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metaforce/gmm/gmm_precond_ilut.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
Copyright (C) 2002-2017 Yves Renard
This file is a part of GetFEM++
GetFEM++ is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version along with the GCC Runtime Library
Exception either version 3.1 or (at your option) any later version.
This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License and GCC Runtime Library Exception for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
As a special exception, you may use this file as it is a part of a free
software library without restriction. Specifically, if other files
instantiate templates or use macros or inline functions from this file,
or you compile this file and link it with other files to produce an
executable, this file does not by itself cause the resulting executable
to be covered by the GNU Lesser General Public License. This exception
does not however invalidate any other reasons why the executable file
might be covered by the GNU Lesser General Public License.
===========================================================================*/
// This file is a modified version of ilut.h from ITL.
// See http://osl.iu.edu/research/itl/
// Following the corresponding Copyright notice.
//===========================================================================
//
// Copyright (c) 1998-2001, University of Notre Dame. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of the University of Notre Dame nor the
// names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE TRUSTEES OF INDIANA UNIVERSITY AND
// CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE TRUSTEES
// OF INDIANA UNIVERSITY AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//===========================================================================
#ifndef GMM_PRECOND_ILUT_H
#define GMM_PRECOND_ILUT_H
/**@file gmm_precond_ilut.h
@author Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu>
@date June 5, 2003.
@brief ILUT: Incomplete LU with threshold and K fill-in Preconditioner.
*/
/*
Performane comparing for SSOR, ILU and ILUT based on sherman 5 matrix
in Harwell-Boeing collection on Sun Ultra 30 UPA/PCI (UltraSPARC-II 296MHz)
Preconditioner & Factorization time & Number of Iteration \\ \hline
SSOR & 0.010577 & 41 \\
ILU & 0.019336 & 32 \\
ILUT with 0 fill-in and threshold of 1.0e-6 & 0.343612 & 23 \\
ILUT with 5 fill-in and threshold of 1.0e-6 & 0.343612 & 18 \\ \hline
*/
#include "gmm_precond.h"
namespace gmm {
template<typename T> struct elt_rsvector_value_less_ {
inline bool operator()(const elt_rsvector_<T>& a,
const elt_rsvector_<T>& b) const
{ return (gmm::abs(a.e) > gmm::abs(b.e)); }
};
/** Incomplete LU with threshold and K fill-in Preconditioner.
The algorithm of ILUT(A, 0, 1.0e-6) is slower than ILU(A). If No
fill-in is arrowed, you can use ILU instead of ILUT.
Notes: The idea under a concrete Preconditioner such as ilut is to
create a Preconditioner object to use in iterative methods.
*/
template <typename Matrix>
class ilut_precond {
public :
typedef typename linalg_traits<Matrix>::value_type value_type;
typedef wsvector<value_type> _wsvector;
typedef rsvector<value_type> _rsvector;
typedef row_matrix<_rsvector> LU_Matrix;
bool invert;
LU_Matrix L, U;
protected:
size_type K;
double eps;
template<typename M> void do_ilut(const M&, row_major);
void do_ilut(const Matrix&, col_major);
public:
void build_with(const Matrix& A, int k_ = -1, double eps_ = double(-1)) {
if (k_ >= 0) K = k_;
if (eps_ >= double(0)) eps = eps_;
invert = false;
gmm::resize(L, mat_nrows(A), mat_ncols(A));
gmm::resize(U, mat_nrows(A), mat_ncols(A));
do_ilut(A, typename principal_orientation_type<typename
linalg_traits<Matrix>::sub_orientation>::potype());
}
ilut_precond(const Matrix& A, int k_, double eps_)
: L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)),
K(k_), eps(eps_) { build_with(A); }
