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 // This file is a modified version of ilut.h from ITL. 33 // See http://osl.iu.edu/research/itl/ 34 // Following the corresponding Copyright notice. 35 //=========================================================================== 36 // 37 // Copyright (c) 1998-2020, University of Notre Dame. All rights reserved. 38 // Redistribution and use in source and binary forms, with or without 39 // modification, are permitted provided that the following conditions are met: 40 // 41 // * Redistributions of source code must retain the above copyright 42 // notice, this list of conditions and the following disclaimer. 43 // * Redistributions in binary form must reproduce the above copyright 44 // notice, this list of conditions and the following disclaimer in the 45 // documentation and/or other materials provided with the distribution. 46 // * Neither the name of the University of Notre Dame nor the 47 // names of its contributors may be used to endorse or promote products 48 // derived from this software without specific prior written permission. 49 // 50 // THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND 51 // CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, 52 // BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 53 // FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES 54 // OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 55 // INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 56 // NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 57 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 58 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 59 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 60 // THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 61 // 62 //=========================================================================== 63 64 #ifndef GMM_PRECOND_ILUT_H 65 #define GMM_PRECOND_ILUT_H 66 67 /**@file gmm_precond_ilut.h 68 @author Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu> 69 @date June 5, 2003. 70 @brief ILUT: Incomplete LU with threshold and K fill-in Preconditioner. 71 */ 72 73 /* 74 Performane comparing for SSOR, ILU and ILUT based on sherman 5 matrix 75 in Harwell-Boeing collection on Sun Ultra 30 UPA/PCI (UltraSPARC-II 296MHz) 76 Preconditioner & Factorization time & Number of Iteration \\ \hline 77 SSOR & 0.010577 & 41 \\ 78 ILU & 0.019336 & 32 \\ 79 ILUT with 0 fill-in and threshold of 1.0e-6 & 0.343612 & 23 \\ 80 ILUT with 5 fill-in and threshold of 1.0e-6 & 0.343612 & 18 \\ \hline 81 */ 82 83 #include "gmm_precond.h" 84 85 namespace gmm { 86 87 template<typename T> struct elt_rsvector_value_less_ { operatorelt_rsvector_value_less_88 inline bool operator()(const elt_rsvector_<T>& a, 89 const elt_rsvector_<T>& b) const 90 { return (gmm::abs(a.e) > gmm::abs(b.e)); } 91 }; 92 93 /** Incomplete LU with threshold and K fill-in Preconditioner. 94 95 The algorithm of ILUT(A, 0, 1.0e-6) is slower than ILU(A). If No 96 fill-in is arrowed, you can use ILU instead of ILUT. 97 98 Notes: The idea under a concrete Preconditioner such as ilut is to 99 create a Preconditioner object to use in iterative methods. 100 */ 101 template <typename Matrix> 102 class ilut_precond { 103 public : 104 typedef typename linalg_traits<Matrix>::value_type value_type; 105 typedef wsvector<value_type> _wsvector; 106 typedef rsvector<value_type> _rsvector; 107 typedef row_matrix<_rsvector> LU_Matrix; 108 109 bool invert; 110 LU_Matrix L, U; 111 112 protected: 113 size_type K; 114 double eps; 115 116 template<typename M> void do_ilut(const M&, row_major); 117 void do_ilut(const Matrix&, col_major); 118 119 public: 120 void build_with(const Matrix& A, int k_ = -1, double eps_ = double(-1)) { 121 if (k_ >= 0) K = k_; 122 if (eps_ >= double(0)) eps = eps_; 123 invert = false; 124 gmm::resize(L, mat_nrows(A), mat_ncols(A)); 125 gmm::resize(U, mat_nrows(A), mat_ncols(A)); 126 do_ilut(A, typename principal_orientation_type<typename 127 linalg_traits<Matrix>::sub_orientation>::potype()); 128 } ilut_precond(const Matrix & A,int k_,double eps_)129 ilut_precond(const Matrix& A, int k_, double eps_) 130 : L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)), 131 K(k_), eps(eps_) { build_with(A); } ilut_precond(size_type k_,double eps_)132 ilut_precond(size_type k_, double eps_) : K(k_), eps(eps_) {} ilut_precond(void)133 ilut_precond(void) { K = 10; eps = 1E-7; } memsize()134 size_type memsize() const { 135 return sizeof(*this) + (nnz(U)+nnz(L))*sizeof(value_type); 136 } 137 }; 138 139 template<typename Matrix> template<typename M> do_ilut(const M & A,row_major)140 void