#include <Laplace.h>

Inheritance diagram for Nektar::Laplace:

Collaboration diagram for Nektar::Laplace:

Static Public Member Functions
static EquationSystemSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of class. More...

Protected Member Functions
	Laplace (const LibUtilities::SessionReaderSharedPtr &pSession)

virtual	~Laplace ()

virtual void	v_InitObject ()
	Initialisation object for EquationSystem. More...

virtual void	v_GenerateSummary (SolverUtils::SummaryList &s)
	Virtual function for generating summary information. More...

virtual void	v_DoSolve ()
	Virtual function for solve implementation. More...

Protected Member Functions inherited from Nektar::SolverUtils::EquationSystem
SOLVER_UTILS_EXPORT	EquationSystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises EquationSystem class members. More...

int	nocase_cmp (const string &s1, const string &s2)

virtual SOLVER_UTILS_EXPORT void	v_DoInitialise ()
	Virtual function for initialisation implementation. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Virtual function for the L_inf error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray, bool Normalised=false)
	Virtual function for the L_2 error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT void	v_TransCoeffToPhys ()
	Virtual function for transformation to physical space. More...

virtual SOLVER_UTILS_EXPORT void	v_TransPhysToCoeff ()
	Virtual function for transformation to coefficient space. More...

virtual SOLVER_UTILS_EXPORT void	v_SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)

virtual SOLVER_UTILS_EXPORT void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time)

SOLVER_UTILS_EXPORT void	SetUpBaseFields (SpatialDomains::MeshGraphSharedPtr &mesh)

SOLVER_UTILS_EXPORT void	ImportFldBase (std::string pInfile, SpatialDomains::MeshGraphSharedPtr pGraph)

virtual SOLVER_UTILS_EXPORT void	v_Output (void)

virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)

virtual SOLVER_UTILS_EXPORT void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Protected Attributes
StdRegions::ConstFactorMap	m_factors

Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
LibUtilities::CommSharedPtr	m_comm
	Communicator. More...

LibUtilities::SessionReaderSharedPtr	m_session
	The session reader. More...

LibUtilities::FieldIOSharedPtr	m_fld
	Field input/output. More...

map< std::string, Array< OneD, Array< OneD, float > > >	m_interpWeights
	Map of the interpolation weights for a specific filename. More...

map< std::string, Array< OneD, Array< OneD, unsigned int > > >	m_interpInds
	Map of the interpolation indices for a specific filename. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_fields
	Array holding all dependent variables. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_base
	Base fields. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_derivedfields
	Array holding all dependent variables. More...

SpatialDomains::BoundaryConditionsSharedPtr	m_boundaryConditions
	Pointer to boundary conditions object. More...

SpatialDomains::MeshGraphSharedPtr	m_graph
	Pointer to graph defining mesh. More...

std::string	m_sessionName
	Name of the session. More...

NekDouble	m_time
	Current time of simulation. More...

int	m_initialStep
	Number of the step where the simulation should begin. More...

NekDouble	m_fintime
	Finish time of the simulation. More...

NekDouble	m_timestep
	Time step size. More...

NekDouble	m_lambda
	Lambda constant in real system if one required. More...

std::set< std::string >	m_loadedFields

NekDouble	m_checktime
	Time between checkpoints. More...

int	m_nchk
	Number of checkpoints written so far. More...

int	m_steps
	Number of steps to take. More...

int	m_checksteps
	Number of steps between checkpoints. More...

int	m_spacedim
	Spatial dimension (>= expansion dim). More...

int	m_expdim
	Expansion dimension. More...

bool	m_singleMode
	Flag to determine if single homogeneous mode is used. More...

bool	m_halfMode
	Flag to determine if half homogeneous mode is used. More...

bool	m_multipleModes
	Flag to determine if use multiple homogenenous modes are used. More...

bool	m_useFFT
	Flag to determine if FFT is used for homogeneous transform. More...

bool	m_homogen_dealiasing
	Flag to determine if dealiasing is used for homogeneous simulations. More...

bool	m_specHP_dealiasing
	Flag to determine if dealisising is usde for the Spectral/hp element discretisation. More...

enum MultiRegions::ProjectionType	m_projectionType
	Type of projection; e.g continuous or discontinuous. More...

Array< OneD, Array< OneD, NekDouble > >	m_traceNormals
	Array holding trace normals for DG simulations in the forwards direction. More...

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_gradtan
	1 x nvariable x nq More...

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_tanbasis
	2 x m_spacedim x nq More...

