A bi conjugate gradient stabilized solver for sparse square problems. More...
#include <BiCGSTAB.h>
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_impl (const MatrixBase< Rhs > &b, Dest &x) const |
| template<typename Rhs , typename Dest > | |
| void | _solve_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, SparseMatrixBase< DestDerived > &aDest) const |
| BiCGSTAB< _MatrixType, _Preconditioner > & | analyzePattern (const EigenBase< MatrixDerived > &A) |
| Index | cols () const |
| BiCGSTAB< _MatrixType, _Preconditioner > & | compute (const EigenBase< MatrixDerived > &A) |
| RealScalar | error () const |
| BiCGSTAB< _MatrixType, _Preconditioner > & | factorize (const EigenBase< MatrixDerived > &A) |
| ComputationInfo | info () const |
| Index | iterations () const |
| IterativeSolverBase () | |
| IterativeSolverBase (const EigenBase< MatrixDerived > &A) | |
| Index | maxIterations () const |
| Preconditioner & | preconditioner () |
| const Preconditioner & | preconditioner () const |
| Index | rows () const |
| 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< BiCGSTAB< _MatrixType, _Preconditioner > > | |
| void | _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const |
| BiCGSTAB< _MatrixType, _Preconditioner > & | derived () |
| const BiCGSTAB< _MatrixType, _Preconditioner > & | derived () const |
| const Solve< BiCGSTAB< _MatrixType, _Preconditioner >, Rhs > | solve (const MatrixBase< Rhs > &b) const |
| const Solve< BiCGSTAB< _MatrixType, _Preconditioner >, Rhs > | solve (const SparseMatrixBase< Rhs > &b) const |
| SparseSolverBase () | |
| ~SparseSolverBase () | |
Private Types | |
| typedef IterativeSolverBase< BiCGSTAB > | Base |
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 |
| Index | m_iterations |
| MatrixWrapper | m_matrixWrapper |
| Index | m_maxIterations |
| Preconditioner | m_preconditioner |
| RealScalar | m_tolerance |
| Protected Attributes inherited from Eigen::SparseSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > > | |
| 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
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 TopicMultiThreading for details.
This class can be used as the direct solver classes. Here is a typical usage example:
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 113 of file BiCGSTAB.h.
Member Typedef Documentation
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private |
Definition at line 160 of file BiCGSTAB.h.
| typedef _MatrixType Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::MatrixType |
Definition at line 167 of file BiCGSTAB.h.
| typedef _Preconditioner Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Preconditioner |
Definition at line 170 of file BiCGSTAB.h.
| typedef MatrixType::RealScalar Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::RealScalar |
Definition at line 169 of file BiCGSTAB.h.
| typedef MatrixType::Scalar Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Scalar |
Definition at line 168 of file BiCGSTAB.h.
Constructor & Destructor Documentation
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inline |
Default constructor.
Definition at line 175 of file BiCGSTAB.h.
|
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 188 of file BiCGSTAB.h.
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inline |
Definition at line 190 of file BiCGSTAB.h.
Member Function Documentation
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inline |
Definition at line 215 of file BiCGSTAB.h.
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inline |
Definition at line 194 of file BiCGSTAB.h.
The documentation for this class was generated from the following file: