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210 lines
7.9 KiB
210 lines
7.9 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2002-2015 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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// This file is a modified version of qmr.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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//
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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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//
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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_solver_qmr.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 Quasi-Minimal Residual iterative solver.
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*/
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#ifndef GMM_QMR_H
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#define GMM_QMR_H
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#include "gmm_kernel.h"
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#include "gmm_iter.h"
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namespace gmm {
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/** Quasi-Minimal Residual.
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This routine solves the unsymmetric linear system Ax = b using
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the Quasi-Minimal Residual method.
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See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual
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method for non-Hermitian linear systems, Numerical Math.,
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60(1991), pp. 315-339
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Preconditioner - Incomplete LU, Incomplete LU with threshold,
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SSOR or identity_preconditioner.
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*/
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template <typename Matrix, typename Vector, typename VectorB,
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typename Precond1>
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void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1,
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iteration& iter) {
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typedef typename linalg_traits<Vector>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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T delta(0), ep(0), beta(0), theta_1(0), gamma_1(0);
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T theta(0), gamma(1), eta(-1);
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R rho_1(0), rho, xi;
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typedef typename temporary_vector<Vector>::vector_type TmpVec;
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size_type nn = vect_size(x);
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TmpVec r(nn), v_tld(nn), y(nn), w_tld(nn), z(nn), v(nn), w(nn);
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TmpVec y_tld(nn), z_tld(nn), p(nn), q(nn), p_tld(nn), d(nn), s(nn);
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iter.set_rhsnorm(double(gmm::vect_norm2(b)));
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if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
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gmm::mult(A, gmm::scaled(x, T(-1)), b, r);
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gmm::copy(r, v_tld);
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gmm::left_mult(M1, v_tld, y);
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rho = gmm::vect_norm2(y);
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gmm::copy(r, w_tld);
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gmm::transposed_right_mult(M1, w_tld, z);
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xi = gmm::vect_norm2(z);
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while (! iter.finished_vect(r)) {
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if (rho == R(0) || xi == R(0)) {
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if (iter.get_maxiter() == size_type(-1))
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{ GMM_ASSERT1(false, "QMR failed to converge"); }
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else { GMM_WARNING1("QMR failed to converge"); return; }
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}
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gmm::copy(gmm::scaled(v_tld, T(R(1)/rho)), v);
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gmm::scale(y, T(R(1)/rho));
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gmm::copy(gmm::scaled(w_tld, T(R(1)/xi)), w);
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gmm::scale(z, T(R(1)/xi));
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delta = gmm::vect_sp(z, y);
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if (delta == T(0)) {
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if (iter.get_maxiter() == size_type(-1))
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{ GMM_ASSERT1(false, "QMR failed to converge"); }
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else { GMM_WARNING1("QMR failed to converge"); return; }
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}
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gmm::right_mult(M1, y, y_tld);
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gmm::transposed_left_mult(M1, z, z_tld);
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if (iter.first()) {
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gmm::copy(y_tld, p);
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gmm::copy(z_tld, q);
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} else {
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gmm::add(y_tld, gmm::scaled(p, -(T(xi * delta) / ep)), p);
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gmm::add(z_tld, gmm::scaled(q, -(T(rho * delta) / ep)), q);
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}
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gmm::mult(A, p, p_tld);
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ep = gmm::vect_sp(q, p_tld);
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if (ep == T(0)) {
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if (iter.get_maxiter() == size_type(-1))
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{ GMM_ASSERT1(false, "QMR failed to converge"); }
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else { GMM_WARNING1("QMR failed to converge"); return; }
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}
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beta = ep / delta;
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if (beta == T(0)) {
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if (iter.get_maxiter() == size_type(-1))
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{ GMM_ASSERT1(false, "QMR failed to converge"); }
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else { GMM_WARNING1("QMR failed to converge"); return; }
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}
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gmm::add(p_tld, gmm::scaled(v, -beta), v_tld);
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gmm::left_mult(M1, v_tld, y);
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rho_1 = rho;
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rho = gmm::vect_norm2(y);
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gmm::mult(gmm::transposed(A), q, w_tld);
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gmm::add(w_tld, gmm::scaled(w, -beta), w_tld);
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gmm::transposed_right_mult(M1, w_tld, z);
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xi = gmm::vect_norm2(z);
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gamma_1 = gamma;
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theta_1 = theta;
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theta = rho / (gamma_1 * beta);
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gamma = T(1) / gmm::sqrt(T(1) + gmm::sqr(theta));
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if (gamma == T(0)) {
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if (iter.get_maxiter() == size_type(-1))
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{ GMM_ASSERT1(false, "QMR failed to converge"); }
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else { GMM_WARNING1("QMR failed to converge"); return; }
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}
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eta = -eta * T(rho_1) * gmm::sqr(gamma) / (beta * gmm::sqr(gamma_1));
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if (iter.first()) {
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gmm::copy(gmm::scaled(p, eta), d);
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gmm::copy(gmm::scaled(p_tld, eta), s);
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} else {
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T tmp = gmm::sqr(theta_1 * gamma);
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gmm::add(gmm::scaled(p, eta), gmm::scaled(d, tmp), d);
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gmm::add(gmm::scaled(p_tld, eta), gmm::scaled(s, tmp), s);
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}
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gmm::add(d, x);
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gmm::add(gmm::scaled(s, T(-1)), r);
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++iter;
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}
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}
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}
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#endif
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