gsPreconditionerFromOp< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsPreconditionerFromOp< T >

Simple class allowing to construct a preconditioner from a linear operator.

The class represents an iteration method in the form

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

Warning

The implemenation pf stepT assumes that P is symmetric.

Inheritance diagram for gsPreconditionerFromOp< T >:

Collaboration diagram for gsPreconditionerFromOp< T >:

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

Public Member Functions
void	apply (const gsMatrix< T > &rhs, gsMatrix< T > &x) const
	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.
T	estimateLargestEigenvalueOfPreconditionedSystem (index_t steps=10) const
	Estimates the largest eigenvalue of \( PA \).
T	getDamping () const
	Get damping parameter.
	gsPreconditionerFromOp (BasePtr underlying, BasePtr preconditioner, T tau=(T) 1)
	Constructor.
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.
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< T > &rhs, gsMatrix< T > &x) const
	Apply the transposed variant of the method for given right hand side and current iterate.
BasePtr	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.
static uPtr	make (BasePtr underlying, BasePtr preconditioner, T tau=(T) 1)
	Make function returning a smart pointer.

Constructor & Destructor Documentation

gsPreconditionerFromOp()

template<class T >

gsPreconditionerFromOp ( BasePtr  underlying, BasePtr  preconditioner, T  tau = (T)1  )

inline

Constructor.

Parameters

underlying	The underlying operator \( A \).
preconditioner	The operator \( P \) to be used as preconditioner.
tau	A damping parameter, defaulted to 1.

Member Function Documentation

apply()

template<class T >

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 >.

estimateLargestEigenvalueOfPreconditionedSystem()

template<class T >

T estimateLargestEigenvalueOfPreconditionedSystem ( index_t  steps = 10 ) const

inlineinherited

Estimates the largest eigenvalue of \( PA \).

Parameters

steps

Number of steps to be performed.

make()

template<class T >

static uPtr make ( BasePtr  underlying, BasePtr  preconditioner, T  tau = (T)1  )

inlinestatic

Make function returning a smart pointer.

Parameters

underlying	The underlying operator \( A \).
preconditioner	The underlying preconditioner \( P \).
tau	A damping parameter, defaulted to 1.

step()

template<class T >

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< T >.

stepT()

template<class T >

virtual void stepT ( const gsMatrix< T > &  rhs, gsMatrix< T > &  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 gsCompositePrecOp< T >, gsGaussSeidelOp< MatrixType, ordering >, and gsMultiGridOp< T >.