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/* -*- c++ -*- (enables emacs c++ mode) *//*===========================================================================
Copyright (C) 2002-2012 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. ===========================================================================*/
// This file is a modified version of qmr.h from ITL.
// See http://osl.iu.edu/research/itl/
// Following the corresponding Copyright notice.
//===========================================================================
//
// Copyright (c) 1997-2001, The Trustees of Indiana University.
// All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of the University of Notre Dame nor the
// names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND
// CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES
// OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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//
//===========================================================================
/**@file gmm_solver_qmr.h
@author Andrew Lumsdaine <lums@osl.iu.edu> @author Lie-Quan Lee <llee@osl.iu.edu> @author Yves Renard <Yves.Renard@insa-lyon.fr> @date October 13, 2002. @brief Quasi-Minimal Residual iterative solver.*/#ifndef GMM_QMR_H
#define GMM_QMR_H
#include "gmm_kernel.h"
#include "gmm_iter.h"
namespace gmm {
/** Quasi-Minimal Residual.
This routine solves the unsymmetric linear system Ax = b using the Quasi-Minimal Residual method. See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual method for non-Hermitian linear systems, Numerical Math., 60(1991), pp. 315-339 Preconditioner - Incomplete LU, Incomplete LU with threshold, SSOR or identity_preconditioner. */ template <typename Matrix, typename Vector, typename VectorB, typename Precond1> void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1, iteration& iter) {
typedef typename linalg_traits<Vector>::value_type T; typedef typename number_traits<T>::magnitude_type R;
T delta(0), ep(0), beta(0), theta_1(0), gamma_1(0); T theta(0), gamma(1), eta(-1); R rho_1(0), rho, xi;
typedef typename temporary_vector<Vector>::vector_type TmpVec; size_type nn = vect_size(x); TmpVec r(nn), v_tld(nn), y(nn), w_tld(nn), z(nn), v(nn), w(nn); TmpVec y_tld(nn), z_tld(nn), p(nn), q(nn), p_tld(nn), d(nn), s(nn);
iter.set_rhsnorm(double(gmm::vect_norm2(b))); if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
gmm::mult(A, gmm::scaled(x, T(-1)), b, r); gmm::copy(r, v_tld);
gmm::left_mult(M1, v_tld, y); rho = gmm::vect_norm2(y);
gmm::copy(r, w_tld); gmm::transposed_right_mult(M1, w_tld, z); xi = gmm::vect_norm2(z); while (! iter.finished_vect(r)) { if (rho == R(0) || xi == R(0)) { if (iter.get_maxiter() == size_type(-1)) { GMM_ASSERT1(false, "QMR failed to converge"); } else { GMM_WARNING1("QMR failed to converge"); return; } } gmm::copy(gmm::scaled(v_tld, T(R(1)/rho)), v); gmm::scale(y, T(R(1)/rho));
gmm::copy(gmm::scaled(w_tld, T(R(1)/xi)), w); gmm::scale(z, T(R(1)/xi));
delta = gmm::vect_sp(z, y); if (delta == T(0)) { if (iter.get_maxiter() == size_type(-1)) { GMM_ASSERT1(false, "QMR failed to converge"); } else { GMM_WARNING1("QMR failed to converge"); return; } } gmm::right_mult(M1, y, y_tld); gmm::transposed_left_mult(M1, z, z_tld);
if (iter.first()) { gmm::copy(y_tld, p); gmm::copy(z_tld, q); } else { gmm::add(y_tld, gmm::scaled(p, -(T(xi * delta) / ep)), p); gmm::add(z_tld, gmm::scaled(q, -(T(rho * delta) / ep)), q); } gmm::mult(A, p, p_tld);
ep = gmm::vect_sp(q, p_tld); if (ep == T(0)) { if (iter.get_maxiter() == size_type(-1)) { GMM_ASSERT1(false, "QMR failed to converge"); } else { GMM_WARNING1("QMR failed to converge"); return; } } beta = ep / delta; if (beta == T(0)) { if (iter.get_maxiter() == size_type(-1)) { GMM_ASSERT1(false, "QMR failed to converge"); } else { GMM_WARNING1("QMR failed to converge"); return; } } gmm::add(p_tld, gmm::scaled(v, -beta), v_tld); gmm::left_mult(M1, v_tld, y);
rho_1 = rho; rho = gmm::vect_norm2(y);
gmm::mult(gmm::transposed(A), q, w_tld); gmm::add(w_tld, gmm::scaled(w, -beta), w_tld); gmm::transposed_right_mult(M1, w_tld, z);
xi = gmm::vect_norm2(z);
gamma_1 = gamma; theta_1 = theta;
theta = rho / (gamma_1 * beta); gamma = T(1) / gmm::sqrt(T(1) + gmm::sqr(theta));
if (gamma == T(0)) { if (iter.get_maxiter() == size_type(-1)) { GMM_ASSERT1(false, "QMR failed to converge"); } else { GMM_WARNING1("QMR failed to converge"); return; } } eta = -eta * T(rho_1) * gmm::sqr(gamma) / (beta * gmm::sqr(gamma_1));
if (iter.first()) { gmm::copy(gmm::scaled(p, eta), d); gmm::copy(gmm::scaled(p_tld, eta), s); } else { T tmp = gmm::sqr(theta_1 * gamma); gmm::add(gmm::scaled(p, eta), gmm::scaled(d, tmp), d); gmm::add(gmm::scaled(p_tld, eta), gmm::scaled(s, tmp), s); } gmm::add(d, x); gmm::add(gmm::scaled(s, T(-1)), r);
++iter; } }
}
#endif
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