GetFEM  5.4.2
gmm_solver_qmr.h
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32 // This file is a modified version of qmr.h from ITL.
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64 
65 /**@file gmm_solver_qmr.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 October 13, 2002.
70  @brief Quasi-Minimal Residual iterative solver.
71 */
72 #ifndef GMM_QMR_H
73 #define GMM_QMR_H
74 
75 #include "gmm_kernel.h"
76 #include "gmm_iter.h"
77 
78 namespace gmm {
79 
80  /** Quasi-Minimal Residual.
81 
82  This routine solves the unsymmetric linear system Ax = b using
83  the Quasi-Minimal Residual method.
84 
85  See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual
86  method for non-Hermitian linear systems, Numerical Math.,
87  60(1991), pp. 315-339
88 
89  Preconditioner - Incomplete LU, Incomplete LU with threshold,
90  SSOR or identity_preconditioner.
91  */
92  template <typename Matrix, typename Vector, typename VectorB,
93  typename Precond1>
94  void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1,
95  iteration& iter) {
96 
97  typedef typename linalg_traits<Vector>::value_type T;
98  typedef typename number_traits<T>::magnitude_type R;
99 
100  T delta(0), ep(0), beta(0), theta_1(0), gamma_1(0);
101  T theta(0), gamma(1), eta(-1);
102  R rho_1(0), rho, xi;
103 
104  typedef typename temporary_vector<Vector>::vector_type TmpVec;
105  size_type nn = vect_size(x);
106  TmpVec r(nn), v_tld(nn), y(nn), w_tld(nn), z(nn), v(nn), w(nn);
107  TmpVec y_tld(nn), z_tld(nn), p(nn), q(nn), p_tld(nn), d(nn), s(nn);
108 
109  iter.set_rhsnorm(double(gmm::vect_norm2(b)));
110  if (iter.get_rhsnorm() == 0.0) { clear(x); return; }
111 
112  gmm::mult(A, gmm::scaled(x, T(-1)), b, r);
113  gmm::copy(r, v_tld);
114 
115  gmm::left_mult(M1, v_tld, y);
116  rho = gmm::vect_norm2(y);
117 
118  gmm::copy(r, w_tld);
119  gmm::transposed_right_mult(M1, w_tld, z);
120  xi = gmm::vect_norm2(z);
121 
122  while (! iter.finished_vect(r)) {
123 
124  if (rho == R(0) || xi == R(0)) {
125  if (iter.get_maxiter() == size_type(-1))
126  { GMM_ASSERT1(false, "QMR failed to converge"); }
127  else { GMM_WARNING1("QMR failed to converge"); return; }
128  }
129  gmm::copy(gmm::scaled(v_tld, T(R(1)/rho)), v);
130  gmm::scale(y, T(R(1)/rho));
131 
132  gmm::copy(gmm::scaled(w_tld, T(R(1)/xi)), w);
133  gmm::scale(z, T(R(1)/xi));
134 
135  delta = gmm::vect_sp(z, y);
136  if (delta == T(0)) {
137  if (iter.get_maxiter() == size_type(-1))
138  { GMM_ASSERT1(false, "QMR failed to converge"); }
139  else { GMM_WARNING1("QMR failed to converge"); return; }
140  }
141  gmm::right_mult(M1, y, y_tld);
142  gmm::transposed_left_mult(M1, z, z_tld);
143 
144  if (iter.first()) {
145  gmm::copy(y_tld, p);
146  gmm::copy(z_tld, q);
147  } else {
148  gmm::add(y_tld, gmm::scaled(p, -(T(xi * delta) / ep)), p);
149  gmm::add(z_tld, gmm::scaled(q, -(T(rho * delta) / ep)), q);
150  }
151 
152  gmm::mult(A, p, p_tld);
153 
154  ep = gmm::vect_sp(q, p_tld);
155  if (ep == T(0)) {
156  if (iter.get_maxiter() == size_type(-1))
157  { GMM_ASSERT1(false, "QMR failed to converge"); }
158  else { GMM_WARNING1("QMR failed to converge"); return; }
159  }
160  beta = ep / delta;
161  if (beta == T(0)) {
162  if (iter.get_maxiter() == size_type(-1))
163  { GMM_ASSERT1(false, "QMR failed to converge"); }
164  else { GMM_WARNING1("QMR failed to converge"); return; }
165  }
166  gmm::add(p_tld, gmm::scaled(v, -beta), v_tld);
167  gmm::left_mult(M1, v_tld, y);
168 
169  rho_1 = rho;
170  rho = gmm::vect_norm2(y);
171 
172  gmm::mult(gmm::transposed(A), q, w_tld);
173  gmm::add(w_tld, gmm::scaled(w, -beta), w_tld);
174  gmm::transposed_right_mult(M1, w_tld, z);
175 
176  xi = gmm::vect_norm2(z);
177 
178  gamma_1 = gamma;
179  theta_1 = theta;
180 
181  theta = rho / (gamma_1 * beta);
182  gamma = T(1) / gmm::sqrt(T(1) + gmm::sqr(theta));
183 
184  if (gamma == T(0)) {
185  if (iter.get_maxiter() == size_type(-1))
186  { GMM_ASSERT1(false, "QMR failed to converge"); }
187  else { GMM_WARNING1("QMR failed to converge"); return; }
188  }
189  eta = -eta * T(rho_1) * gmm::sqr(gamma) / (beta * gmm::sqr(gamma_1));
190 
191  if (iter.first()) {
192  gmm::copy(gmm::scaled(p, eta), d);
193  gmm::copy(gmm::scaled(p_tld, eta), s);
194  } else {
195  T tmp = gmm::sqr(theta_1 * gamma);
196  gmm::add(gmm::scaled(p, eta), gmm::scaled(d, tmp), d);
197  gmm::add(gmm::scaled(p_tld, eta), gmm::scaled(s, tmp), s);
198  }
199  gmm::add(d, x);
200  gmm::add(gmm::scaled(s, T(-1)), r);
201 
202  ++iter;
203  }
204  }
205 
206 
207 }
208 
209 #endif
210 
gmm::qmr
void qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1, iteration &iter)
Quasi-Minimal Residual.
Definition: gmm_solver_qmr.h:94
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::iteration
The Iteration object calculates whether the solution has reached the desired accuracy,...
Definition: gmm_iter.h:53
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
gmm_kernel.h
Include the base gmm files.
gmm_iter.h
Iteration object.