Public Types | Public Member Functions | Private Types | Private Member Functions | Private Attributes | List of all members
Eigen::BiCGSTAB< MatrixType_, Preconditioner_ > Class Template Reference
Sparse linear algebra » Reference » IterativeLinearSolvers module

A bi conjugate gradient stabilized solver for sparse square problems. More...

+ Inheritance diagram for Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >:

Public Types

typedef MatrixType_ MatrixType
 
typedef Preconditioner_ Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
- Public Types inherited from Eigen::IterativeSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > >
enum  
 
typedef internal::traits< BiCGSTAB< MatrixType_, Preconditioner_ > >::MatrixType MatrixType
 
typedef internal::traits< BiCGSTAB< MatrixType_, Preconditioner_ > >::Preconditioner Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
typedef MatrixType::StorageIndex StorageIndex
 

Public Member Functions

template<typename Rhs , typename Dest >
void _solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
 
 BiCGSTAB ()
 
template<typename MatrixDerived >
 BiCGSTAB (const EigenBase< MatrixDerived > &A)
 
 ~BiCGSTAB ()
 
- Public Member Functions inherited from Eigen::IterativeSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > >
void _solve_impl (const Rhs &b, Dest &x) const
 
std::enable_if_t< Rhs::ColsAtCompileTime!=1 &&DestDerived::ColsAtCompileTime!=1 > _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &aDest) const
 
std::enable_if_t< Rhs::ColsAtCompileTime==1||DestDerived::ColsAtCompileTime==1 > _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &dest) const
 
void _solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
 
BiCGSTAB< MatrixType_, Preconditioner_ > & analyzePattern (const EigenBase< MatrixDerived > &A)
 
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
BiCGSTAB< MatrixType_, Preconditioner_ > & compute (const EigenBase< MatrixDerived > &A)
 
BiCGSTAB< MatrixType_, Preconditioner_ > & derived ()
 
const BiCGSTAB< MatrixType_, Preconditioner_ > & derived () const
 
RealScalar error () const
 
BiCGSTAB< MatrixType_, Preconditioner_ > & factorize (const EigenBase< MatrixDerived > &A)
 
ComputationInfo info () const
 
Index iterations () const
 
 IterativeSolverBase ()
 
 IterativeSolverBase (const EigenBase< MatrixDerived > &A)
 
 IterativeSolverBase (IterativeSolverBase &&)=default
 
Index maxIterations () const
 
Preconditioner & preconditioner ()
 
const Preconditioner & preconditioner () const
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
BiCGSTAB< MatrixType_, Preconditioner_ > & setMaxIterations (Index maxIters)
 
BiCGSTAB< MatrixType_, Preconditioner_ > & setTolerance (const RealScalar &tolerance)
 
const SolveWithGuess< BiCGSTAB< MatrixType_, Preconditioner_ >, Rhs, Guess > solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
 
RealScalar tolerance () const
 
 ~IterativeSolverBase ()
 
- Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
Derived & derived ()
 
const Derived & derived () const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const SparseMatrixBase< Rhs > &b) const
 
 SparseSolverBase ()
 
 SparseSolverBase (SparseSolverBase &&other)
 
 ~SparseSolverBase ()
 

Private Types

typedef IterativeSolverBase< BiCGSTAB > Base
 

Private Member Functions

const ActualMatrixType & matrix () const
 

Private Attributes

RealScalar m_error
 
ComputationInfo m_info
 
Index m_iterations
 

Additional Inherited Members

- Protected Types inherited from Eigen::IterativeSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > >
typedef MatrixWrapper::ActualMatrixType ActualMatrixType
 
typedef SparseSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > > Base
 
typedef internal::generic_matrix_wrapper< MatrixType > MatrixWrapper
 
- Protected Member Functions inherited from Eigen::IterativeSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > >
void grab (const InputType &A)
 
void init ()
 
const ActualMatrixType & matrix () const
 
- Protected Attributes inherited from Eigen::IterativeSolverBase< BiCGSTAB< MatrixType_, Preconditioner_ > >
bool m_analysisIsOk
 
RealScalar m_error
 
bool m_factorizationIsOk
 
ComputationInfo m_info
 
bool m_isInitialized
 
Index m_iterations
 
MatrixWrapper m_matrixWrapper
 
Index m_maxIterations
 
Preconditioner m_preconditioner
 
RealScalar m_tolerance
 
- Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool m_isInitialized
 

Detailed Description

template<typename MatrixType_, typename Preconditioner_>
class Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >

A bi conjugate gradient stabilized solver for sparse square problems.

This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient stabilized algorithm. The vectors x and b can be either dense or sparse.

Template Parameters
MatrixType_the type of the sparse matrix A, can be a dense or a sparse matrix.
Preconditioner_the type of the preconditioner. Default is DiagonalPreconditioner

This class follows the sparse solver concept .

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

The tolerance corresponds to the relative residual error: |Ax-b|/|b|

Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format. Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled. See Eigen and multi-threading for details.

