GetFEM  5.4.2
gmm_solver_cg.h
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63 
64 /**@file gmm_solver_cg.h
65  @author Andrew Lumsdaine <lums@osl.iu.edu>
66  @author Lie-Quan Lee <llee@osl.iu.edu>
67  @author Yves Renard <Yves.Renard@insa-lyon.fr>
68  @date October 13, 2002.
69  @brief Conjugate gradient iterative solver.
70 */
71 #ifndef GMM_SOLVER_CG_H__
72 #define GMM_SOLVER_CG_H__
73 
74 #include "gmm_kernel.h"
75 #include "gmm_iter.h"
76 
77 namespace gmm {
78 
79  /* ******************************************************************** */
80  /* conjugate gradient */
81  /* (preconditionned, with parametrable additional scalar product) */
82  /* ******************************************************************** */
83 
84  template <typename Matrix, typename Matps, typename Precond,
85  typename Vector1, typename Vector2>
86  void cg(const Matrix& A, Vector1& x, const Vector2& b, const Matps& PS,
87  const Precond &P, iteration &iter) {
88 
89  typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
90  typedef typename linalg_traits<Vector1>::value_type T;
91 
92  T rho, rho_1(0), a;
93  temp_vector p(vect_size(x)), q(vect_size(x)), r(vect_size(x)),
94  z(vect_size(x));
95  iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(PS, b, b))));
96 
97  if (iter.get_rhsnorm() == 0.0)
98  clear(x);
99  else {
100  mult(A, scaled(x, T(-1)), b, r);
101  mult(P, r, z);
102  rho = vect_hp(PS, z, r);
103  copy(z, p);
104 
105  while (!iter.finished_vect(r)) {
106 
107  if (!iter.first()) {
108  mult(P, r, z);
109  rho = vect_hp(PS, z, r);
110  add(z, scaled(p, rho / rho_1), p);
111  }
112  mult(A, p, q);
113 
114  a = rho / vect_hp(PS, q, p);
115  add(scaled(p, a), x);
116  add(scaled(q, -a), r);
117  rho_1 = rho;
118 
119  ++iter;
120  }
121  }
122  }
123 
124  template <typename Matrix, typename Matps, typename Precond,
125  typename Vector1, typename Vector2>
126  void cg(const Matrix& A, Vector1& x, const Vector2& b, const Matps& PS,
127  const gmm::identity_matrix &, iteration &iter) {
128 
129  typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
130  typedef typename linalg_traits<Vector1>::value_type T;
131 
132  T rho, rho_1(0), a;
133  temp_vector p(vect_size(x)), q(vect_size(x)), r(vect_size(x));
134  iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(PS, b, b))));
135 
136  if (iter.get_rhsnorm() == 0.0)
137  clear(x);
138  else {
139  mult(A, scaled(x, T(-1)), b, r);
140  rho = vect_hp(PS, r, r);
141  copy(r, p);
142 
143  while (!iter.finished_vect(r)) {
144 
145  if (!iter.first()) {
146  rho = vect_hp(PS, r, r);
147  add(r, scaled(p, rho / rho_1), p);
148  }
149  mult(A, p, q);
150  a = rho / vect_hp(PS, q, p);
151  add(scaled(p, a), x);
152  add(scaled(q, -a), r);
153  rho_1 = rho;
154  ++iter;
155  }
156  }
157  }
158 
159  template <typename Matrix, typename Matps, typename Precond,
160  typename Vector1, typename Vector2> inline
161  void cg(const Matrix& A, const Vector1& x, const Vector2& b, const Matps& PS,
162  const Precond &P, iteration &iter)
163  { cg(A, linalg_const_cast(x), b, PS, P, iter); }
164 
165  template <typename Matrix, typename Precond,
166  typename Vector1, typename Vector2> inline
167  void cg(const Matrix& A, Vector1& x, const Vector2& b,
168  const Precond &P, iteration &iter)
169  { cg(A, x , b, identity_matrix(), P, iter); }
170 
171  template <typename Matrix, typename Precond,
172  typename Vector1, typename Vector2> inline
173  void cg(const Matrix& A, const Vector1& x, const Vector2& b,
174  const Precond &P, iteration &iter)
175  { cg(A, x , b , identity_matrix(), P , iter); }
176 
177 }
178 
179 
180 #endif // GMM_SOLVER_CG_H__
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::vect_hp
strongest_value_type< V1, V2 >::value_type vect_hp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:511
gmm_kernel.h
Include the base gmm files.
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:977
gmm_iter.h
Iteration object.
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1268