#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 ()

	PolyEPoints (const PointsKey &key)

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

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

const MatrixSharedPtrType	GetI (const PointsKey &key)

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

const MatrixSharedPtrType	GetI (unsigned int uint, const Array< OneD, const DataType > &x)

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

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

const MatrixSharedPtrType	GetGalerkinProjection (const PointsKey &pkey)

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

Protected Member Functions
virtual const std::shared_ptr< NekMatrix< NekDouble > >	v_GetI (const PointsKey &pkey) override

virtual const std::shared_ptr< NekMatrix< NekDouble > >	v_GetI (const Array< OneD, const NekDouble > &x) override

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

Protected Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual void	v_Initialize (void)

virtual void	v_CalculateBaryWeights ()
	This function calculates the barycentric weights used for enhanced interpolation speed. More...

	Points (const PointsKey &key)

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

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

virtual const MatrixSharedPtrType	v_GetGalerkinProjection (const PointsKey &pkey)

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...

virtual void	v_CalculatePoints () override

virtual void	v_CalculateWeights () override

virtual void	v_CalculateDerivMatrix () override

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 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 51 of file PolyEPoints.h.

Member Typedef Documentation

◆ PointsBaseType

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

Definition at line 54 of file PolyEPoints.h.

Constructor & Destructor Documentation

◆ ~PolyEPoints()

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

inlinevirtual

Definition at line 56 of file PolyEPoints.h.

57 {

58 }

◆ PolyEPoints() [1/3]

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

inline

Definition at line 63 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 79 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 84 of file PolyEPoints.h.

                                            : PointsBaseType(points.m_pointsKey)
     {
     }

Member Function Documentation

◆ 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 v_GetI().

◆ Create()

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

static

Definition at line 126 of file PolyEPoints.cpp.

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

◆ 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 176 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 189 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(), LagrangeInterpolant(), and v_CalculateWeights().

◆ LagrangePolyDeriv()

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

private

Definition at line 207 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 v_CalculateDerivMatrix().

◆ v_CalculateDerivMatrix()

void Nektar::LibUtilities::PolyEPoints::v_CalculateDerivMatrix ( )

overrideprivatevirtual

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

Definition at line 97 of file PolyEPoints.cpp.

 {
     // Allocate the derivative matrix.
     PointsBaseType::v_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::PointsKey::GetNumPoints(), LagrangePolyDeriv(), Nektar::LibUtilities::Points< NekDouble >::m_derivmatrix, Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and Nektar::LibUtilities::Points< NekDouble >::v_CalculateDerivMatrix().

◆ v_CalculatePoints()

void Nektar::LibUtilities::PolyEPoints::v_CalculatePoints ( )

overrideprivatevirtual

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

Definition at line 48 of file PolyEPoints.cpp.

 {
     // Allocate the storage for points
     PointsBaseType::v_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::PointsKey::GetNumPoints(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, and Nektar::LibUtilities::Points< NekDouble >::v_CalculatePoints().

◆ v_CalculateWeights()

void Nektar::LibUtilities::PolyEPoints::v_CalculateWeights ( )

overrideprivatevirtual

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

Definition at line 68 of file PolyEPoints.cpp.

 {
     // Allocate the storage for points
     PointsBaseType::v_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::eGaussLobattoLegendre, Nektar::LibUtilities::PointsKey::GetNumPoints(), LagrangePoly(), Nektar::LibUtilities::Points< NekDouble >::m_points, Nektar::LibUtilities::Points< NekDouble >::m_pointsKey, Nektar::LibUtilities::Points< NekDouble >::m_weights, Nektar::LibUtilities::PointsManager(), and Nektar::LibUtilities::Points< NekDouble >::v_CalculateWeights().

◆ v_GetI() [1/3]

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

overrideprotectedvirtual

Delegate to function below.

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

Definition at line 151 of file PolyEPoints.cpp.

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

References Nektar::LibUtilities::Points< NekDouble >::GetI().

◆ v_GetI() [2/3]

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

overrideprotectedvirtual

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

Definition at line 137 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::Points< NekDouble >::GetI(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetPointsDim(), and Nektar::LibUtilities::PointsManager().

◆ v_GetI() [3/3]

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

overrideprotectedvirtual

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

Definition at line 160 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;
 }