Amesos_Klu: A serial, unblocked code ideal for getting started and for very sparse matrices, such as circuit matrces. More...

#include <Amesos_Klu.h>

Inheritance diagram for Amesos_Klu:

[legend]

Private Attributes
int	SerialXlda_

Teuchos::RCP< Amesos_Klu_Pimpl >	PrivateKluData_

Teuchos::RCP < Amesos_StandardIndex >	StdIndex_

Teuchos::RCP < Amesos_StandardIndex >	StdIndexRange_

Teuchos::RCP < Amesos_StandardIndex >	StdIndexDomain_

std::vector< int >	Ap
	Ap, Ai, Aval form the compressed row storage used by Klu Ai and Aval can point directly into a matrix if it is StorageOptimized(), hence they may either be in vector form or may be a pointer into Epetra_CrsMatrix internals. More...

std::vector< int >	VecAi

std::vector< double >	VecAval

double *	Aval

int *	Ai

int	UseDataInPlace_
	1 if Problem_->GetOperator() is stored entirely on process 0 More...

long long	numentries_
	Number of non-zero entries in Problem_->GetOperator() More...

long long	NumGlobalElements_
	Number of rows and columns in the Problem_->GetOperator() More...

Epetra_RowMatrix *	RowMatrixA_
	Operator converted to a RowMatrix. More...

Epetra_CrsMatrix *	CrsMatrixA_
	Operator converted to a CrsMatrix. More...

Teuchos::RCP< Epetra_Map >	SerialMap_
	Points to a Serial Map (unused if UseDataInPlace_ == 1 ) More...

Teuchos::RCP< Epetra_CrsMatrix >	SerialCrsMatrixA_
	Points to a Serial Copy of A (unused if UseDataInPlace_==1) More...

Epetra_RowMatrix *	StdIndexMatrix_
	Points to a Contiguous Copy of A. More...

Epetra_RowMatrix *	SerialMatrix_
	Points to a Serial Copy of A. More...

bool	TrustMe_
	If `true`, no checks are made and the matrix is assume to be distributed. More...

int	NumVectors_
	Number of vectors in RHS and LHS. More...

double *	SerialXBvalues_
	Pointer to the actual values in the serial version of X and B. More...

double *	SerialBvalues_

Teuchos::RCP< Epetra_MultiVector >	SerialB_
	Serial versions of the LHS and RHS (may point to the original vector if serial) More...

Teuchos::RCP< Epetra_MultiVector >	SerialX_

Teuchos::RCP< Epetra_MultiVector >	SerialXextract_
	Serial versions of the LHS and RHS (if necessary) More...

Teuchos::RCP< Epetra_MultiVector >	SerialBextract_

bool	UseTranspose_
	If `true`, the transpose of A is used. More...

const Epetra_LinearProblem *	Problem_
	Pointer to the linear system problem. More...

std::vector< int >	ColIndicesV_
	Only used for RowMatrices to extract copies. More...

std::vector< double >	RowValuesV_
	Only used for RowMatrices to extract copies. More...

Teuchos::RCP< Epetra_Import >	ImportToSerial_
	Importer to process 0. More...

Teuchos::RCP< Epetra_Import >	ImportRangeToSerial_

Teuchos::RCP< Epetra_Import >	ImportDomainToSerial_

int	MtxRedistTime_
	Quick access ids for the individual timings. More...

int	MtxConvTime_

int	VecRedistTime_

int	SymFactTime_

int	NumFactTime_

int	SolveTime_

int	OverheadTime_

Private Attributes inherited from Amesos_Control
double	AddToDiag_
	Add `this` value to the diagonal. More...

bool	refactorize_

double	rcond_threshold_
	If error is greater than `this` value, perform symbolic and numeric factorization with full partial pivoting. More...

int	ScaleMethod_

bool	AddZeroToDiag_
	Adds zero to diagonal of redistributed matrix (some solvers choke on a matrix with a partly empty diag) More...

int	MatrixProperty_
	Set the matrix property. More...

int	MaxProcesses_

bool	Reindex_
	If true, the Amesos class should reindex the matrix to standard indexing (i.e. More...

