StdExpansion.h

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///////////////////////////////////////////////////////////////////////////////
//
// File Stdexpansion.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// License for the specific language governing rights and limitations under
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Class definition StdExpansion which is the base class
// to all expansion shapes
//
///////////////////////////////////////////////////////////////////////////////

#ifndef NEKTAR_LIB_STDREGIONS_STANDARDEXPANSION_H
#define NEKTAR_LIB_STDREGIONS_STANDARDEXPANSION_H

#include <fstream>
#include <vector>

#include <StdRegions/StdRegions.hpp>
#include <StdRegions/StdRegionsDeclspec.h>
#include <StdRegions/SpatialDomainsDeclarations.hpp>
#include <StdRegions/StdMatrixKey.h>
#include <StdRegions/IndexMapKey.h>
#include <LibUtilities/LinearAlgebra/NekTypeDefs.hpp>
#include <boost/enable_shared_from_this.hpp>
namespace Nektar { namespace LocalRegions { class MatrixKey; class Expansion; } }


namespace Nektar
{
    namespace StdRegions
    {

        class StdExpansion1D;
        class StdExpansion2D;

        typedef Array<OneD, Array<OneD, NekDouble> > NormalVector;

        /** \brief The base class for all shapes
         *
         *  This is the lowest level basic class for all shapes and so
         *  contains the definition of common data and common routine to all
         *  elements
         */
        class StdExpansion : public boost::enable_shared_from_this<StdExpansion>
        {
        public:

            /** \brief Default Constructor */
            STD_REGIONS_EXPORT StdExpansion();

            /** \brief Constructor */
            STD_REGIONS_EXPORT StdExpansion(const int numcoeffs, const int numbases,
                         const LibUtilities::BasisKey &Ba = LibUtilities::NullBasisKey,
                         const LibUtilities::BasisKey &Bb = LibUtilities::NullBasisKey,
                         const LibUtilities::BasisKey &Bc = LibUtilities::NullBasisKey);


            /** \brief Copy Constructor */
            STD_REGIONS_EXPORT StdExpansion(const StdExpansion &T);

            /** \brief Destructor */
            STD_REGIONS_EXPORT virtual ~StdExpansion();


            // Standard Expansion Routines Applicable Regardless of Region

            /** \brief This function returns the number of 1D bases used in
             *  the expansion
             *
             *  \return returns the number of 1D bases used in the expansion,
             *  which is equal to number dimension of the expansion
             */
            inline int GetNumBases() const
            {
                return m_base.num_elements();
            }

            /** \brief This function gets the shared point to basis
             *
             *  \return returns the shared pointer to the bases
             */
            inline const Array<OneD, const LibUtilities::BasisSharedPtr>& GetBase() const
            {
                return(m_base);
            }

            /** \brief This function gets the shared point to basis in
             *  the \a dir direction
             *
             *  \return returns the shared pointer to the basis in
             *  directin \a dir
             */
            inline const LibUtilities::BasisSharedPtr& GetBasis(int dir) const
            {
                ASSERTL1(dir < m_base.num_elements(),
                         "dir is larger than number of bases");
                return(m_base[dir]);
            }

            /** \brief This function returns the total number of coefficients
             *  used in the expansion
             *
             *  \return returns the total number of coefficients (which is
             *  equivalent to the total number of modes) used in the expansion
             */
            inline int GetNcoeffs(void) const
            {
                return(m_ncoeffs);
            }

            /** \brief This function returns the total number of quadrature
             *  points used in the element
             *
             *  \return returns the total number of quadrature points
             */
            inline  int GetTotPoints() const
            {
                int i;
                int nqtot = 1;

                for(i=0; i < m_base.num_elements(); ++i)
                {
                    nqtot *= m_base[i]->GetNumPoints();
                }

                return  nqtot;
            }


            /** \brief This function returns the type of basis used in the \a dir
             *  direction
             *
             *  The different types of bases implemented in the code are defined
             *  in the LibUtilities::BasisType enumeration list. As a result, the
             *  function will return one of the types of this enumeration list.
             *
             *  \param dir the direction
             *  \return returns the type of basis used in the \a dir direction
             */
            inline  LibUtilities::BasisType GetBasisType(const int dir) const
            {
                ASSERTL1(dir < m_base.num_elements(), "dir is larger than m_numbases");
                return(m_base[dir]->GetBasisType());
            }

            /** \brief This function returns the number of expansion modes
             *  in the \a dir direction
             *
             *  \param dir the direction
             *  \return returns the number of expansion modes in the \a dir
             *  direction
             */
            inline int GetBasisNumModes(const int dir) const
            {
                ASSERTL1(dir < m_base.num_elements(),"dir is larger than m_numbases");
                return(m_base[dir]->GetNumModes());
            }


            /** \brief This function returns the maximum number of
             *  expansion modes over all local directions
             *
             *  \return returns the maximum number of expansion modes
             *  over all local directions
             */
            inline int EvalBasisNumModesMax(void) const
            {
                int i;
                int returnval = 0;

                for(i = 0; i < m_base.num_elements(); ++i)
                {
                    returnval = std::max(returnval, m_base[i]->GetNumModes());
                }

                return returnval;
            }

            /** \brief This function returns the type of quadrature points used
             *  in the \a dir direction
             *
             *  The different types of quadrature points implemented in the code
             *  are defined in the LibUtilities::PointsType enumeration list.
             *  As a result, the function will return one of the types of this
             *  enumeration list.
             *
             *  \param dir the direction
             *  \return returns the type of quadrature points  used in the \a dir
             *  direction
             */
            inline LibUtilities::PointsType GetPointsType(const int dir)  const
            {
                ASSERTL1(dir < m_base.num_elements(), "dir is larger than m_numbases");
                return(m_base[dir]->GetPointsType());
            }

            /** \brief This function returns the number of quadrature points
             *  in the \a dir direction
             *
             *  \param dir the direction
             *  \return returns the number of quadrature points in the \a dir
             *  direction
             */
            inline int GetNumPoints(const int dir) const
            {
                ASSERTL1(dir < m_base.num_elements() || dir == 0,
                         "dir is larger than m_numbases");
                return(m_base.num_elements() > 0 ? m_base[dir]->GetNumPoints() : 1);
            }

            /** \brief This function returns a pointer to the array containing
             *  the quadrature points in \a dir direction
             *
             *  \param dir the direction
             *  \return returns a pointer to the array containing
             *  the quadrature points in \a dir direction
             */
            inline const Array<OneD, const NekDouble>& GetPoints(const int dir) const
            {
                return m_base[dir]->GetZ();
            }


            // Wrappers around virtual Functions

            /** \brief This function returns the number of vertices of the
             *  expansion domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetNverts()
             *
             *  \return returns the number of vertices of the expansion domain
             */
            int GetNverts() const
            {
                return v_GetNverts();
            }

            /** \brief This function returns the number of edges of the
             *  expansion domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetNedges()
             *
             *  \return returns the number of edges of the expansion domain
             */
            int GetNedges() const
            {
                return v_GetNedges();
            }

            /** \brief This function returns the number of expansion coefficients
             *  belonging to the \a i-th edge
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetEdgeNcoeffs()
             *
             *  \param i specifies which edge
             *  \return returns the number of expansion coefficients belonging to
             *  the \a i-th edge
             */
            int GetEdgeNcoeffs(const int i) const
            {
                return v_GetEdgeNcoeffs(i);
            }


            int GetTotalEdgeIntNcoeffs() const
            {
                return v_GetTotalEdgeIntNcoeffs();
            }

            /** \brief This function returns the number of quadrature points
             *  belonging to the \a i-th edge
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetEdgeNumPoints()
             *
             *  \param i specifies which edge
             *  \return returns the number of expansion coefficients belonging to
             *  the \a i-th edge
             */
            int GetEdgeNumPoints(const int i) const
            {
                return v_GetEdgeNumPoints(i);
            }


            int DetCartesianDirOfEdge(const int edge)
            {
                return v_DetCartesianDirOfEdge(edge);
            }

            const LibUtilities::BasisKey DetEdgeBasisKey(const int i) const
            {
                return v_DetEdgeBasisKey(i);
            }

            const LibUtilities::BasisKey DetFaceBasisKey(const int i, const int k) const
            {
                return v_DetFaceBasisKey(i, k);
            }
            /**
             * \brief This function returns the number of quadrature points
             * belonging to the \a i-th face.
             *
             * This function is a wrapper around the virtual function \a
             * v_GetFaceNumPoints()
             *
             * \param i specifies which face
             * \return returns the number of expansion coefficients belonging to
             * the \a i-th face
             */
            int GetFaceNumPoints(const int i) const
            {
                return v_GetFaceNumPoints(i);
            }

