BiCGSTAB.h
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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;
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;
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;
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 
191 
193  template<typename Rhs,typename Dest>
194  void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
195  {
198 
200 
201  m_info = (!ret) ? NumericalIssue
203  : NoConvergence;
204  }
205 
206 protected:
207 
208 };
209 
210 } // end namespace Eigen
211 
212 #endif // EIGEN_BICGSTAB_H
w
RowVector3d w
Definition: Matrix_resize_int.cpp:3
Eigen::BiCGSTAB::Scalar
MatrixType::Scalar Scalar
Definition: BiCGSTAB.h:168
Eigen::NumericalIssue
@ NumericalIssue
Definition: Constants.h:444
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
Eigen::BiCGSTAB::m_iterations
Index m_iterations
Definition: IterativeSolverBase.h:437
alpha
RealScalar alpha
Definition: level1_cplx_impl.h:147
s
RealScalar s
Definition: level1_cplx_impl.h:126
MatrixType
MatrixXf MatrixType
Definition: benchmark-blocking-sizes.cpp:52
Eigen::internal::traits< BiCGSTAB< _MatrixType, _Preconditioner > >::MatrixType
_MatrixType MatrixType
Definition: BiCGSTAB.h:120
Eigen::BiCGSTAB::MatrixType
_MatrixType MatrixType
Definition: BiCGSTAB.h:167
b
Scalar * b
Definition: benchVecAdd.cpp:17
Eigen::EigenBase
Definition: EigenBase.h:29
x
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Definition: gnuplot_common_settings.hh:12
Eigen::BiCGSTAB::Preconditioner
_Preconditioner Preconditioner
Definition: BiCGSTAB.h:170
Eigen::internal::bicgstab
bool bicgstab(const MatrixType &mat, const Rhs &rhs, Dest &x, const Preconditioner &precond, Index &iters, typename Dest::RealScalar &tol_error)
Definition: BiCGSTAB.h:29
ret
DenseIndex ret
Definition: level1_cplx_impl.h:44
Eigen::BiCGSTAB::BiCGSTAB
BiCGSTAB(const EigenBase< MatrixDerived > &A)
Definition: BiCGSTAB.h:188
Eigen::Success
@ Success
Definition: Constants.h:442
mat
MatrixXf mat
Definition: Tutorial_AdvancedInitialization_CommaTemporary.cpp:1
beta
double beta(double a, double b)
Definition: beta.c:61
n
int n
Definition: BiCGSTAB_simple.cpp:1
epsilon
static double epsilon
Definition: testRot3.cpp:37
Eigen::BiCGSTAB::m_info
ComputationInfo m_info
Definition: IterativeSolverBase.h:438
Eigen::NoConvergence
@ NoConvergence
Definition: Constants.h:446
A
Definition: test_numpy_dtypes.cpp:298
Eigen::IterativeSolverBase::maxIterations
Index maxIterations() const
Definition: IterativeSolverBase.h:281
Eigen::IterativeSolverBase::m_info
ComputationInfo m_info
Definition: IterativeSolverBase.h:438
Eigen::BiCGSTAB::RealScalar
MatrixType::RealScalar RealScalar
Definition: BiCGSTAB.h:169
pybind_wrapper_test_script.z
z
Definition: pybind_wrapper_test_script.py:61
matrix
Map< Matrix< T, Dynamic, Dynamic, ColMajor >, 0, OuterStride<> > matrix(T *data, int rows, int cols, int stride)
Definition: gtsam/3rdparty/Eigen/blas/common.h:110
Eigen::IterativeSolverBase
Base class for linear iterative solvers.
Definition: IterativeSolverBase.h:143
RealScalar
NumTraits< Scalar >::Real RealScalar
Definition: bench_gemm.cpp:47
Eigen::IterativeSolverBase::m_tolerance
RealScalar m_tolerance
Definition: IterativeSolverBase.h:434
Eigen::BiCGSTAB
A bi conjugate gradient stabilized solver for sparse square problems.
Definition: BiCGSTAB.h:113
Eigen::internal::traits
Definition: ForwardDeclarations.h:17
Eigen::internal::Rhs
@ Rhs
Definition: TensorContractionMapper.h:18
Eigen::internal::y
const Scalar & y
Definition: Eigen/src/Core/MathFunctions.h:821
Eigen::internal::traits< BiCGSTAB< _MatrixType, _Preconditioner > >::Preconditioner
_Preconditioner Preconditioner
Definition: BiCGSTAB.h:121
Eigen::IterativeSolverBase::m_iterations
Index m_iterations
Definition: IterativeSolverBase.h:437
p
float * p
Definition: Tutorial_Map_using.cpp:9
Eigen::IterativeSolverBase::matrix
const ActualMatrixType & matrix() const
Definition: IterativeSolverBase.h:419
v
Array< int, Dynamic, 1 > v
Definition: Array_initializer_list_vector_cxx11.cpp:1
gtsam::tol
const G double tol
Definition: Group.h:79
Eigen::BiCGSTAB::Base
IterativeSolverBase< BiCGSTAB > Base
Definition: BiCGSTAB.h:160
Eigen::Matrix< Scalar, Dynamic, 1 >
abs
#define abs(x)
Definition: datatypes.h:17
internal
Definition: BandTriangularSolver.h:13
VectorType
Definition: FFTW.cpp:65
align_3::t
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Eigen::BiCGSTAB::_solve_vector_with_guess_impl
void _solve_vector_with_guess_impl(const Rhs &b, Dest &x) const
Definition: BiCGSTAB.h:194
Eigen::IterativeSolverBase::m_preconditioner
Preconditioner m_preconditioner
Definition: IterativeSolverBase.h:431
ceres::sqrt
Jet< T, N > sqrt(const Jet< T, N > &f)
Definition: jet.h:418
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9
Eigen::BiCGSTAB::m_error
RealScalar m_error
Definition: IterativeSolverBase.h:436
Eigen::BiCGSTAB::BiCGSTAB
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Definition: BiCGSTAB.h:175
Eigen::IterativeSolverBase::m_error
RealScalar m_error
Definition: IterativeSolverBase.h:436
Scalar
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Definition: bench_gemm.cpp:46
Eigen::BiCGSTAB::~BiCGSTAB
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Definition: BiCGSTAB.h:190
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Eigen::SparseSolverBase::m_isInitialized
bool m_isInitialized
Definition: SparseSolverBase.h:119


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autogenerated on Fri Nov 1 2024 03:32:01