A class for wrapping a CrsMatrix multiply in a Operator. More...

#include <Tpetra_CrsMatrixMultiplyOp.hpp>

Inheritance diagram for Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >:

Public Types
typedef CrsMatrix< MatScalar, LocalOrdinal, GlobalOrdinal, Node >	crs_matrix_type
	The specialization of CrsMatrix which this class wraps. More...

typedef Map< LocalOrdinal, GlobalOrdinal, Node >	map_type
	The specialization of Map which this class uses. More...

Typedefs that give access to the template parameters.
typedef Scalar	scalar_type
	The type of the entries of the input and output multivectors. More...

typedef LocalOrdinal	local_ordinal_type
	The local index type. More...

typedef GlobalOrdinal	global_ordinal_type
	The global index type. More...

typedef Node	node_type
	The Kokkos Node type. More...

Public Member Functions
Constructor and destructor
	CrsMatrixMultiplyOp (const Teuchos::RCP< const crs_matrix_type > &A)
	Constructor. More...

virtual	~CrsMatrixMultiplyOp ()
	Destructor (virtual for memory safety of derived classes). More...

Methods implementing Operator
void	apply (const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &X, MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &Y, Teuchos::ETransp mode=Teuchos::NO_TRANS, Scalar alpha=Teuchos::ScalarTraits< Scalar >::one(), Scalar beta=Teuchos::ScalarTraits< Scalar >::zero()) const
	Compute `Y = betaY + alphaOp(A)*X`, where `Op(A)` is either A, , or . More...

void	gaussSeidel (const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &B, MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &X, const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &D, const Scalar &dampingFactor, const ESweepDirection direction, const int numSweeps) const
	"Hybrid" Jacobi + (Gauss-Seidel or SOR) on . More...

void	gaussSeidelCopy (MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &X, const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &B, const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &D, const Scalar &dampingFactor, const ESweepDirection direction, const int numSweeps) const
	Version of gaussSeidel(), with fewer requirements on X. More...

bool	hasTransposeApply () const
	Whether this Operator's apply() method can apply the transpose or conjugate transpose. More...

Teuchos::RCP< const map_type >	getDomainMap () const
	The domain Map of this Operator. More...

Teuchos::RCP< const map_type >	getRangeMap () const
	The range Map of this Operator. More...

Protected Member Functions
void	applyTranspose (const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &X_in, MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &Y_in, Teuchos::ETransp mode, Scalar alpha, Scalar beta) const
	Apply the transpose or conjugate transpose of the matrix to X_in, producing Y_in. More...

void	applyNonTranspose (const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &X_in, MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &Y_in, Scalar alpha, Scalar beta) const
	Apply the matrix (not its transpose) to X_in, producing Y_in. More...

Protected Attributes
const Teuchos::RCP< const crs_matrix_type >	matrix_
	The underlying CrsMatrix object. More...

Teuchos::RCP< MultiVector < Scalar, LocalOrdinal, GlobalOrdinal, Node > >	importMV_
	Column Map MultiVector used in apply(). More...

Teuchos::RCP< MultiVector < Scalar, LocalOrdinal, GlobalOrdinal, Node > >	exportMV_
	Row Map MultiVector used in apply(). More...

Related Functions
(Note that these are not member functions.)
template<class OpScalar , class MatScalar , class LocalOrdinal , class GlobalOrdinal , class Node >
Teuchos::RCP < CrsMatrixMultiplyOp < OpScalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node > >	createCrsMatrixMultiplyOp (const Teuchos::RCP< const CrsMatrix< MatScalar, LocalOrdinal, GlobalOrdinal, Node > > &A)
	Non-member function to create a CrsMatrixMultiplyOp. More...

Detailed Description

template<class Scalar, class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>
class Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >

A class for wrapping a CrsMatrix multiply in a Operator.

Note: Most Tpetra users do not need to use this class. It will be useful to Tpetra users who want to do mixed-precision sparse matrix-vector multiply, where the sparse matrix's entries have a different precision than that of the input and output vectors. If your sparse matrix and vectors have the same type of entries, then you don't need to use this class.

This class makes a CrsMatrix<MatScalar, ...> "look like" an Operator<Scalar, ...>, where MatScalar and Scalar may be different types. It does so by working around a limitation of C++, namely that template methods of a class can't be virtual.

Here is a detailed description of how the language issue relates to CrsMatrix. If you call the apply method of CrsMatrix, you will always get the version that takes a MultiVector<Scalar, ...> input and produces a MultiVector<Scalar, ...> output. CrsMatrix actually implements a a templated sparse matrix-vector multiply operation (its localMultiply method). It is templated on the scalar types of its input and output multivectors (DomainScalar resp. RangeScalar). However, Operator can't access this templated mat-vec method. This is because Operator::apply is virtual, and therefore cannot have a template parameter for the Scalar type of the MultiVector input and output.

Users who want to access the templated sparse mat-vec in CrsMatrix through the Operator interface may wrap the CrsMatrix in an instance of this class. This class implements an Operator that takes MultiVector<Scalar, ...> input and output, but the CrsMatrix may contain any desired type MatScalar. The type MatScalar may differ from the Scalar type of the MultiVector input and output. That works around the "no virtual template methods" issue for input and output multivectors of the same type.