            /** \brief This function returns the number of expansion coefficients
             *  belonging to the \a i-th face
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetFaceNcoeffs()
             *
             *  \param i specifies which face
             *  \return returns the number of expansion coefficients belonging to
             *  the \a i-th face
             */
            int GetFaceNcoeffs(const int i) const
            {
                return v_GetFaceNcoeffs(i);
            }

            int GetFaceIntNcoeffs(const int i) const
            {
                return v_GetFaceIntNcoeffs(i);
            }

            int GetTotalFaceIntNcoeffs() const
            {
                return v_GetTotalFaceIntNcoeffs();
            }

            /** \brief This function returns the number of expansion coefficients
             *  belonging to the \a i-th edge/face
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetTraceNcoeffs()
             *
             *  \param i specifies which edge/face
             *  \return returns the number of expansion coefficients belonging to
             *  the \a i-th edge/face
             */
            int GetTraceNcoeffs(const int i) const
            {
                return v_GetTraceNcoeffs(i);
            }


            LibUtilities::PointsKey GetFacePointsKey(const int i, const int j) const
            {
                return v_GetFacePointsKey(i, j);
            }

            int NumBndryCoeffs(void)  const
            {
                return v_NumBndryCoeffs();
            }

            int NumDGBndryCoeffs(void)  const
            {
                return v_NumDGBndryCoeffs();
            }

            /** \brief This function returns the type of expansion basis on the
             *  \a i-th edge
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetEdgeBasisType()
             *
             *  The different types of bases implemented in the code are defined
             *  in the LibUtilities::BasisType enumeration list. As a result, the
             *  function will return one of the types of this enumeration list.
             *
             *  \param i specifies which edge
             *  \return returns the expansion basis on the \a i-th edge
             */
            LibUtilities::BasisType GetEdgeBasisType(const int i) const
            {
                return v_GetEdgeBasisType(i);
            }

            /** \brief This function returns the type of expansion
             *  Nodal point type if defined 
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetNodalPointsKey()
             *
             */
            const LibUtilities::PointsKey GetNodalPointsKey() const
            {
                return v_GetNodalPointsKey();
            };

            /** \brief This function returns the number of faces of the
             *  expansion domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetNFaces()
             *
             *  \return returns the number of faces of the expansion domain
             */
            int GetNfaces() const
            {
                return v_GetNfaces();
            }

            /**
             * @brief Returns the number of trace elements connected to this
             * element.
             *
             * For example, a quadrilateral has four edges, so this function
             * would return 4.
             */
            int GetNtrace() const
            {
                const int nBase = m_base.num_elements();
                return
                    nBase == 1 ? 2 :
                    nBase == 2 ? GetNedges() :
                    nBase == 3 ? GetNfaces() : 0;
            }

            /** \brief This function returns the shape of the expansion domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_DetShapeType()
             *
             *  The different shape types implemented in the code are defined
             *  in the ::ShapeType enumeration list. As a result, the
             *  function will return one of the types of this enumeration list.
             *
             *  \return returns the shape of the expansion domain
             */
            LibUtilities::ShapeType DetShapeType() const
            {
                return v_DetShapeType();
            }
            
            boost::shared_ptr<StdExpansion> GetStdExp(void) const
            {
                return v_GetStdExp();
            }


            int GetShapeDimension() const
            {
                return v_GetShapeDimension();
            }

            bool IsBoundaryInteriorExpansion()
            {
                return v_IsBoundaryInteriorExpansion();
            }


            bool IsNodalNonTensorialExp()
            {
                return v_IsNodalNonTensorialExp();
            }

            /** \brief This function performs the Backward transformation from
             *  coefficient space to physical space
             *
             *  This function is a wrapper around the virtual function
             *  \a v_BwdTrans()
             *
             *  Based on the expansion coefficients, this function evaluates the
             *  expansion at the quadrature points. This is equivalent to the
             *  operation \f[ u(\xi_{1i}) =
             *  \sum_{p=0}^{P-1} \hat{u}_p \phi_p(\xi_{1i}) \f] which can be
             *  evaluated as \f$ {\bf u} = {\bf B}^T {\bf \hat{u}} \f$ with
             *  \f${\bf B}[i][j] = \phi_i(\xi_{j})\f$
             *
             *  This function requires that the coefficient array
             *  \f$\mathbf{\hat{u}}\f$ provided as \a inarray.
             *
             *  The resulting array
             *  \f$\mathbf{u}[m]=u(\mathbf{\xi}_m)\f$ containing the
             *  expansion evaluated at the quadrature points, is stored
             *  in the \a outarray.
             *
             *  \param inarray contains the values of the expansion
             *  coefficients (input of the function)
             *
             *  \param outarray contains the values of the expansion evaluated
             *  at the quadrature points (output of the function)
             */

            void  BwdTrans (const Array<OneD, const NekDouble>& inarray,
                            Array<OneD, NekDouble> &outarray)
            {
                v_BwdTrans (inarray, outarray);
            }

            /**
             * @brief This function performs the Forward transformation from
             * physical space to coefficient space.
             */
            inline void FwdTrans (const Array<OneD, const NekDouble>& inarray,
                            Array<OneD, NekDouble> &outarray);

            void FwdTrans_BndConstrained(const Array<OneD, const NekDouble>& inarray,
                                         Array<OneD, NekDouble> &outarray)
            {
                v_FwdTrans_BndConstrained(inarray,outarray);
            }

            /** \brief This function integrates the specified function over the
             *  domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_Integral()
             *
             *  Based on the values of the function evaluated at the quadrature
             *  points (which are stored in \a inarray), this function calculates
             *  the integral of this function over the domain.  This is
             *  equivalent to the numerical evaluation of the operation
             *  \f[ I=\int u(\mathbf{\xi})d \mathbf{\xi}\f]
             *
             *  \param inarray values of the function to be integrated evaluated
             *  at the quadrature points (i.e.
             *  \a inarray[m]=\f$u(\mathbf{\xi}_m)\f$)
             *  \return returns the value of the calculated integral
             *
             *              Inputs:\n

            - \a inarray: definition of function to be returned at quadrature point
            of expansion.

            Outputs:\n

            - returns \f$\int^1_{-1}\int^1_{-1} u(\xi_1, \xi_2) J[i,j] d
            \xi_1 d \xi_2 \f$ where \f$inarray[i,j] =
            u(\xi_{1i},\xi_{2j}) \f$ and \f$ J[i,j] \f$ is the
            Jacobian evaluated at the quadrature point.
             *
             */
            NekDouble Integral(const Array<OneD, const NekDouble>& inarray )
            {
                return v_Integral(inarray);
            }

            /** \brief This function fills the array \a outarray with the
             *  \a mode-th mode of the expansion
             *
             *  This function is a wrapper around the virtual function
             *  \a v_FillMode()
             *
             *  The requested mode is evaluated at the quadrature points
             *
             *  \param mode the mode that should be filled
             *  \param outarray contains the values of the \a mode-th mode of the
             *  expansion evaluated at the quadrature points (output of the
             *  function)
             */
            void FillMode(const int mode, Array<OneD, NekDouble> &outarray)
            {
                v_FillMode(mode, outarray);
            }