Array< OneD, bool >	m_checkIfSystemSingular
	Flag to indicate if the fields should be checked for singularity. More...

LibUtilities::FieldMetaDataMap	m_fieldMetaDataMap
	Map to identify relevant solver info to dump in output fields. More...

int	m_NumQuadPointsError
	Number of Quadrature points used to work out the error. More...

enum HomogeneousType	m_HomogeneousType

NekDouble	m_LhomX
	physical length in X direction (if homogeneous) More...

NekDouble	m_LhomY
	physical length in Y direction (if homogeneous) More...

NekDouble	m_LhomZ
	physical length in Z direction (if homogeneous) More...

int	m_npointsX
	number of points in X direction (if homogeneous) More...

int	m_npointsY
	number of points in Y direction (if homogeneous) More...

int	m_npointsZ
	number of points in Z direction (if homogeneous) More...

int	m_HomoDirec
	number of homogenous directions More...

int	m_NumMode
	Mode to use in case of single mode analysis. More...

Private Member Functions
virtual Array< OneD, bool >	v_GetSystemSingularChecks ()

Friends
class	MemoryManager< Laplace >
	Class may only be instantiated through the MemoryManager. More...

Additional Inherited Members
Public Member Functions inherited from Nektar::SolverUtils::EquationSystem
virtual SOLVER_UTILS_EXPORT	~EquationSystem ()
	Destructor. More...

SOLVER_UTILS_EXPORT void	SetUpTraceNormals (void)

SOLVER_UTILS_EXPORT void	InitObject ()
	Initialises the members of this object. More...

SOLVER_UTILS_EXPORT void	DoInitialise ()
	Perform any initialisation necessary before solving the problem. More...

SOLVER_UTILS_EXPORT void	DoSolve ()
	Solve the problem. More...

SOLVER_UTILS_EXPORT void	TransCoeffToPhys ()
	Transform from coefficient to physical space. More...

SOLVER_UTILS_EXPORT void	TransPhysToCoeff ()
	Transform from physical to coefficient space. More...

SOLVER_UTILS_EXPORT void	Output ()
	Perform output operations after solve. More...

SOLVER_UTILS_EXPORT NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation. More...

SOLVER_UTILS_EXPORT std::string	GetSessionName ()
	Get Session name. More...

template<class T >
boost::shared_ptr< T >	as ()

SOLVER_UTILS_EXPORT void	ResetSessionName (std::string newname)
	Reset Session name. More...

SOLVER_UTILS_EXPORT LibUtilities::SessionReaderSharedPtr	GetSession ()
	Get Session name. More...

SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	GetPressure ()
	Get pressure field if available. More...

SOLVER_UTILS_EXPORT void	PrintSummary (std::ostream &out)
	Print a summary of parameters and solver characteristics. More...

SOLVER_UTILS_EXPORT void	SetLambda (NekDouble lambda)
	Set parameter m_lambda. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (Array< OneD, Array< OneD, NekDouble > > &pArray, std::string pFunctionName, const NekDouble pTime=0.0, const int domain=0)
	Evaluates a function as specified in the session file. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, Array< OneD, NekDouble > > &pFields, const std::string &pName, const NekDouble &pTime=0.0, const int domain=0)
	Populate given fields with the function from session. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const std::string &pName, const NekDouble &pTime=0.0, const int domain=0)
	Populate given fields with the function from session. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::string pFieldName, Array< OneD, NekDouble > &pArray, const std::string &pFunctionName, const NekDouble &pTime=0.0, const int domain=0)

SOLVER_UTILS_EXPORT std::string	DescribeFunction (std::string pFieldName, const std::string &pFunctionName, const int domain)
	Provide a description of a function for a given field name. More...

SOLVER_UTILS_EXPORT void	InitialiseBaseFlow (Array< OneD, Array< OneD, NekDouble > > &base)
	Perform initialisation of the base flow. More...

SOLVER_UTILS_EXPORT void	SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
	Initialise the data in the dependent fields. More...

SOLVER_UTILS_EXPORT void	EvaluateExactSolution (int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
	Evaluates an exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln, bool Normalised=false)
	Compute the L2 error between fields and a given exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, bool Normalised=false)
	Compute the L2 error of the fields. More...

SOLVER_UTILS_EXPORT Array < OneD, NekDouble >	ErrorExtraPoints (unsigned int field)
	Compute error (L2 and L_inf) over an larger set of quadrature points return [L2 Linf]. More...

SOLVER_UTILS_EXPORT void	WeakAdvectionGreensDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\nabla \phi \cdot F)$ . More...

