gsGaussSeidelOp< MatrixType, ordering > Class Template Reference

Detailed Description

template<typename MatrixType, gsGaussSeidel::ordering ordering = gsGaussSeidel::forward>
class gismo::gsGaussSeidelOp< MatrixType, ordering >

Gauss-Seidel preconditioner.

ordering can be gsGaussSeidel::forward, gsGaussSeidel::reverse or gsGaussSeidel::symmetric.

Inheritance diagram for gsGaussSeidelOp< MatrixType, ordering >:

Collaboration diagram for gsGaussSeidelOp< MatrixType, ordering >:

Public Types
typedef gsPreconditionerOp< T >	Base
	Base class.
typedef gsLinearOperator< MatrixType::Scalar >::Ptr	BasePtr
	Base class.
typedef memory::shared_ptr< gsGaussSeidelOp >	Ptr
	Shared pointer for gsGaussSeidelOp.
typedef MatrixType::Scalar	T
	Scalar type.
typedef memory::unique_ptr< gsGaussSeidelOp >	uPtr
	Unique pointer for gsGaussSeidelOp.

Public Member Functions
virtual void	apply (const gsMatrix< T > &input, gsMatrix< T > &x) const =0
	apply the operator on the input vector and store the result in x
index_t	cols () const
	Returns the number of columns of the operator.
MatrixType::Scalar	estimateLargestEigenvalueOfPreconditionedSystem (index_t steps=10) const
	Estimates the largest eigenvalue of \( PA \).
	gsGaussSeidelOp (const MatrixPtr &mat)
	Constructor with shared pointer to matrix.
	gsGaussSeidelOp (const MatrixType &mat)
	Constructor with given matrix.
NestedMatrix	matrix () const
	Returns the matrix.
MatrixPtr	matrixPtr () const
	Returns a shared pinter to the matrix.
index_t	numOfSweeps ()
	Get the number of sweeps to be applied in the member function apply.
index_t	rows () const
	Returns the number of rows of the operator.
void	setNumOfSweeps (index_t n)
	Set the number of sweeps to be applied in the member function apply.
virtual void	setOptions (const gsOptionList &opt)
	Set options based on a gsOptionList object.
void	step (const gsMatrix< T > &rhs, gsMatrix< T > &x) const
	Apply the method for given right hand side and current iterate.
void	stepT (const gsMatrix< T > &rhs, gsMatrix< T > &x) const
	Apply the transposed variant of the method for given right hand side and current iterate.
gsLinearOperator< T >::Ptr	underlyingOp () const
	Return the underlying operator \( A \).

Static Public Member Functions
static gsOptionList	defaultOptions ()
	Get the default options as gsOptionList object.
static gsIdentityOp< T >	Identity (const index_t dim)
	Identity operator.

Private Attributes
NestedMatrix	m_expr
	Nested Eigen expression.
const MatrixPtr	m_mat
	Shared pointer to matrix (if needed)

Related Symbols
(Note that these are not member symbols.)
template<class Derived >
gsGaussSeidelOp< Derived >::uPtr	makeGaussSeidelOp (const gsEigen::EigenBase< Derived > &mat)
	Returns a smart pointer to a Gauss-Seidel operator referring on mat.
template<class Derived >
gsGaussSeidelOp< Derived >::uPtr	makeGaussSeidelOp (const memory::shared_ptr< Derived > &mat)
	Returns a smart pointer to a Jacobi operator referring on mat.
template<class Derived >
gsGaussSeidelOp< Derived, gsGaussSeidel::reverse >::uPtr	makeReverseGaussSeidelOp (const gsEigen::EigenBase< Derived > &mat)
	Returns a smart pointer to a reverse Gauss-Seidel operator referring on mat.
template<class Derived >
gsGaussSeidelOp< Derived, gsGaussSeidel::reverse >::uPtr	makeReverseGaussSeidelOp (const memory::shared_ptr< Derived > &mat)
	Returns a smart pointer to a reverse Gauss-Seidel operator referring on mat.
template<class Derived >
gsGaussSeidelOp< Derived, gsGaussSeidel::symmetric >::uPtr	makeSymmetricGaussSeidelOp (const gsEigen::EigenBase< Derived > &mat)
	Returns a smart pointer to a symmetric Gauss-Seidel operator referring on mat.
template<class Derived >
gsGaussSeidelOp< Derived, gsGaussSeidel::symmetric >::uPtr	makeSymmetricGaussSeidelOp (const memory::shared_ptr< Derived > &mat)
	Returns a smart pointer to a symmetric Gauss-Seidel operator referring on mat.

Member Function Documentation

apply() [1/2]

void apply ( const gsMatrix< MatrixType::Scalar > &  input, gsMatrix< MatrixType::Scalar > &  x  ) const

inlineinherited

apply the operator on the input vector and store the result in x

Parameters

input	Input vector
x	result vector

apply() [2/2]

template<class T >

virtual void apply ( const gsMatrix< T > &  input, gsMatrix< T > &  x  ) const

pure virtualinherited

apply the operator on the input vector and store the result in x

Parameters

input	Input vector
x	result vector

Implemented in gsIterativeSolverOp< SolverType >, gsBlockOp< T >, gsAdditiveOp< T >, gsKroneckerOp< T >, gsScaledOp< T >, gsIdentityOp< T >, gsLinearLambdaOp< T, L >, gsMatrixOp< MatrixType >, gsSolverOp< SolverType >, gsPreconditionerOp< T >, gsProductOp< T >, gsSumOp< T >, and gsPreconditionerFromOp< T >.

estimateLargestEigenvalueOfPreconditionedSystem()

MatrixType::Scalar estimateLargestEigenvalueOfPreconditionedSystem ( index_t  steps = 10 ) const

inlineinherited

Estimates the largest eigenvalue of \( PA \).

Parameters

steps

Number of steps to be performed.

step()

template<typename MatrixType , gsGaussSeidel::ordering ordering = gsGaussSeidel::forward>

void step ( const gsMatrix< T > &  rhs, gsMatrix< T > &  x  ) const

inlinevirtual

Apply the method for given right hand side and current iterate.

Parameters

rhs	Right hand side vector
x	Current iterate vector

Implements gsPreconditionerOp< MatrixType::Scalar >.

stepT()

template<typename MatrixType , gsGaussSeidel::ordering ordering = gsGaussSeidel::forward>

void stepT ( const gsMatrix< T > &  rhs, gsMatrix< T > &  x  ) const

inlinevirtual

Apply the transposed variant of the method for given right hand side and current iterate.

Parameters

rhs	Right hand side vector
x	Current iterate vector

Warning

Derived classes must overwrite this virtual function if the preconditioner is not symmetric.

Reimplemented from gsPreconditionerOp< MatrixType::Scalar >.