This class can be used as the direct solver classes. Here is a typical usage example:

int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
/* ... fill A and b ... */
BiCGSTAB<SparseMatrix<double> > solver;
solver.compute(A);
x = solver.solve(b);
std::cout << "#iterations: " << solver.iterations() << std::endl;
std::cout << "estimated error: " << solver.error() << std::endl;
/* ... update b ... */
x = solver.solve(b); // solve again
b
Array< int, 3, 1 > b
Definition: Array_variadic_ctor_cxx11.cpp:2
solver
BiCGSTAB< SparseMatrix< double > > solver
Definition: BiCGSTAB_simple.cpp:5
n
int n
Definition: BiCGSTAB_simple.cpp:1
x
x
Definition: BiCGSTAB_simple.cpp:7
A
MatrixXcf A
Definition: ComplexEigenSolver_compute.cpp:1
Eigen::VectorXd
Matrix< double, Dynamic, 1 > VectorXd
Dynamic×1 vector of type double.
Definition: Matrix.h:502
Code

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

BiCGSTAB can also be used in a matrix-free context, see the following example .

See also
class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 160 of file BiCGSTAB.h.

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , typename Preconditioner_ >
typedef IterativeSolverBase<BiCGSTAB> Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::Base
private

Definition at line 162 of file BiCGSTAB.h.

◆ MatrixType

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType_ Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::MatrixType

Definition at line 169 of file BiCGSTAB.h.

◆ Preconditioner

template<typename MatrixType_ , typename Preconditioner_ >
typedef Preconditioner_ Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::Preconditioner

Definition at line 172 of file BiCGSTAB.h.

◆ RealScalar

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType::RealScalar Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::RealScalar

Definition at line 171 of file BiCGSTAB.h.

◆ Scalar

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType::Scalar Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::Scalar

Definition at line 170 of file BiCGSTAB.h.

Constructor & Destructor Documentation

◆ BiCGSTAB() [1/2]

template<typename MatrixType_ , typename Preconditioner_ >
Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::BiCGSTAB ( )
inline

Default constructor.

Definition at line 177 of file BiCGSTAB.h.

177 : Base() {}
Eigen::BiCGSTAB::Base
IterativeSolverBase< BiCGSTAB > Base
Definition: BiCGSTAB.h:162
Code

◆ BiCGSTAB() [2/2]

template<typename MatrixType_ , typename Preconditioner_ >
template<typename MatrixDerived >
Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::BiCGSTAB ( const EigenBase< MatrixDerived > &  A)
inlineexplicit

Initialize the solver with matrix A for further Ax=b solving.

This constructor is a shortcut for the default constructor followed by a call to compute().

Warning
this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

Definition at line 190 of file BiCGSTAB.h.

190 : Base(A.derived()) {}
Code

◆ ~BiCGSTAB()

template<typename MatrixType_ , typename Preconditioner_ >
Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::~BiCGSTAB ( )
inline

Definition at line 192 of file BiCGSTAB.h.

192 {}
Code

Member Function Documentation

◆ _solve_vector_with_guess_impl()

template<typename MatrixType_ , typename Preconditioner_ >
template<typename Rhs , typename Dest >
void Eigen::BiCGSTAB< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl ( const Rhs &  b,
Dest &  x 
) const
inline

Definition at line 196 of file BiCGSTAB.h.

197  {
198  m_iterations = Base::maxIterations();
199  m_error = Base::m_tolerance;
200 
201  bool ret = internal::bicgstab(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
202 
203  m_info = (!ret) ? NumericalIssue
204  : m_error <= Base::m_tolerance ? Success
205  : NoConvergence;
206  }
Eigen::BiCGSTAB::m_info
ComputationInfo m_info
Definition: IterativeSolverBase.h:443
Eigen::BiCGSTAB::matrix
const ActualMatrixType & matrix() const
Definition: IterativeSolverBase.h:424
Eigen::NumericalIssue
@ NumericalIssue
Definition: Constants.h:448
Eigen::Success
@ Success
Definition: Constants.h:446
Eigen::NoConvergence
@ NoConvergence
Definition: Constants.h:450
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:31
Code

◆ matrix()

template<typename MatrixType_ , typename Preconditioner_ >
const ActualMatrixType& Eigen::IterativeSolverBase< Derived >::matrix
inlineprivate

Definition at line 424 of file IterativeSolverBase.h.

425  {
426  return m_matrixWrapper.matrix();
427  }
Code

Member Data Documentation

◆ m_error

template<typename MatrixType_ , typename Preconditioner_ >
RealScalar Eigen::IterativeSolverBase< Derived >::m_error
mutableprivate

Definition at line 441 of file IterativeSolverBase.h.

◆ m_info

template<typename MatrixType_ , typename Preconditioner_ >
ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info
mutableprivate

Definition at line 443 of file IterativeSolverBase.h.

◆ m_iterations

template<typename MatrixType_ , typename Preconditioner_ >
Index Eigen::IterativeSolverBase< Derived >::m_iterations
mutableprivate

Definition at line 442 of file IterativeSolverBase.h.

The documentation for this class was generated from the following file:
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