ilut_precond(size_type k_, double eps_) : K(k_), eps(eps_) {}
ilut_precond(void) { K = 10; eps = 1E-7; }
size_type memsize() const {
return sizeof(*this) + (nnz(U)+nnz(L))*sizeof(value_type);
}
};
template<typename Matrix> template<typename M>
void ilut_precond<Matrix>::do_ilut(const M& A, row_major) {
typedef value_type T;
typedef typename number_traits<T>::magnitude_type R;
size_type n = mat_nrows(A);
if (n == 0) return;
std::vector<T> indiag(n);
_wsvector w(mat_ncols(A));
_rsvector ww(mat_ncols(A)), wL(mat_ncols(A)), wU(mat_ncols(A));
T tmp;
gmm::clear(U); gmm::clear(L);
R prec = default_tol(R());
R max_pivot = gmm::abs(A(0,0)) * prec;
for (size_type i = 0; i < n; ++i) {
gmm::copy(mat_const_row(A, i), w);
double norm_row = gmm::vect_norm2(w);
typename _wsvector::iterator wkold = w.end();
for (typename _wsvector::iterator wk = w.begin();
wk != w.end() && wk->first < i; ) {
size_type k = wk->first;
tmp = (wk->second) * indiag[k];
if (gmm::abs(tmp) < eps * norm_row) w.erase(k);
else { wk->second += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); }
if (wkold == w.end()) wk = w.begin(); else { wk = wkold; ++wk; }
if (wk != w.end() && wk->first == k)
{ if (wkold == w.end()) wkold = w.begin(); else ++wkold; ++wk; }
}
tmp = w[i];
if (gmm::abs(tmp) <= max_pivot) {
GMM_WARNING2("pivot " << i << " too small. try with ilutp ?");
w[i] = tmp = T(1);
}
max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
indiag[i] = T(1) / tmp;
gmm::clean(w, eps * norm_row);
gmm::copy(w, ww);
std::sort(ww.begin(), ww.end(), elt_rsvector_value_less_<T>());
typename _rsvector::const_iterator wit = ww.begin(), wite = ww.end();
size_type nnl = 0, nnu = 0;
wL.base_resize(K); wU.base_resize(K+1);
typename _rsvector::iterator witL = wL.begin(), witU = wU.begin();
for (; wit != wite; ++wit)
if (wit->c < i) { if (nnl < K) { *witL++ = *wit; ++nnl; } }
else { if (nnu < K || wit->c == i) { *witU++ = *wit; ++nnu; } }
wL.base_resize(nnl); wU.base_resize(nnu);
std::sort(wL.begin(), wL.end());
std::sort(wU.begin(), wU.end());
gmm::copy(wL, L.row(i));
gmm::copy(wU, U.row(i));
}
}
template<typename Matrix>
void ilut_precond<Matrix>::do_ilut(const Matrix& A, col_major) {
do_ilut(gmm::transposed(A), row_major());
invert = true;
}
template <typename Matrix, typename V1, typename V2> inline
void mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
gmm::copy(v1, v2);
if (P.invert) {
gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
}
else {
gmm::lower_tri_solve(P.L, v2, true);
gmm::upper_tri_solve(P.U, v2, false);
}
}
template <typename Matrix, typename V1, typename V2> inline
void transposed_mult(const ilut_precond<Matrix>& P,const V1 &v1,V2 &v2) {
gmm::copy(v1, v2);
if (P.invert) {
gmm::lower_tri_solve(P.L, v2, true);
gmm::upper_tri_solve(P.U, v2, false);
}
else {
gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
}
}
template <typename Matrix, typename V1, typename V2> inline
void left_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
copy(v1, v2);
if (P.invert) gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
else gmm::lower_tri_solve(P.L, v2, true);
}
template <typename Matrix, typename V1, typename V2> inline
void right_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
copy(v1, v2);
if (P.invert) gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
else gmm::upper_tri_solve(P.U, v2, false);
}
template <typename Matrix, typename V1, typename V2> inline
void transposed_left_mult(const ilut_precond<Matrix>& P, const V1 &v1,
V2 &v2) {
copy(v1, v2);
if (P.invert) gmm::upper_tri_solve(P.U, v2, false);
else gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
}
template <typename Matrix, typename V1, typename V2> inline
void transposed_right_mult(const ilut_precond<Matrix>& P, const V1 &v1,
V2 &v2) {
copy(v1, v2);
if (P.invert) gmm::lower_tri_solve(P.L, v2, true);
else gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
}
}
#endif
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