///////////////////////////////////////////////////////////////////////////////
//
// File StdPyrExp.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: pyramidic routines built upon StdExpansion3D
//
///////////////////////////////////////////////////////////////////////////////

#include <boost/core/ignore_unused.hpp>

#include <StdRegions/StdPyrExp.h>
#include <LibUtilities/Foundations/ManagerAccess.h>
#include <iomanip>

using namespace std;

namespace Nektar
{
    namespace StdRegions
    {
        StdPyrExp::StdPyrExp() // Deafult construct of standard expansion directly called.
        {
        }

        StdPyrExp::StdPyrExp(const LibUtilities::BasisKey &Ba,
                             const LibUtilities::BasisKey &Bb,
                             const LibUtilities::BasisKey &Bc)
            : StdExpansion  (LibUtilities::StdPyrData::getNumberOfCoefficients(
                                 Ba.GetNumModes(),
                                 Bb.GetNumModes(),
                                 Bc.GetNumModes()),
                             3, Ba, Bb, Bc),
              StdExpansion3D(LibUtilities::StdPyrData::getNumberOfCoefficients(
                                 Ba.GetNumModes(),
                                 Bb.GetNumModes(),
                                 Bc.GetNumModes()),
                             Ba, Bb, Bc)
        {

            ASSERTL0(Ba.GetNumModes() <= Bc.GetNumModes(), "order in 'a' direction is higher "
                     "than order in 'c' direction");
            ASSERTL0(Bb.GetNumModes() <= Bc.GetNumModes(), "order in 'b' direction is higher "
                     "than order in 'c' direction");
            ASSERTL1(Bc.GetBasisType() == LibUtilities::eModifiedPyr_C ||
                     Bc.GetBasisType() == LibUtilities::eOrthoPyr_C,
                     "Expected basis type in 'c' direction to be ModifiedPyr_C or OrthoPyr_C");
            
        }

        StdPyrExp::StdPyrExp(const StdPyrExp &T)
            : StdExpansion  (T),
              StdExpansion3D(T)
        {
        }


        // Destructor
        StdPyrExp::~StdPyrExp()
        {
        }


        //---------------------------------------
        // Differentiation/integration Methods
        //---------------------------------------

        /**
         * \brief Calculate the derivative of the physical points
         *
         * The derivative is evaluated at the nodal physical points.
         * Derivatives with respect to the local Cartesian coordinates.
         *
         * \f$\begin{Bmatrix} \frac {\partial} {\partial \xi_1} \\ \frac
         * {\partial} {\partial \xi_2} \\ \frac {\partial} {\partial \xi_3}
         * \end{Bmatrix} = \begin{Bmatrix} \frac 2 {(1-\eta_3)} \frac \partial
         * {\partial \bar \eta_1} \\ \frac {\partial} {\partial \xi_2} \ \
         * \frac {(1 + \bar \eta_1)} {(1 - \eta_3)} \frac \partial {\partial
         * \bar \eta_1} + \frac {\partial} {\partial \eta_3} \end{Bmatrix}\f$
         */
        void StdPyrExp::v_PhysDeriv(
            const Array<OneD, const NekDouble> &u_physical,
                  Array<OneD,       NekDouble> &out_dxi1,
                  Array<OneD,       NekDouble> &out_dxi2,
                  Array<OneD,       NekDouble> &out_dxi3)
        {
            // PhysDerivative implementation based on Spen's book page 152.
            int    Qx = m_base[0]->GetNumPoints();
            int    Qy = m_base[1]->GetNumPoints();
            int    Qz = m_base[2]->GetNumPoints();

            Array<OneD, NekDouble> dEta_bar1(Qx*Qy*Qz,0.0);
            Array<OneD, NekDouble> dXi2     (Qx*Qy*Qz,0.0);
            Array<OneD, NekDouble> dEta3    (Qx*Qy*Qz,0.0);
            PhysTensorDeriv(u_physical, dEta_bar1, dXi2, dEta3);

            Array<OneD, const NekDouble> eta_x, eta_y, eta_z;
            eta_x = m_base[0]->GetZ();
            eta_y = m_base[1]->GetZ();
            eta_z = m_base[2]->GetZ();

            int i, j, k, n;
            
            if (out_dxi1.num_elements() > 0)
            {
                for (k = 0, n = 0; k < Qz; ++k)
                {
                    NekDouble fac = 2.0/(1.0 - eta_z[k]);
                    for (j = 0; j < Qy; ++j)
                    {
                        for (i = 0; i < Qx; ++i, ++n)
                        {
                            out_dxi1[n] = fac * dEta_bar1[n];
                        }
                    }
                }
            }

            if (out_dxi2.num_elements() > 0)
            {
                for (k = 0, n = 0; k < Qz; ++k)
                {
                    NekDouble fac = 2.0/(1.0 - eta_z[k]);
                    for (j = 0; j < Qy; ++j)
                    {
                        for (i = 0; i < Qx; ++i, ++n)
                        {
                            out_dxi2[n] = fac * dXi2[n];
                        }
                    }
                }
            }

            if (out_dxi3.num_elements() > 0)
            {
                for (k = 0, n = 0; k < Qz; ++k)
                {
                    NekDouble fac = 1.0/(1.0 - eta_z[k]);
                    for (j = 0; j < Qy; ++j)
                    {
                        NekDouble fac1 = (1.0+eta_y[j]);
                        for (i = 0; i < Qx; ++i, ++n)
                        {
                            out_dxi3[n] = (1.0+eta_x[i])*fac*dEta_bar1[n] +
                                fac1*fac*dXi2[n] + dEta3[n];
                        }
                    }
                }
            }
        }

        void StdPyrExp::v_PhysDeriv(const int dir,
                                    const Array<OneD, const NekDouble>& inarray,
                                          Array<OneD,       NekDouble>& outarray)
        {
            switch(dir)
            {
                case 0:
                {
                    v_PhysDeriv(inarray, outarray, NullNekDouble1DArray,
                                NullNekDouble1DArray);
                    break;
                }

                case 1:
                {
                    v_PhysDeriv(inarray, NullNekDouble1DArray, outarray,
                                NullNekDouble1DArray);
                    break;
                }

                case 2:
                {
                    v_PhysDeriv(inarray, NullNekDouble1DArray,
                                NullNekDouble1DArray, outarray);
                    break;
                }

                default:
                {
                    ASSERTL1(false,"input dir is out of range");
                }
                break;
            }
        }

        void StdPyrExp::v_StdPhysDeriv(const Array<OneD, const NekDouble> &inarray,
                                             Array<OneD,       NekDouble> &out_d0,
                                             Array<OneD,       NekDouble> &out_d1,
                                             Array<OneD,       NekDouble> &out_d2)
        {
            StdPyrExp::v_PhysDeriv(inarray, out_d0, out_d1, out_d2);
        }

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

        //---------------------------------------
        // Transforms
        //---------------------------------------

	/**
         * \brief Backward transformation is evaluated at the quadrature
         * points.
         *
         * \f$ u^{\delta} (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{m(pqr)} \hat
         * u_{pqr} \phi_{pqr} (\xi_{1i}, \xi_{2j}, \xi_{3k})\f$
         *
         * Backward transformation is three dimensional tensorial expansion
         *
         * \f$ u (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_p^a
	 *  (\xi_{1i}) \lbrace { \sum_{q=0}^{Q_y} \psi_{q}^a (\xi_{2j})
	 *  \lbrace { \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c (\xi_{3k})
	 *  \rbrace} \rbrace}. \f$
	 *
         * And sumfactorizing step of the form is as:\ \ \f$ f_{pqr}
         * (\xi_{3k}) = \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c
         * (\xi_{3k}),\\ g_{p} (\xi_{2j}, \xi_{3k}) = \sum_{r=0}^{Q_y}
         * \psi_{p}^a (\xi_{2j}) f_{pqr} (\xi_{3k}),\\ u(\xi_{1i}, \xi_{2j},
         * \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_{p}^a (\xi_{1i}) g_{p}
         * (\xi_{2j}, \xi_{3k}).  \f$
         **/
        void StdPyrExp::v_BwdTrans(const Array<OneD, const NekDouble> &inarray,
                                         Array<OneD,       NekDouble> &outarray)
        {
            if (m_base[0]->Collocation() &&
                m_base[1]->Collocation() &&
                m_base[2]->Collocation())
            {
                Vmath::Vcopy(m_base[0]->GetNumPoints()*
                             m_base[1]->GetNumPoints()*
                             m_base[2]->GetNumPoints(),
                             inarray, 1, outarray, 1);
            }
            else
            {
                StdPyrExp::v_BwdTrans_SumFac(inarray,outarray);
            }
        }

