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gmm_precond_ildlt.h
gmm_precond_ildlt.h 10.84 KiB
// -*- c++ -*- (enables emacs c++ mode)
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// Copyright (C) 2003-2008 Yves Renard
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// This file is a modified version of cholesky.h from ITL.
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#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