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174 lines
6.8 KiB
174 lines
6.8 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2003-2012 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_dense_sylvester.h
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@author Yves Renard <Yves.Renard@insa-lyon.fr>
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@date June 5, 2003.
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@brief Sylvester equation solver.
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*/
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#ifndef GMM_DENSE_SYLVESTER_H
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#define GMM_DENSE_SYLVESTER_H
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#include "gmm_kernel.h"
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namespace gmm {
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/* ********************************************************************* */
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/* Kronecker system matrix. */
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/* ********************************************************************* */
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template <typename MAT1, typename MAT2, typename MAT3>
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void kron(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3_,
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bool init = true) {
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MAT3 &m3 = const_cast<MAT3 &>(m3_);
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size_type m = mat_nrows(m1), n = mat_ncols(m1);
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size_type l = mat_nrows(m2), k = mat_ncols(m2);
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GMM_ASSERT2(mat_nrows(m3) == m*l && mat_ncols(m3) == n*k,
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"dimensions mismatch");
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for (size_type i = 0; i < m; ++i)
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for (size_type j = 0; j < m; ++j)
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if (init)
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gmm::copy(gmm::scaled(m2, m1(i,j)),
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gmm::sub_matrix(m3, sub_interval(l*i, l),
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sub_interval(k*j, k)));
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else
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gmm::add(gmm::scaled(m2, m1(i,j)),
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gmm::sub_matrix(m3, sub_interval(l*i, l),
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sub_interval(k*j, k)));
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}
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/* ********************************************************************* */
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/* Copy a matrix into a vector. */
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/* ********************************************************************* */
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template <typename MAT, typename VECT>
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colmatrix_to_vector(const MAT &A, VECT &v, col_major) {
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size_type m = mat_nrows(A), n = mat_ncols(A);
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GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
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for (size_type i = 0; i < n; ++i)
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gmm::copy(mat_col(A, i), sub_vector(v, sub_interval(i*m, m)));
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}
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template <typename MAT, typename VECT>
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colmatrix_to_vector(const MAT &A, VECT &v, row_and_col)
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{ colmatrix_to_vector(A, v, col_major()); }
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template <typename MAT, typename VECT>
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colmatrix_to_vector(const MAT &A, VECT &v, col_and_row)
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{ colmatrix_to_vector(A, v, col_major()); }
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template <typename MAT, typename VECT>
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colmatrix_to_vector(const MAT &A, VECT &v, row_major) {
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size_type m = mat_nrows(mat), n = mat_ncols(A);
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GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
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for (size_type i = 0; i < m; ++i)
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gmm::copy(mat_row(A, i), sub_vector(v, sub_slice(i, n, m)));
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}
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template <typename MAT, typename VECT> inline
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colmatrix_to_vector(const MAT &A, const VECT &v_) {
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VECT &v = const_cast<VECT &>(v_);
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colmatrix_to_vector(A, v, typename linalg_traits<MAT>::sub_orientation());
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}
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/* ********************************************************************* */
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/* Copy a vector into a matrix. */
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/* ********************************************************************* */
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template <typename MAT, typename VECT>
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vector_to_colmatrix(const VECT &v, MAT &A, col_major) {
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size_type m = mat_nrows(A), n = mat_ncols(A);
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GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
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for (size_type i = 0; i < n; ++i)
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gmm::copy(sub_vector(v, sub_interval(i*m, m)), mat_col(A, i));
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}
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template <typename MAT, typename VECT>
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vector_to_colmatrix(const VECT &v, MAT &A, row_and_col)
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{ vector_to_colmatrix(v, A, col_major()); }
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template <typename MAT, typename VECT>
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vector_to_colmatrix(const VECT &v, MAT &A, col_and_row)
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{ vector_to_colmatrix(v, A, col_major()); }
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template <typename MAT, typename VECT>
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vector_to_colmatrix(const VECT &v, MAT &A, row_major) {
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size_type m = mat_nrows(mat), n = mat_ncols(A);
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GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
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for (size_type i = 0; i < m; ++i)
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gmm::copy(sub_vector(v, sub_slice(i, n, m)), mat_row(A, i));
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}
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template <typename MAT, typename VECT> inline
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vector_to_colmatrix(const VECT &v, const MAT &A_) {
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MAT &A = const_cast<MAT &>(A_);
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vector_to_colmatrix(v, A, typename linalg_traits<MAT>::sub_orientation());
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}
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/* ********************************************************************* */
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/* Solve sylvester equation. */
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/* ********************************************************************* */
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// very prohibitive solver, to be replaced ...
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template <typename MAT1, typename MAT2, typename MAT3, typename MAT4 >
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void sylvester(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3,
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const MAT4 &m4_) {
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typedef typename linalg_traits<Mat>::value_type T;
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MAT3 &m4 = const_cast<MAT4 &>(m4_);
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size_type m = mat_nrows(m1), n = mat_ncols(m1);
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size_type l = mat_nrows(m2), k = mat_ncols(m2);
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GMM_ASSERT2(m == n && l == k && m == mat_nrows(m3) &&
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l == mat_ncols(m3) && m == mat_nrows(m4) && l == mat_ncols(m4),
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"dimensions mismatch");
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gmm::dense_matrix<T> akronb(m*l, m*l);
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gmm::dense_matrix<T> idm(m, m), idl(l,l);
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gmm::copy(identity_matrix(), idm);
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gmm::copy(identity_matrix(), idl);
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std::vector<T> x(m*l), c(m*l);
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kron(idl, m1, akronb);
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kron(gmm::transposed(m2), idm, akronb, false);
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colmatrix_to_vector(m3, c);
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lu_solve(akronb, c, x);
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vector_to_colmatrix(x, m4);
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}
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}
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#endif
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