        /**
         * Sum-factorisation implementation of the BwdTrans operation.
         */
        void StdPyrExp::v_BwdTrans_SumFac(
            const Array<OneD, const NekDouble>& inarray,
                  Array<OneD,       NekDouble>& outarray)
        {
            int  nquad0 = m_base[0]->GetNumPoints();
            int  nquad1 = m_base[1]->GetNumPoints();
            int  nquad2 = m_base[2]->GetNumPoints();
            int  order0 = m_base[0]->GetNumModes();
            int  order1 = m_base[1]->GetNumModes();

            Array<OneD, NekDouble> wsp(nquad2*order0*order1+
                                       nquad2*nquad1*nquad0);

            v_BwdTrans_SumFacKernel(m_base[0]->GetBdata(),
                                    m_base[1]->GetBdata(),
                                    m_base[2]->GetBdata(),
                                    inarray,outarray,wsp,
                                    true,true,true);
        }

        void StdPyrExp::v_BwdTrans_SumFacKernel(
            const Array<OneD, const NekDouble> &base0,
            const Array<OneD, const NekDouble> &base1,
            const Array<OneD, const NekDouble> &base2,
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray,
                  Array<OneD,       NekDouble> &wsp,
            bool                                doCheckCollDir0,
            bool                                doCheckCollDir1,
            bool                                doCheckCollDir2)
        {
            boost::ignore_unused(doCheckCollDir0, doCheckCollDir1,
                                 doCheckCollDir2);

            int  nquad0 = m_base[0]->GetNumPoints();
            int  nquad1 = m_base[1]->GetNumPoints();
            int  nquad2 = m_base[2]->GetNumPoints();

            int  order0 = m_base[0]->GetNumModes();
            int  order1 = m_base[1]->GetNumModes();
            int  order2 = m_base[2]->GetNumModes();

            Array<OneD, NekDouble > tmp  = wsp;
            Array<OneD, NekDouble > tmp1 = tmp + nquad2*order0*order1;

            int i, j, mode, mode1, cnt;

            // Perform summation over '2' direction
            mode = mode1 = cnt = 0;
            for(i = 0; i < order0; ++i)
            {
                for(j = 0; j < order1; ++j, ++cnt)
                {
                    int ijmax = max(i,j);
                    Blas::Dgemv('N', nquad2, order2-ijmax,
                                1.0, base2.get()+mode*nquad2, nquad2,
                                     inarray.get()+mode1,     1,
                                0.0, tmp.get()+cnt*nquad2,    1);
                    mode  += order2-ijmax;
                    mode1 += order2-ijmax;
                }
                //increment mode in case order1!=order2
                for(j = order1; j < order2-i; ++j)
                {
                    int ijmax = max(i,j);
                    mode += order2-ijmax;
                }
            }

            // fix for modified basis by adding split of top singular
            // vertex mode - currently (1+c)/2 x (1-b)/2 x (1-a)/2
            // component is evaluated
            if(m_base[0]->GetBasisType() == LibUtilities::eModified_A)
            {

                // Not sure why we could not use basis as 1.0 
                // top singular vertex - (1+c)/2 x (1+b)/2 x (1-a)/2 component
                Blas::Daxpy(nquad2,inarray[1],base2.get()+nquad2,1,
                            &tmp[0]+nquad2,1);

                // top singular vertex - (1+c)/2 x (1-b)/2 x (1+a)/2 component
                Blas::Daxpy(nquad2,inarray[1],base2.get()+nquad2,1,
                            &tmp[0]+order1*nquad2,1);

                // top singular vertex - (1+c)/2 x (1+b)/2 x (1+a)/2 component
                Blas::Daxpy(nquad2,inarray[1],base2.get()+nquad2,1,
                            &tmp[0]+order1*nquad2+nquad2,1);
}

            // Perform summation over '1' direction
            mode = 0;
            for(i = 0; i < order0; ++i)
            {
                Blas::Dgemm('N', 'T', nquad1, nquad2, order1,
                            1.0, base1.get(),      nquad1,
                            tmp.get()+mode*nquad2, nquad2,
                            0.0, tmp1.get()+i*nquad1*nquad2, nquad1);
                mode  += order1;
            }

            // Perform summation over '0' direction
            Blas::Dgemm('N', 'T', nquad0, nquad1*nquad2, order0,
                        1.0, base0.get(),    nquad0,
                             tmp1.get(),     nquad1*nquad2,
                        0.0, outarray.get(), nquad0);
            
        }

	/** \brief Forward transform from physical quadrature space
            stored in \a inarray and evaluate the expansion coefficients and
            store in \a outarray

            Inputs:\n

            - \a inarray: array of physical quadrature points to be transformed

            Outputs:\n

            - \a outarray: updated array of expansion coefficients.

        */
        void StdPyrExp::v_FwdTrans(const Array<OneD, const NekDouble> &inarray,
                                         Array<OneD,       NekDouble> &outarray)
        {
            v_IProductWRTBase(inarray,outarray);

            // get Mass matrix inverse
            StdMatrixKey      imasskey(eInvMass,DetShapeType(),*this);
            DNekMatSharedPtr  imatsys = GetStdMatrix(imasskey);

            
            // copy inarray in case inarray == outarray
            DNekVec in (m_ncoeffs, outarray);
            DNekVec out(m_ncoeffs, outarray, eWrapper);

            out = (*imatsys)*in;
        }


        //---------------------------------------
        // Inner product functions
        //---------------------------------------

        /** \brief  Inner product of \a inarray over region with respect to the
            expansion basis m_base[0]->GetBdata(),m_base[1]->GetBdata(), m_base[2]->GetBdata() and return in \a outarray

            Wrapper call to StdPyrExp::IProductWRTBase

            Input:\n

            - \a inarray: array of function evaluated at the physical collocation points

            Output:\n

            - \a outarray: array of inner product with respect to each basis over region

        */
        void StdPyrExp::v_IProductWRTBase(
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray)
        {
            if (m_base[0]->Collocation() &&
                m_base[1]->Collocation() &&
                m_base[2]->Collocation())
            {
                MultiplyByStdQuadratureMetric(inarray, outarray);
            }
            else
            {
                StdPyrExp::v_IProductWRTBase_SumFac(inarray,outarray);
            }
        }

        void StdPyrExp::v_IProductWRTBase_SumFac(
            const Array<OneD, const NekDouble>& inarray,
                  Array<OneD,       NekDouble>& outarray,
            bool                                multiplybyweights)
        {

            int  nquad1 = m_base[1]->GetNumPoints();
            int  nquad2 = m_base[2]->GetNumPoints();
            int  order0 = m_base[0]->GetNumModes();
            int  order1 = m_base[1]->GetNumModes();

            Array<OneD, NekDouble> wsp(order0*nquad2*(nquad1 + order1));

            if(multiplybyweights)
            {
                Array<OneD, NekDouble> tmp(inarray.num_elements());

                v_MultiplyByStdQuadratureMetric(inarray, tmp);

                v_IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                               m_base[1]->GetBdata(),
                                               m_base[2]->GetBdata(),
                                               tmp,outarray,wsp,
                                               true,true,true);
            }
            else
            {
                v_IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                               m_base[1]->GetBdata(),
                                               m_base[2]->GetBdata(),
                                               inarray,outarray,wsp,
                                               true,true,true);
            }
        }

        void StdPyrExp::v_IProductWRTBase_SumFacKernel(
            const Array<OneD, const NekDouble> &base0,
            const Array<OneD, const NekDouble> &base1,
            const Array<OneD, const NekDouble> &base2,
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray,
                  Array<OneD,       NekDouble> &wsp,
            bool                                doCheckCollDir0,
            bool                                doCheckCollDir1,
            bool                                doCheckCollDir2)
        {
            boost::ignore_unused(doCheckCollDir0, doCheckCollDir1,
                                 doCheckCollDir2);

            int  nquad0 = m_base[0]->GetNumPoints();
            int  nquad1 = m_base[1]->GetNumPoints();
            int  nquad2 = m_base[2]->GetNumPoints();

            int  order0 = m_base[0]->GetNumModes();
            int  order1 = m_base[1]->GetNumModes();
            int  order2 = m_base[2]->GetNumModes();