            /** \brief this function calculates the inner product of a given
             *  function \a f with the different modes of the expansion
             *
             *  This function is a wrapper around the virtual function
             *  \a v_IProductWRTBase()
             *
             *  This is equivalent to the numerical evaluation of
             *  \f[ I[p] = \int \phi_p(\mathbf{x}) f(\mathbf{x}) d\mathbf{x}\f]
             *            \f$ \begin{array}{rcl} I_{pq} = (\phi_q \phi_q, u) & = &
            \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \phi_p(\xi_{0,i})
            \phi_q(\xi_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j})
            J_{i,j}\\ & = & \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i})
            \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j}
            J_{i,j} \end{array} \f$

            where

            \f$  \tilde{u}_{i,j} = w^0_i w^1_j u(\xi_{0,i},\xi_{1,j}) \f$

            which can be implemented as

            \f$  f_{qi} = \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j} =
            {\bf B_1 U}  \f$
            \f$  I_{pq} = \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i}) f_{qi} =
            {\bf B_0 F}  \f$
             *
             *  \param inarray contains the values of the function \a f
             *  evaluated at the quadrature points
             *  \param outarray contains the values of the inner product of \a f
             *  with the different modes, i.e. \f$ outarray[p] = I[p]\f$
             *  (output of the function)
             */
            void IProductWRTBase(const Array<OneD, const NekDouble>& inarray,
                                 Array<OneD, NekDouble> &outarray)
            {
                v_IProductWRTBase(inarray, outarray);
            }

            void IProductWRTBase(
                    const Array<OneD, const NekDouble>& base,
                    const Array<OneD, const NekDouble>& inarray,
                    Array<OneD, NekDouble> &outarray,
                    int coll_check)
            {
                v_IProductWRTBase(base, inarray, outarray, coll_check);
            }


            void   IProductWRTDerivBase(const int dir,
                                        const Array<OneD, const NekDouble>& inarray,
                                        Array<OneD, NekDouble> &outarray)
            {
                v_IProductWRTDerivBase(dir,inarray, outarray);
            }

            /// \brief Get the element id of this expansion when used
            /// in a list by returning value of #m_elmt_id
            inline int GetElmtId()
            {
                return m_elmt_id;
            }


            /// \brief Set the element id of this expansion when used
            /// in a list by returning value of #m_elmt_id
            inline void SetElmtId(const int id)
            {
                m_elmt_id = id;
            }

            /** \brief this function returns the physical coordinates of the
             *  quadrature points of the expansion
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetCoords()
             *
             *  \param coords an array containing the coordinates of the
             *  quadrature points (output of the function)
             */
            void GetCoords(Array<OneD, NekDouble> &coords_1,
                           Array<OneD, NekDouble> &coords_2 = NullNekDouble1DArray,
                           Array<OneD, NekDouble> &coords_3 = NullNekDouble1DArray)
            {
                v_GetCoords(coords_1,coords_2,coords_3);
            }

            /** \brief given the coordinates of a point of the element in the
             *  local collapsed coordinate system, this function calculates the
             *  physical coordinates of the point
             *
             *  This function is a wrapper around the virtual function
             *  \a v_GetCoord()
             *
             *  \param Lcoords the coordinates in the local collapsed
             *  coordinate system
             *  \param coords the physical coordinates (output of the function)
             */
            void GetCoord(const Array<OneD, const NekDouble>& Lcoord,
                          Array<OneD, NekDouble> &coord)
            {
                v_GetCoord(Lcoord, coord);
            }

            inline DNekMatSharedPtr GetStdMatrix(const StdMatrixKey &mkey)
            {
                return m_stdMatrixManager[mkey];
            }

            inline DNekBlkMatSharedPtr GetStdStaticCondMatrix(const StdMatrixKey &mkey)
            {
                return m_stdStaticCondMatrixManager[mkey];
            }

            inline IndexMapValuesSharedPtr GetIndexMap(const IndexMapKey &ikey)
            {
                return m_IndexMapManager[ikey];
            }

            const Array<OneD, const NekDouble>& GetPhysNormals(void)
            {
                return v_GetPhysNormals();
            }

            void SetPhysNormals(Array<OneD, const NekDouble> &normal)
            {
                v_SetPhysNormals(normal);
            }

            STD_REGIONS_EXPORT virtual void SetUpPhysNormals(const int edge);
            
            void NormVectorIProductWRTBase(const Array<OneD, const NekDouble> &Fx, Array< OneD, NekDouble> &outarray)
            {
                v_NormVectorIProductWRTBase(Fx,outarray);
            }

            void NormVectorIProductWRTBase(const Array<OneD, const NekDouble> &Fx, const Array<OneD, NekDouble> &Fy, Array< OneD, NekDouble> &outarray)
            {
                v_NormVectorIProductWRTBase(Fx,Fy,outarray);
            }

            void NormVectorIProductWRTBase(const Array<OneD, const NekDouble> &Fx, const Array<OneD, const NekDouble> &Fy, const Array<OneD, const NekDouble> &Fz, Array< OneD, NekDouble> &outarray)
            {
                v_NormVectorIProductWRTBase(Fx,Fy,Fz,outarray);
            }

            void NormVectorIProductWRTBase(const Array<OneD, const Array<OneD, NekDouble> > &Fvec, Array< OneD, NekDouble> &outarray)
            {
                v_NormVectorIProductWRTBase(Fvec, outarray);
            }

            DNekScalBlkMatSharedPtr GetLocStaticCondMatrix(const LocalRegions::MatrixKey &mkey)
            {
                return v_GetLocStaticCondMatrix(mkey);
            }

            STD_REGIONS_EXPORT void DropLocStaticCondMatrix(const LocalRegions::MatrixKey &mkey)
            {
                return v_DropLocStaticCondMatrix(mkey);
            }

            StdRegions::Orientation GetForient(int face)
            {
                return v_GetForient(face);
            }

            StdRegions::Orientation GetEorient(int edge)
            {
                return v_GetEorient(edge);
            }

            StdRegions::Orientation GetPorient(int point)
            {
                return v_GetPorient(point);
            }

            StdRegions::Orientation GetCartesianEorient(int edge)
            {
                return v_GetCartesianEorient(edge);
            }

            void SetCoeffsToOrientation(
                Array<OneD, NekDouble> &coeffs,
                StdRegions::Orientation dir)
            {
                v_SetCoeffsToOrientation(coeffs, dir);
            }

            void SetCoeffsToOrientation(
                StdRegions::Orientation dir,
                Array<OneD, const NekDouble> &inarray,
                Array<OneD, NekDouble> &outarray)
            {
                v_SetCoeffsToOrientation(dir,inarray,outarray);
            }

            int CalcNumberOfCoefficients(const std::vector<unsigned int>  &nummodes, int &modes_offset)
            {
                return v_CalcNumberOfCoefficients(nummodes,modes_offset);
            }

            void ExtractDataToCoeffs(const NekDouble *data,
                                     const std::vector<unsigned int > &nummodes,
                                     const int nmodes_offset,
                                     NekDouble *coeffs)
            {
                v_ExtractDataToCoeffs(data,nummodes,nmodes_offset,coeffs);
            }

            // virtual functions related to LocalRegions
            STD_REGIONS_EXPORT NekDouble StdPhysEvaluate(
                                            const Array<OneD, const NekDouble> &Lcoord,
                                            const Array<OneD, const NekDouble> &physvals);


            int GetCoordim()
            {
                return v_GetCoordim();
            }

            void GetBoundaryMap(Array<OneD, unsigned int> &outarray)
            {
                v_GetBoundaryMap(outarray);
            }

            void GetInteriorMap(Array<OneD, unsigned int> &outarray)
            {
                v_GetInteriorMap(outarray);
            }

            int GetVertexMap(const int localVertexId,
                             bool useCoeffPacking = false)
            {
                return v_GetVertexMap(localVertexId,useCoeffPacking);
            }

            void GetEdgeInteriorMap(const int eid, const Orientation edgeOrient,
                                    Array<OneD, unsigned int> &maparray,
                                    Array<OneD, int> &signarray)
            {
                v_GetEdgeInteriorMap(eid,edgeOrient,maparray,signarray);
            }

            void GetFaceInteriorMap(const int fid, const Orientation faceOrient,
                                    Array<OneD, unsigned int> &maparray,
                                    Array<OneD, int> &signarray)
            {
                v_GetFaceInteriorMap(fid,faceOrient,maparray,signarray);
            }

            void GetEdgeToElementMap(const int eid,
                                     const Orientation edgeOrient,
                                     Array<OneD, unsigned int> &maparray,
                                     Array<OneD, int> &signarray,
                                     int P = -1)
            {
                v_GetEdgeToElementMap(eid, edgeOrient, maparray, signarray, P);
            }

            void GetFaceToElementMap(const int fid, const Orientation faceOrient,
                                     Array<OneD, unsigned int> &maparray,
                                     Array<OneD, int> &signarray,
                                     int nummodesA = -1, int nummodesB = -1)
            {
                v_GetFaceToElementMap(fid,faceOrient,maparray,signarray,
                                      nummodesA,nummodesB);
            }


