GetFEM  5.4.2
gmm_solver_bicgstab.h
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32 // This file is a modified version of bicgstab.h from ITL.
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63 
64 /**@file gmm_solver_bicgstab.h
65  @author Andrew Lumsdaine <[email protected]>
66  @author Lie-Quan Lee <[email protected]>
67  @author Yves Renard <[email protected]>
68  @date October 13, 2002.
69  @brief BiCGStab iterative solver.
70 */
71 
72 #ifndef GMM_SOLVER_BICGSTAB_H__
73 #define GMM_SOLVER_BICGSTAB_H__
74 
75 #include "gmm_kernel.h"
76 #include "gmm_iter.h"
77 
78 namespace gmm {
79 
80  /* ******************************************************************** */
81  /* BiConjugate Gradient Stabilized */
82  /* (preconditionned, with parametrable scalar product) */
83  /* ******************************************************************** */
84 
85  template <typename Matrix, typename Vector, typename VectorB,
86  typename Preconditioner>
87  void bicgstab(const Matrix& A, Vector& x, const VectorB& b,
88  const Preconditioner& M, iteration &iter) {
89 
90  typedef typename linalg_traits<Vector>::value_type T;
91  typedef typename number_traits<T>::magnitude_type R;
92  typedef typename temporary_dense_vector<Vector>::vector_type temp_vector;
93 
94  T rho_1, rho_2(0), alpha(0), beta, omega(0);
95  temp_vector p(vect_size(x)), phat(vect_size(x)), s(vect_size(x)),
96  shat(vect_size(x)),
97  t(vect_size(x)), v(vect_size(x)), r(vect_size(x)), rtilde(vect_size(x));
98 
99  gmm::mult(A, gmm::scaled(x, -T(1)), b, r);
100  gmm::copy(r, rtilde);
101  R norm_r = gmm::vect_norm2(r);
102  iter.set_rhsnorm(gmm::vect_norm2(b));
103 
104  if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
105 
106  while (!iter.finished(norm_r)) {
107 
108  rho_1 = gmm::vect_sp(rtilde, r);
109  if (rho_1 == T(0)) {
110  if (iter.get_maxiter() == size_type(-1))
111  { GMM_ASSERT1(false, "Bicgstab failed to converge"); }
112  else { GMM_WARNING1("Bicgstab failed to converge"); return; }
113  }
114 
115  if (iter.first())
116  gmm::copy(r, p);
117  else {
118  if (omega == T(0)) {
119  if (iter.get_maxiter() == size_type(-1))
120  { GMM_ASSERT1(false, "Bicgstab failed to converge"); }
121  else { GMM_WARNING1("Bicgstab failed to converge"); return; }
122  }
123 
124  beta = (rho_1 / rho_2) * (alpha / omega);
125 
126  gmm::add(gmm::scaled(v, -omega), p);
127  gmm::add(r, gmm::scaled(p, beta), p);
128  }
129  gmm::mult(M, p, phat);
130  gmm::mult(A, phat, v);
131  alpha = rho_1 / gmm::vect_sp(v, rtilde);
132  gmm::add(r, gmm::scaled(v, -alpha), s);
133 
134  if (iter.finished_vect(s))
135  { gmm::add(gmm::scaled(phat, alpha), x); break; }
136 
137  gmm::mult(M, s, shat);
138  gmm::mult(A, shat, t);
139  omega = gmm::vect_sp(t, s) / gmm::vect_norm2_sqr(t);
140 
141  gmm::add(gmm::scaled(phat, alpha), x);
142  gmm::add(gmm::scaled(shat, omega), x);
143  gmm::add(s, gmm::scaled(t, -omega), r);
144  norm_r = gmm::vect_norm2(r);
145  rho_2 = rho_1;
146 
147  ++iter;
148  }
149  }
150 
151  template <typename Matrix, typename Vector, typename VectorB,
152  typename Preconditioner>
153  void bicgstab(const Matrix& A, const Vector& x, const VectorB& b,
154  const Preconditioner& M, iteration &iter)
155  { bicgstab(A, linalg_const_cast(x), b, M, iter); }
156 
157 }
158 
159 
160 #endif // GMM_SOLVER_BICGSTAB_H__
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_norm2_sqr
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2_sqr(const V &v)
squared Euclidean norm of a vector.
Definition: gmm_blas.h:544
gmm::vect_norm2
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2(const V &v)
Euclidean norm of a vector.
Definition: gmm_blas.h:557
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_kernel.h
Include the base gmm files.
gmm_iter.h
Iteration object.