            ASSERTL1(wsp.num_elements() >= nquad1*nquad2*order0 +
                                           nquad2*order0*order1,
                     "Insufficient workspace size");

            Array<OneD, NekDouble > tmp1 = wsp;
            Array<OneD, NekDouble > tmp2 = wsp + nquad1*nquad2*order0;

            int i,j, mode,mode1, cnt;

            // Inner product with respect to the '0' direction
            Blas::Dgemm('T', 'N', nquad1*nquad2, order0, nquad0,
                        1.0, inarray.get(), nquad0,
                             base0.get(),   nquad0,
                        0.0, tmp1.get(),    nquad1*nquad2);

            // Inner product with respect to the '1' direction
            for(mode=i=0; i < order0; ++i)
            {
                Blas::Dgemm('T', 'N', nquad2, order1, nquad1,
                            1.0, tmp1.get()+i*nquad1*nquad2, nquad1,
                                 base1.get(),    nquad1,
                            0.0, tmp2.get()+mode*nquad2,     nquad2);
                mode  += order1;
            }


            // Inner product with respect to the '2' direction
            mode = mode1 = cnt = 0;
            for(i = 0; i < order0; ++i)
            {
                for(j = 0; j < order1; ++j, ++cnt)
                {
                    int ijmax = max(i,j);

                    Blas::Dgemv('T', nquad2, order2-ijmax,
                                1.0, base2.get()+mode*nquad2, nquad2,
                                     tmp2.get()+cnt*nquad2,   1,
                                0.0, outarray.get()+mode1,    1);
                    mode  += order2-ijmax;
                    mode1 += order2-ijmax;
                }
                
                //increment mode in case order1!=order2
                for(j = order1; j < order2; ++j)
                {
                    int ijmax = max(i,j);
                    mode += order2-ijmax;
                }
            }

            // fix for modified basis for top singular vertex component
            // Already have evaluated (1+c)/2 (1-b)/2 (1-a)/2
            if(m_base[0]->GetBasisType() == LibUtilities::eModified_A)
            {
                // add in (1+c)/2 (1+b)/2 (1-a)/2  component
                outarray[1] += Blas::Ddot(nquad2,base2.get()+nquad2,1,
                                          &tmp2[nquad2],1);

                // add in (1+c)/2 (1-b)/2 (1+a)/2 component
                outarray[1] += Blas::Ddot(nquad2,base2.get()+nquad2,1,
                                          &tmp2[nquad2*order1],1);

                // add in (1+c)/2 (1+b)/2 (1+a)/2 component
                outarray[1] += Blas::Ddot(nquad2,base2.get()+nquad2,1,
                                          &tmp2[nquad2*order1+nquad2],1);
            }
        }

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

        /**
         * @param   inarray     Function evaluated at physical collocation
         *                      points.
         * @param   outarray    Inner product with respect to each basis
         *                      function over the element.
         */
        void StdPyrExp::v_IProductWRTDerivBase_SumFac(
            const int dir,
            const Array<OneD, const NekDouble>& inarray,
                  Array<OneD,       NekDouble>& outarray)
        {
            int i;
            int nquad0  = m_base[0]->GetNumPoints();
            int nquad1  = m_base[1]->GetNumPoints();
            int nquad2  = m_base[2]->GetNumPoints();
            int nqtot   = nquad0*nquad1*nquad2;

            Array<OneD, NekDouble> gfac0(nquad0);
            Array<OneD, NekDouble> gfac1(nquad1);
            Array<OneD, NekDouble> gfac2(nquad2);
            Array<OneD, NekDouble> tmp0 (nqtot);


            int  order0 = m_base[0]->GetNumModes();
            int  order1 = m_base[1]->GetNumModes();

            Array<OneD, NekDouble> wsp(nquad1*nquad2*order0 +
                                       nquad2*order0*order1);

            const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
            const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
            const Array<OneD, const NekDouble>& z2 = m_base[2]->GetZ();

            // set up geometric factor: (1+z0)/2
            for(i = 0; i < nquad0; ++i)
            {
                gfac0[i] = 0.5*(1+z0[i]);
            }

            // set up geometric factor: (1+z1)/2
            for(i = 0; i < nquad1; ++i)
            {
                gfac1[i] = 0.5*(1+z1[i]);
            }

            // Set up geometric factor: 2/(1-z2)
            for(i = 0; i < nquad2; ++i)
            {
            	gfac2[i] = 2.0/(1-z2[i]);
            }

            // Derivative in first/second direction is always scaled as follows
            const int nq01 = nquad0*nquad1;
            for(i = 0; i < nquad2; ++i)
            {
                Vmath::Smul(nq01, gfac2[i],
                            &inarray[0] + i*nq01, 1,
                            &tmp0   [0] + i*nq01, 1);
            }

            MultiplyByStdQuadratureMetric(tmp0, tmp0);

            switch(dir)
            {
                case 0:
                {
                    IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
                                                 m_base[1]->GetBdata (),
                                                 m_base[2]->GetBdata (),
                                                 tmp0, outarray, wsp,
                                                 false, true, true);
                    break;
                }
                case 1:
                {
                    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata (),
                                                 m_base[1]->GetDbdata(),
                                                 m_base[2]->GetBdata (),
                                                 tmp0, outarray, wsp,
                                                 true, false, true);
                    break;
                }
                case 2:
                {
                    Array<OneD, NekDouble> tmp3(m_ncoeffs);
                    Array<OneD, NekDouble> tmp4(m_ncoeffs);

                    // Scale eta_1 derivative by gfac0
                    for(i = 0; i < nquad1*nquad2; ++i)
                    {
                        Vmath::Vmul(nquad0, tmp0 .get() + i*nquad0, 1,
                                            gfac0.get(),            1,
                                            tmp0 .get() + i*nquad0, 1);
                    }
                    IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
                                                 m_base[1]->GetBdata(),
                                                 m_base[2]->GetBdata(),
                                                 tmp0,  tmp3, wsp,
                                                 false, true, true);

                    // Scale eta_2 derivative by gfac1*gfac2
                    for(i = 0; i < nquad2; ++i)
                    {
                        Vmath::Smul(nq01, gfac2[i],
                                    &inarray[0] + i*nq01, 1,
                                    &tmp0   [0] + i*nq01, 1);
                    }
                    for(i = 0; i < nquad1*nquad2; ++i)
                    {
                        Vmath::Smul(nquad0, gfac1[i%nquad1],
                                            &tmp0[0] + i*nquad0, 1,
                                            &tmp0[0] + i*nquad0, 1);
                    }

                    MultiplyByStdQuadratureMetric(tmp0, tmp0);
                    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                                 m_base[1]->GetDbdata(),
                                                 m_base[2]->GetBdata(),
                                                 tmp0, tmp4,  wsp,
                                                 true, false, true);

                    MultiplyByStdQuadratureMetric(inarray,tmp0);
                    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
                                                 m_base[1]->GetBdata(),
                                                 m_base[2]->GetDbdata(),
                                                 tmp0,outarray,wsp,
                                                 true, true, false);

                    Vmath::Vadd(m_ncoeffs,&tmp3[0],1,&outarray[0],1,&outarray[0],1);
                    Vmath::Vadd(m_ncoeffs,&tmp4[0],1,&outarray[0],1,&outarray[0],1);
                    break;
                }
                default:
                {
                    ASSERTL1(false, "input dir is out of range");
                    break;
                }
            }
        }