            /**
             * @brief Extract the physical values along edge \a edge from \a
             * inarray into \a outarray following the local edge orientation
             * and point distribution defined by defined in \a EdgeExp.
             */

            void GetEdgePhysVals(const int edge, const Array<OneD,
                                 const NekDouble> &inarray,
                                       Array<OneD,NekDouble> &outarray)
            {
                v_GetEdgePhysVals(edge,inarray,outarray);
            }

            void GetEdgePhysVals(const int edge,
                                 const boost::shared_ptr<StdExpansion> &EdgeExp,
                                 const Array<OneD, const NekDouble> &inarray,
                                       Array<OneD,NekDouble> &outarray)
            {
                v_GetEdgePhysVals(edge,EdgeExp,inarray,outarray);
            }
            
            void GetTracePhysVals(const int edge, const boost::shared_ptr<StdExpansion> &EdgeExp, const Array<OneD, const NekDouble> &inarray, Array<OneD,NekDouble> &outarray)
            {
                v_GetTracePhysVals(edge,EdgeExp,inarray,outarray);
            }

            void GetVertexPhysVals(const int vertex,
                                   const Array<OneD, const NekDouble> &inarray,
                                         NekDouble &outarray)
            {
                v_GetVertexPhysVals(vertex, inarray, outarray);
            }

            void GetEdgeInterpVals(const int edge,const Array<OneD,
                                   const NekDouble> &inarray,
                                         Array<OneD,NekDouble> &outarray)
            {
                v_GetEdgeInterpVals(edge, inarray, outarray);
            }

            /**
             * @brief Extract the metric factors to compute the contravariant
             * fluxes along edge \a edge and stores them into \a outarray
             * following the local edge orientation (i.e. anticlockwise
             * convention).
             */
            void GetEdgeQFactors(
                    const int edge,
                    Array<OneD, NekDouble> &outarray)
            {
                v_GetEdgeQFactors(edge, outarray);
            }

            void GetFacePhysVals(
                const int                                face,
                const boost::shared_ptr<StdExpansion>   &FaceExp,
                const Array<OneD, const NekDouble>      &inarray,
                      Array<OneD,       NekDouble>      &outarray,
                StdRegions::Orientation                  orient = eNoOrientation)
            {
                v_GetFacePhysVals(face, FaceExp, inarray, outarray, orient);
            }

            void GetEdgePhysMap(
                const int           edge,
                Array<OneD, int>   &outarray)
            {
                v_GetEdgePhysMap(edge, outarray);
            }
            
            void GetFacePhysMap(
                const int           face,
                Array<OneD, int>   &outarray)
            {
                v_GetFacePhysMap(face, outarray);
            }

            void MultiplyByQuadratureMetric(
                    const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> &outarray)
            {
                v_MultiplyByQuadratureMetric(inarray, outarray);
            }

            void MultiplyByStdQuadratureMetric(
                    const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> & outarray)
            {
                v_MultiplyByStdQuadratureMetric(inarray, outarray);
            }

            // Matrix Routines

            /** \brief this function generates the mass matrix
             *  \f$\mathbf{M}[i][j] =
             *  \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\f$
             *
             *  \return returns the mass matrix
             */

            STD_REGIONS_EXPORT DNekMatSharedPtr CreateGeneralMatrix(const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void GeneralMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                 Array<OneD,NekDouble> &outarray,
                                 const StdMatrixKey &mkey);

            void MassMatrixOp(const Array<OneD, const NekDouble> &inarray,
                              Array<OneD,NekDouble> &outarray,
                              const StdMatrixKey &mkey)
            {
                v_MassMatrixOp(inarray,outarray,mkey);
            }

            void LaplacianMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD,NekDouble> &outarray,
                                   const StdMatrixKey &mkey)
            {
                v_LaplacianMatrixOp(inarray,outarray,mkey);
            }

            void ReduceOrderCoeffs(int numMin,
                                   const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD,NekDouble> &outarray)
            {
                v_ReduceOrderCoeffs(numMin,inarray,outarray);
            }

            void SVVLaplacianFilter(Array<OneD,NekDouble> &array,
                                    const StdMatrixKey &mkey)
            {
                v_SVVLaplacianFilter(array,mkey);
            }

            void LaplacianMatrixOp(const int k1, const int k2,
                                   const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD,NekDouble> &outarray,
                                   const StdMatrixKey &mkey)
            {
                v_LaplacianMatrixOp(k1,k2,inarray,outarray,mkey);
            }

            void WeakDerivMatrixOp(const int i,
                                   const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD,NekDouble> &outarray,
                                   const StdMatrixKey &mkey)
            {
                v_WeakDerivMatrixOp(i,inarray,outarray,mkey);
            }

            void WeakDirectionalDerivMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                              Array<OneD,NekDouble> &outarray,
                                              const StdMatrixKey &mkey)
            {
                v_WeakDirectionalDerivMatrixOp(inarray,outarray,mkey);
            }

            void MassLevelCurvatureMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                            Array<OneD,NekDouble> &outarray,
                                            const StdMatrixKey &mkey)
            {
                v_MassLevelCurvatureMatrixOp(inarray,outarray,mkey);
            }

            void LinearAdvectionDiffusionReactionMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                                 Array<OneD,NekDouble> &outarray,
                                                          const StdMatrixKey &mkey,
                                                          bool addDiffusionTerm = true)
            {
                v_LinearAdvectionDiffusionReactionMatrixOp(inarray,outarray,mkey,addDiffusionTerm);
            }

            /**
             * @param   inarray     Input array @f$ \mathbf{u} @f$.
             * @param   outarray    Output array @f$ \boldsymbol{\nabla^2u}
             *                          + \lambda \boldsymbol{u} @f$.
             * @param   mkey
             */
            void HelmholtzMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD,NekDouble> &outarray,
                                   const StdMatrixKey &mkey)
            {
                v_HelmholtzMatrixOp(inarray,outarray,mkey);
            }

            DNekMatSharedPtr GenMatrix (const StdMatrixKey &mkey)
            {
                return v_GenMatrix(mkey);
            }

            void PhysDeriv (const Array<OneD, const NekDouble>& inarray,
                            Array<OneD, NekDouble> &out_d0,
                            Array<OneD, NekDouble> &out_d1 = NullNekDouble1DArray,
                            Array<OneD, NekDouble> &out_d2 = NullNekDouble1DArray)
            {
                v_PhysDeriv (inarray, out_d0, out_d1, out_d2);
            }

            void PhysDeriv(const int dir,
                           const Array<OneD, const NekDouble>& inarray,
                           Array<OneD, NekDouble> &outarray)
            {
                v_PhysDeriv (dir, inarray, outarray);
            }

            void PhysDeriv_s(const Array<OneD, const NekDouble>& inarray,
                             Array<OneD, NekDouble> &out_ds)
            {
                v_PhysDeriv_s(inarray,out_ds);
            }

            void PhysDeriv_n(const Array<OneD, const NekDouble>& inarray,
                             Array<OneD, NekDouble>& out_dn)
            {
                 v_PhysDeriv_n(inarray,out_dn);
            }

            void PhysDirectionalDeriv(const Array<OneD, const NekDouble>& inarray,
                                      const Array<OneD, const NekDouble>& direction,
                                      Array<OneD, NekDouble> &outarray)
            {
                v_PhysDirectionalDeriv (inarray, direction, outarray);
            }

            void StdPhysDeriv(const Array<OneD, const NekDouble>& inarray,
                              Array<OneD, NekDouble> &out_d0,
                              Array<OneD, NekDouble> &out_d1 = NullNekDouble1DArray,
                              Array<OneD, NekDouble> &out_d2 = NullNekDouble1DArray)
            {
                v_StdPhysDeriv(inarray, out_d0, out_d1, out_d2);
            }

            void StdPhysDeriv (const int dir,
                               const Array<OneD, const NekDouble>& inarray,
                               Array<OneD, NekDouble> &outarray)
            {
                v_StdPhysDeriv(dir,inarray,outarray);
            }

            void AddRobinMassMatrix(const int edgeid, const Array<OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
            {
                v_AddRobinMassMatrix(edgeid,primCoeffs,inoutmat);
            }

            void AddRobinEdgeContribution(const int edgeid, const Array<OneD, const NekDouble> &primCoeffs, Array<OneD, NekDouble> &coeffs)
            {
                v_AddRobinEdgeContribution(edgeid, primCoeffs, coeffs);
            }