Interestingly enough, CrsMatrix implements its apply method using an instance of this class with Scalar == MatScalar. CrsMatrix does not actually contain an implementation of "nonlocal" (distributed over multiple MPI processes) mat-vec; its apply defers the nonlocal part to this class' apply() method. The same is true for the gaussSeidel() method.

Template Parameters

Scalar	The type of the entries of the input and output MultiVector of the apply() method. Same as the first template parameter of Operator.
MatScalar	The type of the entries of the CrsMatrix; the first template parameter of CrsMatrix.
LocalOrdinal	The type of the local indices of the CrsMatrix; the second template parameter of CrsMatrix and Operator.
GlobalOrdinal	The type of the global indices of the CrsMatrix; the third template parameter of CrsMatrix and Operator.
Node	The fourth template parameter of CrsMatrix and Operator.

Definition at line 126 of file Tpetra_CrsMatrixMultiplyOp.hpp.

Member Typedef Documentation

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

typedef CrsMatrix<MatScalar, LocalOrdinal, GlobalOrdinal, Node> Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::crs_matrix_type

The specialization of CrsMatrix which this class wraps.

Definition at line 131 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

typedef Map<LocalOrdinal, GlobalOrdinal, Node> Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::map_type

The specialization of Map which this class uses.

Definition at line 133 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>

typedef Scalar Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >::scalar_type

inherited

The type of the entries of the input and output multivectors.

Definition at line 92 of file Tpetra_Operator.hpp.

template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>

typedef LocalOrdinal Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >::local_ordinal_type

inherited

The local index type.

Definition at line 95 of file Tpetra_Operator.hpp.

template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>

typedef GlobalOrdinal Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >::global_ordinal_type

inherited

The global index type.

Definition at line 98 of file Tpetra_Operator.hpp.

template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>

typedef Node Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >::node_type

inherited

The Kokkos Node type.

Definition at line 101 of file Tpetra_Operator.hpp.

Constructor & Destructor Documentation

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::CrsMatrixMultiplyOp ( const Teuchos::RCP< const crs_matrix_type > & A )

inline

Constructor.

Parameters

A	[in] The CrsMatrix to wrap as an `Operator<Scalar, ...>`.

Definition at line 142 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

virtual Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::~CrsMatrixMultiplyOp ( )

inlinevirtual

Destructor (virtual for memory safety of derived classes).

Definition at line 150 of file Tpetra_CrsMatrixMultiplyOp.hpp.

Member Function Documentation

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

void Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::apply	(	const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	X,
		MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	Y,
		Teuchos::ETransp	mode = `Teuchos::NO_TRANS`,
		Scalar	alpha = `Teuchos::ScalarTraits<Scalar>::one ()`,
		Scalar	beta = `Teuchos::ScalarTraits<Scalar>::zero ()`
	)		const

inlinevirtual

Compute Y = beta*Y + alpha*Op(A)*X, where Op(A) is either A, $A^T$ , or $A^H$ .

This method calls the underlying CrsMatrix object's localMultiply<Scalar,Scalar>() method.

Implements Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >.

Definition at line 162 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

void Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::gaussSeidel	(	const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	B,
		MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	X,
		const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	D,
		const Scalar &	dampingFactor,
		const ESweepDirection	direction,
		const int	numSweeps
	)		const

inline

"Hybrid" Jacobi + (Gauss-Seidel or SOR) on $B = A X$ .

"Hybrid" means Jacobi for interprocess communication, but Successive Over-Relaxation (SOR) or Gauss-Seidel for intraprocess computation. Gauss-Seidel is a special case of SOR, where the damping factor is one.

The Forward or Backward sweep directions have their usual SOR meaning within the process. Interprocess communication occurs once before the sweep, as it would in Jacobi.

The Symmetric sweep direction means first Forward, then Backward. Before each sweep is an interprocess communication, as in Jacobi. Thus, Symmetric results in two interprocess communication steps.

Parameters

B	[in] Right-hand side(s), in the range Map of the matrix.
X	[in/out] On input: initial guess(es). On output: result multivector(s). This must be a domain Map view of a column Map multivector.
D	[in] Inverse of diagonal entries of the matrix A, in the row Map of the matrix.
dampingFactor	[in] SOR damping factor. A damping factor of one results in Gauss-Seidel.
direction	[in] Sweep direction: Forward, Backward, or Symmetric.
numSweeps	[in] Number of sweeps. We count each Symmetric sweep (including both its Forward and its Backward sweep) as one.

Precondition: Domain, range, and row Maps of the sparse matrix are all the same. (The domain and range Maps must be the same because this kernel overwrites its input. The row Map must be the same because the kernel uses the same local indices for the rows of the sparse matrix, and for the rows of the input / output multivector.); No other argument aliases X.

Definition at line 225 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

void Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::gaussSeidelCopy	(	MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	X,
		const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	B,
		const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	D,
		const Scalar &	dampingFactor,
		const ESweepDirection	direction,
		const int	numSweeps
	)		const

inline

Version of gaussSeidel(), with fewer requirements on X.