Private Attributes inherited from Amesos_Status
bool	IsSymbolicFactorizationOK_
	If `true`, SymbolicFactorization() has been successfully called. More...

bool	IsNumericFactorizationOK_
	If `true`, NumericFactorization() has been successfully called. More...

bool	PrintTiming_
	If `true`, prints timing information in the destructor. More...

bool	PrintStatus_
	If `true`, print additional information in the destructor. More...

bool	ComputeVectorNorms_
	If `true`, prints the norms of X and B in Solve(). More...

bool	ComputeTrueResidual_
	If `true`, computes the true residual in Solve(). More...

int	verbose_
	Toggles the output level. More...

int	debug_
	Sets the level of debug_ output. More...

int	NumSymbolicFact_
	Number of symbolic factorization phases. More...

int	NumNumericFact_
	Number of numeric factorization phases. More...

int	NumSolve_
	Number of solves. More...

double	Threshold_

int	MyPID_

int	NumProcs_

	Amesos_Klu (const Epetra_LinearProblem &LinearProblem)
	Amesos_Klu Constructor. More...

	~Amesos_Klu (void)
	Amesos_Klu Destructor. More...

int	SymbolicFactorization ()
	Performs SymbolicFactorization on the matrix A. More...

int	NumericFactorization ()
	Performs NumericFactorization on the matrix A. More...

int	Solve ()
	Solves A X = B (or A^T x = B) More...

const Epetra_LinearProblem *	GetProblem () const
	Get a pointer to the Problem. More...

bool	MatrixShapeOK () const
	Returns true if KLU can handle this matrix shape. More...

int	SetUseTranspose (bool UseTranspose_in)
	SetUseTranpose(true) is more efficient in Amesos_Klu. More...

bool	UseTranspose () const
	Returns the current UseTranspose setting. More...

const Epetra_Comm &	Comm () const
	Returns a pointer to the Epetra_Comm communicator associated with this operator. More...

int	SetParameters (Teuchos::ParameterList &ParameterList)
	Updates internal variables. More...

int	NumSymbolicFact () const
	Returns the number of symbolic factorizations performed by this object. More...

int	NumNumericFact () const
	Returns the number of numeric factorizations performed by this object. More...

int	NumSolve () const
	Returns the number of solves performed by this object. More...

void	PrintTiming () const
	Prints timing information. More...

void	PrintStatus () const
	Prints information about the factorization and solution phases. More...

void	GetTiming (Teuchos::ParameterList &TimingParameterList) const
	Extracts timing information and places in parameter list. More...

int	CreateLocalMatrixAndExporters ()

int	ExportToSerial ()

int	ConvertToKluCRS (bool firsttime)

int	PerformSymbolicFactorization ()

int	PerformNumericFactorization ()

Additional Inherited Members
Public Member Functions inherited from Amesos_BaseSolver
virtual	~Amesos_BaseSolver ()
	Destructor. More...

virtual void	setParameterList (Teuchos::RCP< Teuchos::ParameterList > const &paramList)
	Redefined from Teuchos::ParameterListAcceptor (Does Not Work) More...

virtual Teuchos::RCP < Teuchos::ParameterList >	getNonconstParameterList ()
	This is an empty stub. More...

virtual Teuchos::RCP < Teuchos::ParameterList >	unsetParameterList ()
	This is an empty stub. More...

Public Member Functions inherited from Teuchos::ParameterListAcceptor
virtual RCP< const ParameterList >	getParameterList () const

virtual RCP< const ParameterList >	getValidParameters () const

Private Member Functions inherited from Amesos_Time
	Amesos_Time ()
	Default constructor to create `size` timers. More...

virtual	~Amesos_Time ()
	Default destructor. More...

void	CreateTimer (const Epetra_Comm &Comm, int size=1)
	Initializes the Time object. More...

void	ResetTimer (const int timerID=0)
	Resets the internally stored time object. More...

int	AddTime (const std::string what, int dataID, const int timerID=0)
	Adds to field `what` the time elapsed since last call to ResetTimer(). More...

double	GetTime (const std::string what) const
	Gets the cumulative time using the string. More...

double	GetTime (const int dataID) const
	Gets the cumulative time using the dataID. More...

void	GetTiming (Teuchos::ParameterList &list) const
	Load up the current timing information into the parameter list. More...