        //---------------------------------------
        // Evaluation functions
        //---------------------------------------

        void StdPyrExp::v_LocCoordToLocCollapsed(
            const Array<OneD, const NekDouble>& xi,
                  Array<OneD,       NekDouble>& eta)
        {
            if (fabs(xi[2]-1.0) < NekConstants::kNekZeroTol)
            {
                // Very top point of the pyramid
                eta[0] = -1.0;
                eta[1] = -1.0;
                eta[2] = xi[2];
            }
            else
            {
                // Below the line-singularity -- Common case
                eta[2] = xi[2]; // eta_z = xi_z
                eta[1] = 2.0*(1.0 + xi[1])/(1.0 - xi[2]) - 1.0;
                eta[0] = 2.0*(1.0 + xi[0])/(1.0 - xi[2]) - 1.0;
            }
        }

        void StdPyrExp::v_GetCoords(Array<OneD, NekDouble> &xi_x,
                                    Array<OneD, NekDouble> &xi_y,
                                    Array<OneD, NekDouble> &xi_z)
        {
            Array<OneD, const NekDouble> etaBar_x = m_base[0]->GetZ();
            Array<OneD, const NekDouble> eta_y    = m_base[1]->GetZ();
            Array<OneD, const NekDouble> eta_z    = m_base[2]->GetZ();
            int Qx = GetNumPoints(0);
            int Qy = GetNumPoints(1);
            int Qz = GetNumPoints(2);

            // Convert collapsed coordinates into cartesian coordinates: eta --> xi
            for (int k = 0; k < Qz; ++k )
            {
                for (int j = 0; j < Qy; ++j)
                {
                    for (int i = 0; i < Qx; ++i)
                    {
                        int s = i + Qx*(j + Qy*k);

                        xi_z[s] = eta_z[k];
                        xi_y[s] = (1.0 + eta_y[j]) * (1.0 - eta_z[k]) / 2.0  -  1.0;
                        xi_x[s] = (1.0 + etaBar_x[i]) * (1.0 - eta_z[k]) / 2.0  -  1.0;
                    }
                }
            }
        }

        void StdPyrExp::v_FillMode(const int mode, Array<OneD, NekDouble> &outarray)
        {
            Array<OneD, NekDouble> tmp(m_ncoeffs, 0.0);
            tmp[mode] = 1.0;
            v_BwdTrans(tmp, outarray);
        }

        void StdPyrExp::v_GetFaceNumModes(
                    const int                  fid,
                    const Orientation          faceOrient,
                    int &numModes0,
                    int &numModes1)
        {
            int nummodes [3] = {m_base[0]->GetNumModes(),
                                m_base[1]->GetNumModes(),
                                m_base[2]->GetNumModes()};
            switch(fid)
            {
            // quad
            case 0:
                {
                    numModes0 = nummodes[0];
                    numModes1 = nummodes[1];
                }
                break;
            case 1:
            case 3:
                {
                    numModes0 = nummodes[0];
                    numModes1 = nummodes[2];
                }
                break;
            case 2:
            case 4:
                {
                    numModes0 = nummodes[1];
                    numModes1 = nummodes[2];
                }
                break;
            }

            if ( faceOrient >= 9 )
            {
                std::swap(numModes0, numModes1);
            }
        }

        //---------------------------------------
        // Helper functions
        //---------------------------------------

        int StdPyrExp::v_GetNverts() const
        {
            return 5;
        }

        int StdPyrExp::v_GetNedges() const
        {
            return 8;
        }

        int StdPyrExp::v_GetNfaces() const
        {
            return 5;
        }

        LibUtilities::ShapeType StdPyrExp::v_DetShapeType() const
        {
            return LibUtilities::ePyramid;
        }

        int StdPyrExp::v_NumBndryCoeffs() const
        {
            ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                     GetBasisType(0) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(1) == LibUtilities::eModified_A ||
                     GetBasisType(1) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(2) == LibUtilities::eModifiedPyr_C ||
                     GetBasisType(2) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");

            int P = m_base[0]->GetNumModes();
            int Q = m_base[1]->GetNumModes();
            int R = m_base[2]->GetNumModes();

            return LibUtilities::StdPyrData::
                                    getNumberOfBndCoefficients(P, Q, R);
        }

        int StdPyrExp::v_NumDGBndryCoeffs() const
        {
            ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                     GetBasisType(0) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(1) == LibUtilities::eModified_A ||
                     GetBasisType(1) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(2) == LibUtilities::eModifiedPyr_C ||
                     GetBasisType(2) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");

            int P = m_base[0]->GetNumModes()-1;
            int Q = m_base[1]->GetNumModes()-1;
            int R = m_base[2]->GetNumModes()-1;

            return (P+1)*(Q+1)               // 1 rect. face on base
                + 2*(R+1) + P*(1 + 2*R - P)  // 2 tri. (P,R) faces
                + 2*(R+1) + Q*(1 + 2*R - Q); // 2 tri. (Q,R) faces
        }
        
        int StdPyrExp::v_GetEdgeNcoeffs(const int i) const
        {
            ASSERTL2(i >= 0 && i <= 7, "edge id is out of range");

            if (i == 0 || i == 2)
            {
                return GetBasisNumModes(0);
            }
            else if (i == 1 || i == 3)
            {
                return GetBasisNumModes(1);
            }
            else
            {
                return GetBasisNumModes(2);
            }
        }

        int StdPyrExp::v_GetFaceNcoeffs(const int i) const
        {
            ASSERTL2(i >= 0 && i <= 4, "face id is out of range");

            if (i == 0)
            {
                return GetBasisNumModes(0)*GetBasisNumModes(1);
            }
            else if (i == 1 || i == 3)
            {
                int P = GetBasisNumModes(0)-1, Q = GetBasisNumModes(2)-1;
                return Q+1 + (P*(1 + 2*Q - P))/2;
            }
            else
            {
                int P = GetBasisNumModes(1)-1, Q = GetBasisNumModes(2)-1;
                return Q+1 + (P*(1 + 2*Q - P))/2;
            }
        }

        int StdPyrExp::v_GetFaceIntNcoeffs(const int i) const
        {
            ASSERTL2(i >= 0 && i <= 4, "face id is out of range");

            int P = m_base[0]->GetNumModes()-1;
            int Q = m_base[1]->GetNumModes()-1;
            int R = m_base[2]->GetNumModes()-1;

            if (i == 0)
            {
                return (P-1)*(Q-1);
            }
            else if (i == 1 || i == 3)
            {
                return (P-1) * (2*(R-1) - (P-1) - 1) / 2;
            }
            else
            {
                return (Q-1) * (2*(R-1) - (Q-1) - 1) / 2;
            }
        }

        int StdPyrExp::v_GetFaceNumPoints(const int i) const
        {
            ASSERTL2(i >= 0 && i <= 4, "face id is out of range");

            if (i == 0)
            {
                return m_base[0]->GetNumPoints()*
                       m_base[1]->GetNumPoints();
            }
            else if (i == 1 || i == 3)
            {
                return m_base[0]->GetNumPoints()*
                       m_base[2]->GetNumPoints();
            }
            else
            {
                return m_base[1]->GetNumPoints()*
                       m_base[2]->GetNumPoints();
            }
        }


        const LibUtilities::BasisKey StdPyrExp::v_DetFaceBasisKey(
            const int i, const int k) const
        {
            ASSERTL2(i >= 0 && i <= 4, "face id is out of range");
            ASSERTL2(k >= 0 && k <= 1, "basis key id is out of range");

            switch(i)
            {
                case 0:
                {
                    return EvaluateQuadFaceBasisKey(k,
                                                    m_base[k]->GetBasisType(),
                                                    m_base[k]->GetNumPoints(),
                                                    m_base[k]->GetNumModes());

                }
                case 1:
                case 3:
                {
                    return EvaluateTriFaceBasisKey(k,
                                                   m_base[2*k]->GetBasisType(),
                                                   m_base[2*k]->GetNumPoints(),
                                                   m_base[2*k]->GetNumModes());
                }
                case 2:
                case 4:
                {
                    return EvaluateTriFaceBasisKey(k,
                                                   m_base[k+1]->GetBasisType(),
                                                   m_base[k+1]->GetNumPoints(),
                                                   m_base[k+1]->GetNumModes());
                }
            }

