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