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165 lines
6.0 KiB
165 lines
6.0 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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/**@file gmm_solver_constrained_cg.h
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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 Constrained conjugate gradient. */
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// preconditionning does not work
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#ifndef GMM_SOLVER_CCG_H__
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#define GMM_SOLVER_CCG_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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template <typename CMatrix, typename CINVMatrix, typename Matps,
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typename VectorX>
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void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV,
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const Matps& /* PS */, VectorX&) {
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// compute the pseudo inverse of the non-square matrix C such
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// CINV = inv(C * trans(C)) * C.
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// based on a conjugate gradient method.
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// optimisable : copie de la ligne, precalcul de C * trans(C).
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typedef VectorX TmpVec;
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typedef typename linalg_traits<VectorX>::value_type value_type;
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size_type nr = mat_nrows(C), nc = mat_ncols(C);
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TmpVec d(nr), e(nr), l(nc), p(nr), q(nr), r(nr);
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value_type rho, rho_1, alpha;
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clear(d);
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clear(CINV);
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for (size_type i = 0; i < nr; ++i) {
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d[i] = 1.0; rho = 1.0;
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clear(e);
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copy(d, r);
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copy(d, p);
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while (rho >= 1E-38) { /* conjugate gradient to compute e */
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/* which is the i nd row of inv(C * trans(C)) */
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mult(gmm::transposed(C), p, l);
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mult(C, l, q);
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alpha = rho / vect_sp(p, q);
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add(scaled(p, alpha), e);
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add(scaled(q, -alpha), r);
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rho_1 = rho;
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rho = vect_sp(r, r);
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add(r, scaled(p, rho / rho_1), p);
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}
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mult(transposed(C), e, l); /* l is the i nd row of CINV */
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// cout << "l = " << l << endl;
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clean(l, 1E-15);
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copy(l, mat_row(CINV, i));
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d[i] = 0.0;
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}
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}
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/** Compute the minimum of @f$ 1/2((Ax).x) - bx @f$ under the contraint @f$ Cx <= f @f$ */
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template < typename Matrix, typename CMatrix, typename Matps,
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typename VectorX, typename VectorB, typename VectorF,
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typename Preconditioner >
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void constrained_cg(const Matrix& A, const CMatrix& C, VectorX& x,
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const VectorB& b, const VectorF& f,const Matps& PS,
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const Preconditioner& M, iteration &iter) {
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typedef typename temporary_dense_vector<VectorX>::vector_type TmpVec;
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typedef typename temporary_vector<CMatrix>::vector_type TmpCVec;
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typedef row_matrix<TmpCVec> TmpCmat;
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typedef typename linalg_traits<VectorX>::value_type value_type;
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value_type rho = 1.0, rho_1, lambda, gamma;
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TmpVec p(vect_size(x)), q(vect_size(x)), q2(vect_size(x)),
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r(vect_size(x)), old_z(vect_size(x)), z(vect_size(x)),
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memox(vect_size(x));
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std::vector<bool> satured(mat_nrows(C));
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clear(p);
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iter.set_rhsnorm(sqrt(vect_sp(PS, b, b)));
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if (iter.get_rhsnorm() == 0.0) iter.set_rhsnorm(1.0);
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TmpCmat CINV(mat_nrows(C), mat_ncols(C));
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pseudo_inverse(C, CINV, PS, x);
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while(true) {
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// computation of residu
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copy(z, old_z);
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copy(x, memox);
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mult(A, scaled(x, -1.0), b, r);
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mult(M, r, z); // preconditionner not coherent
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bool transition = false;
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for (size_type i = 0; i < mat_nrows(C); ++i) {
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value_type al = vect_sp(mat_row(C, i), x) - f[i];
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if (al >= -1.0E-15) {
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if (!satured[i]) { satured[i] = true; transition = true; }
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value_type bb = vect_sp(mat_row(CINV, i), z);
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if (bb > 0.0) add(scaled(mat_row(C, i), -bb), z);
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}
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else
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satured[i] = false;
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}
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// descent direction
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rho_1 = rho; rho = vect_sp(PS, r, z); // ...
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if (iter.finished(rho)) break;
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if (iter.get_noisy() > 0 && transition) std::cout << "transition\n";
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if (transition || iter.first()) gamma = 0.0;
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else gamma = std::max(0.0, (rho - vect_sp(PS, old_z, z) ) / rho_1);
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// std::cout << "gamma = " << gamma << endl;
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// itl::add(r, itl::scaled(p, gamma), p);
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add(z, scaled(p, gamma), p); // ...
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++iter;
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// one dimensionnal optimization
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mult(A, p, q);
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lambda = rho / vect_sp(PS, q, p);
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for (size_type i = 0; i < mat_nrows(C); ++i)
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if (!satured[i]) {
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value_type bb = vect_sp(mat_row(C, i), p) - f[i];
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if (bb > 0.0)
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lambda = std::min(lambda, (f[i]-vect_sp(mat_row(C, i), x)) / bb);
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}
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add(x, scaled(p, lambda), x);
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add(memox, scaled(x, -1.0), memox);
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}
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}
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}
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#endif // GMM_SOLVER_CCG_H__
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