            /** \brief This function evaluates the expansion at a single
             *  (arbitrary) point of the domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_PhysEvaluate()
             *
             *  Based on the value of the expansion at the quadrature
             *  points provided in \a physvals, this function
             *  calculates the value of the expansion at an arbitrary
             *  single points (with coordinates \f$ \mathbf{x_c}\f$
             *  given by the pointer \a coords). This operation,
             *  equivalent to \f[ u(\mathbf{x_c}) = \sum_p
             *  \phi_p(\mathbf{x_c}) \hat{u}_p \f] is evaluated using
             *  Lagrangian interpolants through the quadrature points:
             *  \f[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\f]
             *
             *  \param coords the coordinates of the single point
             *  \param physvals the interpolated field at the quadrature points
             *
             *  \return returns the value of the expansion at the
             *  single point
             */
            NekDouble PhysEvaluate(const Array<OneD, const NekDouble>& coords,
                                   const Array<OneD, const NekDouble>& physvals)
            {
                return v_PhysEvaluate(coords,physvals);
            }


            /** \brief This function evaluates the expansion at a single
             *  (arbitrary) point of the domain
             *
             *  This function is a wrapper around the virtual function
             *  \a v_PhysEvaluate()
             *
             *  Based on the value of the expansion at the quadrature
             *  points provided in \a physvals, this function
             *  calculates the value of the expansion at an arbitrary
             *  single points associated with the interpolation
             *  matrices provided in \f$ I \f$.
             *
             *  \param I an Array of lagrange interpolantes evaluated
             *  at the coordinate and going through the local physical
             *  quadrature
             *  \param physvals the interpolated field at the quadrature points
             *
             *  \return returns the value of the expansion at the
             *  single point
             */
            NekDouble PhysEvaluate(const Array<OneD, DNekMatSharedPtr>& I,
                                   const Array<OneD, const NekDouble >& physvals)
            {
                return v_PhysEvaluate(I,physvals);
            }


            /**
             * \brief Convert local cartesian coordinate \a xi into local
             * collapsed coordinates \a eta
             **/
            void LocCoordToLocCollapsed(const Array<OneD, const NekDouble>& xi,
                                        Array<OneD, NekDouble>& eta)
            {
                v_LocCoordToLocCollapsed(xi,eta);
            }

            const boost::shared_ptr<SpatialDomains::GeomFactors>& GetMetricInfo(void) const
            {
                return v_GetMetricInfo();
            }

            /// \brief Get the element id of this expansion when used
            /// in a list by returning value of #m_elmt_id
            STD_REGIONS_EXPORT virtual int v_GetElmtId();

            STD_REGIONS_EXPORT virtual const Array<OneD, const NekDouble>& v_GetPhysNormals(void);

            STD_REGIONS_EXPORT virtual void v_SetPhysNormals(Array<OneD, const NekDouble> &normal);

            STD_REGIONS_EXPORT virtual void v_SetUpPhysNormals(const int edge);

            STD_REGIONS_EXPORT virtual int v_CalcNumberOfCoefficients(const std::vector<unsigned int>  &nummodes, int &modes_offset);

            /**
             * @brief Unpack data from input file assuming it comes from the
             * same expansion type.
             * @see StdExpansion::ExtractDataToCoeffs
             */
            STD_REGIONS_EXPORT virtual  void v_ExtractDataToCoeffs(const NekDouble *data,
                                                const std::vector<unsigned int > &nummodes,
                                                const int nmode_offset,
                                                NekDouble *coeffs);
            
            STD_REGIONS_EXPORT virtual void v_NormVectorIProductWRTBase(const Array<OneD, const NekDouble> &Fx, Array< OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_NormVectorIProductWRTBase(
                     const Array<OneD, const NekDouble> &Fx, 
                     const Array<OneD, const NekDouble> &Fy, 
                     Array< OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_NormVectorIProductWRTBase(const Array<OneD, const NekDouble> &Fx, const Array<OneD, const NekDouble> &Fy, const Array<OneD, const NekDouble> &Fz, Array< OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_NormVectorIProductWRTBase(const Array<OneD, const Array<OneD, NekDouble> > &Fvec, Array< OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual DNekScalBlkMatSharedPtr v_GetLocStaticCondMatrix(const LocalRegions::MatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_DropLocStaticCondMatrix(const LocalRegions::MatrixKey &mkey);


            STD_REGIONS_EXPORT virtual StdRegions::Orientation v_GetForient(int face);

            STD_REGIONS_EXPORT virtual StdRegions::Orientation v_GetEorient(int edge);

            STD_REGIONS_EXPORT virtual StdRegions::Orientation v_GetCartesianEorient(int edge);

            STD_REGIONS_EXPORT virtual StdRegions::Orientation v_GetPorient(int point);

            /** \brief Function to evaluate the discrete \f$ L_\infty\f$
             *  error \f$ |\epsilon|_\infty = \max |u - u_{exact}|\f$ where \f$
             *    u_{exact}\f$ is given by the array \a sol.
             *
             *    This function takes the physical value space array \a m_phys as
             *  approximate solution
             *
             *  \param sol array of solution function  at physical quadrature
             *  points
             *  \return returns the \f$ L_\infty \f$ error as a NekDouble.
             */
             STD_REGIONS_EXPORT NekDouble Linf(const Array<OneD, const NekDouble>& phys, const Array<OneD, const NekDouble>& sol = NullNekDouble1DArray);

            /** \brief Function to evaluate the discrete \f$ L_2\f$ error,
             *  \f$ | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2
             *  dx \right]^{1/2} d\xi_1 \f$ where \f$ u_{exact}\f$ is given by
             *  the array \a sol.
             *
             *    This function takes the physical value space array \a m_phys as
             *  approximate solution
             *
             *  \param sol array of solution function  at physical quadrature
             *  points
             *  \return returns the \f$ L_2 \f$ error as a double.
             */
             STD_REGIONS_EXPORT NekDouble L2(const Array<OneD, const NekDouble>& phys, const Array<OneD, const NekDouble>& sol = NullNekDouble1DArray);

            /** \brief Function to evaluate the discrete \f$ H^1\f$
             *  error, \f$ | \epsilon |^1_{2} = \left [ \int^1_{-1} [u -
             *  u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u -
             *  u_{exact})\cdot dx \right]^{1/2} d\xi_1 \f$ where \f$
             *  u_{exact}\f$ is given by the array \a sol.
             *
             *    This function takes the physical value space array
             *  \a m_phys as approximate solution
             *
             *  \param sol array of solution function  at physical quadrature
             *  points
             *  \return returns the \f$ H_1 \f$ error as a double.
             */
             STD_REGIONS_EXPORT NekDouble H1(const Array<OneD, const NekDouble>& phys, const Array<OneD, const NekDouble>& sol = NullNekDouble1DArray);

            // I/O routines
            const NormalVector & GetEdgeNormal(const int edge) const
            {
                return v_GetEdgeNormal(edge);
            }

            void ComputeEdgeNormal(const int edge)
            {
                v_ComputeEdgeNormal(edge);
            }

            void NegateEdgeNormal(const int edge)
            {
                v_NegateEdgeNormal(edge);
            }

            bool EdgeNormalNegated(const int edge)
            {
                return v_EdgeNormalNegated(edge);
            }

            void ComputeFaceNormal(const int face)
            {
                v_ComputeFaceNormal(face);
            }

            void NegateFaceNormal(const int face)
            {
                v_NegateFaceNormal(face);
            }

            bool FaceNormalNegated(const int face)
            {
                return v_FaceNormalNegated(face);
            }

            void ComputeVertexNormal(const int vertex)
            {
                v_ComputeVertexNormal(vertex);
            }

            const NormalVector & GetFaceNormal(const int face) const
            {
                return v_GetFaceNormal(face);
            }

            const NormalVector & GetVertexNormal(const int vertex) const
            {
                return v_GetVertexNormal(vertex);
            }

            const NormalVector & GetSurfaceNormal(const int id) const
            {
                return v_GetSurfaceNormal(id);
            }

            const LibUtilities::PointsKeyVector GetPointsKeys() const
            {
                LibUtilities::PointsKeyVector p;
                for (int i = 0; i < m_base.num_elements(); ++i)
                {
                    p.push_back(m_base[i]->GetPointsKey());
                }
                return p;
            }

            STD_REGIONS_EXPORT Array<OneD, unsigned int>
                GetEdgeInverseBoundaryMap(int eid)
            {
                return v_GetEdgeInverseBoundaryMap(eid);
            }