This method is just like gaussSeidel(), except that X need only be in the domain Map. This method does not require that X be a domain Map view of a column Map multivector. As a result, this method must copy X into a domain Map multivector before operating on it.

Parameters

X	[in/out] On input: initial guess(es). On output: result multivector(s).
B	[in] Right-hand side(s), in the range Map.
D	[in] Inverse of diagonal entries of the matrix, in the row Map.
dampingFactor	[in] SOR damping factor. A damping factor of one results in Gauss-Seidel.
direction	[in] Sweep direction: Forward, Backward, or Symmetric.
numSweeps	[in] Number of sweeps. We count each Symmetric sweep (including both its Forward and its Backward sweep) as one.

Precondition: Domain, range, and row Maps of the sparse matrix are all the same.; No other argument aliases X.

Definition at line 463 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

bool Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::hasTransposeApply ( ) const

inlinevirtual

Whether this Operator's apply() method can apply the transpose or conjugate transpose.

This is always true, since it is true for the CrsMatrix that this object wraps.

Reimplemented from Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >.

Definition at line 662 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

Teuchos::RCP<const map_type> Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::getDomainMap ( ) const

inlinevirtual

The domain Map of this Operator.

Implements Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >.

Definition at line 667 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

Teuchos::RCP<const map_type> Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::getRangeMap ( ) const

inlinevirtual

The range Map of this Operator.

Implements Tpetra::Operator< Scalar, LocalOrdinal, GlobalOrdinal, Node >.

Definition at line 672 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

void Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::applyTranspose	(	const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	X_in,
		MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	Y_in,
		Teuchos::ETransp	mode,
		Scalar	alpha,
		Scalar	beta
	)		const

inlineprotected

Apply the transpose or conjugate transpose of the matrix to X_in, producing Y_in.

Definition at line 715 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

void Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::applyNonTranspose	(	const MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	X_in,
		MultiVector< Scalar, LocalOrdinal, GlobalOrdinal, Node > &	Y_in,
		Scalar	alpha,
		Scalar	beta
	)		const

inlineprotected

Apply the matrix (not its transpose) to X_in, producing Y_in.

Definition at line 809 of file Tpetra_CrsMatrixMultiplyOp.hpp.

Friends And Related Function Documentation

template<class OpScalar , class MatScalar , class LocalOrdinal , class GlobalOrdinal , class Node >

Teuchos::RCP< CrsMatrixMultiplyOp< OpScalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node > > createCrsMatrixMultiplyOp ( const Teuchos::RCP< const CrsMatrix< MatScalar, LocalOrdinal, GlobalOrdinal, Node > > & A )

The function has the same template parameters of CrsMatrixMultiplyOp.

Parameters

A	[in] The CrsMatrix instance to wrap in an CrsMatrixMultiplyOp.

Returns: The CrsMatrixMultiplyOp wrapper for the given CrsMatrix.

Definition at line 1114 of file Tpetra_CrsMatrixMultiplyOp.hpp.

Member Data Documentation

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

const Teuchos::RCP<const crs_matrix_type> Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::matrix_

protected

The underlying CrsMatrix object.

Definition at line 682 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

Teuchos::RCP<MultiVector<Scalar,LocalOrdinal,GlobalOrdinal,Node> > Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::importMV_

mutableprotected

Column Map MultiVector used in apply().

This is a column Map MultiVector. It is used as the target of the forward mode Import operation (if necessary) in applyNonTranspose(), and the source of the reverse mode Export operation (if necessary) in applyTranspose(). Both of these methods create this MultiVector on demand if needed, and reuse it (if possible) for subsequent calls.

This is declared mutable because the apply() method is const, yet the method needs to cache the MultiVector for later use.

Definition at line 696 of file Tpetra_CrsMatrixMultiplyOp.hpp.

template<class Scalar , class MatScalar = Scalar, class LocalOrdinal = ::Tpetra::Details::DefaultTypes::local_ordinal_type, class GlobalOrdinal = ::Tpetra::Details::DefaultTypes::global_ordinal_type, class Node = ::Tpetra::Details::DefaultTypes::node_type>

Teuchos::RCP<MultiVector<Scalar,LocalOrdinal,GlobalOrdinal,Node> > Tpetra::CrsMatrixMultiplyOp< Scalar, MatScalar, LocalOrdinal, GlobalOrdinal, Node >::exportMV_

mutableprotected

Row Map MultiVector used in apply().

This is a row Map MultiVector. It is uses as the source of the forward mode Export operation (if necessary) in applyNonTranspose(), and the target of the reverse mode Import operation (if necessary) in applyTranspose(). Both of these methods create this MultiVector on demand if needed, and reuse it (if possible) for subsequent calls.

This is declared mutable because the apply() method is const, yet the method needs to cache the MultiVector for later use.

Definition at line 710 of file Tpetra_CrsMatrixMultiplyOp.hpp.

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

Tpetra_CrsMatrixMultiplyOp.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Related Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation