#include <PolyEPoints.h>

Inheritance diagram for Nektar::LibUtilities::PolyEPoints:

Public Types
typedef Points< NekDouble >	PointsBaseType

Public Types inherited from Nektar::LibUtilities::Points< NekDouble >
typedef NekDouble	DataType

typedef std::shared_ptr< NekMatrix< DataType > >	MatrixSharedPtrType

Public Member Functions
virtual	~PolyEPoints ()

const std::shared_ptr< NekMatrix< NekDouble > >	GetI (const PointsKey &pkey)

const std::shared_ptr< NekMatrix< NekDouble > >	GetI (const Array< OneD, const NekDouble > &x)

const std::shared_ptr< NekMatrix< NekDouble > >	GetI (unsigned int numpoints, const Array< OneD, const NekDouble > &x)

	PolyEPoints (const PointsKey &key)

Public Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual	~Points ()

virtual void	Initialize (void)

unsigned int	GetPointsDim () const

unsigned int	GetNumPoints () const

unsigned int	GetTotNumPoints () const

PointsType	GetPointsType () const

const Array< OneD, const DataType > &	GetZ () const

const Array< OneD, const DataType > &	GetW () const

void	GetZW (Array< OneD, const DataType > &z, Array< OneD, const DataType > &w) const

const Array< OneD, const NekDouble > &	GetBaryWeights () const

void	GetPoints (Array< OneD, const DataType > &x) const

void	GetPoints (Array< OneD, const DataType > &x, Array< OneD, const DataType > &y) const

void	GetPoints (Array< OneD, const DataType > &x, Array< OneD, const DataType > &y, Array< OneD, const DataType > &z) const

const MatrixSharedPtrType &	GetD (Direction dir=xDir) const

virtual const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y)

virtual const MatrixSharedPtrType	GetI (const Array< OneD, const DataType > &x, const Array< OneD, const DataType > &y, const Array< OneD, const DataType > &z)

virtual const MatrixSharedPtrType	GetGalerkinProjection (const PointsKey &pkey)

Static Public Member Functions
static std::shared_ptr< PointsBaseType >	Create (const PointsKey &key)

Private Member Functions
	PolyEPoints ()
	Default constructor should not be called except by Create method. More...

	PolyEPoints (const PolyEPoints &points)
	Copy constructor should not be called. More...

void	CalculatePoints ()

void	CalculateWeights ()

void	CalculateDerivMatrix ()

void	CalculateInterpMatrix (unsigned int npts, const Array< OneD, const NekDouble > &xpoints, Array< OneD, NekDouble > &interp)

NekDouble	LagrangeInterpolant (NekDouble x, int npts, const Array< OneD, const NekDouble > &xpts, const Array< OneD, const NekDouble > &funcvals)

NekDouble	LagrangePoly (NekDouble x, int pt, int npts, const Array< OneD, const NekDouble > &xpts)

NekDouble	LagrangePolyDeriv (NekDouble x, int pt, int npts, const Array< OneD, const NekDouble > &xpts)

Static Private Attributes
static bool	initPointsManager []

Additional Inherited Members
Protected Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual void	CalculateBaryWeights ()
	This function calculates the barycentric weights used for enhanced interpolation speed. More...

	Points (const PointsKey &key)

Protected Attributes inherited from Nektar::LibUtilities::Points< NekDouble >
PointsKey	m_pointsKey
	Points type for this points distributions. More...

Array< OneD, DataType >	m_points [3]
	Storage for the point locations, allowing for up to a 3D points storage. More...

Array< OneD, DataType >	m_weights
	Quadrature weights for the weights. More...

Array< OneD, DataType >	m_bcweights
	Barycentric weights. More...

MatrixSharedPtrType	m_derivmatrix [3]
	Derivative matrices. More...

NekManager< PointsKey, NekMatrix< DataType >, PointsKey::opLess >	m_InterpManager

NekManager< PointsKey, NekMatrix< DataType >, PointsKey::opLess >	m_GalerkinProjectionManager

Detailed Description

Definition at line 53 of file PolyEPoints.h.

Member Typedef Documentation

◆ PointsBaseType

typedef Points<NekDouble> Nektar::LibUtilities::PolyEPoints::PointsBaseType

Definition at line 56 of file PolyEPoints.h.

Constructor & Destructor Documentation

◆ ~PolyEPoints()

virtual Nektar::LibUtilities::PolyEPoints::~PolyEPoints ( )

inlinevirtual

Definition at line 58 of file PolyEPoints.h.

59 {

60 }

◆ PolyEPoints() [1/3]

Nektar::LibUtilities::PolyEPoints::PolyEPoints ( const PointsKey & key )

inline

Definition at line 68 of file PolyEPoints.h.

                                              :PointsBaseType(key)
             {
             }

◆ PolyEPoints() [2/3]

Nektar::LibUtilities::PolyEPoints::PolyEPoints ( )

inlineprivate

Default constructor should not be called except by Create method.

Definition at line 76 of file PolyEPoints.h.

