Public Types | Public Member Functions | Private Types | Private Member Functions | Private Attributes | List of all members
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

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

#include <MINRES.h>

Public Types

enum  { UpLo = _UpLo }
 
typedef _MatrixType MatrixType
 
typedef _Preconditioner Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 

Public Member Functions

template<typename Rhs , typename Dest >
void _solve_impl (const Rhs &b, Dest &x) const
 
template<typename Rhs , typename Dest >
void _solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
 
 MINRES ()
 
template<typename MatrixDerived >
 MINRES (const EigenBase< MatrixDerived > &A)
 
 ~MINRES ()
 

Private Types

typedef IterativeSolverBase< MINRESBase
 

Private Member Functions

const ActualMatrixType & matrix () const
 

Private Attributes

RealScalar m_error
 
ComputationInfo m_info
 
bool m_isInitialized
 
Index m_iterations
 

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 143 of file MINRES.h.

Member Typedef Documentation

◆ Base

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

Definition at line 198 of file MINRES.h.

◆ MatrixType

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

Definition at line 206 of file MINRES.h.

◆ Preconditioner

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

Definition at line 209 of file MINRES.h.

◆ RealScalar

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

Definition at line 208 of file MINRES.h.

◆ Scalar

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

Definition at line 207 of file MINRES.h.

Member Enumeration Documentation

◆ anonymous enum

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

Definition at line 211 of file MINRES.h.

Constructor & Destructor Documentation

◆ MINRES() [1/2]

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

Default constructor.

Definition at line 216 of file MINRES.h.

◆ MINRES() [2/2]

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 229 of file MINRES.h.

◆ ~MINRES()

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

Destructor.

Definition at line 232 of file MINRES.h.

Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
template<typename Rhs , typename Dest >
void Eigen::IterativeSolverBase< Derived >::_solve_impl ( typename Rhs  ,
typename Dest   
)
inline

Definition at line 400 of file IterativeSolverBase.h.

◆ _solve_vector_with_guess_impl()

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

Definition at line 236 of file MINRES.h.

◆ matrix()

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
const ActualMatrixType& Eigen::IterativeSolverBase< Derived >::matrix
inlineprivate

Definition at line 419 of file IterativeSolverBase.h.

Member Data Documentation

◆ m_error

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
RealScalar Eigen::IterativeSolverBase< Derived >::m_error
mutableprivate

Definition at line 436 of file IterativeSolverBase.h.

◆ m_info

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info
mutableprivate

Definition at line 438 of file IterativeSolverBase.h.

◆ m_isInitialized

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
bool Eigen::SparseSolverBase< Derived >::m_isInitialized
mutableprivate

Definition at line 119 of file SparseSolverBase.h.

◆ m_iterations

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
Index Eigen::IterativeSolverBase< Derived >::m_iterations
mutableprivate

Definition at line 437 of file IterativeSolverBase.h.


The documentation for this class was generated from the following file:
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Scalar * b
Definition: benchVecAdd.cpp:17
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Definition: gnuplot_common_settings.hh:12
n
int n
Definition: BiCGSTAB_simple.cpp:1
A
Definition: test_numpy_dtypes.cpp:298


gtsam
Author(s):
autogenerated on Fri Nov 1 2024 03:45:23