metaforce/gmm/gmm_precond_mr_approx_inver...

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
Copyright (C) 2002-2017 Yves Renard
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// This file is a modified version of approximate_inverse.h from ITL.
// See http://osl.iu.edu/research/itl/
// Following the corresponding Copyright notice.
//===========================================================================
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/**@file gmm_precond_mr_approx_inverse.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 Approximate inverse via MR iteration.
*/
#ifndef GMM_PRECOND_MR_APPROX_INVERSE_H
#define GMM_PRECOND_MR_APPROX_INVERSE_H
#include "gmm_precond.h"
namespace gmm {
/** Approximate inverse via MR iteration (see P301 of Saad book).
*/
template <typename Matrix>
struct mr_approx_inverse_precond {
typedef typename linalg_traits<Matrix>::value_type value_type;
typedef typename number_traits<value_type>::magnitude_type magnitude_type;
typedef typename principal_orientation_type<typename
linalg_traits<Matrix>::sub_orientation>::potype sub_orientation;
typedef wsvector<value_type> VVector;
typedef col_matrix<VVector> MMatrix;
MMatrix M;
size_type nb_it;
magnitude_type threshold;
void build_with(const Matrix& A);
mr_approx_inverse_precond(const Matrix& A, size_type nb_it_,
magnitude_type threshold_)
: M(mat_nrows(A), mat_ncols(A))
{ threshold = threshold_; nb_it = nb_it_; build_with(A); }
mr_approx_inverse_precond(void)
{ threshold = magnitude_type(1E-7); nb_it = 5; }
mr_approx_inverse_precond(size_type nb_it_, magnitude_type threshold_)
{ threshold = threshold_; nb_it = nb_it_; }
const MMatrix &approx_inverse(void) const { return M; }
};
template <typename Matrix, typename V1, typename V2> inline
void mult(const mr_approx_inverse_precond<Matrix>& P, const V1 &v1, V2 &v2)
{ mult(P.M, v1, v2); }
template <typename Matrix, typename V1, typename V2> inline
void transposed_mult(const mr_approx_inverse_precond<Matrix>& P,
const V1 &v1,V2 &v2)
{ mult(gmm::conjugated(P.M), v1, v2); }
template <typename Matrix>
void mr_approx_inverse_precond<Matrix>::build_with(const Matrix& A) {
gmm::resize(M, mat_nrows(A), mat_ncols(A));
typedef value_type T;
typedef magnitude_type R;
VVector m(mat_ncols(A)),r(mat_ncols(A)),ei(mat_ncols(A)),Ar(mat_ncols(A));
T alpha = mat_trace(A)/ mat_euclidean_norm_sqr(A);
if (alpha == T(0)) alpha = T(1);
for (size_type i = 0; i < mat_nrows(A); ++i) {
gmm::clear(m); gmm::clear(ei);
m[i] = alpha;
ei[i] = T(1);
for (size_type j = 0; j < nb_it; ++j) {
gmm::mult(A, gmm::scaled(m, T(-1)), r);
gmm::add(ei, r);
gmm::mult(A, r, Ar);
T nAr = vect_sp(Ar,Ar);
if (gmm::abs(nAr) > R(0)) {
gmm::add(gmm::scaled(r, gmm::safe_divide(vect_sp(r, Ar), vect_sp(Ar, Ar))), m);
gmm::clean(m, threshold * gmm::vect_norm2(m));
} else gmm::clear(m);
}
if (gmm::vect_norm2(m) == R(0)) m[i] = alpha;
gmm::copy(m, M.col(i));
}
}
}
#endif