SOLVER_UTILS_EXPORT void	WeakAdvectionDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\phi, \nabla \cdot F)$ . More...

SOLVER_UTILS_EXPORT void	WeakAdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, bool UseContCoeffs=false)
	Compute the inner product $(\phi, V\cdot \nabla u)$ . More...

f SOLVER_UTILS_EXPORT void	AdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wk=NullNekDouble1DArray)
	Compute the non-conservative advection. More...

SOLVER_UTILS_EXPORT void	WeakDGAdvection (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false, int nvariables=0)
	Calculate the weak discontinuous Galerkin advection. More...

SOLVER_UTILS_EXPORT void	WeakDGDiffusion (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false)
	Calculate weak DG Diffusion in the LDG form. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n)
	Write checkpoint file of m_fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write checkpoint file of custom data fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_BaseFlow (const int n)
	Write base flow file of m_fields. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname)
	Write field data to the given filename. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write input fields to the given filename. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields)
	Input field data from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFldToMultiDomains (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const int ndomains)
	Input field data from the given file to multiple domains. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, std::vector< std::string > &fieldStr, Array< OneD, Array< OneD, NekDouble > > &coeffs)
	Output a field. Input field data into array from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, MultiRegions::ExpListSharedPtr &pField, std::string &pFieldName)
	Output a field. Input field data into ExpList from the given file. More...

SOLVER_UTILS_EXPORT void	ScanForHistoryPoints ()
	Builds map of which element holds each history point. More...

SOLVER_UTILS_EXPORT void	WriteHistoryData (std::ostream &out)
	Probe each history point and write to file. More...

SOLVER_UTILS_EXPORT void	SessionSummary (SummaryList &vSummary)
	Write out a session summary. More...

SOLVER_UTILS_EXPORT Array < OneD, MultiRegions::ExpListSharedPtr > &	UpdateFields ()

SOLVER_UTILS_EXPORT LibUtilities::FieldMetaDataMap &	UpdateFieldMetaDataMap ()
	Get hold of FieldInfoMap so it can be updated. More...

SOLVER_UTILS_EXPORT NekDouble	GetFinalTime ()
	Return final time. More...

SOLVER_UTILS_EXPORT int	GetNcoeffs ()

SOLVER_UTILS_EXPORT int	GetNcoeffs (const int eid)

SOLVER_UTILS_EXPORT int	GetNumExpModes ()

SOLVER_UTILS_EXPORT const Array< OneD, int >	GetNumExpModesPerExp ()

SOLVER_UTILS_EXPORT int	GetNvariables ()

SOLVER_UTILS_EXPORT const std::string	GetVariable (unsigned int i)

SOLVER_UTILS_EXPORT int	GetTraceTotPoints ()

SOLVER_UTILS_EXPORT int	GetTraceNpoints ()

SOLVER_UTILS_EXPORT int	GetExpSize ()

SOLVER_UTILS_EXPORT int	GetPhys_Offset (int n)

SOLVER_UTILS_EXPORT int	GetCoeff_Offset (int n)

SOLVER_UTILS_EXPORT int	GetTotPoints ()

SOLVER_UTILS_EXPORT int	GetTotPoints (int n)

SOLVER_UTILS_EXPORT int	GetNpoints ()

SOLVER_UTILS_EXPORT int	GetNumElmVelocity ()

SOLVER_UTILS_EXPORT int	GetSteps ()

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()

SOLVER_UTILS_EXPORT void	CopyFromPhysField (const int i, Array< OneD, NekDouble > &output)

SOLVER_UTILS_EXPORT void	CopyToPhysField (const int i, Array< OneD, NekDouble > &output)

SOLVER_UTILS_EXPORT void	SetSteps (const int steps)

SOLVER_UTILS_EXPORT void	ZeroPhysFields ()

SOLVER_UTILS_EXPORT void	FwdTransFields ()

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &fluxX, Array< OneD, Array< OneD, NekDouble > > &fluxY)

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, const int j, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)

SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)

SOLVER_UTILS_EXPORT void	NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)

SOLVER_UTILS_EXPORT void	NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)

SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)

SOLVER_UTILS_EXPORT int	NoCaseStringCompare (const string &s1, const string &s2)
	Perform a case-insensitive string comparison. More...

