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/* -*- c++ -*- (enables emacs c++ mode) *//*===========================================================================
Copyright (C) 2003-2012 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 cholesky.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
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// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//===========================================================================
#ifndef GMM_PRECOND_ILDLT_H
#define GMM_PRECOND_ILDLT_H
/**@file gmm_precond_ildlt.h
@author Andrew Lumsdaine <lums@osl.iu.edu> @author Lie-Quan Lee <llee@osl.iu.edu> @author Yves Renard <yves.renard@insa-lyon.fr> @date June 5, 2003. @brief Incomplete Level 0 ILDLT Preconditioner.*/
#include "gmm_precond.h"
namespace gmm {
/** Incomplete Level 0 LDLT Preconditioner.
For use with symmetric real or hermitian complex sparse matrices.
Notes: The idea under a concrete Preconditioner such as Incomplete Cholesky is to create a Preconditioner object to use in iterative methods.
Y. Renard : Transformed in LDLT for stability reason. U=LT is stored in csr format. D is stored on the diagonal of U. */ template <typename Matrix> class ildlt_precond {
public : typedef typename linalg_traits<Matrix>::value_type value_type; typedef typename number_traits<value_type>::magnitude_type magnitude_type; typedef csr_matrix_ref<value_type *, size_type *, size_type *, 0> tm_type;
tm_type U;
protected : std::vector<value_type> Tri_val; std::vector<size_type> Tri_ind, Tri_ptr; template<typename M> void do_ildlt(const M& A, row_major); void do_ildlt(const Matrix& A, col_major);
public:
size_type nrows(void) const { return mat_nrows(U); } size_type ncols(void) const { return mat_ncols(U); } value_type &D(size_type i) { return Tri_val[Tri_ptr[i]]; } const value_type &D(size_type i) const { return Tri_val[Tri_ptr[i]]; } ildlt_precond(void) {} void build_with(const Matrix& A) { Tri_ptr.resize(mat_nrows(A)+1); do_ildlt(A, typename principal_orientation_type<typename linalg_traits<Matrix>::sub_orientation>::potype()); } ildlt_precond(const Matrix& A) { build_with(A); } size_type memsize() const { return sizeof(*this) + Tri_val.size() * sizeof(value_type) + (Tri_ind.size()+Tri_ptr.size()) * sizeof(size_type); } };
template <typename Matrix> template<typename M> void ildlt_precond<Matrix>::do_ildlt(const M& A, row_major) { typedef typename linalg_traits<Matrix>::storage_type store_type; typedef value_type T; typedef typename number_traits<T>::magnitude_type R; size_type Tri_loc = 0, n = mat_nrows(A), d, g, h, i, j, k; if (n == 0) return; T z, zz; Tri_ptr[0] = 0; R prec = default_tol(R()); R max_pivot = gmm::abs(A(0,0)) * prec; for (int count = 0; count < 2; ++count) { if (count) { Tri_val.resize(Tri_loc); Tri_ind.resize(Tri_loc); } for (Tri_loc = 0, i = 0; i < n; ++i) { typedef typename linalg_traits<M>::const_sub_row_type row_type; row_type row = mat_const_row(A, i); typename linalg_traits<row_type>::const_iterator it = vect_const_begin(row), ite = vect_const_end(row);
if (count) { Tri_val[Tri_loc] = T(0); Tri_ind[Tri_loc] = i; } ++Tri_loc; // diagonal element
for (k = 0; it != ite; ++it, ++k) { j = index_of_it(it, k, store_type()); if (i == j) { if (count) Tri_val[Tri_loc-1] = *it; } else if (j > i) { if (count) { Tri_val[Tri_loc] = *it; Tri_ind[Tri_loc]=j; } ++Tri_loc; } } Tri_ptr[i+1] = Tri_loc; } } if (A(0,0) == T(0)) { Tri_val[Tri_ptr[0]] = T(1); GMM_WARNING2("pivot 0 is too small"); } for (k = 0; k < n; k++) { d = Tri_ptr[k]; z = T(gmm::real(Tri_val[d])); Tri_val[d] = z; if (gmm::abs(z) <= max_pivot) { Tri_val[d] = z = T(1); GMM_WARNING2("pivot " << k << " is too small [" << gmm::abs(z) << "]"); } max_pivot = std::max(max_pivot, std::min(gmm::abs(z) * prec, R(1))); for (i = d + 1; i < Tri_ptr[k+1]; ++i) Tri_val[i] /= z; for (i = d + 1; i < Tri_ptr[k+1]; ++i) { zz = gmm::conj(Tri_val[i] * z); h = Tri_ind[i]; g = i; for (j = Tri_ptr[h] ; j < Tri_ptr[h+1]; ++j) for ( ; g < Tri_ptr[k+1] && Tri_ind[g] <= Tri_ind[j]; ++g) if (Tri_ind[g] == Tri_ind[j]) Tri_val[j] -= zz * Tri_val[g]; } } U = tm_type(&(Tri_val[0]), &(Tri_ind[0]), &(Tri_ptr[0]), n, mat_ncols(A)); } template <typename Matrix> void ildlt_precond<Matrix>::do_ildlt(const Matrix& A, col_major) { do_ildlt(gmm::conjugated(A), row_major()); }
template <typename Matrix, typename V1, typename V2> inline void mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) { gmm::copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); gmm::upper_tri_solve(P.U, v2, true); }
template <typename Matrix, typename V1, typename V2> inline void transposed_mult(const ildlt_precond<Matrix>& P,const V1 &v1,V2 &v2) { mult(P, v1, v2); }
template <typename Matrix, typename V1, typename V2> inline void left_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); }
template <typename Matrix, typename V1, typename V2> inline void right_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true); }
template <typename Matrix, typename V1, typename V2> inline void transposed_left_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); }
template <typename Matrix, typename V1, typename V2> inline void transposed_right_mult(const ildlt_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); }
// for compatibility with old versions
template <typename Matrix> struct cholesky_precond : public ildlt_precond<Matrix> { cholesky_precond(const Matrix& A) : ildlt_precond<Matrix>(A) {} cholesky_precond(void) {} } IS_DEPRECATED;
template <typename Matrix, typename V1, typename V2> inline void mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) { gmm::copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); gmm::upper_tri_solve(P.U, v2, true); }
template <typename Matrix, typename V1, typename V2> inline void transposed_mult(const cholesky_precond<Matrix>& P,const V1 &v1,V2 &v2) { mult(P, v1, v2); }
template <typename Matrix, typename V1, typename V2> inline void left_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); }
template <typename Matrix, typename V1, typename V2> inline void right_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true); }
template <typename Matrix, typename V1, typename V2> inline void transposed_left_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true); for (size_type i = 0; i < mat_nrows(P.U); ++i) v2[i] /= P.D(i); }
template <typename Matrix, typename V1, typename V2> inline void transposed_right_mult(const cholesky_precond<Matrix>& P, const V1 &v1, V2 &v2) { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); } }
#endif
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