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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. ===========================================================================*/
/**@file gmm_tri_solve.h
@author Yves Renard @date October 13, 2002. @brief Solve triangular linear system for dense matrices.*/
#ifndef GMM_TRI_SOLVE_H__
#define GMM_TRI_SOLVE_H__
#include "gmm_interface.h"
namespace gmm {
template <typename TriMatrix, typename VecX> void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, col_major, abstract_sparse, bool is_unit) { typename linalg_traits<TriMatrix>::value_type x_j; for (int j = int(k) - 1; j >= 0; --j) { typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; COL c = mat_const_col(T, j); typename linalg_traits<COL>::const_iterator it = vect_const_begin(c), ite = vect_const_end(c); if (!is_unit) x[j] /= c[j]; for (x_j = x[j]; it != ite ; ++it) if (int(it.index()) < j) x[it.index()] -= x_j * (*it); } }
template <typename TriMatrix, typename VecX> void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, col_major, abstract_dense, bool is_unit) { typename linalg_traits<TriMatrix>::value_type x_j; for (int j = int(k) - 1; j >= 0; --j) { typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; COL c = mat_const_col(T, j); typename linalg_traits<COL>::const_iterator it = vect_const_begin(c), ite = it + j; typename linalg_traits<VecX>::iterator itx = vect_begin(x); if (!is_unit) x[j] /= c[j]; for (x_j = x[j]; it != ite ; ++it, ++itx) *itx -= x_j * (*it); } }
template <typename TriMatrix, typename VecX> void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, col_major, abstract_sparse, bool is_unit) { typename linalg_traits<TriMatrix>::value_type x_j; // cout << "(lower col)The Tri Matrix = " << T << endl;
// cout << "k = " << endl;
for (int j = 0; j < int(k); ++j) { typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; COL c = mat_const_col(T, j); typename linalg_traits<COL>::const_iterator it = vect_const_begin(c), ite = vect_const_end(c); if (!is_unit) x[j] /= c[j]; for (x_j = x[j]; it != ite ; ++it) if (int(it.index()) > j && it.index() < k) x[it.index()] -= x_j*(*it); } } template <typename TriMatrix, typename VecX> void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, col_major, abstract_dense, bool is_unit) { typename linalg_traits<TriMatrix>::value_type x_j; for (int j = 0; j < int(k); ++j) { typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; COL c = mat_const_col(T, j); typename linalg_traits<COL>::const_iterator it = vect_const_begin(c) + (j+1), ite = vect_const_begin(c) + k; typename linalg_traits<VecX>::iterator itx = vect_begin(x) + (j+1); if (!is_unit) x[j] /= c[j]; for (x_j = x[j]; it != ite ; ++it, ++itx) *itx -= x_j * (*it); } }
template <typename TriMatrix, typename VecX> void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, row_major, abstract_sparse, bool is_unit) { typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; typename linalg_traits<TriMatrix>::value_type t; typename linalg_traits<TriMatrix>::const_row_iterator itr = mat_row_const_end(T); for (int i = int(k) - 1; i >= 0; --i) { --itr; ROW c = linalg_traits<TriMatrix>::row(itr); typename linalg_traits<ROW>::const_iterator it = vect_const_begin(c), ite = vect_const_end(c); for (t = x[i]; it != ite; ++it) if (int(it.index()) > i && it.index() < k) t -= (*it) * x[it.index()]; if (!is_unit) x[i] = t / c[i]; else x[i] = t; } }
template <typename TriMatrix, typename VecX> void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, row_major, abstract_dense, bool is_unit) { typename linalg_traits<TriMatrix>::value_type t; for (int i = int(k) - 1; i >= 0; --i) { typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; ROW c = mat_const_row(T, i); typename linalg_traits<ROW>::const_iterator it = vect_const_begin(c) + (i + 1), ite = vect_const_begin(c) + k; typename linalg_traits<VecX>::iterator itx = vect_begin(x) + (i+1); for (t = x[i]; it != ite; ++it, ++itx) t -= (*it) * (*itx); if (!is_unit) x[i] = t / c[i]; else x[i] = t; } }
template <typename TriMatrix, typename VecX> void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, row_major, abstract_sparse, bool is_unit) { typename linalg_traits<TriMatrix>::value_type t; for (int i = 0; i < int(k); ++i) { typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; ROW c = mat_const_row(T, i); typename linalg_traits<ROW>::const_iterator it = vect_const_begin(c), ite = vect_const_end(c);
for (t = x[i]; it != ite; ++it) if (int(it.index()) < i) t -= (*it) * x[it.index()]; if (!is_unit) x[i] = t / c[i]; else x[i] = t; } }
template <typename TriMatrix, typename VecX> void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, row_major, abstract_dense, bool is_unit) { typename linalg_traits<TriMatrix>::value_type t; for (int i = 0; i < int(k); ++i) { typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; ROW c = mat_const_row(T, i); typename linalg_traits<ROW>::const_iterator it = vect_const_begin(c), ite = it + i; typename linalg_traits<VecX>::iterator itx = vect_begin(x);
for (t = x[i]; it != ite; ++it, ++itx) t -= (*it) * (*itx); if (!is_unit) x[i] = t / c[i]; else x[i] = t; } }
// Triangular Solve: x <-- T^{-1} * x
template <typename TriMatrix, typename VecX> inline void upper_tri_solve(const TriMatrix& T, VecX &x_, bool is_unit = false) { upper_tri_solve(T, x_, mat_nrows(T), is_unit); } template <typename TriMatrix, typename VecX> inline void lower_tri_solve(const TriMatrix& T, VecX &x_, bool is_unit = false) { lower_tri_solve(T, x_, mat_nrows(T), is_unit); }
template <typename TriMatrix, typename VecX> inline void upper_tri_solve(const TriMatrix& T, VecX &x_, size_t k, bool is_unit) { VecX& x = const_cast<VecX&>(x_); GMM_ASSERT2(mat_nrows(T) >= k && vect_size(x) >= k && mat_ncols(T) >= k && !is_sparse(x_), "dimensions mismatch"); upper_tri_solve__(T, x, k, typename principal_orientation_type<typename linalg_traits<TriMatrix>::sub_orientation>::potype(), typename linalg_traits<TriMatrix>::storage_type(), is_unit); } template <typename TriMatrix, typename VecX> inline void lower_tri_solve(const TriMatrix& T, VecX &x_, size_t k, bool is_unit) { VecX& x = const_cast<VecX&>(x_); GMM_ASSERT2(mat_nrows(T) >= k && vect_size(x) >= k && mat_ncols(T) >= k && !is_sparse(x_), "dimensions mismatch"); lower_tri_solve__(T, x, k, typename principal_orientation_type<typename linalg_traits<TriMatrix>::sub_orientation>::potype(), typename linalg_traits<TriMatrix>::storage_type(), is_unit); }
}
#endif // GMM_TRI_SOLVE_H__
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