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Eigen  3.4.0
 
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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
14namespace Eigen {
15
16namespace internal {
17
28template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
29bool 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
111template< typename _MatrixType,
112 typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
113class BiCGSTAB;
114
115namespace internal {
116
117template< typename _MatrixType, typename _Preconditioner>
118struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
119{
120 typedef _MatrixType MatrixType;
121 typedef _Preconditioner Preconditioner;
122};
123
124}
125
157template< typename _MatrixType, typename _Preconditioner>
158class 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;
166public:
167 typedef _MatrixType MatrixType;
168 typedef typename MatrixType::Scalar Scalar;
169 typedef typename MatrixType::RealScalar RealScalar;
170 typedef _Preconditioner Preconditioner;
171
172public:
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_vector_with_guess_impl(const Rhs& b, Dest& x) const
195 {
196 m_iterations = Base::maxIterations();
197 m_error = Base::m_tolerance;
198
199 bool ret = internal::bicgstab(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
200
201 m_info = (!ret) ? NumericalIssue
202 : m_error <= Base::m_tolerance ? Success
204 }
205
206protected:
207
208};
209
210} // end namespace Eigen
211
212#endif // EIGEN_BICGSTAB_H
A bi conjugate gradient stabilized solver for sparse square problems.
Definition: BiCGSTAB.h:159
BiCGSTAB(const EigenBase< MatrixDerived > &A)
Definition: BiCGSTAB.h:188
BiCGSTAB()
Definition: BiCGSTAB.h:175
Base class for linear iterative solvers.
Definition: IterativeSolverBase.h:144
Index maxIterations() const
Definition: IterativeSolverBase.h:281
@ NumericalIssue
Definition: Constants.h:444
@ Success
Definition: Constants.h:442
@ NoConvergence
Definition: Constants.h:446
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Definition: EigenBase.h:30