GetFEM  5.4.2
gmm_precond_mr_approx_inverse.h
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33 // This file is a modified version of approximate_inverse.h from ITL.
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64 
65 /**@file gmm_precond_mr_approx_inverse.h
66  @author Andrew Lumsdaine <lums@osl.iu.edu>
67  @author Lie-Quan Lee <llee@osl.iu.edu>
68  @author Yves Renard <Yves.Renard@insa-lyon.fr>
69  @date June 5, 2003.
70  @brief Approximate inverse via MR iteration.
71 */
72 
73 #ifndef GMM_PRECOND_MR_APPROX_INVERSE_H
74 #define GMM_PRECOND_MR_APPROX_INVERSE_H
75 
76 
77 #include "gmm_precond.h"
78 
79 namespace gmm {
80 
81  /** Approximate inverse via MR iteration (see P301 of Saad book).
82  */
83  template <typename Matrix>
84  struct mr_approx_inverse_precond {
85 
86  typedef typename linalg_traits<Matrix>::value_type value_type;
87  typedef typename number_traits<value_type>::magnitude_type magnitude_type;
88  typedef typename principal_orientation_type<typename
89  linalg_traits<Matrix>::sub_orientation>::potype sub_orientation;
90  typedef wsvector<value_type> VVector;
91  typedef col_matrix<VVector> MMatrix;
92 
93  MMatrix M;
94  size_type nb_it;
95  magnitude_type threshold;
96 
97  void build_with(const Matrix& A);
98  mr_approx_inverse_precond(const Matrix& A, size_type nb_it_,
99  magnitude_type threshold_)
100  : M(mat_nrows(A), mat_ncols(A))
101  { threshold = threshold_; nb_it = nb_it_; build_with(A); }
102  mr_approx_inverse_precond(void)
103  { threshold = magnitude_type(1E-7); nb_it = 5; }
104  mr_approx_inverse_precond(size_type nb_it_, magnitude_type threshold_)
105  { threshold = threshold_; nb_it = nb_it_; }
106  const MMatrix &approx_inverse(void) const { return M; }
107  };
108 
109  template <typename Matrix, typename V1, typename V2> inline
110  void mult(const mr_approx_inverse_precond<Matrix>& P, const V1 &v1, V2 &v2)
111  { mult(P.M, v1, v2); }
112 
113  template <typename Matrix, typename V1, typename V2> inline
114  void transposed_mult(const mr_approx_inverse_precond<Matrix>& P,
115  const V1 &v1,V2 &v2)
116  { mult(gmm::conjugated(P.M), v1, v2); }
117 
118  template <typename Matrix>
119  void mr_approx_inverse_precond<Matrix>::build_with(const Matrix& A) {
120  gmm::resize(M, mat_nrows(A), mat_ncols(A));
121  typedef value_type T;
122  typedef magnitude_type R;
123  VVector m(mat_ncols(A)),r(mat_ncols(A)),ei(mat_ncols(A)),Ar(mat_ncols(A));
124  T alpha = mat_trace(A)/ mat_euclidean_norm_sqr(A);
125  if (alpha == T(0)) alpha = T(1);
126 
127  for (size_type i = 0; i < mat_nrows(A); ++i) {
128  gmm::clear(m); gmm::clear(ei);
129  m[i] = alpha;
130  ei[i] = T(1);
131 
132  for (size_type j = 0; j < nb_it; ++j) {
133  gmm::mult(A, gmm::scaled(m, T(-1)), r);
134  gmm::add(ei, r);
135  gmm::mult(A, r, Ar);
136  T nAr = vect_sp(Ar,Ar);
137  if (gmm::abs(nAr) > R(0)) {
138  gmm::add(gmm::scaled(r, gmm::safe_divide(vect_sp(r, Ar), vect_sp(Ar, Ar))), m);
139  gmm::clean(m, threshold * gmm::vect_norm2(m));
140  } else gmm::clear(m);
141  }
142  if (gmm::vect_norm2(m) == R(0)) m[i] = alpha;
143  gmm::copy(m, M.col(i));
144  }
145  }
146 }
147 
148 #endif
149 
gmm::resize
void resize(M &v, size_type m, size_type n)
*‍/
Definition: gmm_blas.h:231
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::vect_sp
strongest_value_type< V1, V2 >::value_type vect_sp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:263
gmm::mat_euclidean_norm_sqr
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_euclidean_norm_sqr(const M &m)
*‍/
Definition: gmm_blas.h:626
bgeot::alpha
size_type alpha(short_type n, short_type d)
Return the value of which is the number of monomials of a polynomial of variables and degree .
Definition: bgeot_poly.cc:47
gmm_precond.h
gmm preconditioners.
gmm::mat_trace
linalg_traits< M >::value_type mat_trace(const M &m)
Trace of a matrix.
Definition: gmm_blas.h:528
gmm::mr_approx_inverse_precond
Approximate inverse via MR iteration (see P301 of Saad book).
Definition: gmm_precond_mr_approx_inverse.h:84
gmm::wsvector
sparse vector built upon std::map.
Definition: gmm_def.h:487