            // Should never get here.
            return LibUtilities::NullBasisKey;
        }

        int StdPyrExp::v_CalcNumberOfCoefficients(
            const std::vector<unsigned int> &nummodes,
            int &modes_offset)
        {
            int nmodes = LibUtilities::StdPyrData::getNumberOfCoefficients(
                nummodes[modes_offset],
                nummodes[modes_offset+1],
                nummodes[modes_offset+2]);

            modes_offset += 3;
            return nmodes;
        }

        LibUtilities::BasisType StdPyrExp::v_GetEdgeBasisType(const int i) const
        {
            ASSERTL2(i >= 0 && i <= 7, "edge id is out of range");
            if (i == 0 || i == 2)
            {
                return GetBasisType(0);
            }
            else if (i == 1 || i == 3)
            {
                return GetBasisType(1);
            }
            else
            {
                return GetBasisType(2);
            }
        }


        //---------------------------------------
        // Mappings
        //---------------------------------------

        void StdPyrExp::v_GetFaceToElementMap(
            const int                  fid,
            const Orientation          faceOrient,
            Array<OneD, unsigned int> &maparray,
            Array<OneD,          int> &signarray,
            int                        P,
            int                        Q)
        {
            ASSERTL1(GetEdgeBasisType(0) == GetEdgeBasisType(1),
                     "Method only implemented if BasisType is identical"
                     "in x and y directions");
            ASSERTL1(GetEdgeBasisType(0) == LibUtilities::eModified_A &&
                     GetEdgeBasisType(4) == LibUtilities::eModifiedPyr_C,
                     "Method only implemented for Modified_A BasisType"
                     "(x and y direction) and ModifiedPyr_C BasisType (z "
                     "direction)");

            int i, j, k, p, q, r, nFaceCoeffs, idx = 0;
            int nummodesA=0, nummodesB=0;

            int order0 = m_base[0]->GetNumModes();
            int order1 = m_base[1]->GetNumModes();
            int order2 = m_base[2]->GetNumModes();

            switch (fid)
            {
            case 0:
                nummodesA = order0;
                nummodesB = order1;
                break;
            case 1:
            case 3:
                nummodesA = order0;
                nummodesB = order2;
                break;
            case 2:
            case 4:
                nummodesA = order1;
                nummodesB = order2;
                break;
            default:
                ASSERTL0(false,"fid must be between 0 and 4");
            }

            bool CheckForZeroedModes = false;

            if (P == -1)
            {
                P = nummodesA;
                Q = nummodesB;
                nFaceCoeffs = GetFaceNcoeffs(fid);
            }
            else if (fid > 0)
            {
                nFaceCoeffs = P*(2*Q-P+1)/2;
                CheckForZeroedModes = true;
            }
            else
            {
                nFaceCoeffs = P*Q;
                CheckForZeroedModes = true;
            }

            // Allocate the map array and sign array; set sign array to ones (+)
            if (maparray.num_elements() != nFaceCoeffs)
            {
                maparray = Array<OneD, unsigned int>(nFaceCoeffs);
            }

            if (signarray.num_elements() != nFaceCoeffs)
            {
                signarray = Array<OneD, int>(nFaceCoeffs,1);
            }
            else
            {
                fill(signarray.get(), signarray.get() + nFaceCoeffs, 1);
            }

            // Set up an array indexing for quads, since the ordering may need
            // to be transposed.
            Array<OneD, int> arrayindx(nFaceCoeffs,-1);

            if (fid == 0)
            {
                for (i = 0; i < Q; i++)
                {
                    for (j = 0; j < P; j++)
                    {
                        if (faceOrient < 9)
                        {
                            arrayindx[i*P+j] = i*P+j;
                        }
                        else
                        {
                            arrayindx[i*P+j] = j*Q+i;
                        }
                    }
                }
            }

            // Set up ordering inside each 2D face. Also for triangular faces,
            // populate signarray.
            switch (fid)
            {
            case 0: // Bottom quad

                for (q = 0; q < Q; ++q)
                {
                    for (p = 0; p < P; ++p)
                    {
                        maparray[arrayindx[q*P+p]] = GetMode(p,q,0);
                    }
                }
                break;
                
            case 1: // Front triangle
                for (p = 0; p < P; ++p)
                {
                    for (r = 0; r < Q-p; ++r)
                    {
                        if ((int)faceOrient == 7 && p > 1)
                        {
                            signarray[idx] = p % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(p,0,r);
                    }
                }
                break;
                
            case 2: // Right triangle
                maparray[idx++] = GetMode(1,0,0);
                maparray[idx++] = GetMode(0,0,1);
                for (r = 1; r < Q-1; ++r)
                {
                    maparray[idx++] = GetMode(1,0,r);
                }

                for (q = 1; q < P; ++q)
                {
                    for (r = 0; r < Q-q; ++r)
                    {
                        if ((int)faceOrient == 7 && q > 1)
                        {
                            signarray[idx] = q % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(1,q,r);
                    }
                }
                break;

            case 3: // Rear triangle
                maparray[idx++] = GetMode(0,1,0);
                maparray[idx++] = GetMode(0,0,1);
                for (r = 1; r < Q-1; ++r)
                {
                    maparray[idx++] = GetMode(0,1,r);
                }

                for (p = 1; p < P; ++p)
                {
                    for (r = 0; r < Q-p; ++r)
                    {
                        if ((int)faceOrient == 7 && p > 1)
                        {
                            signarray[idx] = p % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(p, 1, r);
                    }
                }
                break;
                
            case 4: // Left triangle
                for (q = 0; q < P; ++q)
                {
                    for (r = 0; r < Q-q; ++r)
                    {
                        if ((int)faceOrient == 7 && q > 1)
                        {
                            signarray[idx] = q % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(0,q,r);
                    }
                }
                break;

            default:
                ASSERTL0(false, "Face to element map unavailable.");
            }

            if (fid > 0)
            {
               if(CheckForZeroedModes)
                {
                    // zero signmap and set maparray to zero if elemental
                    // modes are not as large as face modesl
                    int idx = 0;
                    for (j = 0; j < P; ++j)
                    {
                        idx += Q-j;
                        for (k = Q-j; k < Q-j; ++k)
                        {
                            signarray[idx]  = 0.0;
                            maparray[idx++] = maparray[0];
                        }
                    }

                    for (j = P; j < P; ++j)
                    {
                        for (k = 0; k < Q-j; ++k)
                        {
                            signarray[idx]  = 0.0;
                            maparray[idx++] = maparray[0];
                        }
                    }
                }

                // Triangles only have one possible orientation (base
                // direction reversed); swap edge modes.
                if ((int)faceOrient == 7)
                {
                    swap(maparray[0], maparray[Q]);
                    for (i = 1; i < Q-1; ++i)
                    {
                        swap(maparray[i+1], maparray[Q+i]);
                    }
                }
            }
            else
            {
                if(CheckForZeroedModes)
                {
                    // zero signmap and set maparray to zero if elemental
                    // modes are not as large as face modesl
                    for (j = 0; j < P; ++j)
                    {
                        for (k = Q; k < Q; ++k)
                        {
                            signarray[arrayindx[j+k*P]] = 0.0;
                            maparray[arrayindx[j+k*P]]  = maparray[0];
                        }
                    }

                    for (j = P; j < P; ++j)
                    {
                        for (k = 0; k < Q; ++k)
                        {
                            signarray[arrayindx[j+k*P]] = 0.0;
                            maparray[arrayindx[j+k*P]]  = maparray[0];
                        }
                    }
                }

                // The code below is exactly the same as that taken from
                // StdHexExp and reverses the 'b' and 'a' directions as
                // appropriate (1st and 2nd if statements respectively) in
                // quadrilateral faces.
                if (faceOrient == 6 || faceOrient == 8 ||
                    faceOrient == 11 || faceOrient == 12)
                {
                    if (faceOrient < 9)
                    {
                        for (i = 3; i < Q; i += 2)
                        {
                            for (j = 0; j < P; j++)
                            {
                                signarray[arrayindx[i*P+j]] *= -1;
                            }
                        }