                          :PointsBaseType(NullPointsKey)
             {
             }

◆ PolyEPoints() [3/3]

Nektar::LibUtilities::PolyEPoints::PolyEPoints ( const PolyEPoints & points )

inlineprivate

Copy constructor should not be called.

Definition at line 81 of file PolyEPoints.h.

                                                   :PointsBaseType(points.m_pointsKey)
             {
             }

Member Function Documentation

◆ CalculateDerivMatrix()

void Nektar::LibUtilities::PolyEPoints::CalculateDerivMatrix ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 98 of file PolyEPoints.cpp.

         {
             // Allocate the derivative matrix.
             PointsBaseType::CalculateDerivMatrix();
  
             for(unsigned int i=0;i<m_pointsKey.GetNumPoints();++i)
             {
                 for(unsigned int j=0;j<m_pointsKey.GetNumPoints();++j)
                 {
                     (*m_derivmatrix[0])(i,j) = LagrangePolyDeriv(m_points[0][i],j,m_pointsKey.GetNumPoints(),m_points[0]);
                 }
             }
         }

References Nektar::LibUtilities::Points< NekDouble >::CalculateDerivMatrix(), Nektar::LibUtilities::PointsKey::GetNumPoints(), LagrangePolyDeriv(), Nektar::LibUtilities::Points< NekDouble >::m_derivmatrix, Nektar::LibUtilities::Points< NekDouble >::m_points, and Nektar::LibUtilities::Points< NekDouble >::m_pointsKey.

◆ CalculateInterpMatrix()

void Nektar::LibUtilities::PolyEPoints::CalculateInterpMatrix	(	unsigned int	npts,
		const Array< OneD, const NekDouble > &	xpoints,
		Array< OneD, NekDouble > &	interp
	)

private

Definition at line 112 of file PolyEPoints.cpp.

         {
             for(unsigned int i=0;i<npts;++i)
             {
                 for(unsigned int j=0;j<m_pointsKey.GetNumPoints();++j)
                 {
                     interp[i + j*npts] = LagrangePoly(xpoints[i],j,m_pointsKey.GetNumPoints(),m_points[0]);
                 }
             }
         }

References Nektar::LibUtilities::PointsKey::GetNumPoints(), LagrangePoly(), Nektar::LibUtilities::Points< NekDouble >::m_points, and Nektar::LibUtilities::Points< NekDouble >::m_pointsKey.

Referenced by GetI().

◆ CalculatePoints()

void Nektar::LibUtilities::PolyEPoints::CalculatePoints ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 49 of file PolyEPoints.cpp.

         {
             // Allocate the storage for points
             PointsBaseType::CalculatePoints();
  
             unsigned int npts = m_pointsKey.GetNumPoints();
             if(npts==1)
             {
                 m_points[0][0] = 0.0;
             }
             else
             {
                 NekDouble dx = 2.0/(NekDouble)(npts-1);
                 for(unsigned int i=0;i<npts;++i)
                 {
                     m_points[0][i] = -1.0 + i*dx;
                 }
             }
         }

References Nektar::LibUtilities::Points< NekDouble >::CalculatePoints(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_points, and Nektar::LibUtilities::Points< NekDouble >::m_pointsKey.

◆ CalculateWeights()

void Nektar::LibUtilities::PolyEPoints::CalculateWeights ( )

privatevirtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 69 of file PolyEPoints.cpp.

         {
             // Allocate the storage for points
             PointsBaseType::CalculateWeights();
  
             unsigned int npts = m_pointsKey.GetNumPoints();
             if(npts==1)
             {
                 m_weights[0] = 2.0; //midpoint rule
             }
             else
             {
                 PointsKey gaussKey(npts, eGaussLobattoLegendre);
                 std::shared_ptr<PointsBaseType> ptr = PointsManager()[gaussKey];
                 Array<OneD, const NekDouble> z;
                 Array<OneD, const NekDouble> w;
  
                 ptr->GetZW(z,w);
                 for(unsigned int i=0; i<npts;++i)
                 {
                     m_weights[i] = 0.0;
                     for(unsigned j=0;j<npts;++j)
                     {
                         m_weights[i] += w[j]*LagrangePoly(z[j],i,npts,m_points[0]);
                     }
                 }
             }
         }

References Nektar::LibUtilities::Points< NekDouble >::CalculateWeights(), Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::PointsKey::GetNumPoints(), LagrangePoly(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, Nektar::LibUtilities::Points< NekDouble >::m_weights, and Nektar::LibUtilities::PointsManager().

◆ Create()

std::shared_ptr< PolyEPoints::PointsBaseType > Nektar::LibUtilities::PolyEPoints::Create ( const PointsKey & key )

static

Definition at line 123 of file PolyEPoints.cpp.

         {
             std::shared_ptr<PointsBaseType> returnval(MemoryManager<PolyEPoints>::AllocateSharedPtr(key));
  
             returnval->Initialize();
  
             return returnval;
         }

◆ GetI() [1/3]

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::PolyEPoints::GetI ( const Array< OneD, const NekDouble > & x )

virtual

Delegate to function below.

