Eigen::MINRES< MatrixType_, UpLo_, Preconditioner_ > Class Template Reference

#include <Eigen/src/IterativeLinearSolvers/MINRES.h>

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

MatrixType_	the type of the sparse matrix A, can be a dense or a sparse matrix.
UpLo_	the 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.
Preconditioner_	the type of the preconditioner. Default is IdentityPreconditioner

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are twice the number of columns of the matrix 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

Inheritance diagram for Eigen::MINRES< MatrixType_, UpLo_, Preconditioner_ >:

Public Member Functions
	MINRES ()
template<typename MatrixDerived>
	MINRES (const EigenBase< MatrixDerived > &A)
Public Member Functions inherited from Eigen::IterativeSolverBase< MINRES< MatrixType_, UpLo_, Preconditioner_ > >
MINRES< MatrixType_, UpLo_, Preconditioner_ > &	analyzePattern (const EigenBase< MatrixDerived > &A)
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
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
void	solveWithGuessInPlace (const Rhs &b, Dest &x) const
RealScalar	tolerance () const
Public Member Functions inherited from Eigen::SparseSolverBase< MINRES< MatrixType_, UpLo_, Preconditioner_ > >
Solve< MINRES< MatrixType_, UpLo_, Preconditioner_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
Solve< MINRES< MatrixType_, UpLo_, Preconditioner_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()=default

Constructor & Destructor Documentation

MINRES() [1/2]

template<typename MatrixType_, int UpLo_, typename Preconditioner_>

Eigen::MINRES< MatrixType_, UpLo_, Preconditioner_ >::MINRES ( )

inline

Default constructor.

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.

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

• /builds/libeigen/eigen/Eigen/src/IterativeLinearSolvers/MINRES.h