                        for (i = 0; i < P; i++)
                        {
                            swap(maparray [i], maparray [i+P]);
                            swap(signarray[i], signarray[i+P]);
                        }
                    }
                    else
                    {
                        for (i = 0; i < Q; i++)
                        {
                            for (j = 3; j < P; j += 2)
                            {
                                signarray[arrayindx[i*P+j]] *= -1;
                            }
                        }

                        for (i = 0; i < Q; i++)
                        {
                            swap (maparray [i], maparray [i+Q]);
                            swap (signarray[i], signarray[i+Q]);
                        }
                    }
                }

                if (faceOrient == 7 || faceOrient == 8 ||
                    faceOrient == 10 || faceOrient == 12)
                {
                    if (faceOrient < 9)
                    {
                        for (i = 0; i < Q; i++)
                        {
                            for (j = 3; j < P; j += 2)
                            {
                                signarray[arrayindx[i*P+j]] *= -1;
                            }
                        }

                        for(i = 0; i < Q; i++)
                        {
                            swap(maparray [i*P], maparray [i*P+1]);
                            swap(signarray[i*P], signarray[i*P+1]);
                        }
                    }
                    else
                    {
                        for (i = 3; i < Q; i += 2)
                        {
                            for (j = 0; j < P; j++)
                            {
                                signarray[arrayindx[i*P+j]] *= -1;
                            }
                        }

                        for (i = 0; i < P; i++)
                        {
                            swap(maparray [i*Q], maparray [i*Q+1]);
                            swap(signarray[i*Q], signarray[i*Q+1]);
                        }
                    }
                }
            }
        }

        int StdPyrExp::v_GetVertexMap(int vId, bool useCoeffPacking)
        {
            ASSERTL0(GetEdgeBasisType(vId) == LibUtilities::eModified_A ||
                     GetEdgeBasisType(vId) == LibUtilities::eModified_A ||
                     GetEdgeBasisType(vId) == LibUtilities::eModifiedPyr_C,
                     "Mapping not defined for this type of basis");



            int l = 0;

            if(useCoeffPacking == true) // follow packing of coefficients i.e q,r,p
            {
                switch (vId)
                {
                case 0:
                    l = GetMode(0,0,0);
                    break;
                case 1:
                    l = GetMode(0,0,1);
                    break;
                case 2:
                    l = GetMode(0,1,0);
                    break;
                case 3:
                    l = GetMode(1,0,0);
                    break;
                case 4:
                    l = GetMode(1,1,0);
                    break;
                default:
                    ASSERTL0(false, "local vertex id must be between 0 and 4");
                }
            }
            else
            {
                switch (vId)
                {
                case 0:
                    l = GetMode(0,0,0);
                    break;
                case 1:
                    l = GetMode(1,0,0);
                    break;
                case 2:
                    l = GetMode(1,1,0);
                    break;
                case 3:
                    l = GetMode(0,1,0);
                    break;
                case 4:
                    l = GetMode(0,0,1);
                    break;
                default:
                    ASSERTL0(false, "local vertex id must be between 0 and 4");
                }
            }
            
            return l;
        }

        void StdPyrExp::v_GetEdgeInteriorMap(
            const int                  eid,
            const Orientation          edgeOrient,
            Array<OneD, unsigned int> &maparray,
            Array<OneD, int>          &signarray)
        {
            int       i;
            bool      signChange;
            const int P              = m_base[0]->GetNumModes() - 1;
            const int Q              = m_base[1]->GetNumModes() - 1;
            const int R              = m_base[2]->GetNumModes() - 1;
            const int nEdgeIntCoeffs = v_GetEdgeNcoeffs(eid) - 2;

            if (maparray.num_elements() != nEdgeIntCoeffs)
            {
                maparray = Array<OneD, unsigned int>(nEdgeIntCoeffs);
            }

            if(signarray.num_elements() != nEdgeIntCoeffs)
            {
                signarray = Array<OneD, int>(nEdgeIntCoeffs,1);
            }
            else
            {
                fill(signarray.get(), signarray.get()+nEdgeIntCoeffs, 1);
            }

            // If edge is oriented backwards, change sign of modes which have
            // degree 2n+1, n >= 1.
            signChange = edgeOrient == eBackwards;

            switch (eid)
            {
            case 0:
                for (i = 2; i <= P; ++i)
                {
                    maparray[i-2] = GetMode(i,0,0);
                }
                break;
                
            case 1:
                for (i = 2; i <= Q; ++i)
                {
                    maparray[i-2] = GetMode(1,i,0);
                }
                break;
            case 2:
                for (i = 2; i <= P; ++i)
                {
                    maparray[i-2] = GetMode(i,1,0);
                }
                break;
                
            case 3:
                for (i = 2; i <= Q; ++i)
                {
                    maparray[i-2] = GetMode(0,i,0);
                }
                break;
            case 4:
                for (i = 2; i <= R; ++i)
                {
                    maparray[i-2] = GetMode(0,0,i);
                }
                break;
                
            case 5:
                for (i = 1; i <= R-1; ++i)
                {
                    maparray[i-1] = GetMode(1,0,i);
                }
                break;                
            case 6:
                for (i = 1; i <= R-1; ++i)
                {
                    maparray[i-1] = GetMode(1,1,i);
                }
                break;
                
            case 7:
                for (i = 1; i <= R-1; ++i)
                {
                    maparray[i-1] = GetMode(0,1,i);
                }
                break;
            default:
                ASSERTL0(false, "Edge not defined.");
                break;
            }
            
            if (signChange)
            {
                for (i = 1; i < nEdgeIntCoeffs; i += 2)
                {
                    signarray[i] = -1;
                }
            }
        }

        void StdPyrExp::v_GetFaceInteriorMap(
            const int                  fid,
            const Orientation          faceOrient,
            Array<OneD, unsigned int> &maparray,
            Array<OneD, int>          &signarray)
        {
            const int P              = m_base[0]->GetNumModes() - 1;
            const int Q              = m_base[1]->GetNumModes() - 1;
            const int R              = m_base[2]->GetNumModes() - 1;
            const int nFaceIntCoeffs = v_GetFaceIntNcoeffs(fid);
            int       p, q, r, idx   = 0;
            int       nummodesA      = 0;
            int       nummodesB      = 0;
            int       i, j;

            if (maparray.num_elements() != nFaceIntCoeffs)
            {
                maparray = Array<OneD, unsigned int>(nFaceIntCoeffs);
            }

            if (signarray.num_elements() != nFaceIntCoeffs)
            {
                signarray = Array<OneD, int>(nFaceIntCoeffs, 1);
            }
            else
            {
                fill(signarray.get(), signarray.get()+nFaceIntCoeffs, 1);
            }

            // Set up an array indexing for quad faces, since the ordering may
            // need to be transposed depending on orientation.
            Array<OneD, int> arrayindx(nFaceIntCoeffs);
            if (fid == 0)
            {
                nummodesA = P-1;
                nummodesB = Q-1;

                for (i = 0; i < nummodesB; i++)
                {
                    for (j = 0; j < nummodesA; j++)
                    {
                        if (faceOrient < 9)
                        {
                            arrayindx[i*nummodesA+j] = i*nummodesA+j;
                        }
                        else
                        {
                            arrayindx[i*nummodesA+j] = j*nummodesB+i;
                        }
                    }
                }
            }

            switch (fid)
            {
            case 0: // Bottom quad
                for (q = 2; q <= Q; ++q)
                {
                    for (p = 2; p <= P; ++p)
                    {
                        maparray[arrayindx[(q-2)*nummodesA+(p-2)]] = GetMode(p,q,0);
                    }
                }
                break;
            case 1: // Front triangle
                for (p = 2; p <= P; ++p)
                {
                    for (r = 1; r <= R-p; ++r)
                    {
                        if ((int)faceOrient == 7)
                        {
                                signarray[idx] = p % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(p,0,r);
                    }
                }
                break;
            case 2: // Right triangle
                for (q = 2; q <= Q; ++q)
                {
                    for (r = 1; r <= R-q; ++r)
                    {
                        if ((int)faceOrient == 7)
                        {
                            signarray[idx] = q % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(1, q, r);
                    }
                }
                    break;
                    
            case 3: // Rear triangle
                for (p = 2; p <= P; ++p)
                {
                    for (r = 1; r <= R-p; ++r)
                    {
                        if ((int)faceOrient == 7)
                        {
                            signarray[idx] = p % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(p, 1, r);
                    }
                }
                break;
                
            case 4: // Left triangle
                for (q = 2; q <= Q; ++q)
                {
                    for (r = 1; r <= R-q; ++r)
                    {
                        if ((int)faceOrient == 7)
                        {
                            signarray[idx] = q % 2 ? -1 : 1;
                        }
                        maparray[idx++] = GetMode(0, q, r);
                        }
                }
                break;
            default:
                ASSERTL0(false, "Face interior map not available.");
            }
            