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 144 of file PolyEPoints.cpp.

         {
             int numpoints = 1;
  
             /// Delegate to function below.
             return GetI(numpoints, x);
         }

References GetI().

◆ GetI() [2/3]

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::PolyEPoints::GetI ( const PointsKey & pkey )

virtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 132 of file PolyEPoints.cpp.

         {
             ASSERTL0(pkey.GetPointsDim()==1, "Gauss Points can only interp to other 1d point distributions");
  
             int numpoints = pkey.GetNumPoints();
             Array<OneD, const NekDouble> xpoints;
  
             PointsManager()[pkey]->GetPoints(xpoints);
  
             return GetI(numpoints, xpoints);
         }

References ASSERTL0, Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsDim(), and Nektar::LibUtilities::PointsManager().

Referenced by GetI().

◆ GetI() [3/3]

const std::shared_ptr< NekMatrix< NekDouble > > Nektar::LibUtilities::PolyEPoints::GetI	(	unsigned int	numpoints,
		const Array< OneD, const NekDouble > &	x
	)

virtual

Reimplemented from Nektar::LibUtilities::Points< NekDouble >.

Definition at line 152 of file PolyEPoints.cpp.

         {
             Array<OneD, NekDouble> interp(GetNumPoints()*numpoints);
  
             CalculateInterpMatrix(numpoints, x, interp);
  
             unsigned int np = GetTotNumPoints();
             NekDouble* d = interp.data();
             std::shared_ptr< NekMatrix<NekDouble> > returnval(MemoryManager<NekMatrix<NekDouble> >::AllocateSharedPtr(numpoints,np, d));
  
             return returnval;
         }

References CalculateInterpMatrix(), Nektar::LibUtilities::Points< NekDouble >::GetNumPoints(), and Nektar::LibUtilities::Points< NekDouble >::GetTotNumPoints().

◆ LagrangeInterpolant()

NekDouble Nektar::LibUtilities::PolyEPoints::LagrangeInterpolant	(	NekDouble	x,
		int	npts,
		const Array< OneD, const NekDouble > &	xpts,
		const Array< OneD, const NekDouble > &	funcvals
	)

private

Definition at line 166 of file PolyEPoints.cpp.

         {
             NekDouble sum = 0.0;
  
             for(int i=0;i<npts;++i)
             {
                 sum += funcvals[i]*LagrangePoly(x,i,npts,xpts);
             }
             return sum;
         }

References LagrangePoly().

◆ LagrangePoly()

NekDouble Nektar::LibUtilities::PolyEPoints::LagrangePoly	(	NekDouble	x,
		int	pt,
		int	npts,
		const Array< OneD, const NekDouble > &	xpts
	)

private

Definition at line 179 of file PolyEPoints.cpp.

         {
             NekDouble h=1.0;
  
             for(int i=0;i<pt; ++i)
             {
                 h = h * (x - xpts[i])/(xpts[pt]-xpts[i]);
             }
  
             for(int i=pt+1;i<npts;++i)
             {
                 h = h * (x - xpts[i])/(xpts[pt]-xpts[i]);
             }
  
             return h;
         }

Referenced by CalculateInterpMatrix(), CalculateWeights(), and LagrangeInterpolant().

◆ LagrangePolyDeriv()

NekDouble Nektar::LibUtilities::PolyEPoints::LagrangePolyDeriv	(	NekDouble	x,
		int	pt,
		int	npts,
		const Array< OneD, const NekDouble > &	xpts
	)

private

Definition at line 196 of file PolyEPoints.cpp.

         {
             NekDouble h;
             NekDouble y=0.0;
  
             for(int j=0;j<npts;++j)
             {
                 if(j!=pt)
                 {
                     h=1.0;
                     for(int i=0;i<npts;++i)
                     {
                         if(i!=pt)
                         {
                             if(i!=j)
                             {
                                 h = h*(x-xpts[i]);
                             }
                             h = h/(xpts[pt]-xpts[i]);
                         }
                     }
                     y = y + h;
                 }
             }
             return y;
         }

Referenced by CalculateDerivMatrix().

Member Data Documentation

◆ initPointsManager

bool Nektar::LibUtilities::PolyEPoints::initPointsManager

staticprivate

Initial value:

= {
            PointsManager().RegisterCreator(PointsKey(0, ePolyEvenlySpaced), PolyEPoints::Create)
        }

Definition at line 73 of file PolyEPoints.h.

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ PointsBaseType

Constructor & Destructor Documentation

◆ ~PolyEPoints()

◆ PolyEPoints() [1/3]

◆ PolyEPoints() [2/3]

◆ PolyEPoints() [3/3]

Member Function Documentation

◆ CalculateDerivMatrix()

◆ CalculateInterpMatrix()

◆ CalculatePoints()

◆ CalculateWeights()

◆ Create()

◆ GetI() [1/3]

◆ GetI() [2/3]

◆ GetI() [3/3]

◆ LagrangeInterpolant()

◆ LagrangePoly()

◆ LagrangePolyDeriv()

Member Data Documentation

◆ initPointsManager