Private Member Functions inherited from Amesos_NoCopiable
	Amesos_NoCopiable ()
	Default constructor. More...

	~Amesos_NoCopiable ()
	Default destructor. More...

Private Member Functions inherited from Amesos_Utils
	Amesos_Utils ()
	Default constructor. More...

	~Amesos_Utils ()
	Default destructor. More...

void	ComputeTrueResidual (const Epetra_RowMatrix &Matrix, const Epetra_MultiVector &X, const Epetra_MultiVector &B, const bool UseTranspose, const std::string prefix) const
	Computes the true residual, B - Matrix * X, and prints the results. More...

void	ComputeVectorNorms (const Epetra_MultiVector &X, const Epetra_MultiVector &B, const std::string prefix) const
	Computes the norms of X and B and print the results. More...

void	PrintLine () const
	Prints line on std::cout. More...

void	SetMaxProcesses (int &MaxProcesses, const Epetra_RowMatrix &A)

Private Member Functions inherited from Amesos_Control
	Amesos_Control ()
	Default constructor. More...

	~Amesos_Control ()
	Default destructor. More...

void	SetControlParameters (const Teuchos::ParameterList &ParameterList)

Private Member Functions inherited from Amesos_Status
	Amesos_Status ()
	Default constructor. More...

	~Amesos_Status ()
	Default destructor. More...

void	SetStatusParameters (const Teuchos::ParameterList &ParameterList)

Detailed Description

Amesos_Klu: A serial, unblocked code ideal for getting started and for very sparse matrices, such as circuit matrces.

Interface to UMFPACK.

Interface to KLU internal solver.

Class Amesos_Klu is an object-oriented wrapper for KLU. KLU, whose sources are distributed within Amesos, is a serial solver for sparse matrices. KLU will solve a linear system of equations: $A X = B$ , where A is an Epetra_RowMatrix and X and B are Epetra_MultiVector objects.

Amesos_Klu computes $A^T X = B$ more efficiently than $>A X = B$ . The latter requires a matrix transpose – which costs both time and space.

KLU is Tim Davis' implementation of Gilbert-Peierl's left-looking sparse partial pivoting algorithm, with Eisenstat & Liu's symmetric pruning. Gilbert's version appears as [L,U,P]=lu(A) in MATLAB. It doesn't exploit dense matrix kernels, but it is the only sparse LU factorization algorithm known to be asymptotically optimal, in the sense that it takes time proportional to the number of floating-point operations. It is the precursor to SuperLU, thus the name ("clark Kent LU"). For very sparse matrices that do not suffer much fill-in (such as most circuit matrices when permuted properly) dense matrix kernels do not help, and the asymptotic run-time is of practical importance.

The klu_btf code first permutes the matrix to upper block triangular form (using two algorithms by Duff and Reid, MC13 and MC21, in the ACM Collected Algorithms). It then permutes each block via a symmetric minimum degree ordering (AMD, by Amestoy, Davis, and Duff). This ordering phase can be done just once for a sequence of matrices. Next, it factorizes each reordered block via the klu routine, which also attempts to preserve diagonal pivoting, but allows for partial pivoting if the diagonal is to small.

Date: Last updated on 24-May-05.

Definition at line 111 of file Amesos_Klu.h.

Constructor & Destructor Documentation

Amesos_Klu::Amesos_Klu ( const Epetra_LinearProblem & LinearProblem )

Amesos_Klu Constructor.

Creates an Amesos_Klu instance, using an Epetra_LinearProblem, passing in an already-defined Epetra_LinearProblem object.

Note: The operator in LinearProblem must be an Epetra_RowMatrix.

Definition at line 89 of file Amesos_Klu.cpp.

Amesos_Klu::~Amesos_Klu ( void )

Amesos_Klu Destructor.

Definition at line 111 of file Amesos_Klu.cpp.

Member Function Documentation

int Amesos_Klu::SymbolicFactorization ( )

virtual

Performs SymbolicFactorization on the matrix A.

In addition to performing symbolic factorization on the matrix A, the call to SymbolicFactorization() implies that no change will be made to the non-zero structure of the underlying matrix without a subsequent call to SymbolicFactorization().

