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//===========================================================================
//
// Copyright (C) 2002-2008 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 2.1 of the License, 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 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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