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284 lines
9.8 KiB
284 lines
9.8 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2004-2012 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_precond_ilutp.h
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@author Yves Renard <Yves.Renard@insa-lyon.fr>
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@date October 14, 2004.
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@brief ILUTP: Incomplete LU with threshold and K fill-in Preconditioner and
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column pivoting.
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*/
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#ifndef GMM_PRECOND_ILUTP_H
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#define GMM_PRECOND_ILUTP_H
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#include "gmm_precond_ilut.h"
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namespace gmm {
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/**
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ILUTP: Incomplete LU with threshold and K fill-in Preconditioner and
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column pivoting.
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See Yousef Saad, Iterative Methods for
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sparse linear systems, PWS Publishing Company, section 10.4.4
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TODO : store the permutation by cycles to avoid the temporary vector
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*/
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template <typename Matrix>
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class ilutp_precond {
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public :
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typedef typename linalg_traits<Matrix>::value_type value_type;
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typedef wsvector<value_type> _wsvector;
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typedef rsvector<value_type> _rsvector;
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typedef row_matrix<_rsvector> LU_Matrix;
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typedef col_matrix<_wsvector> CLU_Matrix;
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bool invert;
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LU_Matrix L, U;
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gmm::unsorted_sub_index indperm;
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gmm::unsorted_sub_index indperminv;
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mutable std::vector<value_type> temporary;
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protected:
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size_type K;
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double eps;
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template<typename M> void do_ilutp(const M&, row_major);
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void do_ilutp(const Matrix&, col_major);
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public:
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void build_with(const Matrix& A, int k_ = -1, double eps_ = double(-1)) {
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if (k_ >= 0) K = k_;
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if (eps_ >= double(0)) eps = eps_;
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invert = false;
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gmm::resize(L, mat_nrows(A), mat_ncols(A));
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gmm::resize(U, mat_nrows(A), mat_ncols(A));
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do_ilutp(A, typename principal_orientation_type<typename
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linalg_traits<Matrix>::sub_orientation>::potype());
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}
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ilutp_precond(const Matrix& A, size_type k_, double eps_)
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: L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)),
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K(k_), eps(eps_) { build_with(A); }
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ilutp_precond(int k_, double eps_) : K(k_), eps(eps_) {}
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ilutp_precond(void) { K = 10; eps = 1E-7; }
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size_type memsize() const {
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return sizeof(*this) + (nnz(U)+nnz(L))*sizeof(value_type);
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}
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};
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template<typename Matrix> template<typename M>
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void ilutp_precond<Matrix>::do_ilutp(const M& A, row_major) {
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typedef value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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size_type n = mat_nrows(A);
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CLU_Matrix CU(n,n);
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if (n == 0) return;
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std::vector<T> indiag(n);
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temporary.resize(n);
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std::vector<size_type> ipvt(n), ipvtinv(n);
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for (size_type i = 0; i < n; ++i) ipvt[i] = ipvtinv[i] = i;
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indperm = unsorted_sub_index(ipvt);
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indperminv = unsorted_sub_index(ipvtinv);
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_wsvector w(mat_ncols(A));
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_rsvector ww(mat_ncols(A));
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T tmp = T(0);
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gmm::clear(L); gmm::clear(U);
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R prec = default_tol(R());
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R max_pivot = gmm::abs(A(0,0)) * prec;
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for (size_type i = 0; i < n; ++i) {
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copy(sub_vector(mat_const_row(A, i), indperm), w);
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double norm_row = gmm::vect_norm2(mat_const_row(A, i));
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typename _wsvector::iterator wkold = w.end();
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for (typename _wsvector::iterator wk = w.begin();
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wk != w.end() && wk->first < i; ) {
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size_type k = wk->first;
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tmp = (wk->second) * indiag[k];
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if (gmm::abs(tmp) < eps * norm_row) w.erase(k);
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else { wk->second += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); }
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if (wkold == w.end()) wk = w.begin(); else { wk = wkold; ++wk; }
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if (wk != w.end() && wk->first == k)
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{ if (wkold == w.end()) wkold = w.begin(); else ++wkold; ++wk; }
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}
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gmm::clean(w, eps * norm_row);
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gmm::copy(w, ww);
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std::sort(ww.begin(), ww.end(), elt_rsvector_value_less_<T>());
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typename _rsvector::const_iterator wit = ww.begin(), wite = ww.end();
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size_type ip = size_type(-1);
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for (; wit != wite; ++wit)
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if (wit->c >= i) { ip = wit->c; tmp = wit->e; break; }
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if (ip == size_type(-1) || gmm::abs(tmp) <= max_pivot)
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{ GMM_WARNING2("pivot " << i << " too small"); ip=i; ww[i]=tmp=T(1); }
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max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
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indiag[i] = T(1) / tmp;
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wit = ww.begin();
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size_type nnl = 0, nnu = 0;
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L[i].base_resize(K); U[i].base_resize(K+1);
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typename _rsvector::iterator witL = L[i].begin(), witU = U[i].begin();
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for (; wit != wite; ++wit) {
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if (wit->c < i) { if (nnl < K) { *witL++ = *wit; ++nnl; } }
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else if (nnu < K || wit->c == i)
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{ CU(i, wit->c) = wit->e; *witU++ = *wit; ++nnu; }
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}
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L[i].base_resize(nnl); U[i].base_resize(nnu);
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std::sort(L[i].begin(), L[i].end());
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std::sort(U[i].begin(), U[i].end());
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if (ip != i) {
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typename _wsvector::const_iterator iti = CU.col(i).begin();
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typename _wsvector::const_iterator itie = CU.col(i).end();
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typename _wsvector::const_iterator itp = CU.col(ip).begin();
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typename _wsvector::const_iterator itpe = CU.col(ip).end();
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while (iti != itie && itp != itpe) {
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if (iti->first < itp->first)
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{ U.row(iti->first).swap_indices(i, ip); ++iti; }
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else if (iti->first > itp->first)
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{ U.row(itp->first).swap_indices(i,ip);++itp; }
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else
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{ U.row(iti->first).swap_indices(i, ip); ++iti; ++itp; }
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}
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for( ; iti != itie; ++iti) U.row(iti->first).swap_indices(i, ip);
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for( ; itp != itpe; ++itp) U.row(itp->first).swap_indices(i, ip);
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CU.swap_col(i, ip);
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indperm.swap(i, ip);
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indperminv.swap(ipvt[i], ipvt[ip]);
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std::swap(ipvtinv[ipvt[i]], ipvtinv[ipvt[ip]]);
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std::swap(ipvt[i], ipvt[ip]);
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}
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}
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}
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template<typename Matrix>
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void ilutp_precond<Matrix>::do_ilutp(const Matrix& A, col_major) {
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do_ilutp(gmm::transposed(A), row_major());
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invert = true;
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}
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template <typename Matrix, typename V1, typename V2> inline
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void mult(const ilutp_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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if (P.invert) {
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gmm::copy(gmm::sub_vector(v1, P.indperm), v2);
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gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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}
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else {
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gmm::copy(v1, P.temporary);
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gmm::lower_tri_solve(P.L, P.temporary, true);
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gmm::upper_tri_solve(P.U, P.temporary, false);
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gmm::copy(gmm::sub_vector(P.temporary, P.indperminv), v2);
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}
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}
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template <typename Matrix, typename V1, typename V2> inline
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void transposed_mult(const ilutp_precond<Matrix>& P,const V1 &v1,V2 &v2) {
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if (P.invert) {
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gmm::copy(v1, P.temporary);
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gmm::lower_tri_solve(P.L, P.temporary, true);
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gmm::upper_tri_solve(P.U, P.temporary, false);
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gmm::copy(gmm::sub_vector(P.temporary, P.indperminv), v2);
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}
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else {
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gmm::copy(gmm::sub_vector(v1, P.indperm), v2);
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gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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}
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}
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template <typename Matrix, typename V1, typename V2> inline
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void left_mult(const ilutp_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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if (P.invert) {
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gmm::copy(gmm::sub_vector(v1, P.indperm), v2);
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gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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}
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else {
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copy(v1, v2);
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gmm::lower_tri_solve(P.L, v2, true);
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}
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}
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template <typename Matrix, typename V1, typename V2> inline
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void right_mult(const ilutp_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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if (P.invert) {
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copy(v1, v2);
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gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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}
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else {
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copy(v1, P.temporary);
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gmm::upper_tri_solve(P.U, P.temporary, false);
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gmm::copy(gmm::sub_vector(P.temporary, P.indperminv), v2);
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}
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}
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template <typename Matrix, typename V1, typename V2> inline
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void transposed_left_mult(const ilutp_precond<Matrix>& P, const V1 &v1,
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V2 &v2) {
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if (P.invert) {
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copy(v1, P.temporary);
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gmm::upper_tri_solve(P.U, P.temporary, false);
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gmm::copy(gmm::sub_vector(P.temporary, P.indperminv), v2);
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}
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else {
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copy(v1, v2);
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gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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}
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}
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template <typename Matrix, typename V1, typename V2> inline
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void transposed_right_mult(const ilutp_precond<Matrix>& P, const V1 &v1,
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V2 &v2) {
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if (P.invert) {
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copy(v1, v2);
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gmm::lower_tri_solve(P.L, v2, true);
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}
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else {
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gmm::copy(gmm::sub_vector(v1, P.indperm), v2);
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gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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}
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}
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}
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#endif
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