            STD_REGIONS_EXPORT Array<OneD, unsigned int>
                GetFaceInverseBoundaryMap(int fid, StdRegions::Orientation faceOrient = eNoOrientation)
            {
                return v_GetFaceInverseBoundaryMap(fid,faceOrient);
            }

            STD_REGIONS_EXPORT DNekMatSharedPtr BuildInverseTransformationMatrix(
                const DNekScalMatSharedPtr & m_transformationmatrix)
            {
                return v_BuildInverseTransformationMatrix(
                    m_transformationmatrix);
            }


            /** \brief This function performs an interpolation from
             * the physical space points provided at input into an
             * array of equispaced points which are not the collapsed
             * coordinate. So for a tetrahedron you will only get a
             * tetrahedral number of values.
             *
             * This is primarily used for output purposes to get a
             * better distribution of points more suitable for most
             * postprocessing
             */
            STD_REGIONS_EXPORT void PhysInterpToSimplexEquiSpaced(
                const Array<OneD, const NekDouble> &inarray,
                Array<OneD, NekDouble>       &outarray,
                int npset = -1);

            /** \brief This function provides the connectivity of
             *   local simplices (triangles or tets) to connect the
             *   equispaced data points provided by
             *   PhysInterpToSimplexEquiSpaced
             *
             *  This is a virtual call to the function 
             *  \a v_GetSimplexEquiSpaceConnectivity
             */ 
            STD_REGIONS_EXPORT void GetSimplexEquiSpacedConnectivity(
                Array<OneD, int> &conn,
                bool              standard = true)
            {
                v_GetSimplexEquiSpacedConnectivity(conn,standard);
            }

            /** \brief This function performs a
             * projection/interpolation from the equispaced points
             * sometimes used in post-processing onto the coefficient
             * space 
             *
             * This is primarily used for output purposes to use a
             * more even distribution of points more suitable for alot of
             * postprocessing
             */
             STD_REGIONS_EXPORT void EquiSpacedToCoeffs(
                           const Array<OneD, const NekDouble> &inarray,
                           Array<OneD, NekDouble>       &outarray);

            template<class T>
            boost::shared_ptr<T> as()
            {
#if defined __INTEL_COMPILER && BOOST_VERSION > 105200
                typedef typename boost::shared_ptr<T>::element_type E;
                E * p = dynamic_cast< E* >( shared_from_this().get() );
                ASSERTL1(p, "Cannot perform cast");
                return boost::shared_ptr<T>( shared_from_this(), p );
#else
                return boost::dynamic_pointer_cast<T>( shared_from_this() );
#endif
            }

            void IProductWRTBase_SumFac(const Array<OneD, const NekDouble>& inarray,
                                        Array<OneD, NekDouble> &outarray,
                                        bool multiplybyweights = true)
            {
                v_IProductWRTBase_SumFac(inarray,outarray,multiplybyweights);
            }

        protected:
            Array<OneD, LibUtilities::BasisSharedPtr> m_base; /**< Bases needed for the expansion */
            int m_elmt_id;
            int m_ncoeffs;                                   /**< Total number of coefficients used in the expansion */
            LibUtilities::NekManager<StdMatrixKey, DNekMat, StdMatrixKey::opLess> m_stdMatrixManager;
            LibUtilities::NekManager<StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess> m_stdStaticCondMatrixManager;
        LibUtilities::NekManager<IndexMapKey, IndexMapValues, IndexMapKey::opLess> m_IndexMapManager;

            DNekMatSharedPtr CreateStdMatrix(const StdMatrixKey &mkey)
            {
                return v_CreateStdMatrix(mkey);
            }

            /** \brief Create the static condensation of a matrix when
                using a boundary interior decomposition

                If a matrix system can be represented by
                \f$ Mat = \left [ \begin{array}{cc}
                A & B \\
                C & D \end{array} \right ] \f$
                This routine creates a matrix containing the statically
                condense system of the form
                \f$ Mat = \left [ \begin{array}{cc}
                A - B D^{-1} C & B D^{-1} \\
                D^{-1} C       & D^{-1} \end{array} \right ] \f$
            **/
            STD_REGIONS_EXPORT DNekBlkMatSharedPtr CreateStdStaticCondMatrix(const StdMatrixKey &mkey);

            /** \brief Create an IndexMap which contains mapping information linking any specific
                element shape with either its boundaries, edges, faces, verteces, etc.

                The index member of the IndexMapValue struct gives back an integer associated with an entity index
                The sign member of the same struct gives back a sign to algebrically apply entities orientation
            **/
            STD_REGIONS_EXPORT IndexMapValuesSharedPtr CreateIndexMap(const IndexMapKey &ikey);

            STD_REGIONS_EXPORT void BwdTrans_MatOp(const Array<OneD, const NekDouble>& inarray,
                                Array<OneD, NekDouble> &outarray);

            void BwdTrans_SumFac(const Array<OneD, const NekDouble>& inarray,
                                 Array<OneD, NekDouble> &outarray)
            {
                v_BwdTrans_SumFac(inarray,outarray);
            }


            void IProductWRTDerivBase_SumFac(const int dir,
                                             const Array<OneD, const NekDouble>& inarray,
                                             Array<OneD, NekDouble> &outarray)
            {
                v_IProductWRTDerivBase_SumFac(dir,inarray,outarray);
            }

            // The term _MatFree denotes that the action of the MatrixOperation
            // is done withouth actually using the matrix (which then needs to be stored/calculated).
            // Although this does not strictly mean that no matrix operations are involved in the
            // evaluation of the operation, we use this term in the same context used as in the following
            // paper:
            // R. C. Kirby, M. G. Knepley, A. Logg, and L. R. Scott,
            // "Optimizing the evaluation of finite element matrices," SISC 27:741-758 (2005)
            STD_REGIONS_EXPORT void GeneralMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                               Array<OneD,NekDouble> &outarray,
                                               const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void MassMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                            Array<OneD,NekDouble> &outarray,
                                            const StdMatrixKey &mkey);

            void LaplacianMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                 Array<OneD,NekDouble> &outarray,
                                                 const StdMatrixKey &mkey)
            {
                v_LaplacianMatrixOp_MatFree(inarray,outarray,mkey);
            }

            STD_REGIONS_EXPORT void LaplacianMatrixOp_MatFree_Kernel(
                const Array<OneD, const NekDouble> &inarray,
                      Array<OneD,       NekDouble> &outarray,
                      Array<OneD,       NekDouble> &wsp)
            {
                v_LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp);
            }

            STD_REGIONS_EXPORT void LaplacianMatrixOp_MatFree_GenericImpl(const Array<OneD, const NekDouble> &inarray,
                                                             Array<OneD,NekDouble> &outarray,
                                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void LaplacianMatrixOp_MatFree(const int k1, const int k2,
                                                 const Array<OneD, const NekDouble> &inarray,
                                                 Array<OneD,NekDouble> &outarray,
                                                 const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void WeakDerivMatrixOp_MatFree(const int i,
                                                 const Array<OneD, const NekDouble> &inarray,
                                                 Array<OneD,NekDouble> &outarray,
                                                 const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void WeakDirectionalDerivMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                      Array<OneD,NekDouble> &outarray,
                                                      const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void MassLevelCurvatureMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                    Array<OneD,NekDouble> &outarray,
                                                    const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT void LinearAdvectionDiffusionReactionMatrixOp_MatFree( const Array<OneD, const NekDouble> &inarray,
                                                                   Array<OneD,NekDouble> &outarray,
                                                                   const StdMatrixKey &mkey,
                                                                   bool addDiffusionTerm = true);

            void HelmholtzMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                 Array<OneD,NekDouble> &outarray,
                                                 const StdMatrixKey &mkey)
            {
                v_HelmholtzMatrixOp_MatFree(inarray,outarray,mkey);
            }

            STD_REGIONS_EXPORT void HelmholtzMatrixOp_MatFree_GenericImpl(const Array<OneD, const NekDouble> &inarray,
                                                             Array<OneD,NekDouble> &outarray,
                                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_SetCoeffsToOrientation(StdRegions::Orientation dir,
                                                  Array<OneD, const NekDouble> &inarray,
                                                  Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_SetCoeffsToOrientation(
                Array<OneD, NekDouble> &coeffs,
                StdRegions::Orientation dir);

