StdSegExp.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File StdSegExp.cpp
//
// 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).
//
// 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: Routines within Standard Segment Expansions
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <StdRegions/StdSegExp.h>
#include <LibUtilities/Foundations/InterpCoeff.h>
 
 
using namespace std;
 
namespace Nektar
{
    namespace StdRegions
    {
 
        /** \brief Default constructor */
 
        StdSegExp::StdSegExp()
        {
        }
 
 
        /** \brief Constructor using BasisKey class for quadrature points and
         *  order definition
         *
         *  \param Ba BasisKey class definition containing order and quadrature
         *  points.
         */
 
        StdSegExp::StdSegExp(const LibUtilities::BasisKey &Ba):
        StdExpansion(Ba.GetNumModes(), 1, Ba),
        StdExpansion1D(Ba.GetNumModes(),Ba)
        {
        }
 
 
        /** \brief Copy Constructor */
 
        StdSegExp::StdSegExp(const StdSegExp &T):
                StdExpansion(T),
                StdExpansion1D(T)
        {
        }
 
 
        StdSegExp::~StdSegExp()
        {
        }
 
        /** \brief Return Shape of region, using  ShapeType enum list.
         *  i.e. Segment
         */
        LibUtilities::ShapeType StdSegExp::v_DetShapeType() const
        {
            return LibUtilities::eSegment;
        }
 
        bool StdSegExp::v_IsBoundaryInteriorExpansion()
        {
 
            bool returnval = false;
 
            if(m_base[0]->GetBasisType() == LibUtilities::eModified_A)
            {
                returnval = true;
            }
 
            if(m_base[0]->GetBasisType() == LibUtilities::eGLL_Lagrange)
            {
                returnval = true;
            }
 
            return returnval;
        }
 
 
 
 
        //---------------------------------------------------------------------
        // Integration Methods
        //---------------------------------------------------------------------
 
        /** \brief Integrate the physical point list \a inarray over region
         *  and return the value
         *
         *  \param inarray definition of function to be integrated evauluated at
         *  quadrature point of expansion.
         *  \return returns \f$\int^1_{-1} u(\xi_1)d \xi_1 \f$ where \f$inarray[i]
         *  = u(\xi_{1i}) \f$
         */
        NekDouble StdSegExp::v_Integral(const Array<OneD, const NekDouble>& inarray )
        {
            NekDouble Int = 0.0;
            int    nquad0 = m_base[0]->GetNumPoints();
            Array<OneD, NekDouble> tmp(nquad0);
            Array<OneD, const NekDouble> z  = m_base[0]->GetZ();
            Array<OneD, const NekDouble> w0 = m_base[0]->GetW();
 
            // multiply by integration constants
            Vmath::Vmul(nquad0, inarray, 1, w0, 1, tmp, 1);
 
            Int = Vmath::Vsum(nquad0, tmp, 1);
 
            return Int;
        }
 
 
 
 
        //---------------------------------------------------------------------
        // Differentiation Methods
        //---------------------------------------------------------------------
 
 
        /** \brief Evaluate the derivative \f$ d/d{\xi_1} \f$ at the physical
         *  quadrature points given by \a inarray and return in \a outarray.
         *
         *  This is a wrapper around StdExpansion1D::Tensor_Deriv
         *  \param inarray array of a function evaluated at the quadrature points
         *  \param  outarray the resulting array of the derivative \f$
         *  du/d_{\xi_1}|_{\xi_{1i}} \f$ will be stored in the array \a outarra
         */
 
        void StdSegExp::v_PhysDeriv(const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &out_d0,
                Array<OneD, NekDouble> &out_d1,
                Array<OneD, NekDouble> &out_d2)
        {
            boost::ignore_unused(out_d1, out_d2);
            PhysTensorDeriv(inarray,out_d0);
        }
 
 
        void StdSegExp::v_PhysDeriv(const int dir,
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            boost::ignore_unused(dir);
            ASSERTL1(dir==0,"input dir is out of range");
            PhysTensorDeriv(inarray,outarray);
            // PhysDeriv(inarray, outarray);
        }
 
        void StdSegExp::v_StdPhysDeriv(
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &out_d0,
                Array<OneD, NekDouble> &out_d1,
                Array<OneD, NekDouble> &out_d2)
        {
            boost::ignore_unused(out_d1, out_d2);
            PhysTensorDeriv(inarray,out_d0);
            // PhysDeriv(inarray, out_d0);
        }
 
        void StdSegExp::v_StdPhysDeriv(
                const int dir,
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            boost::ignore_unused(dir);
            ASSERTL1(dir==0,"input dir is out of range");
            PhysTensorDeriv(inarray,outarray);
            // PhysDeriv(inarray, outarray);
        }
 
