Public Types | Public Member Functions | Private Types | List of all members
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner > Class Template Reference
Sparse linear algebra » Reference » IterativeLinearSolvers_Module

A minimal residual solver for sparse symmetric problems. More...

#include <MINRES.h>

Inheritance diagram for Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >:
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Public Types

enum  { UpLo = _UpLo }
 
typedef _MatrixType MatrixType
 
typedef _Preconditioner Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
- Public Types inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
enum  
 
typedef internal::traits< MINRES< _MatrixType, _UpLo, _Preconditioner > >::MatrixType MatrixType
 
typedef internal::traits< MINRES< _MatrixType, _UpLo, _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 Rhs &b, MatrixBase< Dest > &x) const
 
template<typename Rhs , typename Dest >
void _solve_with_guess_impl (const Rhs &b, Dest &x) const
 
 MINRES ()
 
template<typename MatrixDerived >
 MINRES (const EigenBase< MatrixDerived > &A)
 
 ~MINRES ()
 
- Public Member Functions inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
void _solve_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
 
MINRES< _MatrixType, _UpLo, _Preconditioner > & analyzePattern (const EigenBase< MatrixDerived > &A)
 
Index cols () const
 
MINRES< _MatrixType, _UpLo, _Preconditioner > & compute (const EigenBase< MatrixDerived > &A)
 
RealScalar error () const
 
MINRES< _MatrixType, _UpLo, _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
 
MINRES< _MatrixType, _UpLo, _Preconditioner > & setMaxIterations (Index maxIters)
 
MINRES< _MatrixType, _UpLo, _Preconditioner > & setTolerance (const RealScalar &tolerance)
 
const SolveWithGuess< MINRES< _MatrixType, _UpLo, _Preconditioner >, Rhs, Guess > solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
 
RealScalar tolerance () const
 
 ~IterativeSolverBase ()
 
- Public Member Functions inherited from Eigen::SparseSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
void _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
 
MINRES< _MatrixType, _UpLo, _Preconditioner > & derived ()
 
const MINRES< _MatrixType, _UpLo, _Preconditioner > & derived () const
 
const Solve< MINRES< _MatrixType, _UpLo, _Preconditioner >, Rhs > solve (const MatrixBase< Rhs > &b) const
 
const Solve< MINRES< _MatrixType, _UpLo, _Preconditioner >, Rhs > solve (const SparseMatrixBase< Rhs > &b) const
 
 SparseSolverBase ()
 
 ~SparseSolverBase ()
 

Private Types

typedef IterativeSolverBase< MINRES > Base
 

Additional Inherited Members

- Protected Types inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
typedef MatrixWrapper::ActualMatrixType ActualMatrixType
 
typedef SparseSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > > Base
 
typedef internal::generic_matrix_wrapper< MatrixType > MatrixWrapper
 
- Protected Member Functions inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
void grab (const InputType &A)
 
void init ()
 
const ActualMatrixType & matrix () const
 
- Protected Attributes inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _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< MINRES< _MatrixType, _UpLo, _Preconditioner > >
bool m_isInitialized
 

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
class Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >

A minimal residual solver for sparse symmetric problems.

This class allows to solve for A.x = b sparse linear problems using the MINRES algorithm of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite). The vectors x and b can be either dense or sparse.

Template Parameters
_MatrixTypethe type of the sparse matrix A, can be a dense or a sparse matrix.
_UpLothe triangular part that will be used for the computations. It can be Lower, Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.
_Preconditionerthe 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.

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
MINRES<SparseMatrix<double> > mr;
mr.compute(A);
x = mr.solve(b);
std::cout << "#iterations: " << mr.iterations() << std::endl;
std::cout << "estimated error: " << mr.error() << std::endl;
// update b, and solve again
x = mr.solve(b);

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

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

See also
class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 147 of file MINRES.h.

Member Typedef Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
typedef IterativeSolverBase<MINRES> Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Base
private

Definition at line 202 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
typedef _MatrixType Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MatrixType

Definition at line 210 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
typedef _Preconditioner Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Preconditioner

Definition at line 213 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
typedef MatrixType::RealScalar Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::RealScalar

Definition at line 212 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
typedef MatrixType::Scalar Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Scalar

Definition at line 211 of file MINRES.h.

Member Enumeration Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
anonymous enum
Enumerator
UpLo 

Definition at line 215 of file MINRES.h.

Constructor & Destructor Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES ( )
inline

Default constructor.

Definition at line 220 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
template<typename MatrixDerived >
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES ( 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 233 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::~MINRES ( )
inline

Destructor.

Definition at line 236 of file MINRES.h.

Member Function Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
template<typename Rhs , typename Dest >
void Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::_solve_impl ( const Rhs &  b,
MatrixBase< Dest > &  x 
) const
inline

Definition at line 276 of file MINRES.h.

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
template<typename Rhs , typename Dest >
void Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::_solve_with_guess_impl ( const Rhs &  b,
Dest &  x 
) const
inline

Definition at line 240 of file MINRES.h.

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

gtsam
Author(s):
autogenerated on Sat May 8 2021 02:53:23