            // Triangular faces are processed in the above switch loop; for
            // remaining quad faces, set up orientation if necessary.
            if (fid > 0)
            {
                return;
            }

            if (faceOrient == 6 || faceOrient == 8 ||
                faceOrient == 11 || faceOrient == 12)
            {
                if (faceOrient < 9)
                {
                    for (i = 1; i < nummodesB; i += 2)
                    {
                        for (j = 0; j < nummodesA; j++)
                        {
                            signarray[arrayindx[i*nummodesA+j]] *= -1;
                        }
                    }
                }
                else
                {
                    for (i = 0; i < nummodesB; i++)
                    {
                        for (j = 1; j < nummodesA; j += 2)
                        {
                            signarray[arrayindx[i*nummodesA+j]] *= -1;
                        }
                    }
                }
            }

            if (faceOrient == 7 || faceOrient == 8 ||
                faceOrient == 10 || faceOrient == 12)
            {
                if (faceOrient < 9)
                {
                    for (i = 0; i < nummodesB; i++)
                    {
                        for (j = 1; j < nummodesA; j += 2)
                        {
                            signarray[arrayindx[i*nummodesA+j]] *= -1;
                        }
                    }
                }
                else
                {
                    for (i = 1; i < nummodesB; i += 2)
                    {
                        for (j = 0; j < nummodesA; j++)
                        {
                            signarray[arrayindx[i*nummodesA+j]] *= -1;
                        }
                    }
                }
            }
        }

        void StdPyrExp::v_GetInteriorMap(Array<OneD, unsigned int> &outarray)
        {
            ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                     GetBasisType(0) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(1) == LibUtilities::eModified_A ||
                     GetBasisType(1) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(2) == LibUtilities::eModifiedPyr_C ||
                     GetBasisType(2) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");


            int P   = m_base[0]->GetNumModes() - 1, p;
            int Q   = m_base[1]->GetNumModes() - 1, q;
            int R   = m_base[2]->GetNumModes() - 1, r;

            int nIntCoeffs = m_ncoeffs - NumBndryCoeffs();

            if(outarray.num_elements()!=nIntCoeffs)
            {
                outarray = Array<OneD, unsigned int>(nIntCoeffs);
            }

            int idx = 0;

            // Loop over all interior modes.
            for (p = 2; p <= P; ++p)
            {
            	for (q = 2; q <= Q; ++q)
            	{
                    int maxpq = max(p,q);
                    for (r = 1; r <= R-maxpq; ++r)
                    {
                        outarray[idx++] = GetMode(p,q,r);
                    }
                }
            }
        }

        void StdPyrExp::v_GetBoundaryMap(Array<OneD, unsigned int> &maparray)
        {
            ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A ||
                     GetBasisType(0) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(1) == LibUtilities::eModified_A ||
                     GetBasisType(1) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");
            ASSERTL1(GetBasisType(2) == LibUtilities::eModifiedPyr_C ||
                     GetBasisType(2) == LibUtilities::eGLL_Lagrange,
                     "BasisType is not a boundary interior form");

            int P   = m_base[0]->GetNumModes() - 1, p;
            int Q   = m_base[1]->GetNumModes() - 1, q;
            int R   = m_base[2]->GetNumModes() - 1, r;
            int idx = 0;

            int nBnd = NumBndryCoeffs();

            if (maparray.num_elements() != nBnd)
            {
                maparray = Array<OneD, unsigned int>(nBnd);
            }

            // Loop over all boundary modes (in ascending order).
            for (p = 0; p <= P; ++p)
            {
                // First two q-r planes are entirely boundary modes.
                if (p <= 1)
                {
                    for (q = 0; q <= Q; ++q)
                    {
                        int maxpq = max(p,q);
                        for (r = 0; r <= R-maxpq; ++r)
                        {
                            maparray[idx++] = GetMode(p,q,r);
                        }
                    }
                }
                else
                {
                    // Remaining q-r planes contain boundary modes on the two
                    // front and back sides and edges 0 2.
                    for (q = 0; q <= Q; ++q)
                    {
                        if (q <= 1)
                        {
                            for (r = 0; r <= R-p; ++r)
                            {
                                maparray[idx++] = GetMode(p,q,r);
                            }
                        }
                        else
                        {
                            maparray[idx++] = GetMode(p,q,0);
                        }
                    }
                }
            }
        }

        //---------------------------------------
        // Wrapper functions
        //---------------------------------------

        DNekMatSharedPtr StdPyrExp::v_GenMatrix(const StdMatrixKey &mkey)
        {
            return CreateGeneralMatrix(mkey);
        }

        DNekMatSharedPtr StdPyrExp::v_CreateStdMatrix(const StdMatrixKey &mkey)
        {
            return v_GenMatrix(mkey);
        }


        /**
         * @brief Compute the mode number in the expansion for a
         * particular tensorial combination.
         *
         * Modes are numbered with the r index travelling fastest,
         * followed by q and then p, and each q-r plane is of size
         * 
         * (R+1-p)*(Q+1) - l(l+1)/2 where l = max(0,Q-p) 
         *
         * For example, when P=2, Q=3 and R=4 the indexing inside each
         * q-r plane (with r increasing upwards and q to the right)
         * is:
         *
         * p = 0:      p = 1:       p = 2:
         * ----------------------------------
         * 4
         * 3 8         17 21
         * 2 7 11      16 20 24     29 32 35
         * 1 6 10 13   15 19 23 26  28 31 34 37 
         * 0 5 9  12   14 18 22 25  27 30 33 36 
         *
         * Note that in this element, we must have that \f$ P,Q \leq
         * R\f$.
         */
        int StdPyrExp::GetMode(const int I, const int J, const int K)
        {
            const int Q = m_base[1]->GetNumModes()-1;
            const int R = m_base[2]->GetNumModes()-1;

            int i,l; 
            int cnt = 0;

            // Traverse to q-r plane number I
            for (i = 0; i < I; ++i)
            {
                // Size of triangle part
                l = max(0,Q-i);
                
                // Size of rectangle part
                cnt += (R+1-i)*(Q+1) - l*(l+1)/2;
            }

            // Traverse to q column J (Pretend this is a face of width J)
            l = max(0,J-1-I);
            cnt += (R+1-I)*J - l*(l+1)/2;
            
            // Traverse up stacks to K
            cnt += K;

            return cnt;
        }


        void StdPyrExp::v_MultiplyByStdQuadratureMetric(
            const Array<OneD, const NekDouble>& inarray,
                  Array<OneD,       NekDouble>& outarray)
        {
            int i, j;

            int  nquad0 = m_base[0]->GetNumPoints();
            int  nquad1 = m_base[1]->GetNumPoints();
            int  nquad2 = m_base[2]->GetNumPoints();

            const Array<OneD, const NekDouble>& w0 = m_base[0]->GetW();
            const Array<OneD, const NekDouble>& w1 = m_base[1]->GetW();
            const Array<OneD, const NekDouble>& w2 = m_base[2]->GetW();

            const Array<OneD, const NekDouble>& z2 = m_base[2]->GetZ();