Preconditions:

GetProblem().GetOperator() != 0 (return -1)
MatrixShapeOk(GetProblem().GetOperator()) == true (return -6)

Postconditions:

Symbolic Factorization will be performed (or marked to be performed) allowing NumericFactorization() and Solve() to be called.

Returns: Integer error code, set to 0 if successful.

Implements Amesos_BaseSolver.

Definition at line 617 of file Amesos_Klu.cpp.

int Amesos_Klu::NumericFactorization ( )

virtual

Performs NumericFactorization on the matrix A.

In addition to performing numeric factorization on the matrix A, the call to NumericFactorization() implies that no change will be made to the underlying matrix without a subsequent call to NumericFactorization().

Preconditions:

GetProblem().GetOperator() != 0 (return -1)
MatrixShapeOk(GetProblem().GetOperator()) == true (return -6)
The non-zero structure of the matrix should not have changed since the last call to SymbolicFactorization(). (return -2 if the number of non-zeros changes) Other changes can have arbitrary consequences.
The distribution of the matrix should not have changed since the last call to SymbolicFactorization()
The matrix should be indexed from 0 to n-1, unless the parameter "Reindex" was set to "true" prior to the call to SymbolicFactorization(). (return -3 - if caught)
The paremeter "Reindex" should not be set to "true" except on CrsMatrices. (return -4)
The paremeter "Reindex" should not be set to "true" unless Amesos was built with EpetraExt, i.e. with –enable-epetraext on the configure line. (return -4)
Internal errors retur -5.

Postconditions:

Numeric Factorization will be performed (or marked to be performed) allowing Solve() to be performed correctly despite a potential change in in the matrix values (though not in the non-zero structure).

Returns: Integer error code, set to 0 if successful.

Implements Amesos_BaseSolver.

Definition at line 681 of file Amesos_Klu.cpp.

int Amesos_Klu::Solve ( )

virtual

Solves A X = B (or A^T x = B)

Preconditions:

GetProblem().GetOperator() != 0 (return -1)
MatrixShapeOk(GetProblem().GetOperator()) == true (return -6)
GetProblem()->CheckInput (see Epetra_LinearProblem::CheckInput() for return values)
The non-zero structure of the matrix should not have changed since the last call to SymbolicFactorization().
The distribution of the matrix should not have changed since the last call to SymbolicFactorization()
The matrix should not have changed since the last call to NumericFactorization().

Postconditions:

X will be set such that A X = B (or A^T X = B), within the limits of the accuracy of the underlying solver.

Returns: Integer error code, set to 0 if successful.

Implements Amesos_BaseSolver.

Definition at line 729 of file Amesos_Klu.cpp.

const Epetra_LinearProblem* Amesos_Klu::GetProblem ( ) const

inlinevirtual

Get a pointer to the Problem.

Implements Amesos_BaseSolver.

Definition at line 147 of file Amesos_Klu.h.

bool Amesos_Klu::MatrixShapeOK ( ) const

virtual

Returns true if KLU can handle this matrix shape.

Returns true if the matrix shape is one that KLU can handle. KLU only works with square matrices.

Implements Amesos_BaseSolver.

Definition at line 603 of file Amesos_Klu.cpp.

int Amesos_Klu::SetUseTranspose ( bool UseTranspose_in )

inlinevirtual

SetUseTranpose(true) is more efficient in Amesos_Klu.

If SetUseTranspose() is set to true, $A^T X = B$ is computed.

Implements Amesos_BaseSolver.

Definition at line 160 of file Amesos_Klu.h.

bool Amesos_Klu::UseTranspose ( ) const

inlinevirtual

Returns the current UseTranspose setting.

Implements Amesos_BaseSolver.

Definition at line 162 of file Amesos_Klu.h.

const Epetra_Comm& Amesos_Klu::Comm ( ) const

inlinevirtual

Returns a pointer to the Epetra_Comm communicator associated with this operator.

Implements Amesos_BaseSolver.

Definition at line 164 of file Amesos_Klu.h.

int Amesos_Klu::SetParameters ( Teuchos::ParameterList & ParameterList )

virtual

Updates internal variables.

  <br \>Preconditions:<ul>
  <li>None.</li>
  </ul>

  <br \>Postconditions:<ul> 
  <li>Internal variables controlling the factorization and solve will
  be updated and take effect on all subseuent calls to NumericFactorization() 
  and Solve().</li>
  <li>All parameters whose value are to differ from the default values must

be included in ParameterList. Parameters not specified in ParameterList revert to their default values.

Returns: Integer error code, set to 0 if successful.

Implements Amesos_BaseSolver.

Definition at line 449 of file Amesos_Klu.cpp.

int Amesos_Klu::NumSymbolicFact ( ) const

inlinevirtual

Returns the number of symbolic factorizations performed by this object.

Implements Amesos_BaseSolver.

Definition at line 169 of file Amesos_Klu.h.

int Amesos_Klu::NumNumericFact ( ) const

inlinevirtual

Returns the number of numeric factorizations performed by this object.

Implements Amesos_BaseSolver.

Definition at line 172 of file Amesos_Klu.h.

int Amesos_Klu::NumSolve ( ) const

inlinevirtual

Returns the number of solves performed by this object.

Implements Amesos_BaseSolver.

Definition at line 175 of file Amesos_Klu.h.

void Amesos_Klu::PrintTiming ( ) const

virtual

Prints timing information.

Implements Amesos_BaseSolver.

Definition at line 949 of file Amesos_Klu.cpp.

void Amesos_Klu::PrintStatus ( ) const

virtual

Prints information about the factorization and solution phases.

Implements Amesos_BaseSolver.

Definition at line 926 of file Amesos_Klu.cpp.

void Amesos_Klu::GetTiming ( Teuchos::ParameterList & TimingParameterList ) const

inlinevirtual

Extracts timing information and places in parameter list.

Reimplemented from Amesos_BaseSolver.

Definition at line 184 of file Amesos_Klu.h.

int Amesos_Klu::CreateLocalMatrixAndExporters ( )

private

Definition at line 196 of file Amesos_Klu.cpp.

int Amesos_Klu::ExportToSerial ( )

private

Definition at line 119 of file Amesos_Klu.cpp.

int Amesos_Klu::ConvertToKluCRS ( bool firsttime )

private

Definition at line 337 of file Amesos_Klu.cpp.

int Amesos_Klu::PerformSymbolicFactorization ( )

private

Definition at line 478 of file Amesos_Klu.cpp.

int Amesos_Klu::PerformNumericFactorization ( )

private

Definition at line 516 of file Amesos_Klu.cpp.

Member Data Documentation

int Amesos_Klu::SerialXlda_

private

Definition at line 258 of file Amesos_Klu.h.

Teuchos::RCP<Amesos_Klu_Pimpl> Amesos_Klu::PrivateKluData_

private

Definition at line 267 of file Amesos_Klu.h.

Teuchos::RCP<Amesos_StandardIndex> Amesos_Klu::StdIndex_

private

Definition at line 268 of file Amesos_Klu.h.

Teuchos::RCP<Amesos_StandardIndex> Amesos_Klu::StdIndexRange_

private

Definition at line 269 of file Amesos_Klu.h.

Teuchos::RCP<Amesos_StandardIndex> Amesos_Klu::StdIndexDomain_

private

Definition at line 270 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::Ap

private

Ap, Ai, Aval form the compressed row storage used by Klu Ai and Aval can point directly into a matrix if it is StorageOptimized(), hence they may either be in vector form or may be a pointer into Epetra_CrsMatrix internals.

Ap must always be constructed.

Definition at line 276 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::VecAi

private

Definition at line 277 of file Amesos_Klu.h.

std::vector<double> Amesos_Klu::VecAval

private

Definition at line 278 of file Amesos_Klu.h.

double* Amesos_Klu::Aval

private

Definition at line 279 of file Amesos_Klu.h.

int* Amesos_Klu::Ai

private

Definition at line 280 of file Amesos_Klu.h.

int Amesos_Klu::UseDataInPlace_

private

1 if Problem_->GetOperator() is stored entirely on process 0

Definition at line 283 of file Amesos_Klu.h.

long long Amesos_Klu::numentries_

private

Number of non-zero entries in Problem_->GetOperator()

Definition at line 285 of file Amesos_Klu.h.

long long Amesos_Klu::NumGlobalElements_

private

Number of rows and columns in the Problem_->GetOperator()

Definition at line 287 of file Amesos_Klu.h.

