Please, help us to better know about our user community by answering the following short survey: https://forms.gle/wpyrxWi18ox9Z5ae9
Eigen  3.3.9
BiCGSTAB.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_BICGSTAB_H
12 #define EIGEN_BICGSTAB_H
13 
14 namespace Eigen {
15 
16 namespace internal {
17 
28 template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
29 bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
30  const Preconditioner& precond, Index& iters,
31  typename Dest::RealScalar& tol_error)
32 {
33  using std::sqrt;
34  using std::abs;
35  typedef typename Dest::RealScalar RealScalar;
36  typedef typename Dest::Scalar Scalar;
37  typedef Matrix<Scalar,Dynamic,1> VectorType;
38  RealScalar tol = tol_error;
39  Index maxIters = iters;
40 
41  Index n = mat.cols();
42  VectorType r = rhs - mat * x;
43  VectorType r0 = r;
44 
45  RealScalar r0_sqnorm = r0.squaredNorm();
46  RealScalar rhs_sqnorm = rhs.squaredNorm();
47  if(rhs_sqnorm == 0)
48  {
49  x.setZero();
50  return true;
51  }
52  Scalar rho = 1;
53  Scalar alpha = 1;
54  Scalar w = 1;
55 
56  VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
57  VectorType y(n), z(n);
58  VectorType kt(n), ks(n);
59 
60  VectorType s(n), t(n);
61 
62  RealScalar tol2 = tol*tol*rhs_sqnorm;
63  RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
64  Index i = 0;
65  Index restarts = 0;
66 
67  while ( r.squaredNorm() > tol2 && i<maxIters )
68  {
69  Scalar rho_old = rho;
70 
71  rho = r0.dot(r);
72  if (abs(rho) < eps2*r0_sqnorm)
73  {
74  // The new residual vector became too orthogonal to the arbitrarily chosen direction r0
75  // Let's restart with a new r0:
76  r = rhs - mat * x;
77  r0 = r;
78  rho = r0_sqnorm = r.squaredNorm();
79  if(restarts++ == 0)
80  i = 0;
81  }
82  Scalar beta = (rho/rho_old) * (alpha / w);
83  p = r + beta * (p - w * v);
84 
85  y = precond.solve(p);
86 
87  v.noalias() = mat * y;
88 
89  alpha = rho / r0.dot(v);
90  s = r - alpha * v;
91 
92  z = precond.solve(s);
93  t.noalias() = mat * z;
94 
95  RealScalar tmp = t.squaredNorm();
96  if(tmp>RealScalar(0))
97  w = t.dot(s) / tmp;
98  else
99  w = Scalar(0);
100  x += alpha * y + w * z;
101  r = s - w * t;
102  ++i;
103  }
104  tol_error = sqrt(r.squaredNorm()/rhs_sqnorm);
105  iters = i;
106  return true;
107 }
108 
109 }
110 
111 template< typename _MatrixType,
112  typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
113 class BiCGSTAB;
114 
115 namespace internal {
116 
117 template< typename _MatrixType, typename _Preconditioner>
118 struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
119 {
120  typedef _MatrixType MatrixType;
121  typedef _Preconditioner Preconditioner;
122 };
123 
124 }
125 
157 template< typename _MatrixType, typename _Preconditioner>
158 class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >
159 {
161  using Base::matrix;
162  using Base::m_error;
163  using Base::m_iterations;
164  using Base::m_info;
165  using Base::m_isInitialized;
166 public:
167  typedef _MatrixType MatrixType;
168  typedef typename MatrixType::Scalar Scalar;
169  typedef typename MatrixType::RealScalar RealScalar;
170  typedef _Preconditioner Preconditioner;
171 
172 public:
173 
175  BiCGSTAB() : Base() {}
176 
187  template<typename MatrixDerived>
188  explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
189 
190  ~BiCGSTAB() {}
191 
193  template<typename Rhs,typename Dest>
194  void _solve_with_guess_impl(const Rhs& b, Dest& x) const
195  {
196  bool failed = false;
197  for(Index j=0; j<b.cols(); ++j)
198  {
199  m_iterations = Base::maxIterations();
200  m_error = Base::m_tolerance;
201 
202  typename Dest::ColXpr xj(x,j);
203  if(!internal::bicgstab(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))
204  failed = true;
205  }
206  m_info = failed ? NumericalIssue
207  : m_error <= Base::m_tolerance ? Success
208  : NoConvergence;
209  m_isInitialized = true;
210  }
211 
213  using Base::_solve_impl;
214  template<typename Rhs,typename Dest>
215  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const
216  {
217  x.resize(this->rows(),b.cols());
218  x.setZero();
219  _solve_with_guess_impl(b,x);
220  }
221 
222 protected:
223 
224 };
225 
226 } // end namespace Eigen
227 
228 #endif // EIGEN_BICGSTAB_H
Eigen::NumericalIssue
@ NumericalIssue
Definition: Constants.h:434
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:309
Eigen::sqrt
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Eigen::EigenBase
Definition: EigenBase.h:30
Eigen::BiCGSTAB::BiCGSTAB
BiCGSTAB(const EigenBase< MatrixDerived > &A)
Definition: BiCGSTAB.h:188
Eigen::Success
@ Success
Definition: Constants.h:432
Eigen::NoConvergence
@ NoConvergence
Definition: Constants.h:436
Eigen::IterativeSolverBase::maxIterations
Index maxIterations() const
Definition: IterativeSolverBase.h:281
Eigen::abs
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Eigen::IterativeSolverBase
Base class for linear iterative solvers.
Definition: IterativeSolverBase.h:144
Eigen::BiCGSTAB
A bi conjugate gradient stabilized solver for sparse square problems.
Definition: BiCGSTAB.h:159
Eigen::BiCGSTAB::BiCGSTAB
BiCGSTAB()
Definition: BiCGSTAB.h:175
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33