SOLVER_UTILS_EXPORT int	GetCheckpointNumber ()

SOLVER_UTILS_EXPORT void	SetCheckpointNumber (int num)

SOLVER_UTILS_EXPORT int	GetCheckpointSteps ()

SOLVER_UTILS_EXPORT void	SetCheckpointSteps (int num)

SOLVER_UTILS_EXPORT void	SetTime (const NekDouble time)

SOLVER_UTILS_EXPORT void	SetInitialStep (const int step)

SOLVER_UTILS_EXPORT void	SetBoundaryConditions (NekDouble time)
	Evaluates the boundary conditions at the given time. More...

virtual SOLVER_UTILS_EXPORT bool	v_NegatedOp ()
	Virtual function to identify if operator is negated in DoSolve. More...

Protected Types inherited from Nektar::SolverUtils::EquationSystem
enum	HomogeneousType { eHomogeneous1D, eHomogeneous2D, eHomogeneous3D, eNotHomogeneous }
	Parameter for homogeneous expansions. More...

Detailed Description

Definition at line 45 of file Laplace.h.

Constructor & Destructor Documentation

Nektar::Laplace::Laplace ( const LibUtilities::SessionReaderSharedPtr & pSession )

protected

Definition at line 43 of file Laplace.cpp.

References Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorTau, and m_factors.

         : EquationSystem(pSession),
           m_factors()
     {
         m_factors[StdRegions::eFactorLambda] = 0.0;
         m_factors[StdRegions::eFactorTau] = 1.0;
     }

Nektar::Laplace::~Laplace ( )

protectedvirtual

Definition at line 57 of file Laplace.cpp.

     {
 
     }

Member Function Documentation

static EquationSystemSharedPtr Nektar::Laplace::create ( const LibUtilities::SessionReaderSharedPtr & pSession )

inlinestatic

Creates an instance of this class.

Definition at line 52 of file Laplace.h.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr().

         {
             EquationSystemSharedPtr p = MemoryManager<Laplace>::AllocateSharedPtr(pSession);
             p->InitObject();
             return p;
         }

void Nektar::Laplace::v_DoSolve ( void )

protectedvirtual

Virtual function for solve implementation.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 69 of file Laplace.cpp.

References Nektar::SolverUtils::EquationSystem::GetNcoeffs(), m_factors, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::NullFlagList, and Vmath::Zero().

     {
         for(int i = 0; i < m_fields.num_elements(); ++i)
         {
             // Zero field so initial conditions are zero
             Vmath::Zero(m_fields[i]->GetNcoeffs(),
                         m_fields[i]->UpdateCoeffs(), 1);
             m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                                    m_fields[i]->UpdateCoeffs(),
                                    NullFlagList,
                                    m_factors);
             m_fields[i]->SetPhysState(false);
         }
     }

void Nektar::Laplace::v_GenerateSummary ( SolverUtils::SummaryList & l )

protectedvirtual

Virtual function for generating summary information.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::Helmholtz, and Nektar::Poisson.

Definition at line 62 of file Laplace.cpp.

References Nektar::SolverUtils::AddSummaryItem(), Nektar::StdRegions::eFactorLambda, and m_factors.

Referenced by Nektar::Poisson::v_GenerateSummary().

     {
         EquationSystem::SessionSummary(s);
         SolverUtils::AddSummaryItem(s, "Lambda",
                                     m_factors[StdRegions::eFactorLambda]);
     }

Array< OneD, bool > Nektar::Laplace::v_GetSystemSingularChecks ( )

privatevirtual

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::Helmholtz, and Nektar::Poisson.

Definition at line 84 of file Laplace.cpp.

References Nektar::SolverUtils::EquationSystem::m_session.

     {
         return Array<OneD, bool>(m_session->GetVariables().size(), true);
     }

void Nektar::Laplace::v_InitObject ( )

protectedvirtual

Initialisation object for EquationSystem.

Continuous field

Setting up the normals

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::Helmholtz, and Nektar::Poisson.

Definition at line 52 of file Laplace.cpp.

Referenced by Nektar::Poisson::v_InitObject().

     {
         EquationSystem::v_InitObject();
     }

Friends And Related Function Documentation

friend class MemoryManager< Laplace >

friend

Class may only be instantiated through the MemoryManager.

Definition at line 49 of file Laplace.h.

Member Data Documentation

string Nektar::Laplace::className

static

Initial value:

= GetEquationSystemFactory().

RegisterCreatorFunction("Laplace", Laplace::create)

Name of class.

Definition at line 61 of file Laplace.h.

StdRegions::ConstFactorMap Nektar::Laplace::m_factors

protected

Definition at line 64 of file Laplace.h.

Referenced by Nektar::Helmholtz::Helmholtz(), Laplace(), v_DoSolve(), v_GenerateSummary(), and Nektar::Helmholtz::v_GetSystemSingularChecks().

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation