1 /* -*- c++ -*- (enables emacs c++ mode) */ 2 /*=========================================================================== 3 4 Copyright (C) 2002-2020 Yves Renard 5 6 This file is a part of GetFEM 7 8 GetFEM is free software; you can redistribute it and/or modify it 9 under the terms of the GNU Lesser General Public License as published 10 by the Free Software Foundation; either version 3 of the License, or 11 (at your option) any later version along with the GCC Runtime Library 12 Exception either version 3.1 or (at your option) any later version. 13 This program is distributed in the hope that it will be useful, but 14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16 License and GCC Runtime Library Exception for more details. 17 You should have received a copy of the GNU Lesser General Public License 18 along with this program; if not, write to the Free Software Foundation, 19 Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. 20 21 As a special exception, you may use this file as it is a part of a free 22 software library without restriction. Specifically, if other files 23 instantiate templates or use macros or inline functions from this file, 24 or you compile this file and link it with other files to produce an 25 executable, this file does not by itself cause the resulting executable 26 to be covered by the GNU Lesser General Public License. This exception 27 does not however invalidate any other reasons why the executable file 28 might be covered by the GNU Lesser General Public License. 29 30 ===========================================================================*/ 31 32 /**@file gmm_tri_solve.h 33 @author Yves Renard 34 @date October 13, 2002. 35 @brief Solve triangular linear system for dense matrices. 36 */ 37 38 #ifndef GMM_TRI_SOLVE_H__ 39 #define GMM_TRI_SOLVE_H__ 40 41 #include "gmm_interface.h" 42 43 namespace gmm { 44 45 template <typename TriMatrix, typename VecX> upper_tri_solve__(const TriMatrix & T,VecX & x,size_t k,col_major,abstract_sparse,bool is_unit)46 void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 47 col_major, abstract_sparse, bool is_unit) { 48 typename linalg_traits<TriMatrix>::value_type x_j; 49 for (int j = int(k) - 1; j >= 0; --j) { 50 typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; 51 COL c = mat_const_col(T, j); 52 typename linalg_traits<typename org_type<COL>::t>::const_iterator 53 it = vect_const_begin(c), ite = vect_const_end(c); 54 if (!is_unit) x[j] /= c[j]; 55 for (x_j = x[j]; it != ite ; ++it) 56 if (int(it.index()) < j) x[it.index()] -= x_j * (*it); 57 } 58 } 59 60 template <typename TriMatrix, typename VecX> upper_tri_solve__(const TriMatrix & T,VecX & x,size_t k,col_major,abstract_dense,bool is_unit)61 void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 62 col_major, abstract_dense, bool is_unit) { 63 typename linalg_traits<TriMatrix>::value_type x_j; 64 for (int j = int(k) - 1; j >= 0; --j) { 65 typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; 66 COL c = mat_const_col(T, j); 67 typename linalg_traits<typename org_type<COL>::t>::const_iterator 68 it = vect_const_begin(c), ite = it + j; 69 typename linalg_traits<VecX>::iterator itx = vect_begin(x); 70 if (!is_unit) x[j] /= c[j]; 71 for (x_j = x[j]; it != ite ; ++it, ++itx) *itx -= x_j * (*it); 72 } 73 } 74 75 template <typename TriMatrix, typename VecX> lower_tri_solve__(const TriMatrix & T,VecX & x,size_t k,col_major,abstract_sparse,bool is_unit)76 void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 77 col_major, abstract_sparse, bool is_unit) { 78 typename linalg_traits<TriMatrix>::value_type x_j; 79 // cout << "(lower col)The Tri Matrix = " << T << endl; 80 // cout << "k = " << endl; 81 for (int j = 0; j < int(k); ++j) { 82 typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; 83 COL c = mat_const_col(T, j); 84 typename linalg_traits<typename org_type<COL>::t>::const_iterator 85 it = vect_const_begin(c), ite = vect_const_end(c); 86 if (!is_unit) x[j] /= c[j]; 87 for (x_j = x[j]; it != ite ; ++it) 88 if (int(it.index()) > j && it.index() < k) x[it.index()] -= x_j*(*it); 89 } 90 } 91 92 template <typename TriMatrix, typename VecX> lower_tri_solve__(const TriMatrix & T,VecX & x,size_t k,col_major,abstract_dense,bool is_unit)93 void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 94 col_major, abstract_dense, bool is_unit) { 95 typename linalg_traits<TriMatrix>::value_type x_j; 96 for (int j = 0; j < int(k); ++j) { 97 typedef typename linalg_traits<TriMatrix>::const_sub_col_type COL; 98 COL c = mat_const_col(T, j); 99 typename linalg_traits<typename org_type<COL>::t>::const_iterator 100 it = vect_const_begin(c) + (j+1), ite = vect_const_begin(c) + k; 101 typename linalg_traits<VecX>::iterator itx = vect_begin(x) + (j+1); 102 if (!is_unit) x[j] /= c[j]; 103 for (x_j = x[j]; it != ite ; ++it, ++itx) *itx -= x_j * (*it); 