MINRES< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

Detailed Description

template<typename _MatrixType, int _UpLo = Lower, typename _Preconditioner = IdentityPreconditioner>
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 or Upper. Default is Lower.
_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.

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.

See Also

class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Inherits IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >.

Public Member Functions
	MINRES ()
template<typename MatrixDerived >
	MINRES (const EigenBase< MatrixDerived > &A)
template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess < MINRES, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
	~MINRES ()

Constructor & Destructor Documentation

MINRES ( )

inline

Default constructor.

Referenced by MINRES< _MatrixType, _UpLo, _Preconditioner >::solveWithGuess().

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.

~MINRES ( )

inline

Destructor.

Member Function Documentation

const internal::solve_retval_with_guess<MINRES, Rhs, Guess> solveWithGuess ( const MatrixBase< Rhs > &  b, const Guess &  x0  ) const

inline

Returns

the solution x of using the current decomposition of A x0 as an initial solution.

See Also

compute()

References MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES().

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

• MINRES.h