c_rot[i], s_rot[i]);
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++inner, ++outer, ++i;
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} while (! inner.finished(gmm::abs(s[i])));
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upper_tri_solve(H, s, i, false);
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combine(KS, s, x, i);
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mult(A, gmm::scaled(x, -1), b, w);
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beta_old = std::min(beta, beta_old); beta = gmm::vect_norm2(r);
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if (int(inner.get_iteration()) < restart -1 || beta_old <= beta)
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++blocked; else blocked = 0;
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if (outer.get_noisy()) cout << "Gmres is blocked, exiting\n";
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t_tot = MPI_Wtime() - t_ref;
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cout << "temps GMRES : " << t_tot << endl;
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template <typename Mat, typename Vec, typename VecB, typename Precond >
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void gmres(const Mat &A, Vec &x, const VecB &b,
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const Precond &M, int restart, iteration& outer) {
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typedef typename linalg_traits<Vec>::value_type T;
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modified_gram_schmidt<T> orth(restart, vect_size(x));
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gmres(A, x, b, M, restart, outer, orth);
added
removed
contrib/gmm/gmm_solver_gmres.h