 
 
        //---------------------------------------------------------------------
        // Transforms
        //---------------------------------------------------------------------
 
        /** \brief Backward transform from coefficient space given
         *  in \a inarray and evaluate at the physical quadrature
         *  points \a outarray
         *
         *  Operation can be evaluated as \f$ u(\xi_{1i}) =
         *  \sum_{p=0}^{order-1} \hat{u}_p \phi_p(\xi_{1i}) \f$ or equivalently
         *  \f$ {\bf u} = {\bf B}^T {\bf \hat{u}} \f$ where
         *  \f${\bf B}[i][j] = \phi_i(\xi_{1j}), \mbox{\_coeffs}[p] = {\bf
         *  \hat{u}}[p] \f$
         *
         *  The function takes the coefficient array \a inarray as
         *  input for the transformation
         *
         *  \param inarray: the coeffficients of the expansion
         *
         *  \param outarray: the resulting array of the values of the function at
         *  the physical quadrature points will be stored in the array \a outarray
         */
 
        void StdSegExp::v_BwdTrans(
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            int  nquad = m_base[0]->GetNumPoints();
 
            if(m_base[0]->Collocation())
            {
                Vmath::Vcopy(nquad, inarray, 1, outarray, 1);
            }
            else
            {
 
            Blas::Dgemv('N',nquad,m_base[0]->GetNumModes(),1.0,
                        (m_base[0]->GetBdata()).get(),
                        nquad,&inarray[0],1,0.0,&outarray[0],1);
 
            }
        }
 
        void StdSegExp::v_ReduceOrderCoeffs(
            int                                 numMin,
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray)
        {
            int n_coeffs = inarray.size();
 
            Array<OneD, NekDouble> coeff(n_coeffs);
            Array<OneD, NekDouble> coeff_tmp(n_coeffs,0.0);
            Array<OneD, NekDouble> tmp;
            Array<OneD, NekDouble> tmp2;
 
            int       nmodes0 = m_base[0]->GetNumModes();
 
            Vmath::Vcopy(n_coeffs,inarray,1,coeff_tmp,1);
 
            const LibUtilities::PointsKey Pkey0(
                nmodes0, LibUtilities::eGaussLobattoLegendre);
 
            LibUtilities::BasisKey b0(m_base[0]->GetBasisType(),nmodes0,Pkey0);
 
            LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A,nmodes0,Pkey0);
 
            LibUtilities::InterpCoeff1D(
                b0, coeff_tmp, bortho0, coeff);
 
            Vmath::Zero(n_coeffs,coeff_tmp,1);
 
            Vmath::Vcopy(numMin,
                         tmp  = coeff,1,
                         tmp2 = coeff_tmp,1);
 
            LibUtilities::InterpCoeff1D(
                bortho0, coeff_tmp, b0, outarray);
        }
 
        /**
         * \brief Forward transform from physical quadrature space stored in \a
         * inarray and evaluate the expansion coefficients and store in \a
         * outarray
         *
         * Perform a forward transform using a Galerkin projection by taking the
         * inner product of the physical points and multiplying by the inverse
         * of the mass matrix using the Solve method of the standard matrix
         * container holding the local mass matrix, i.e. \f$ {\bf \hat{u}} =
         * {\bf M}^{-1} {\bf I} \f$ where \f$ {\bf I}[p] = \int^1_{-1}
         * \phi_p(\xi_1) u(\xi_1) d\xi_1 \f$
         *
         * This function stores the expansion coefficients calculated by the
         * transformation in the coefficient space array \a outarray
         *
         * \param inarray: array of physical quadrature points to be transformed
         * \param outarray: the coeffficients of the expansion
         */
        void StdSegExp::v_FwdTrans(const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            if(m_base[0]->Collocation())
            {
                Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
            }
            else
            {
                v_IProductWRTBase(inarray,outarray);
 
                // get Mass matrix inverse
                StdMatrixKey      masskey(eInvMass,v_DetShapeType(),*this);
                DNekMatSharedPtr  matsys = GetStdMatrix(masskey);
 
                NekVector<NekDouble> in(m_ncoeffs,outarray,eCopy);
                NekVector<NekDouble> out(m_ncoeffs,outarray,eWrapper);
 
                out = (*matsys)*in;
            }
        }
 
        void StdSegExp::v_FwdTrans_BndConstrained(
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            if(m_base[0]->Collocation())
            {
                Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
            }
            else
            {
                int nInteriorDofs = m_ncoeffs-2;
                int offset        = 0;
 
                switch(m_base[0]->GetBasisType())
                {
                case LibUtilities::eGLL_Lagrange:
                    {
                        offset = 1;
                    }
                    break;
                case LibUtilities::eGauss_Lagrange:
                {
                    nInteriorDofs = m_ncoeffs;
                    offset = 0;
                }
                break;
                case LibUtilities::eModified_A:
                case LibUtilities::eModified_B:
                    {
                        offset = 2;
                    }
                    break;
                default:
                    ASSERTL0(false,"This type of FwdTrans is not defined for this expansion type");
                }
 
                fill(outarray.get(), outarray.get()+m_ncoeffs, 0.0 );
 
                if(m_base[0]->GetBasisType() != LibUtilities::eGauss_Lagrange)
                {
                    outarray[GetVertexMap(0)] = inarray[0];
                    outarray[GetVertexMap(1)] = inarray[m_base[0]->GetNumPoints()-1];
 
                    if(m_ncoeffs>2)
                    {
                        // ideally, we would like to have tmp0 to be replaced by
                        // outarray (currently MassMatrixOp does not allow aliasing)
                        Array<OneD, NekDouble> tmp0(m_ncoeffs);
                        Array<OneD, NekDouble> tmp1(m_ncoeffs);
 
                        StdMatrixKey      masskey(eMass,v_DetShapeType(),*this);
                        MassMatrixOp(outarray,tmp0,masskey);
                        v_IProductWRTBase(inarray,tmp1);
 
                        Vmath::Vsub(m_ncoeffs, tmp1, 1, tmp0, 1, tmp1, 1);
 
                        // get Mass matrix inverse (only of interior DOF)
                        DNekMatSharedPtr  matsys =
                        (m_stdStaticCondMatrixManager[masskey])-> GetBlock(1,1);
 
                        Blas::Dgemv('N',nInteriorDofs,nInteriorDofs,1.0,
                                &(matsys->GetPtr())[0],nInteriorDofs,tmp1.get()
                                +offset,1,0.0,outarray.get()+offset,1);
                    }
                }
                else
                {
                    StdSegExp::v_FwdTrans(inarray, outarray);
                }
            }
 
        }
 
 
        void StdSegExp::v_BwdTrans_SumFac(const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            v_BwdTrans(inarray, outarray);
        }
 
 
 
        //---------------------------------------------------------------------
        // Inner product functions
        //---------------------------------------------------------------------
 
 
 
        /** \brief  Inner product of \a inarray over region with respect to
         *  expansion basis \a base and return in \a outarray
         *
         *  Calculate \f$ I[p] = \int^{1}_{-1} \phi_p(\xi_1) u(\xi_1) d\xi_1
         *  = \sum_{i=0}^{nq-1} \phi_p(\xi_{1i}) u(\xi_{1i}) w_i \f$ where
         *  \f$ outarray[p] = I[p], inarray[i] = u(\xi_{1i}), base[p*nq+i] =
         *  \phi_p(\xi_{1i}) \f$.
         *
         *  \param  base an array defining the local basis for the inner product
         *  usually passed from Basis->GetBdata() or Basis->GetDbdata()
         *  \param inarray: physical point array of function to be integrated
         *  \f$ u(\xi_1) \f$
         *  \param coll_check flag to identify when a Basis->Collocation() call
         *  should be performed to see if this is a GLL_Lagrange basis with a
         *  collocation property. (should be set to 0 if taking the inner
         *  product with respect to the derivative of basis)
         *  \param outarray  the values of the inner product with respect to
         *  each basis over region will be stored in the array \a outarray as
         *  output of the function
         */
 
        void StdSegExp::v_IProductWRTBase(
            const Array<OneD, const NekDouble> &base,
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray,
            int coll_check)
        {
            boost::ignore_unused(coll_check);
 
            int    nquad = m_base[0]->GetNumPoints();
            Array<OneD, NekDouble> tmp(nquad);
            Array<OneD, const NekDouble> w =  m_base[0]->GetW();
 
            Vmath::Vmul(nquad, inarray, 1, w, 1, tmp, 1);
 
            /* Comment below was a bug for collocated basis
            if(coll_check&&m_base[0]->Collocation())
            {
                Vmath::Vcopy(nquad, tmp, 1, outarray, 1);
            }
            else
            {
                Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                            &tmp[0],1,0.0,outarray.get(),1);
            }*/
 
            // Correct implementation
            Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                        &tmp[0],1,0.0,outarray.get(),1);
        }
 
        /** \brief Inner product of \a inarray over region with respect to the
         *  expansion basis (this)->m_base[0] and return in \a outarray
         *
         *  Wrapper call to StdSegExp::IProductWRTBase
         *  \param inarray array of function values evaluated at the physical
         *  collocation points
         *  \param outarray  the values of the inner product with respect to
         *  each basis over region will be stored in the array \a outarray as
         *  output of the function
         */
        void StdSegExp::v_IProductWRTBase(const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray)
        {
            v_IProductWRTBase(m_base[0]->GetBdata(),inarray,outarray,1);
        }
 
        void StdSegExp::v_IProductWRTDerivBase(
                const int dir,
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> & outarray)
        {
            boost::ignore_unused(dir);
            ASSERTL1(dir >= 0 && dir < 1,"input dir is out of range");
            v_IProductWRTBase(m_base[0]->GetDbdata(),inarray,outarray,1);
        }
 
        void StdSegExp::v_IProductWRTBase_SumFac(
                const Array<OneD, const NekDouble>& inarray,
                Array<OneD, NekDouble> &outarray,
                bool multiplybyweights)
        {
            int    nquad = m_base[0]->GetNumPoints();
            Array<OneD, NekDouble> tmp(nquad);
            Array<OneD, const NekDouble> w =  m_base[0]->GetW();
            Array<OneD, const NekDouble> base =  m_base[0]->GetBdata();
 
            if(multiplybyweights)
            {
                Vmath::Vmul(nquad, inarray, 1, w, 1, tmp, 1);
 
                Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                                &tmp[0],1,0.0,outarray.get(),1);
            }
            else
            {
                Blas::Dgemv('T',nquad,m_ncoeffs,1.0,base.get(),nquad,
                            &inarray[0],1,0.0,outarray.get(),1);
            }
        }
 
 
 
 
 
        //----------------------------
        // Evaluation
        //----------------------------
        void StdSegExp::v_LocCoordToLocCollapsed(const Array<OneD, const NekDouble>& xi,
                                                 Array<OneD, NekDouble>& eta)
        {
            eta[0] = xi[0];
        }
 
        void StdSegExp::v_LocCollapsedToLocCoord
                          (const Array<OneD, const NekDouble>& eta,
                           Array<OneD, NekDouble>& xi)
        {
            xi[0] = eta[0];
        }
 
        void StdSegExp::v_FillMode(const int mode, Array<OneD, NekDouble> &outarray)
        {
            int   nquad = m_base[0]->GetNumPoints();
            const NekDouble * base  = m_base[0]->GetBdata().get();
 
            ASSERTL2(mode <= m_ncoeffs,
             "calling argument mode is larger than total expansion order");
 
            Vmath::Vcopy(nquad,(NekDouble *)base+mode*nquad,1, &outarray[0],1);
        }
 
        NekDouble StdSegExp::v_PhysEvaluateBasis(
            const Array<OneD, const NekDouble>& coords,
            int mode)
        {
            return StdExpansion::BaryEvaluateBasis<0>(coords[0], mode);
        }
 
        void StdSegExp::v_LaplacianMatrixOp(
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray,
            const StdMatrixKey                 &mkey)
        {
            boost::ignore_unused(mkey);
 
            int    nquad = m_base[0]->GetNumPoints();
 
            Array<OneD,NekDouble> physValues(nquad);
            Array<OneD,NekDouble> dPhysValuesdx(nquad);
 
            v_BwdTrans(inarray,physValues);
 
            // Laplacian matrix operation
            v_PhysDeriv(physValues,dPhysValuesdx);
            v_IProductWRTBase(m_base[0]->GetDbdata(),dPhysValuesdx,outarray,1);
        }
 
 
        void StdSegExp::v_HelmholtzMatrixOp(
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray,
            const StdMatrixKey                 &mkey)
        {
            int    nquad = m_base[0]->GetNumPoints();
 
            Array<OneD,NekDouble> physValues(nquad);
            Array<OneD,NekDouble> dPhysValuesdx(nquad);
            Array<OneD,NekDouble> wsp(m_ncoeffs);
 
            v_BwdTrans(inarray,physValues);
 
            // mass matrix operation
            v_IProductWRTBase((m_base[0]->GetBdata()),physValues,wsp,1);
 
            // Laplacian matrix operation
            v_PhysDeriv(physValues,dPhysValuesdx);
            v_IProductWRTBase(m_base[0]->GetDbdata(),dPhysValuesdx,outarray,1);
            Blas::Daxpy(m_ncoeffs, mkey.GetConstFactor(eFactorLambda), wsp.get(), 1, outarray.get(), 1);
        }
 
        void StdSegExp::v_SVVLaplacianFilter(Array<OneD, NekDouble> &array,
                                            const StdMatrixKey &mkey)
        {
            // Generate an orthogonal expansion
            int nq = m_base[0]->GetNumPoints();
            int nmodes = m_base[0]->GetNumModes();
            // Declare orthogonal basis.
            LibUtilities::PointsKey pKey(nq,m_base[0]->GetPointsType());
 
            LibUtilities::BasisKey B(LibUtilities::eOrtho_A, nmodes, pKey);
            StdSegExp OrthoExp(B);
 
            //SVV parameters loaded from the .xml case file
            NekDouble  SvvDiffCoeff  = mkey.GetConstFactor(eFactorSVVDiffCoeff);
            int cutoff = (int) (mkey.GetConstFactor(eFactorSVVCutoffRatio))*nmodes;
 
            Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
 
            // project onto modal  space.
            OrthoExp.FwdTrans(array,orthocoeffs);
 
            //
            for(int j = 0; j < nmodes; ++j)
            {
                if(j >= cutoff)//to filter out only the "high-modes"
                {
                     orthocoeffs[j] *=
                         (SvvDiffCoeff*exp(-(j-nmodes)*(j-nmodes)/
                                            ((NekDouble)((j-cutoff+1)*
                                                 (j-cutoff+1)))));
                 }
                else
                {
                     orthocoeffs[j] *= 0.0;
                }
            }
 
            // backward transform to physical space
            OrthoExp.BwdTrans(orthocoeffs,array);
        }
 
        void StdSegExp::v_ExponentialFilter(
                                          Array<OneD, NekDouble> &array,
                                    const NekDouble        alpha,
                                    const NekDouble        exponent,
                                    const NekDouble        cutoff)
        {
            // Generate an orthogonal expansion
            int nq     = m_base[0]->GetNumPoints();
            int nmodes = m_base[0]->GetNumModes();
            int P  = nmodes - 1;
            // Declare orthogonal basis.
            LibUtilities::PointsKey pKey(nq,m_base[0]->GetPointsType());
 
            LibUtilities::BasisKey B(LibUtilities::eOrtho_A, nmodes, pKey);
            StdSegExp OrthoExp(B);
 
            // Cutoff
            int Pcut = cutoff*P;
 
            // Project onto orthogonal space.
            Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
            OrthoExp.FwdTrans(array,orthocoeffs);
 
            //
            NekDouble fac;
            for(int j = 0; j < nmodes; ++j)
            {
                //to filter out only the "high-modes"
                if(j > Pcut)
                {
                    fac = (NekDouble) (j - Pcut) / ( (NekDouble) (P - Pcut) );
                    fac = pow(fac, exponent);
                    orthocoeffs[j] *= exp(-alpha*fac);
                }
            }
 
            // backward transform to physical space
            OrthoExp.BwdTrans(orthocoeffs,array);
        }
 
        //up to here
        void StdSegExp::v_MultiplyByStdQuadratureMetric(
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray)
        {
            int nquad0 = m_base[0]->GetNumPoints();
 
            const Array<OneD, const NekDouble>& w0 = m_base[0]->GetW();
 
            Vmath::Vmul(nquad0, inarray.get(),1,
                        w0.get(),1,outarray.get(),1);
        }
 
        void StdSegExp::v_GetCoords(
                Array<OneD, NekDouble> &coords_0,
                Array<OneD, NekDouble> &coords_1,
                Array<OneD, NekDouble> &coords_2)
        {
            boost::ignore_unused(coords_1, coords_2);
            Blas::Dcopy(GetNumPoints(0),(m_base[0]->GetZ()).get(),
                        1,&coords_0[0],1);
        }
 
 
 
 
 
        //---------------------------------------------------------------------
        // Helper functions
        //---------------------------------------------------------------------
 
        int StdSegExp::v_GetNverts() const
        {
            return 2;
        }
 
        int StdSegExp::v_GetNtraces() const
        {
            return 2;
        }
 
        int StdSegExp::v_GetTraceNcoeffs(const int i) const
        {
            boost::ignore_unused(i);
            return 1;
        }
 
        int StdSegExp::v_GetTraceNumPoints(const int i) const
        {
            boost::ignore_unused(i);
            return 1;
        }
        
        int StdSegExp::v_NumBndryCoeffs() const
        {
            return 2;
        }
 
        int StdSegExp::v_NumDGBndryCoeffs() const
        {
            return 2;
        }
 
        int StdSegExp::v_CalcNumberOfCoefficients(
                const std::vector<unsigned int> &nummodes,
                int &modes_offset)
        {
            int nmodes = nummodes[modes_offset];
            modes_offset += 1;
 
            return nmodes;
        }
 
        //---------------------------------------------------------------------
        // Wrapper functions
        //---------------------------------------------------------------------
 
        DNekMatSharedPtr StdSegExp::v_GenMatrix(const StdMatrixKey &mkey)
        {
            DNekMatSharedPtr Mat;
            MatrixType mattype;
 
            switch(mattype = mkey.GetMatrixType())
            {
            case ePhysInterpToEquiSpaced:
                {
                    int nq = m_base[0]->GetNumPoints();
 
                    // take definition from key
                    if(mkey.ConstFactorExists(eFactorConst))
                    {
                        nq = (int) mkey.GetConstFactor(eFactorConst);
                    }
 
                    int neq = LibUtilities::StdSegData::
                                              getNumberOfCoefficients(nq);
                    Array<OneD, NekDouble >   coords (1);
                    DNekMatSharedPtr          I     ;
                    Mat                     = MemoryManager<DNekMat>::
                                                AllocateSharedPtr(neq, nq);
 
                    for(int i = 0; i < neq; ++i)
                    {
                        coords[0] = -1.0 + 2*i/(NekDouble)(neq-1);
                        I         = m_base[0]->GetI(coords);
                        Vmath::Vcopy(nq, I->GetRawPtr(), 1,
                                         Mat->GetRawPtr()+i,neq);
                    }
                }
                break;
            case eFwdTrans:
                {
                    Mat = MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs,m_ncoeffs);
                    StdMatrixKey iprodkey(eIProductWRTBase,v_DetShapeType(),*this);
                    DNekMat &Iprod = *GetStdMatrix(iprodkey);
                    StdMatrixKey imasskey(eInvMass,v_DetShapeType(),*this);
                    DNekMat &Imass = *GetStdMatrix(imasskey);
 
                    (*Mat) = Imass*Iprod;
                }
                break;
            default:
                {
                    Mat = StdExpansion::CreateGeneralMatrix(mkey);
 
                    if(mattype ==  eMass)
                    {
                        // For Fourier basis set the imaginary component
                        // of mean mode to have a unit diagonal component
                        // in mass matrix
                        if(m_base[0]->GetBasisType() == LibUtilities::eFourier)
                        {
                            (*Mat)(1,1) = 1.0;
                        }
                    }
                }
                break;
            }
 
            return Mat;
        }
 
 
        DNekMatSharedPtr StdSegExp::v_CreateStdMatrix(const StdMatrixKey &mkey)
        {
            return v_GenMatrix(mkey);
        }
 