            STD_REGIONS_EXPORT virtual NekDouble v_StdPhysEvaluate(
                                                   const Array<OneD, const NekDouble> &Lcoord,
                                                   const Array<OneD, const NekDouble> &physvals);

        private:
            // Virtual functions
            STD_REGIONS_EXPORT virtual int v_GetNverts() const = 0;
            STD_REGIONS_EXPORT virtual int v_GetNedges() const;

            STD_REGIONS_EXPORT virtual int v_GetNfaces() const;

            STD_REGIONS_EXPORT virtual int v_NumBndryCoeffs() const;

            STD_REGIONS_EXPORT virtual int v_NumDGBndryCoeffs() const;

            STD_REGIONS_EXPORT virtual int v_GetEdgeNcoeffs(const int i) const;

            STD_REGIONS_EXPORT virtual int v_GetTotalEdgeIntNcoeffs() const;

            STD_REGIONS_EXPORT virtual int v_GetEdgeNumPoints(const int i) const;

            STD_REGIONS_EXPORT virtual int v_DetCartesianDirOfEdge(const int edge);

            STD_REGIONS_EXPORT virtual const LibUtilities::BasisKey v_DetEdgeBasisKey(const int i) const;

            STD_REGIONS_EXPORT virtual const LibUtilities::BasisKey v_DetFaceBasisKey(const int i, const int k) const;

            STD_REGIONS_EXPORT virtual int v_GetFaceNumPoints(const int i) const;

            STD_REGIONS_EXPORT virtual int v_GetFaceNcoeffs(const int i) const;

            STD_REGIONS_EXPORT virtual int v_GetFaceIntNcoeffs(const int i) const;

            STD_REGIONS_EXPORT virtual int v_GetTotalFaceIntNcoeffs() const;


            STD_REGIONS_EXPORT virtual int v_GetTraceNcoeffs(const int i) const;

            STD_REGIONS_EXPORT virtual LibUtilities::PointsKey v_GetFacePointsKey(const int i, const int j) const;

            STD_REGIONS_EXPORT virtual LibUtilities::BasisType v_GetEdgeBasisType(const int i) const;

            STD_REGIONS_EXPORT virtual const LibUtilities::PointsKey v_GetNodalPointsKey() const;

            STD_REGIONS_EXPORT virtual LibUtilities::ShapeType v_DetShapeType() const;

            STD_REGIONS_EXPORT virtual boost::shared_ptr<StdExpansion> 
                v_GetStdExp(void) const;

            STD_REGIONS_EXPORT virtual int v_GetShapeDimension() const;

            STD_REGIONS_EXPORT virtual bool  v_IsBoundaryInteriorExpansion();

            STD_REGIONS_EXPORT virtual bool  v_IsNodalNonTensorialExp();

            STD_REGIONS_EXPORT virtual void   v_BwdTrans   (const Array<OneD, const NekDouble>& inarray,
                                         Array<OneD, NekDouble> &outarray) = 0;

            /**
             * @brief Transform a given function from physical quadrature space
             * to coefficient space.
             * @see StdExpansion::FwdTrans
             */
            STD_REGIONS_EXPORT virtual void   v_FwdTrans   (
                            const Array<OneD, const NekDouble>& inarray,
                                  Array<OneD,       NekDouble> &outarray) = 0;

            /**
             * @brief Calculates the inner product of a given function \a f
             * with the different modes of the expansion
             */
            STD_REGIONS_EXPORT virtual void  v_IProductWRTBase(
                            const Array<OneD, const NekDouble>& inarray,
                                  Array<OneD,       NekDouble> &outarray) = 0;

            STD_REGIONS_EXPORT virtual void v_IProductWRTBase(
                            const Array<OneD, const NekDouble>& base,
                            const Array<OneD, const NekDouble>& inarray,
                                  Array<OneD,       NekDouble>& outarray,
                                  int coll_check)
            {
                ASSERTL0(false, "StdExpansion::v_IProductWRTBase has no (and should have no) implementation");
            }

            STD_REGIONS_EXPORT virtual void  v_IProductWRTDerivBase (const int dir,
                                                   const Array<OneD, const NekDouble>& inarray,
                                                   Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_FwdTrans_BndConstrained(const Array<OneD, const NekDouble>& inarray,
                                                   Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual NekDouble v_Integral(const Array<OneD, const NekDouble>& inarray );

            STD_REGIONS_EXPORT virtual void   v_PhysDeriv (const Array<OneD, const NekDouble>& inarray,
                                        Array<OneD, NekDouble> &out_d1,
                                        Array<OneD, NekDouble> &out_d2,
                                        Array<OneD, NekDouble> &out_d3);

        STD_REGIONS_EXPORT virtual void v_PhysDeriv_s (const Array<OneD, const NekDouble>& inarray,
                            Array<OneD, NekDouble> &out_ds);

            STD_REGIONS_EXPORT virtual void v_PhysDeriv_n(const Array<OneD, const NekDouble>& inarray,
                                        Array<OneD, NekDouble>& out_dn);
            STD_REGIONS_EXPORT virtual void v_PhysDeriv(const int dir,
                                     const Array<OneD, const NekDouble>& inarray,
                                     Array<OneD, NekDouble> &out_d0);

            STD_REGIONS_EXPORT virtual void v_PhysDirectionalDeriv(const Array<OneD, const NekDouble>& inarray,
                                                const Array<OneD, const NekDouble>& direction,
                                                Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_StdPhysDeriv (const Array<OneD, const NekDouble>& inarray,
                                         Array<OneD, NekDouble> &out_d1,
                                         Array<OneD, NekDouble> &out_d2,
                                         Array<OneD, NekDouble> &out_d3);

            STD_REGIONS_EXPORT virtual void   v_StdPhysDeriv (const int dir,
                                           const Array<OneD, const NekDouble>& inarray,
                                           Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_AddRobinMassMatrix(const int edgeid, const Array<OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat);

            STD_REGIONS_EXPORT virtual void v_AddRobinEdgeContribution(const int edgeid, const Array<OneD, const NekDouble> &primCoeffs, Array<OneD, NekDouble> &coeffs);

            STD_REGIONS_EXPORT virtual NekDouble v_PhysEvaluate(const Array<OneD, const NekDouble>& coords, const Array<OneD, const NekDouble> & physvals);

            STD_REGIONS_EXPORT virtual NekDouble v_PhysEvaluate(const Array<OneD, DNekMatSharedPtr >& I, const Array<OneD, const NekDouble> & physvals);

            STD_REGIONS_EXPORT virtual void v_LocCoordToLocCollapsed(
                                        const Array<OneD, const NekDouble>& xi,
                                        Array<OneD, NekDouble>& eta);


            STD_REGIONS_EXPORT virtual void v_FillMode(const int mode, Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual DNekMatSharedPtr v_GenMatrix(const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual DNekMatSharedPtr v_CreateStdMatrix(const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_GetCoords(Array<OneD, NekDouble> &coords_0,
                                     Array<OneD, NekDouble> &coords_1,
                                     Array<OneD, NekDouble> &coords_2);

            STD_REGIONS_EXPORT virtual void v_GetCoord(const Array<OneD, const NekDouble>& Lcoord,
                                    Array<OneD, NekDouble> &coord);

            STD_REGIONS_EXPORT virtual int v_GetCoordim(void);

            STD_REGIONS_EXPORT virtual void v_GetBoundaryMap(Array<OneD, unsigned int>& outarray);

            STD_REGIONS_EXPORT virtual void v_GetInteriorMap(Array<OneD, unsigned int>& outarray);

            STD_REGIONS_EXPORT virtual int v_GetVertexMap(int localVertexId,
                                                          bool useCoeffPacking = false);

            STD_REGIONS_EXPORT virtual void v_GetEdgeInteriorMap(const int eid, const Orientation edgeOrient,
                                              Array<OneD, unsigned int> &maparray,
                                              Array<OneD, int> &signarray);

            STD_REGIONS_EXPORT virtual void v_GetFaceInteriorMap(const int fid, const Orientation faceOrient,
                                              Array<OneD, unsigned int> &maparray,
                                              Array<OneD, int> &signarray);

            STD_REGIONS_EXPORT virtual void v_GetEdgeToElementMap(
                const int                  eid,
                const Orientation          edgeOrient,
                Array<OneD, unsigned int>& maparray,
                Array<OneD, int>&          signarray,
                int                        P = -1);

            STD_REGIONS_EXPORT virtual void v_GetFaceToElementMap(const int fid, const Orientation faceOrient,
                                               Array<OneD, unsigned int> &maparray,
                                               Array<OneD, int> &signarray,
                                               int nummodesA = -1, int nummodesB = -1);

            /**
             * @brief Extract the physical values along edge \a edge from \a
             * inarray into \a outarray following the local edge orientation
             * and point distribution defined by defined in \a EdgeExp.
             */
            STD_REGIONS_EXPORT virtual void v_GetEdgePhysVals(const int edge, const Array<OneD, const NekDouble> &inarray, Array<OneD,NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_GetEdgePhysVals(const int edge,  const boost::shared_ptr<StdExpansion>  &EdgeExp, const Array<OneD, const NekDouble> &inarray, Array<OneD,NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_GetTracePhysVals(const int edge,  const boost::shared_ptr<StdExpansion>  &EdgeExp, const Array<OneD, const NekDouble> &inarray, Array<OneD,NekDouble> &outarray, StdRegions::Orientation  orient = eNoOrientation);

            STD_REGIONS_EXPORT virtual void v_GetVertexPhysVals(const int vertex, const Array<OneD, const NekDouble> &inarray, NekDouble &outarray);

            STD_REGIONS_EXPORT virtual void v_GetEdgeInterpVals(const int edge,
                const Array<OneD, const NekDouble> &inarray,Array<OneD,NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_GetEdgeQFactors(
                const int edge,
                Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_GetFacePhysVals(
                const int                                face,
                const boost::shared_ptr<StdExpansion>   &FaceExp,
                const Array<OneD, const NekDouble>      &inarray,
                      Array<OneD,       NekDouble>      &outarray,
                StdRegions::Orientation                  orient);

            STD_REGIONS_EXPORT virtual void v_GetEdgePhysMap(
                const int       edge,
                Array<OneD,int> &outarray);
            
            STD_REGIONS_EXPORT virtual void v_GetFacePhysMap(
                const int       face,
                Array<OneD,int> &outarray);

            STD_REGIONS_EXPORT virtual void v_MultiplyByQuadratureMetric(
                    const Array<OneD, const NekDouble> &inarray,
                    Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_MultiplyByStdQuadratureMetric(
                    const Array<OneD, const NekDouble> &inarray,
                    Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual const  boost::shared_ptr<SpatialDomains::GeomFactors>& v_GetMetricInfo() const;

            STD_REGIONS_EXPORT virtual void v_BwdTrans_SumFac(const Array<OneD, const NekDouble>& inarray,
                                           Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_IProductWRTBase_SumFac(const Array<OneD, const NekDouble>& inarray,
                                                                     Array<OneD, NekDouble> &outarray, bool multiplybyweights = true);

            STD_REGIONS_EXPORT virtual void v_IProductWRTDerivBase_SumFac(const int dir,
                                                       const Array<OneD, const NekDouble>& inarray,
                                                       Array<OneD, NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_MassMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                        Array<OneD,NekDouble> &outarray,
                                        const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_LaplacianMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                             Array<OneD,NekDouble> &outarray,
                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_SVVLaplacianFilter(Array<OneD,NekDouble> &array,
                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_ReduceOrderCoeffs(
                                            int numMin,
                                            const Array<OneD, const NekDouble> &inarray,
                                            Array<OneD,NekDouble> &outarray);

            STD_REGIONS_EXPORT virtual void v_LaplacianMatrixOp(const int k1, const int k2,
                                             const Array<OneD, const NekDouble> &inarray,
                                             Array<OneD,NekDouble> &outarray,
                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_WeakDerivMatrixOp(const int i,
                                             const Array<OneD, const NekDouble> &inarray,
                                             Array<OneD,NekDouble> &outarray,
                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_WeakDirectionalDerivMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                                        Array<OneD,NekDouble> &outarray,
                                                        const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_MassLevelCurvatureMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                                        Array<OneD,NekDouble> &outarray,
                                                        const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_LinearAdvectionDiffusionReactionMatrixOp(const Array<OneD,
                                                                    const NekDouble> &inarray,
                                                                    Array<OneD,NekDouble> &outarray,
                                                                    const StdMatrixKey &mkey,
                                                                    bool addDiffusionTerm=true);

            STD_REGIONS_EXPORT virtual void v_HelmholtzMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                             Array<OneD,NekDouble> &outarray,
                                             const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_LaplacianMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                           Array<OneD,NekDouble> &outarray,
                                                           const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual void v_LaplacianMatrixOp_MatFree_Kernel(
                                const Array<OneD, const NekDouble> &inarray,
                                      Array<OneD,       NekDouble> &outarray,
                                      Array<OneD,       NekDouble> &wsp);

            STD_REGIONS_EXPORT virtual void v_HelmholtzMatrixOp_MatFree(const Array<OneD, const NekDouble> &inarray,
                                                           Array<OneD,NekDouble> &outarray,
                                                           const StdMatrixKey &mkey);

            STD_REGIONS_EXPORT virtual const NormalVector & v_GetEdgeNormal(const int edge) const;

            STD_REGIONS_EXPORT virtual void v_ComputeEdgeNormal(const int edge);

            STD_REGIONS_EXPORT virtual void v_NegateEdgeNormal(const int edge);

            STD_REGIONS_EXPORT virtual bool v_EdgeNormalNegated(const int edge);

            STD_REGIONS_EXPORT virtual void v_ComputeFaceNormal(const int face);

            STD_REGIONS_EXPORT virtual void v_NegateFaceNormal(const int face);

            STD_REGIONS_EXPORT virtual bool v_FaceNormalNegated(const int face);

            STD_REGIONS_EXPORT virtual const NormalVector & v_GetVertexNormal(const int vertex) const;

            STD_REGIONS_EXPORT virtual void v_ComputeVertexNormal(const int vertex);

            STD_REGIONS_EXPORT virtual const NormalVector & v_GetFaceNormal(const int face) const;
            STD_REGIONS_EXPORT virtual const NormalVector &
                v_GetSurfaceNormal(const int id) const;

            STD_REGIONS_EXPORT virtual Array<OneD, unsigned int>
                v_GetEdgeInverseBoundaryMap(int eid);

            STD_REGIONS_EXPORT virtual Array<OneD, unsigned int>
                v_GetFaceInverseBoundaryMap(int fid, StdRegions::Orientation faceOrient = eNoOrientation);

            STD_REGIONS_EXPORT virtual DNekMatSharedPtr v_BuildInverseTransformationMatrix(const DNekScalMatSharedPtr & m_transformationmatrix);

            STD_REGIONS_EXPORT virtual void v_GetSimplexEquiSpacedConnectivity(
                Array<OneD, int> &conn,
                bool              standard = true);
        };


        typedef boost::shared_ptr<StdExpansion> StdExpansionSharedPtr;
        typedef std::vector< StdExpansionSharedPtr > StdExpansionVector;
        typedef std::vector< StdExpansionSharedPtr >::iterator StdExpansionVectorIter;

        /**
         *  This function is a wrapper around the virtual function
         *  \a v_FwdTrans()
         *
         *  Given a function evaluated at the quadrature points, this
         *  function calculates the expansion coefficients such that the
         *  resulting expansion approximates the original function.
         *
         *  The calculation of the expansion coefficients is done using a
         *  Galerkin projection. This is equivalent to the operation:
         *  \f[ \mathbf{\hat{u}} = \mathbf{M}^{-1} \mathbf{I}\f]
         *  where
         *  - \f$\mathbf{M}[p][q]= \int\phi_p(\mathbf{\xi})\phi_q(
         *  \mathbf{\xi}) d\mathbf{\xi}\f$ is the Mass matrix
         *  - \f$\mathbf{I}[p] = \int\phi_p(\mathbf{\xi}) u(\mathbf{\xi})
         *  d\mathbf{\xi}\f$
         *
         *  This function takes the array \a inarray as the values of the
         *  function evaluated at the quadrature points
         *  (i.e. \f$\mathbf{u}\f$),
         *  and stores the resulting coefficients \f$\mathbf{\hat{u}}\f$
         *  in the \a outarray
         *
         *  @param inarray array of the function discretely evaluated at the
         *  quadrature points
         *
         *  @param outarray array of the function coefficieints
         */
        inline void StdExpansion::FwdTrans (const Array<OneD, const NekDouble>& inarray,
                        Array<OneD, NekDouble> &outarray)
        {
            v_FwdTrans(inarray,outarray);
        }

    } //end of namespace
} //end of namespace

#endif //STANDARDDEXPANSION_H