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263 lines
10 KiB
263 lines
10 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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// This file is a modified version of ilut.h from ITL.
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// See http://osl.iu.edu/research/itl/
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// Following the corresponding Copyright notice.
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//===========================================================================
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//
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// Copyright (c) 1998-2001, University of Notre Dame. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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// * Neither the name of the University of Notre Dame nor the
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// names of its contributors may be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND
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// CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
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// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES
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// OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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//===========================================================================
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#ifndef GMM_PRECOND_ILUT_H
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#define GMM_PRECOND_ILUT_H
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/**@file gmm_precond_ilut.h
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@author Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu>
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@date June 5, 2003.
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@brief ILUT: Incomplete LU with threshold and K fill-in Preconditioner.
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*/
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/*
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Performane comparing for SSOR, ILU and ILUT based on sherman 5 matrix
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in Harwell-Boeing collection on Sun Ultra 30 UPA/PCI (UltraSPARC-II 296MHz)
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Preconditioner & Factorization time & Number of Iteration \\ \hline
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SSOR & 0.010577 & 41 \\
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ILU & 0.019336 & 32 \\
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ILUT with 0 fill-in and threshold of 1.0e-6 & 0.343612 & 23 \\
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ILUT with 5 fill-in and threshold of 1.0e-6 & 0.343612 & 18 \\ \hline
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*/
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#include "gmm_precond.h"
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namespace gmm {
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template<typename T> struct elt_rsvector_value_less_ {
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inline bool operator()(const elt_rsvector_<T>& a,
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const elt_rsvector_<T>& b) const
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{ return (gmm::abs(a.e) > gmm::abs(b.e)); }
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};
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/** Incomplete LU with threshold and K fill-in Preconditioner.
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The algorithm of ILUT(A, 0, 1.0e-6) is slower than ILU(A). If No
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fill-in is arrowed, you can use ILU instead of ILUT.
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Notes: The idea under a concrete Preconditioner such as ilut is to
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create a Preconditioner object to use in iterative methods.
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*/
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template <typename Matrix>
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class ilut_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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bool invert;
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LU_Matrix L, U;
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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_ilut(const M&, row_major);
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void do_ilut(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_ilut(A, typename principal_orientation_type<typename
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linalg_traits<Matrix>::sub_orientation>::potype());
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}
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ilut_precond(const Matrix& A, int 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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ilut_precond(size_type k_, double eps_) : K(k_), eps(eps_) {}
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ilut_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 ilut_precond<Matrix>::do_ilut(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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if (n == 0) return;
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std::vector<T> indiag(n);
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_wsvector w(mat_ncols(A));
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_rsvector ww(mat_ncols(A)), wL(mat_ncols(A)), wU(mat_ncols(A));
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T tmp;
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gmm::clear(U); gmm::clear(L);
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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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gmm::copy(mat_const_row(A, i), w);
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double norm_row = gmm::vect_norm2(w);
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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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tmp = w[i];
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if (gmm::abs(tmp) <= max_pivot) {
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GMM_WARNING2("pivot " << i << " too small. try with ilutp ?");
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w[i] = tmp = T(1);
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}
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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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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 nnl = 0, nnu = 0;
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wL.base_resize(K); wU.base_resize(K+1);
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typename _rsvector::iterator witL = wL.begin(), witU = wU.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) { *witU++ = *wit; ++nnu; } }
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wL.base_resize(nnl); wU.base_resize(nnu);
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std::sort(wL.begin(), wL.end());
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std::sort(wU.begin(), wU.end());
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gmm::copy(wL, L.row(i));
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gmm::copy(wU, U.row(i));
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}
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}
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template<typename Matrix>
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void ilut_precond<Matrix>::do_ilut(const Matrix& A, col_major) {
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do_ilut(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 ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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gmm::copy(v1, v2);
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if (P.invert) {
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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::lower_tri_solve(P.L, v2, true);
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gmm::upper_tri_solve(P.U, v2, false);
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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 ilut_precond<Matrix>& P,const V1 &v1,V2 &v2) {
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gmm::copy(v1, v2);
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if (P.invert) {
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gmm::lower_tri_solve(P.L, v2, true);
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gmm::upper_tri_solve(P.U, v2, false);
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}
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else {
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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 ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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copy(v1, v2);
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if (P.invert) gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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else gmm::lower_tri_solve(P.L, v2, true);
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}
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template <typename Matrix, typename V1, typename V2> inline
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void right_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
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copy(v1, v2);
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if (P.invert) gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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else gmm::upper_tri_solve(P.U, v2, false);
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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 ilut_precond<Matrix>& P, const V1 &v1,
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V2 &v2) {
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copy(v1, v2);
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if (P.invert) gmm::upper_tri_solve(P.U, v2, false);
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else gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
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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 ilut_precond<Matrix>& P, const V1 &v1,
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V2 &v2) {
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copy(v1, v2);
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if (P.invert) gmm::lower_tri_solve(P.L, v2, true);
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else gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
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}
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}
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#endif
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