Detailed Description

template<typename MatrixType>
class gismo::gsRichardsonOp< MatrixType >

Richardson preconditioner.

Inheritance diagram for gsRichardsonOp< MatrixType >:

Collaboration diagram for gsRichardsonOp< MatrixType >:

Public Types
typedef gsPreconditionerOp< T >	Base
	Base class.

typedef gsLinearOperator< MatrixType::Scalar >::Ptr	BasePtr
	Base class.

typedef memory::shared_ptr< gsRichardsonOp >	Ptr
	Shared pointer for gsRichardsonOp.

typedef MatrixType::Scalar	T
	Scalar type.

typedef memory::unique_ptr< gsRichardsonOp >	uPtr
	Unique pointer for gsRichardsonOp.

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 \( PA \).

void	getDamping ()
	Get damping parameter.

	gsRichardsonOp (const MatrixPtr &mat, T tau=1)
	Constructor with shared pointer to matrix.

	gsRichardsonOp (const MatrixType &mat, T tau=1)
	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	setDamping (const T tau)
	Set damping parameter.

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.

virtual void	stepT (const gsMatrix< MatrixType::Scalar > &rhs, gsMatrix< MatrixType::Scalar > &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 >
gsRichardsonOp< Derived >::uPtr	makeRichardsonOp (const gsEigen::EigenBase< Derived > &mat, typename Derived::Scalar tau=1)
	Returns a smart pointer to a Richardson operator referring on mat.

template<class Derived >
gsRichardsonOp< Derived >::uPtr	makeRichardsonOp (const memory::shared_ptr< Derived > &mat, typename Derived::Scalar tau=1)
	Returns a smart pointer to a Richardson operator referring on mat.

Member Function Documentation

◆ apply()

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 >, gsINSPrecondBlockF< T, MatOrder >, gsINSPrecondBlockFwhole< T, MatOrder >, gsINSPrecondBlockFdiag< T, MatOrder >, gsINSPrecondBlockFmod< T, MatOrder >, gsINSBlockPrecondBase< T, MatOrder >, gsINSBlockPrecondSIMPLE< T, MatOrder, BlockFType >, gsINSBlockPrecondSIMPLE< T, MatOrder, gsINSPrecondBlockF< T, MatOrder > >, gsINSBlockPrecondSIMPLER< T, MatOrder, BlockFType >, gsINSBlockPrecondMSIMPLER< T, MatOrder, BlockFType >, gsBlockPrecondStokes< T, MatOrder, BlockFType >, 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 >

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()

virtual void stepT	(	const gsMatrix< MatrixType::Scalar > &	rhs,
		gsMatrix< MatrixType::Scalar > &	x
	)		const

inlinevirtualinherited

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 in gsGaussSeidelOp< MatrixType, ordering >.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Related Symbols

Member Function Documentation

◆ apply()

◆ estimateLargestEigenvalueOfPreconditionedSystem()

◆ step()

◆ stepT()