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// This file is a modified version of ilut.h from ITL.
// See http://osl.iu.edu/research/itl/
// Following the corresponding Copyright notice.
//===========================================================================
//
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#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