104 } 105 } 106 107 108 template <typename TriMatrix, typename VecX> upper_tri_solve__(const TriMatrix & T,VecX & x,size_t k,row_major,abstract_sparse,bool is_unit)109 void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 110 row_major, abstract_sparse, bool is_unit) { 111 typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; 112 typename linalg_traits<TriMatrix>::value_type t; 113 typename linalg_traits<TriMatrix>::const_row_iterator 114 itr = mat_row_const_end(T); 115 for (int i = int(k) - 1; i >= 0; --i) { 116 --itr; 117 ROW c = linalg_traits<TriMatrix>::row(itr); 118 typename linalg_traits<typename org_type<ROW>::t>::const_iterator 119 it = vect_const_begin(c), ite = vect_const_end(c); 120 for (t = x[i]; it != ite; ++it) 121 if (int(it.index()) > i && it.index() < k) t -= (*it) * x[it.index()]; 122 if (!is_unit) x[i] = t / c[i]; else x[i] = t; 123 } 124 } 125 126 template <typename TriMatrix, typename VecX> upper_tri_solve__(const TriMatrix & T,VecX & x,size_t k,row_major,abstract_dense,bool is_unit)127 void upper_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 128 row_major, abstract_dense, bool is_unit) { 129 typename linalg_traits<TriMatrix>::value_type t; 130 131 for (int i = int(k) - 1; i >= 0; --i) { 132 typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; 133 ROW c = mat_const_row(T, i); 134 typename linalg_traits<typename org_type<ROW>::t>::const_iterator 135 it = vect_const_begin(c) + (i + 1), ite = vect_const_begin(c) + k; 136 typename linalg_traits<VecX>::iterator itx = vect_begin(x) + (i+1); 137 138 for (t = x[i]; it != ite; ++it, ++itx) t -= (*it) * (*itx); 139 if (!is_unit) x[i] = t / c[i]; else x[i] = t; 140 } 141 } 142 143 template <typename TriMatrix, typename VecX> lower_tri_solve__(const TriMatrix & T,VecX & x,size_t k,row_major,abstract_sparse,bool is_unit)144 void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 145 row_major, abstract_sparse, bool is_unit) { 146 typename linalg_traits<TriMatrix>::value_type t; 147 148 for (int i = 0; i < int(k); ++i) { 149 typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; 150 ROW c = mat_const_row(T, i); 151 typename linalg_traits<typename org_type<ROW>::t>::const_iterator 152 it = vect_const_begin(c), ite = vect_const_end(c); 153 154 for (t = x[i]; it != ite; ++it) 155 if (int(it.index()) < i) t -= (*it) * x[it.index()]; 156 if (!is_unit) x[i] = t / c[i]; else x[i] = t; 157 } 158 } 159 160 template <typename TriMatrix, typename VecX> lower_tri_solve__(const TriMatrix & T,VecX & x,size_t k,row_major,abstract_dense,bool is_unit)161 void lower_tri_solve__(const TriMatrix& T, VecX& x, size_t k, 162 row_major, abstract_dense, bool is_unit) { 163 typename linalg_traits<TriMatrix>::value_type t; 164 165 for (int i = 0; i < int(k); ++i) { 166 typedef typename linalg_traits<TriMatrix>::const_sub_row_type ROW; 167 ROW c = mat_const_row(T, i); 168 typename linalg_traits<typename org_type<ROW>::t>::const_iterator 169 it = vect_const_begin(c), ite = it + i; 170 typename linalg_traits<VecX>::iterator itx = vect_begin(x); 171 172 for (t = x[i]; it != ite; ++it, ++itx) t -= (*it) * (*itx); 173 if (!is_unit) x[i] = t / c[i]; else x[i] = t; 174 } 175 } 176 177 178 // Triangular Solve: x <-- T^{-1} * x 179 180 template <typename TriMatrix, typename VecX> inline 181 void upper_tri_solve(const TriMatrix& T, VecX &x_, bool is_unit = false) 182 { upper_tri_solve(T, x_, mat_nrows(T), is_unit); } 183 184 template <typename TriMatrix, typename VecX> inline 185 void lower_tri_solve(const TriMatrix& T, VecX &x_, bool is_unit = false) 186 { lower_tri_solve(T, x_, mat_nrows(T), is_unit); } 187 188 template <typename TriMatrix, typename VecX> inline upper_tri_solve(const TriMatrix & T,VecX & x_,size_t k,bool is_unit)189 void upper_tri_solve(const TriMatrix& T, VecX &x_, size_t k, 190 bool is_unit) { 191 VecX& x = const_cast<VecX&>(x_); 192 GMM_ASSERT2(mat_nrows(T) >= k && vect_size(x) >= k 193 && mat_ncols(T) >= k && !is_sparse(x_), "dimensions mismatch"); 194 upper_tri_solve__(T, x, k, 195 typename principal_orientation_type<typename 196 linalg_traits<TriMatrix>::sub_orientation>::potype(), 197 typename linalg_traits<TriMatrix>::storage_type(), 198 is_unit); 199 } 200 201 template <typename TriMatrix, typename VecX> inline lower_tri_solve(const TriMatrix & T,VecX & x_,size_t k,bool is_unit)202 void lower_tri_solve(const TriMatrix& T, VecX &x_, size_t k, 203 bool is_unit) { 204 VecX& x = const_cast<VecX&>(x_); 205 GMM_ASSERT2(mat_nrows(T) >= k && vect_size(x) >= k 206 && mat_ncols(T) >= k && !is_sparse(x_), "dimensions mismatch"); 207 lower_tri_solve__(T, x, k, 208 typename principal_orientation_type<typename 209 linalg_traits<TriMatrix>::sub_orientation>::potype(), 210 typename linalg_traits<TriMatrix>::storage_type(), 211 is_unit); 212 } 213 214 215 216 217 218 219 } 220 221 222 #endif // GMM_TRI_SOLVE_H__ 223