 Eigen-unsupported  3.3.7 Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

## 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 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 .

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)

~MINRES ()

## ◆ 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.

## ◆ ~MINRES()

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

Destructor.

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