gsPreconditionerOp< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsPreconditionerOp< T >

Simple abstract class for perconditioners.

The class represents an iteration method in the form

\( x_{new} = x_{old} + P(f - A*x_{old}).\)

If the number of steps is set to 1, the member function apply represents the application of \( P \). If setNumOfSweeps is used to set the number of sweeps to some \( \nu>0 \), the member function apply realizes \( I-(I-PA)^{\nu} A^{-1} \). The same interpretation applies if the object is used as a gsLinearOperator.

The member function step represents one step of the above iteration method.

Usually, the step operation can be performed in an optimized way.

The derived classes have to contain the functions: step, stepT, rows, cols.

Inheritance diagram for gsPreconditionerOp< T >:

Collaboration diagram for gsPreconditionerOp< T >:

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

Public Member Functions
void	apply (const gsMatrix< T > &input, gsMatrix< T > &x) const
	apply the operator on the input vector and store the result in x More...
virtual index_t	cols () const =0
	Returns the number of columns of the operator.
T	estimateLargestEigenvalueOfPreconditionedSystem (index_t steps=10) const
	Estimates the largest eigenvalue of \( PA \). More...
index_t	numOfSweeps ()
	Get the number of sweeps to be applied in the member function apply.
virtual index_t	rows () const =0
	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.
virtual void	step (const gsMatrix< T > &rhs, gsMatrix< T > &x) const =0
	Apply the method for given right hand side and current iterate. More...
virtual 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. More...
virtual BasePtr	underlyingOp () const =0
	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.

Member Function Documentation

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

inlinevirtual

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

Parameters

input	Input vector
x	result vector

Implements gsLinearOperator< T >.

Reimplemented in gsPreconditionerFromOp< T >.

T estimateLargestEigenvalueOfPreconditionedSystem ( index_t  steps = 10 ) const

inline

Estimates the largest eigenvalue of \( PA \).

Parameters

steps

Number of steps to be performed.

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

pure virtual

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

Parameters

rhs	Right hand side vector
x	Current iterate vector

Implemented in gsIncompleteLUOp< MatrixType >, gsGaussSeidelOp< MatrixType, ordering >, gsMultiGridOp< T >, gsPreconditionerFromOp< T >, gsJacobiOp< MatrixType >, gsCompositePrecOp< T >, and gsRichardsonOp< MatrixType >.

virtual 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 in gsGaussSeidelOp< MatrixType, ordering >, gsMultiGridOp< T >, and gsCompositePrecOp< T >.