        //---------------------------------------------------------------------
        // Mappings
        //---------------------------------------------------------------------
 
 
        void StdSegExp::v_GetBoundaryMap(Array<OneD, unsigned int>& outarray)
        {
            if(outarray.size() != NumBndryCoeffs())
            {
                outarray = Array<OneD, unsigned int>(NumBndryCoeffs());
            }
            const LibUtilities::BasisType Btype = GetBasisType(0);
            int nummodes = m_base[0]->GetNumModes();
 
            outarray[0] = 0;
 
            switch(Btype)
            {
            case LibUtilities::eGLL_Lagrange:
            case LibUtilities::eGauss_Lagrange:
            case LibUtilities::eChebyshev:
            case LibUtilities::eFourier:
                outarray[1]= nummodes-1;
                break;
            case LibUtilities::eModified_A:
            case LibUtilities::eModified_B:
                outarray[1] = 1;
                break;
            default:
                ASSERTL0(0,"Mapping array is not defined for this expansion");
                break;
            }
        }
 
        void StdSegExp::v_GetInteriorMap(Array<OneD, unsigned int>& outarray)
        {
            int i;
            if(outarray.size()!=GetNcoeffs()-NumBndryCoeffs())
            {
                outarray = Array<OneD, unsigned int>(GetNcoeffs()-NumBndryCoeffs());
            }
            const LibUtilities::BasisType Btype = GetBasisType(0);
 
            switch(Btype)
            {
            case LibUtilities::eGLL_Lagrange:
            case LibUtilities::eGauss_Lagrange:
            case LibUtilities::eChebyshev:
            case LibUtilities::eFourier:
                for(i = 0 ; i < GetNcoeffs()-2;i++)
                {
                    outarray[i] = i+1;
                }
                break;
            case LibUtilities::eModified_A:
            case LibUtilities::eModified_B:
                for(i = 0 ; i < GetNcoeffs()-2;i++)
                {
                    outarray[i] = i+2;
                }
                break;
            default:
                ASSERTL0(0,"Mapping array is not defined for this expansion");
                break;
            }
        }
 
        int StdSegExp::v_GetVertexMap(int localVertexId,bool useCoeffPacking)
        {
            boost::ignore_unused(useCoeffPacking);
            ASSERTL0((localVertexId==0)||(localVertexId==1),"local vertex id"
                     "must be between 0 or 1");
 
            int localDOF = localVertexId;
 
            if( (m_base[0]->GetBasisType()==LibUtilities::eGLL_Lagrange) &&
                (localVertexId==1) )
            {
                localDOF = m_base[0]->GetNumModes()-1;
            }
            return localDOF;
        }
 
        void StdSegExp::v_GetSimplexEquiSpacedConnectivity(
            Array<OneD, int> &conn,
            bool              standard)
        {
            boost::ignore_unused(standard);
            int np = m_base[0]->GetNumPoints();
 
            conn     = Array<OneD, int>(2*(np-1));
            int cnt  = 0;
            for(int i = 0; i < np-1; ++i)
            {
                conn[cnt++] = i;
                conn[cnt++] = i+1;
            }
        }
 
        void StdSegExp::v_GetTraceToElementMap(
             const int                  tid,
             Array<OneD, unsigned int>& maparray,
             Array<OneD, int>&          signarray,
             Orientation                orient,
             int P,  int Q)
        {
            boost::ignore_unused(P,Q,orient);
            int order0 = m_base[0]->GetNumModes();
    
            ASSERTL0(tid < 2,"eid must be between 0 and 1");
 
            if (maparray.size() != 2)
            {
                maparray = Array<OneD, unsigned int>(2);
            }
 
            if(signarray.size() != 2)
            {
                signarray = Array<OneD, int>(2, 1);
            }
            else
            {
                fill(signarray.get(), signarray.get()+2, 1);
            }
 
            const LibUtilities::BasisType bType = GetBasisType(0);
 
            if (bType == LibUtilities::eModified_A)
            {
                maparray[0] = 0;
                maparray[1] = 1;
            }
            else if(bType == LibUtilities::eGLL_Lagrange ||
                    bType == LibUtilities::eGauss_Lagrange)
            {
                maparray[0] = 0;
                maparray[1] = order0-1;
            }
            else
            {
                ASSERTL0(false,"Unknown Basis");
            }
        }
 
    }//end namespace
}//end namespace