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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 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, int& 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  int maxIters = iters;
40 
41  int n = mat.cols();
42  x = precond.solve(x);
43  VectorType r = rhs - mat * x;
44  VectorType r0 = r;
45 
46  RealScalar r0_sqnorm = r0.squaredNorm();
47  RealScalar rhs_sqnorm = rhs.squaredNorm();
48  if(rhs_sqnorm == 0)
49  {
50  x.setZero();
51  return true;
52  }
53  Scalar rho = 1;
54  Scalar alpha = 1;
55  Scalar w = 1;
56 
57  VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
58  VectorType y(n), z(n);
59  VectorType kt(n), ks(n);
60 
61  VectorType s(n), t(n);
62 
63  RealScalar tol2 = tol*tol;
64  RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
65  int i = 0;
66  int restarts = 0;
67 
68  while ( r.squaredNorm()/rhs_sqnorm > tol2 && i<maxIters )
69  {
70  Scalar rho_old = rho;
71 
72  rho = r0.dot(r);
73  if (abs(rho) < eps2*r0_sqnorm)
74  {
75  // The new residual vector became too orthogonal to the arbitrarily choosen direction r0
76  // Let's restart with a new r0:
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 
172 template< typename _MatrixType, typename _Preconditioner>
173 class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >
174 {
175  typedef IterativeSolverBase<BiCGSTAB> Base;
176  using Base::mp_matrix;
177  using Base::m_error;
178  using Base::m_iterations;
179  using Base::m_info;
180  using Base::m_isInitialized;
181 public:
182  typedef _MatrixType MatrixType;
183  typedef typename MatrixType::Scalar Scalar;
184  typedef typename MatrixType::Index Index;
185  typedef typename MatrixType::RealScalar RealScalar;
186  typedef _Preconditioner Preconditioner;
187 
188 public:
189 
191  BiCGSTAB() : Base() {}
192 
203  BiCGSTAB(const MatrixType& A) : Base(A) {}
204 
205  ~BiCGSTAB() {}
206 
212  template<typename Rhs,typename Guess>
213  inline const internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess>
214  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
215  {
216  eigen_assert(m_isInitialized && "BiCGSTAB is not initialized.");
217  eigen_assert(Base::rows()==b.rows()
218  && "BiCGSTAB::solve(): invalid number of rows of the right hand side matrix b");
219  return internal::solve_retval_with_guess
220  <BiCGSTAB, Rhs, Guess>(*this, b.derived(), x0);
221  }
222 
224  template<typename Rhs,typename Dest>
225  void _solveWithGuess(const Rhs& b, Dest& x) const
226  {
227  bool failed = false;
228  for(int j=0; j<b.cols(); ++j)
229  {
230  m_iterations = Base::maxIterations();
231  m_error = Base::m_tolerance;
232 
233  typename Dest::ColXpr xj(x,j);
234  if(!internal::bicgstab(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))
235  failed = true;
236  }
237  m_info = failed ? NumericalIssue
238  : m_error <= Base::m_tolerance ? Success
239  : NoConvergence;
240  m_isInitialized = true;
241  }
242 
244  template<typename Rhs,typename Dest>
245  void _solve(const Rhs& b, Dest& x) const
246  {
247 // x.setZero();
248  x = b;
249  _solveWithGuess(b,x);
250  }
251 
252 protected:
253 
254 };
255 
256 
257 namespace internal {
258 
259  template<typename _MatrixType, typename _Preconditioner, typename Rhs>
260 struct solve_retval<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs>
261  : solve_retval_base<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs>
262 {
263  typedef BiCGSTAB<_MatrixType, _Preconditioner> Dec;
264  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
265 
266  template<typename Dest> void evalTo(Dest& dst) const
267  {
268  dec()._solve(rhs(),dst);
269  }
270 };
271 
272 } // end namespace internal
273 
274 } // end namespace Eigen
275 
276 #endif // EIGEN_BICGSTAB_H
A bi conjugate gradient stabilized solver for sparse square problems.
Definition: BiCGSTAB.h:113
Definition: Constants.h:378
Definition: LDLT.h:16
BiCGSTAB(const MatrixType &A)
Definition: BiCGSTAB.h:203
BiCGSTAB()
Definition: BiCGSTAB.h:191
Definition: Eigen_Colamd.h:54
Definition: Constants.h:380
Definition: Constants.h:376
const internal::solve_retval_with_guess< BiCGSTAB, Rhs, Guess > solveWithGuess(const MatrixBase< Rhs > &b, const Guess &x0) const
Definition: BiCGSTAB.h:214
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
int maxIterations() const
Definition: IterativeSolverBase.h:136