GetFEM  5.4.2
gmm_modified_gram_schmidt.h
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60 
61 /**@file gmm_modified_gram_schmidt.h
62  @author Andrew Lumsdaine <[email protected]>, Lie-Quan Lee <[email protected]>
63  @date October 13, 2002.
64  @brief Modified Gram-Schmidt orthogonalization
65 */
66 
67 #ifndef GMM_MODIFIED_GRAM_SCHMIDT_H
68 #define GMM_MODIFIED_GRAM_SCHMIDT_H
69 
70 #include "gmm_kernel.h"
71 
72 namespace gmm {
73 
74  template <typename T>
75  class modified_gram_schmidt {
76  protected:
77  typedef dense_matrix<T> MAT;
78  MAT M;
79 
80  public:
81 
82  modified_gram_schmidt(int restart, size_t s) : M(s, restart+1) {}
83 
84  typename linalg_traits<MAT>::const_sub_col_type
85  operator[](size_t i) const { return mat_const_col(M, i); }
86 
87  typename linalg_traits<MAT>::sub_col_type
88  operator[](size_t i) { return mat_col(M, i); }
89 
90  inline size_type nrows(void) const { return M.nrows(); }
91  inline size_type ncols(void) const { return M.ncols(); }
92  MAT &mat(void) { return M; }
93  const MAT &mat(void) const { return M; }
94 
95  };
96 
97  template <typename T, typename VecHi> inline
98  void orthogonalize(modified_gram_schmidt<T>& V, const VecHi& Hi_, size_t i) {
99  VecHi& Hi = const_cast<VecHi&>(Hi_);
100 
101  for (size_t k = 0; k <= i; k++) {
102  Hi[k] = gmm::vect_hp(V[i+1], V[k]);
103  gmm::add(gmm::scaled(V[k], -Hi[k]), V[i+1]);
104  }
105  }
106 
107  template <typename T, typename VecHi>
108  void orthogonalize_with_refinment(modified_gram_schmidt<T>& V,
109  const VecHi& Hi_, size_t i) {
110  VecHi& Hi = const_cast<VecHi&>(Hi_);
111  orthogonalize(V, Hi_, i);
112 
113  sub_interval SUBI(0, V.nrows()), SUBJ(0, i+1);
114  std::vector<T> corr(i+1);
115  gmm::mult(conjugated(sub_matrix(V.mat(), SUBI, SUBJ)),
116  V[i+1], corr);
117  gmm::mult(sub_matrix(V.mat(), SUBI, SUBJ),
118  scaled(corr, T(-1)), V[i+1],V[i+1]);
119  gmm::add(corr, sub_vector(Hi, SUBJ));
120  }
121 
122  template <typename T, typename VecS, typename VecX>
123  void combine(modified_gram_schmidt<T>& V, const VecS& s, VecX& x, size_t i)
124  { for (size_t j = 0; j < i; ++j) gmm::add(gmm::scaled(V[j], s[j]), x); }
125 }
126 
127 #endif
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
gmm::conjugated
conjugated_return< L >::return_type conjugated(const L &v)
return a conjugated view of the input matrix or vector.
Definition: gmm_conjugated.h:294
gmm_kernel.h
Include the base gmm files.