Nektar::LibUtilities::PolyEPoints Class Reference

#include <PolyEPoints.h>

Inheritance diagram for Nektar::LibUtilities::PolyEPoints:

Collaboration diagram for Nektar::LibUtilities::PolyEPoints:

Public Types
typedef Points< NekDouble >	PointsBaseType
Public Types inherited from Nektar::LibUtilities::Points< NekDouble >
typedef NekDouble	DataType
typedef boost::shared_ptr < NekMatrix< DataType > >	MatrixSharedPtrType

Public Member Functions
virtual	~PolyEPoints ()
const boost::shared_ptr < NekMatrix< NekDouble > >	GetI (const PointsKey &pkey)
const boost::shared_ptr < NekMatrix< NekDouble > >	GetI (const Array< OneD, const NekDouble > &x)
const boost::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
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 boost::shared_ptr < PointsBaseType >	Create (const PointsKey &key)

Private Member Functions
	PolyEPoints ()
	Default constructor should not be called except by Create method.
	PolyEPoints (const PolyEPoints &points)
	Copy constructor should not be called.
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)

Additional Inherited Members
Protected Member Functions inherited from Nektar::LibUtilities::Points< NekDouble >
virtual void	CalculatePoints ()
virtual void	CalculateWeights ()
virtual void	CalculateDerivMatrix ()
	Points (const PointsKey &key)
Protected Attributes inherited from Nektar::LibUtilities::Points< NekDouble >
PointsKey	m_pointsKey
Array< OneD, DataType >	m_points [3]
Array< OneD, DataType >	m_weights
MatrixSharedPtrType	m_derivmatrix [3]
NekManager< PointsKey, NekMatrix< DataType > , PointsKey::opLess >	m_InterpManager
NekManager< PointsKey, NekMatrix< DataType > , PointsKey::opLess >	m_GalerkinProjectionManager

Detailed Description

Definition at line 55 of file PolyEPoints.h.

Member Typedef Documentation

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

Definition at line 58 of file PolyEPoints.h.

Constructor & Destructor Documentation

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

inlinevirtual

Definition at line 60 of file PolyEPoints.h.

            {
            }            

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

inline

Definition at line 70 of file PolyEPoints.h.

                                             :PointsBaseType(key)
            {
            }

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)
            {
            }

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

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

private

Definition at line 95 of file PolyEPoints.cpp.

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.

        {
            // 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]);
                }
            }
        }

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

private

Definition at line 109 of file PolyEPoints.cpp.

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

Referenced by GetI().

        {
            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]);
                }
            }
        }

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

private

Definition at line 46 of file PolyEPoints.cpp.

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

        {
            // 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;
                }
            }
        }

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

private

Definition at line 66 of file PolyEPoints.cpp.

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, npts, and Nektar::LibUtilities::PointsManager().

        {
            // 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);
                boost::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]);
                    }
                }
            }
        }

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

static

Definition at line 120 of file PolyEPoints.cpp.

        {
            boost::shared_ptr<PointsBaseType> returnval(MemoryManager<PolyEPoints>::AllocateSharedPtr(key));

            returnval->Initialize();

            return returnval;
        }

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

virtual

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

Definition at line 129 of file PolyEPoints.cpp.

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

Referenced by GetI().

        {
            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);
        }

const boost::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 141 of file PolyEPoints.cpp.

References GetI().

        {
            int numpoints = 1;

            /// Delegate to function below.
            return GetI(numpoints, x);
        }

const boost::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 149 of file PolyEPoints.cpp.

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

        {
            Array<OneD, NekDouble> interp(GetNumPoints()*numpoints);

            CalculateInterpMatrix(numpoints, x, interp);

            unsigned int np = GetTotNumPoints();
            NekDouble* d = interp.data();
            boost::shared_ptr< NekMatrix<NekDouble> > returnval(MemoryManager<NekMatrix<NekDouble> >::AllocateSharedPtr(numpoints,np, d));

            return returnval;
        }

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 163 of file PolyEPoints.cpp.

References LagrangePoly(), and npts.

        {
            NekDouble sum = 0.0;

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

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

private

Definition at line 176 of file PolyEPoints.cpp.

References npts.

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

        {
            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;
        }

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

private

Definition at line 193 of file PolyEPoints.cpp.

References npts.

Referenced by CalculateDerivMatrix().

        {
            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;
        }