The gmres algorithm. -*- c++ -*-. More...

#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/vector_of_vector.hpp>
#include <boost/numeric/ublas/vector_expression.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/operation_sparse.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/banded.hpp>

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Functions
template<class Vector >
std::vector< Vector >	orthogonal_system (std::vector< Vector > &basis)
	returns the orthogonal system of a given set of vectors More...

template<class Vector >
Vector	orthogonal_vector (std::vector< Vector > &basis, Vector &v)
	preforms the orthogonalization of a given vector to a given basis using the arnoldi approach More...

template<class Matrix , class Vector >
Vector	arnoldi_step (std::vector< Vector > &q, Matrix &A, Matrix &H, int n)
	preforms the orthogonalization of a given vector to a given basis using the arnoldi approach the basis is represented as a matrix More...

template<class Matrix , class Vector >
void	gmres (const Matrix &A, Vector &x, const Vector &b, double tol)
	the standard gmres algorithm, without linear operator or any improvements More...

template<class Matrix , class LinOp , class Vector , class Precond >
unsigned int	gmres_step (LinOp const &A, Vector &x, const Vector &b, Precond const &B, unsigned int const maxiter, double const tol)
	a single step of the gmres algorithm, one iteration. Returns true if the approach converges. More...

template<class Matrix , class LinOp , class Vector , class Precond >
int	gmres_restarts (LinOp const &A, Vector &x, const Vector &b, Precond const &B, unsigned int const maxiter, unsigned int const nrestarts, double const tol)
	the gmres algorithm restarting after maxiter steps. nrestarts is the number of the allowed restarts More...

template<class Matrix , class LinOp , class Vector , class Precond >
int	gmres_short (LinOp const &A, Vector &x, const Vector &b, Precond const &B, int number, int maxiter, double tol)
	/QGMRES. Only the last "number" vectors are taken into account, i.e. the orthogonalization depends only on the last number vectors. More...

Detailed Description

The gmres algorithm. -*- c++ -*-.

Function Documentation

template<class Matrix , class Vector >

Vector arnoldi_step	(	std::vector< Vector > &	q,
		Matrix &	A,
		Matrix &	H,
		int	n
	)

preforms the orthogonalization of a given vector to a given basis using the arnoldi approach the basis is represented as a matrix

Parameters

Vector is the type of the vectors
Parameters

Matrix is the type of the matrix

template<class Matrix , class Vector >

void gmres	(	const Matrix &	A,
		Vector &	x,
		const Vector &	b,
		double	tol
	)

the standard gmres algorithm, without linear operator or any improvements

Parameters

Vector is the type of the vectors
Parameters

Matrix is the type of the matrix
Note
the input parameter x must be predefined

template<class Matrix , class LinOp , class Vector , class Precond >

int gmres_restarts	(	LinOp const &	A,
		Vector &	x,
		const Vector &	b,
		Precond const &	B,
		unsigned int const	maxiter,
		unsigned int const	nrestarts,
		double const	tol
	)

the gmres algorithm restarting after maxiter steps. nrestarts is the number of the allowed restarts

Parameters

LinOp is the type of the linear opeartor representing the matrix
Parameters

Vector is the type of the vectors
Parameters

Matrix is the type of the matrix
Parameters

Precond is the type of the used preconditioner
Note
the input parameter x must be predefined

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template<class Matrix , class LinOp , class Vector , class Precond >

int gmres_short	(	LinOp const &	A,
		Vector &	x,
		const Vector &	b,
		Precond const &	B,
		int	number,
		int	maxiter,
		double	tol
	)

/QGMRES. Only the last "number" vectors are taken into account, i.e. the orthogonalization depends only on the last number vectors.

The solution x is updated at the end of each iteration.
Parameters

LinOp is the type of the linear opeartor representing the matrix
Parameters

Vector is the type of the vectors
Parameters

Matrix is the type of the matrix
Parameters

Precond is the type of the used preconditioner
Note
the input parameter x must be predefined

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template<class Matrix , class LinOp , class Vector , class Precond >

unsigned int gmres_step	(	LinOp const &	A,
		Vector &	x,
		const Vector &	b,
		Precond const &	B,
		unsigned int const	maxiter,
		double const	tol
	)

a single step of the gmres algorithm, one iteration. Returns true if the approach converges.

Parameters

LinOp is the type of the linear opeartor representing the matrix
Parameters

Vector is the type of the vectors
Parameters

Matrix is the type of the matrix
Parameters

Precond is the type of the used preconditioner
Note
the input parameter x must be predefined, assume maxiter < A.image_size()

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template<class Vector >

std::vector< Vector > orthogonal_system ( std::vector< Vector > & basis )

returns the orthogonal system of a given set of vectors

Parameters

Vector is the type of the vectors

template<class Vector >

Vector orthogonal_vector	(	std::vector< Vector > &	basis,
		Vector &	v
	)

preforms the orthogonalization of a given vector to a given basis using the arnoldi approach

Parameters

Vector is the type of the vectors

Functions

Detailed Description

Function Documentation