ilut_precond<Matrix>::do_ilut(const M& A, row_major) { 141 typedef value_type T; 142 typedef typename number_traits<T>::magnitude_type R; 143 144 size_type n = mat_nrows(A); 145 if (n == 0) return; 146 std::vector<T> indiag(n); 147 _wsvector w(mat_ncols(A)); 148 _rsvector ww(mat_ncols(A)), wL(mat_ncols(A)), wU(mat_ncols(A)); 149 T tmp; 150 gmm::clear(U); gmm::clear(L); 151 R prec = default_tol(R()); 152 R max_pivot = gmm::abs(A(0,0)) * prec; 153 154 for (size_type i = 0; i < n; ++i) { 155 gmm::copy(mat_const_row(A, i), w); 156 double norm_row = gmm::vect_norm2(w); 157 158 typename _wsvector::iterator wkold = w.end(); 159 for (typename _wsvector::iterator wk = w.begin(); 160 wk != w.end() && wk->first < i; ) { 161 size_type k = wk->first; 162 tmp = (wk->second) * indiag[k]; 163 if (gmm::abs(tmp) < eps * norm_row) w.erase(k); 164 else { wk->second += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); } 165 if (wkold == w.end()) wk = w.begin(); else { wk = wkold; ++wk; } 166 if (wk != w.end() && wk->first == k) 167 { if (wkold == w.end()) wkold = w.begin(); else ++wkold; ++wk; } 168 } 169 tmp = w[i]; 170 171 if (gmm::abs(tmp) <= max_pivot) { 172 GMM_WARNING2("pivot " << i << " too small. try with ilutp ?"); 173 w[i] = tmp = T(1); 174 } 175 176 max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1))); 177 indiag[i] = T(1) / tmp; 178 gmm::clean(w, eps * norm_row); 179 gmm::copy(w, ww); 180 std::sort(ww.begin(), ww.end(), elt_rsvector_value_less_<T>()); 181 typename _rsvector::const_iterator wit = ww.begin(), wite = ww.end(); 182 183 size_type nnl = 0, nnu = 0; 184 wL.base_resize(K); wU.base_resize(K+1); 185 typename _rsvector::iterator witL = wL.begin(), witU = wU.begin(); 186 for (; wit != wite; ++wit) 187 if (wit->c < i) { if (nnl < K) { *witL++ = *wit; ++nnl; } } 188 else { if (nnu < K || wit->c == i) { *witU++ = *wit; ++nnu; } } 189 wL.base_resize(nnl); wU.base_resize(nnu); 190 std::sort(wL.begin(), wL.end()); 191 std::sort(wU.begin(), wU.end()); 192 gmm::copy(wL, L.row(i)); 193 gmm::copy(wU, U.row(i)); 194 } 195 196 } 197 198 template<typename Matrix> do_ilut(const Matrix & A,col_major)199 void ilut_precond<Matrix>::do_ilut(const Matrix& A, col_major) { 200 do_ilut(gmm::transposed(A), row_major()); 201 invert = true; 202 } 203 204 template <typename Matrix, typename V1, typename V2> inline mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)205 void mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) { 206 gmm::copy(v1, v2); 207 if (P.invert) { 208 gmm::lower_tri_solve(gmm::transposed(P.U), v2, false); 209 gmm::upper_tri_solve(gmm::transposed(P.L), v2, true); 210 } 211 else { 212 gmm::lower_tri_solve(P.L, v2, true); 213 gmm::upper_tri_solve(P.U, v2, false); 214 } 215 } 216 217 template <typename Matrix, typename V1, typename V2> inline transposed_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)218 void transposed_mult(const ilut_precond<Matrix>& P,const V1 &v1,V2 &v2) { 219 gmm::copy(v1, v2); 220 if (P.invert) { 221 gmm::lower_tri_solve(P.L, v2, true); 222 gmm::upper_tri_solve(P.U, v2, false); 223 } 224 else { 225 gmm::lower_tri_solve(gmm::transposed(P.U), v2, false); 226 gmm::upper_tri_solve(gmm::transposed(P.L), v2, true); 227 } 228 } 229 230 template <typename Matrix, typename V1, typename V2> inline left_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)231 void left_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) { 232 copy(v1, v2); 233 if (P.invert) gmm::lower_tri_solve(gmm::transposed(P.U), v2, false); 234 else gmm::lower_tri_solve(P.L, v2, true); 235 } 236 237 template <typename Matrix, typename V1, typename V2> inline right_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)238 void right_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) { 239 copy(v1, v2); 240 if (P.invert) gmm::upper_tri_solve(gmm::transposed(P.L), v2, true); 241 else gmm::upper_tri_solve(P.U, v2, false); 242 } 243 244 template <typename Matrix, typename V1, typename V2> inline transposed_left_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)245 void transposed_left_mult(const ilut_precond<Matrix>& P, const V1 &v1, 246 V2 &v2) { 247 copy(v1, v2); 248 if (P.invert) gmm::upper_tri_solve(P.U, v2, false); 249 else gmm::upper_tri_solve(gmm::transposed(P.L), v2, true); 250 } 251 252 template <typename Matrix, typename V1, typename V2> inline transposed_right_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)253 void transposed_right_mult(const ilut_precond<Matrix>& P, const V1 &v1, 254 V2 &v2) { 255 copy(v1, v2); 256 if (P.invert) gmm::lower_tri_solve(P.L, v2, true); 257 else gmm::lower_tri_solve(gmm::transposed(P.U), v2, false); 258 } 259 260 } 261 262 #endif 263 264