Public Types | Public Member Functions | Private Types
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

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

#include <MINRES.h>

Inheritance diagram for Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >:
Inheritance graph
[legend]

List of all members.

Public Types

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

Public Member Functions

template<typename Rhs , typename Dest >
void _solve (const Rhs &b, Dest &x) const
template<typename Rhs , typename Dest >
void _solveWithGuess (const Rhs &b, Dest &x) const
 MINRES ()
 MINRES (const MatrixType &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 ()

Private Types

typedef IterativeSolverBase
< MINRES
Base

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 or Upper. 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. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error: *

 x = VectorXd::Random(n);
 mr.setMaxIterations(1);
 int i = 0;
 do {
   x = mr.solveWithGuess(b,x);
   std::cout << i << " : " << mr.error() << std::endl;
   ++i;
 } while (mr.info()!=Success && i<100);

Note that such a step by step excution is slightly slower.

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

Definition at line 195 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 198 of file MINRES.h.

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

Member Enumeration Documentation

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

Definition at line 211 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 216 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES ( const MatrixType A) [inline]

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 228 of file MINRES.h.

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

Destructor.

Definition at line 231 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 ( const Rhs &  b,
Dest &  x 
) const [inline]

Definition at line 272 of file MINRES.h.

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

Definition at line 251 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >
template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess<MINRES, Rhs, Guess> Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::solveWithGuess ( const MatrixBase< Rhs > &  b,
const Guess &  x0 
) const [inline]
Returns:
the solution x of $ A x = b $ using the current decomposition of A x0 as an initial solution.
See also:
compute()

Definition at line 240 of file MINRES.h.


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


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Thu Aug 27 2015 12:02:00