Weighted diagonal preconditioner for the binary Wavelets. More...

#include <operator.hh>

Inheritance diagram for aglowav::CGt2< F >:

Collaboration diagram for aglowav::CGt2< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
typedef Realtype< F >::type	r_type
	Real type of data type.
typedef F	type
	Type of data, e.g. matrix entries.
Public Member Functions
	CGt2 (const Haar3d< F > &spc, concepts::Real t)
	Constructor.
virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix)
virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix)
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator for real function `fncY`.
void	operator() (const concepts::Function< F > &fncY, concepts::Function< F > &fncX)
	Matrix vector multiplication.
void	operator() (const concepts::Vector< F > &fncY, concepts::Vector< F > &fncX)
const Haar3d< F > &	spaceX () const
	Spaces of the transformation.
const Haar3d< F > &	spaceY () const
Protected Member Functions
std::ostream &	info (std::ostream &os) const
	Information about the operator.
Protected Attributes
uint	dimX_
	Dimension of image space and the source space.
uint	dimY_
Private Attributes
const Haar3d< F > &	spc_
	Spaces of the transformation.
concepts::Real	t_
std::vector< concepts::Real >	val_
	Values of the diagonal entries.

Detailed Description

template<class F = concepts::Real>
class aglowav::CGt2< F >

Weighted diagonal preconditioner for the binary Wavelets.

The weights are $\left( \frac{\Gamma_{l,j}}{\Gamma_{0,0}} \right)^{t/2}$ where $t$ is a parameter ( $-1/2 < t \leq 0$ normally) and $\Gamma_{0,0}$ the support size on top level and $\Gamma_{l,j}$ the support size of the wavelet $\psi_{l,j}$ . param F Field (Real or Cmplx)

Definition at line 205 of file operator.hh.

Member Typedef Documentation

template<class F>

typedef Cmplxtype<F>::type concepts::Operator< F >::c_type [inherited]

Real type of data type.

Reimplemented in concepts::VecOperator< F >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::DiagonalSolver< F >, concepts::Matrix< F >, concepts::Permutation< F >, concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::Transpose< F >, concepts::VecOperator< Real >, concepts::DenseMatrix< Cmplx >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< concepts::Real >, concepts::Matrix< F::type >, concepts::Matrix< FX >, concepts::Matrix< T >, concepts::Matrix< Cmplx >, concepts::Matrix< Real >, concepts::Permutation< Real >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 47 of file compositions.hh.

template<class F>

typedef Realtype<F>::type concepts::Operator< F >::r_type [inherited]

Real type of data type.

Reimplemented in concepts::VecOperator< F >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::DiagonalSolver< F >, concepts::Matrix< F >, concepts::Permutation< F >, concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::Transpose< F >, concepts::VecOperator< Real >, concepts::DenseMatrix< Cmplx >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< concepts::Real >, concepts::Matrix< F::type >, concepts::Matrix< FX >, concepts::Matrix< T >, concepts::Matrix< Cmplx >, concepts::Matrix< Real >, concepts::Permutation< Real >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 45 of file compositions.hh.

template<class F>

typedef F concepts::Operator< F >::type [inherited]

Type of data, e.g. matrix entries.

Reimplemented in concepts::AfterIteration< F >, and concepts::SubMatrixN< F >.

Definition at line 43 of file compositions.hh.

Constructor & Destructor Documentation

template<class F = concepts::Real>

aglowav::CGt2< F >::CGt2	(	const Haar3d< F > &	spc,
		concepts::Real	t
	)

Constructor.

Member Function Documentation

template<class F>

virtual const uint concepts::Operator< F >::dimX ( ) const [inline, virtual, inherited]

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Definition at line 87 of file compositions.hh.

template<class F>

virtual const uint concepts::Operator< F >::dimY ( ) const [inline, virtual, inherited]

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Definition at line 92 of file compositions.hh.

template<class F = concepts::Real>

std::ostream& aglowav::CGt2< F >::info ( std::ostream & os ) const [protected, virtual]

Information about the operator.

Reimplemented from concepts::Operator< F >.

template<class F>

virtual void concepts::Operator< F >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)		`[virtual, inherited]`

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function fncY is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< F >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::DiagonalSolver< F >, concepts::Matrix< F >, concepts::Permutation< F >, concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::Transpose< F >, concepts::VecOperator< Real >, concepts::DenseMatrix< Cmplx >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< concepts::Real >, concepts::Matrix< F::type >, concepts::Matrix< FX >, concepts::Matrix< T >, concepts::Matrix< Cmplx >, concepts::Matrix< Real >, concepts::Permutation< Real >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

template<class F = concepts::Real>

void aglowav::CGt2< F >::operator()	(	const concepts::Function< F > &	fncY,
		concepts::Function< F > &	fncX
	)

Matrix vector multiplication.

Exceptions:

MissingFeature

template<class F = concepts::Real>

void aglowav::CGt2< F >::operator()	(	const concepts::Vector< F > &	fncY,
		concepts::Vector< F > &	fncX
	)

template<class F>

virtual void concepts::Operator< F >::operator()	(	const Function< r_type > &	fncY,
		Function< F > &	fncX
	)		`[virtual, inherited]`

Application operator for real function fncY.

Computes fncX = A(fncY) where A is this operator.

fncX becomes the type of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the function fncY is transformed to a complex function and then the application operator for complex functions is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

Reimplemented in concepts::VecOperator< F >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::DiagonalSolver< F >, concepts::Matrix< F >, concepts::Permutation< F >, concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::Transpose< F >, concepts::VecOperator< Real >, concepts::DenseMatrix< Cmplx >, concepts::DenseMatrix< Real >, concepts::DiagonalMatrix< Real >, concepts::Matrix< concepts::Real >, concepts::Matrix< F::type >, concepts::Matrix< FX >, concepts::Matrix< T >, concepts::Matrix< Cmplx >, concepts::Matrix< Real >, concepts::Permutation< Real >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

template<class F = concepts::Real>

const Haar3d<F>& aglowav::CGt2< F >::spaceX ( ) const [inline]

Spaces of the transformation.

Definition at line 218 of file operator.hh.

template<class F = concepts::Real>

const Haar3d<F>& aglowav::CGt2< F >::spaceY ( ) const [inline]

Definition at line 219 of file operator.hh.

Member Data Documentation

template<class F>

uint concepts::Operator< F >::dimX_ [protected, inherited]

Dimension of image space and the source space.

Definition at line 96 of file compositions.hh.

template<class F>

uint concepts::Operator< F >::dimY_ [protected, inherited]

Definition at line 96 of file compositions.hh.

template<class F = concepts::Real>

const Haar3d<F>& aglowav::CGt2< F >::spc_ [private]

Spaces of the transformation.

Definition at line 227 of file operator.hh.

template<class F = concepts::Real>

concepts::Real aglowav::CGt2< F >::t_ [private]

Definition at line 228 of file operator.hh.

template<class F = concepts::Real>

std::vector<concepts::Real> aglowav::CGt2< F >::val_ [private]

Values of the diagonal entries.

Definition at line 230 of file operator.hh.

The documentation for this class was generated from the following file:

aglowav/operator.hh

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

template<class F = concepts::Real> class aglowav::CGt2< F >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class F = concepts::Real>
class aglowav::CGt2< F >