Epetra_RowMatrix* Amesos_Klu::RowMatrixA_

private

Operator converted to a RowMatrix.

Definition at line 290 of file Amesos_Klu.h.

Epetra_CrsMatrix* Amesos_Klu::CrsMatrixA_

private

Operator converted to a CrsMatrix.

Definition at line 292 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_Map> Amesos_Klu::SerialMap_

private

Points to a Serial Map (unused if UseDataInPlace_ == 1 )

Definition at line 302 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_CrsMatrix> Amesos_Klu::SerialCrsMatrixA_

private

Points to a Serial Copy of A (unused if UseDataInPlace_==1)

Definition at line 304 of file Amesos_Klu.h.

Epetra_RowMatrix* Amesos_Klu::StdIndexMatrix_

private

Points to a Contiguous Copy of A.

Definition at line 306 of file Amesos_Klu.h.

Epetra_RowMatrix* Amesos_Klu::SerialMatrix_

private

Points to a Serial Copy of A.

Definition at line 308 of file Amesos_Klu.h.

bool Amesos_Klu::TrustMe_

private

If true, no checks are made and the matrix is assume to be distributed.

Definition at line 314 of file Amesos_Klu.h.

int Amesos_Klu::NumVectors_

private

Number of vectors in RHS and LHS.

Definition at line 316 of file Amesos_Klu.h.

double* Amesos_Klu::SerialXBvalues_

private

Pointer to the actual values in the serial version of X and B.

Definition at line 318 of file Amesos_Klu.h.

double* Amesos_Klu::SerialBvalues_

private

Definition at line 319 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_MultiVector> Amesos_Klu::SerialB_

private

Serial versions of the LHS and RHS (may point to the original vector if serial)

Definition at line 321 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_MultiVector> Amesos_Klu::SerialX_

private

Definition at line 322 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_MultiVector> Amesos_Klu::SerialXextract_

private

Serial versions of the LHS and RHS (if necessary)

Definition at line 324 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_MultiVector> Amesos_Klu::SerialBextract_

private

Definition at line 325 of file Amesos_Klu.h.

bool Amesos_Klu::UseTranspose_

private

If true, the transpose of A is used.

Definition at line 328 of file Amesos_Klu.h.

const Epetra_LinearProblem* Amesos_Klu::Problem_

private

Pointer to the linear system problem.

Definition at line 330 of file Amesos_Klu.h.

std::vector<int> Amesos_Klu::ColIndicesV_

private

Only used for RowMatrices to extract copies.

Definition at line 333 of file Amesos_Klu.h.

std::vector<double> Amesos_Klu::RowValuesV_

private

Only used for RowMatrices to extract copies.

Definition at line 335 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_Import> Amesos_Klu::ImportToSerial_

private

Importer to process 0.

Definition at line 337 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_Import> Amesos_Klu::ImportRangeToSerial_

private

Definition at line 338 of file Amesos_Klu.h.

Teuchos::RCP<Epetra_Import> Amesos_Klu::ImportDomainToSerial_

private

Definition at line 339 of file Amesos_Klu.h.

int Amesos_Klu::MtxRedistTime_

private

Quick access ids for the individual timings.

Definition at line 341 of file Amesos_Klu.h.

int Amesos_Klu::MtxConvTime_

private

Definition at line 341 of file Amesos_Klu.h.

int Amesos_Klu::VecRedistTime_

private

Definition at line 341 of file Amesos_Klu.h.

int Amesos_Klu::SymFactTime_

private

Definition at line 342 of file Amesos_Klu.h.

int Amesos_Klu::NumFactTime_

private

Definition at line 342 of file Amesos_Klu.h.

int Amesos_Klu::SolveTime_

private

Definition at line 342 of file Amesos_Klu.h.

int Amesos_Klu::OverheadTime_

private

Definition at line 342 of file Amesos_Klu.h.

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

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation