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