            // Multiply by integration constants in x-direction
            for(i = 0; i < nquad1*nquad2; ++i)
            {
                Vmath::Vmul(nquad0, inarray.get()+i*nquad0, 1,
                            w0.get(), 1, outarray.get()+i*nquad0,1);
            }

            // Multiply by integration constants in y-direction
            for(j = 0; j < nquad2; ++j)
            {
                for(i = 0; i < nquad1; ++i)
                {
                    Blas::Dscal(nquad0,w1[i], &outarray[0]+i*nquad0 +
                                j*nquad0*nquad1,1);
                }
            }

            // Multiply by integration constants in z-direction; need to
            // incorporate factor [(1-eta_3)/2]^2 into weights, but only if
            // using GLL quadrature points.
            switch(m_base[2]->GetPointsType())
            {
                // (2,0) Jacobi inner product.
                case LibUtilities::eGaussRadauMAlpha2Beta0:
                    for(i = 0; i < nquad2; ++i)
                    {
                        Blas::Dscal(nquad0*nquad1, 0.25*w2[i],
                                    &outarray[0]+i*nquad0*nquad1, 1);
                    }
                    break;

                default:
                    for(i = 0; i < nquad2; ++i)
                    {
                        Blas::Dscal(nquad0*nquad1,0.25*(1-z2[i])*(1-z2[i])*w2[i],
                                    &outarray[0]+i*nquad0*nquad1,1);
                    }
                    break;
            }
        }


        void StdPyrExp::v_SVVLaplacianFilter(Array<OneD, NekDouble> &array,
                                             const StdMatrixKey &mkey)
        {
            // Generate an orthonogal expansion
            int qa = m_base[0]->GetNumPoints();
            int qb = m_base[1]->GetNumPoints();
            int qc = m_base[2]->GetNumPoints();
            int nmodes_a = m_base[0]->GetNumModes();
            int nmodes_b = m_base[1]->GetNumModes();
            int nmodes_c = m_base[2]->GetNumModes();
            // Declare orthogonal basis.
            LibUtilities::PointsKey pa(qa,m_base[0]->GetPointsType());
            LibUtilities::PointsKey pb(qb,m_base[1]->GetPointsType());
            LibUtilities::PointsKey pc(qc,m_base[2]->GetPointsType());

            LibUtilities::BasisKey Ba(LibUtilities::eOrtho_A,nmodes_a,pa);
            LibUtilities::BasisKey Bb(LibUtilities::eOrtho_A,nmodes_b,pb);
            LibUtilities::BasisKey Bc(LibUtilities::eOrthoPyr_C,nmodes_c,pc);
            StdPyrExp OrthoExp(Ba,Bb,Bc);

            Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
            int i,j,k,cnt = 0;

            // project onto modal  space.
            OrthoExp.FwdTrans(array,orthocoeffs);

            if(mkey.ConstFactorExists(eFactorSVVPowerKerDiffCoeff)) 
            {
                // Rodrigo's power kernel                
                NekDouble cutoff = mkey.GetConstFactor(eFactorSVVCutoffRatio); 
                NekDouble  SvvDiffCoeff  =
                    mkey.GetConstFactor(eFactorSVVPowerKerDiffCoeff)*
                    mkey.GetConstFactor(eFactorSVVDiffCoeff);
                
                for(int i = 0; i < nmodes_a; ++i)
                {
                    for(int j = 0; j < nmodes_b; ++j)
                    {
                        int maxij = max(i,j);
                        NekDouble fac1 = std::max(
                                   pow((1.0*i)/(nmodes_a-1),cutoff*nmodes_a),
                                   pow((1.0*j)/(nmodes_b-1),cutoff*nmodes_b));

                        for(int k = 0; k < nmodes_c-maxij; ++k)
                        {
                            NekDouble fac = std::max(fac1,
                                   pow((1.0*k)/(nmodes_c-1),cutoff*nmodes_c));
                            
                            orthocoeffs[cnt] *= SvvDiffCoeff * fac;
                            cnt++;
                        }
                    }
                }
            }
            else if(mkey.ConstFactorExists(eFactorSVVDGKerDiffCoeff))  // Rodrigo/Mansoor's DG Kernel
            {
                NekDouble  SvvDiffCoeff  =
                    mkey.GetConstFactor(eFactorSVVDGKerDiffCoeff)*
                    mkey.GetConstFactor(eFactorSVVDiffCoeff);

                int max_abc = max(nmodes_a-kSVVDGFiltermodesmin,
                                  nmodes_b-kSVVDGFiltermodesmin);
                max_abc = max(max_abc, nmodes_c-kSVVDGFiltermodesmin);
                // clamp max_abc
                max_abc = max(max_abc,0);
                max_abc = min(max_abc,kSVVDGFiltermodesmax-kSVVDGFiltermodesmin);
                
                for(int i = 0; i < nmodes_a; ++i)
                {
                    for(int j = 0; j < nmodes_b; ++j)
                    {
                        int maxij = max(i,j);

                        for(int k = 0; k < nmodes_c-maxij; ++k)
                        {
                            int maxijk = max(maxij,k);
                            maxijk = min(maxijk,kSVVDGFiltermodesmax-1);
                        
                            orthocoeffs[cnt] *= SvvDiffCoeff *
                                kSVVDGFilter[max_abc][maxijk];
                            cnt++;
                        }
                    }
                }
            }
            else
            {
                //SVV filter paramaters (how much added diffusion relative
                // to physical one and fraction of modes from which you
                // start applying this added diffusion)
                //
                NekDouble  SvvDiffCoeff = mkey.GetConstFactor(StdRegions::eFactorSVVDiffCoeff);
                NekDouble  SVVCutOff    = mkey.GetConstFactor(StdRegions::eFactorSVVCutoffRatio);
                
                //Defining the cut of mode
                int cutoff_a = (int) (SVVCutOff*nmodes_a);
                int cutoff_b = (int) (SVVCutOff*nmodes_b);
                int cutoff_c = (int) (SVVCutOff*nmodes_c);
                //To avoid the fac[j] from blowing up
                NekDouble epsilon = 1;
                
                int nmodes = min(min(nmodes_a,nmodes_b),nmodes_c);
                NekDouble cutoff = min(min(cutoff_a,cutoff_b),cutoff_c);
                
                for(i = 0; i < nmodes_a; ++i)//P
                {
                    for(j = 0; j < nmodes_b; ++j) //Q
                    {
                        int maxij = max(i,j);
                        for(k = 0; k < nmodes_c-maxij; ++k) //R
                        {
                            if(j + k >= cutoff ||  i + k >= cutoff)
                            {
                                orthocoeffs[cnt] *=
                                    (SvvDiffCoeff*exp(-(i+k-nmodes)*(i+k-nmodes)/
                                ((NekDouble)((i+k-cutoff+epsilon)*
                                             (i+k-cutoff+epsilon))))*
                                     exp(-(j-nmodes)*(j-nmodes)/
                                ((NekDouble)((j-cutoff+epsilon)*
                                             (j-cutoff+epsilon)))));
                            }
                            else
                            {
                                orthocoeffs[cnt] *= 0.0;
                            }
                            cnt++;
                        }
                    }
                }
            }
            
            // backward transform to physical space
            OrthoExp.BwdTrans(orthocoeffs,array);
        }

        void StdPyrExp::v_ReduceOrderCoeffs(
            int                                 numMin,
            const Array<OneD, const NekDouble> &inarray,
                  Array<OneD,       NekDouble> &outarray)
        {
            int nquad0   = m_base[0]->GetNumPoints();
            int nquad1   = m_base[1]->GetNumPoints();
            int nquad2   = m_base[2]->GetNumPoints();
            int nqtot    = nquad0*nquad1*nquad2;
            int nmodes0  = m_base[0]->GetNumModes();
            int nmodes1  = m_base[1]->GetNumModes();
            int nmodes2  = m_base[2]->GetNumModes();
            int numMax   = nmodes0;

            Array<OneD, NekDouble> coeff     (m_ncoeffs);
            Array<OneD, NekDouble> coeff_tmp1(m_ncoeffs, 0.0);
            Array<OneD, NekDouble> phys_tmp  (nqtot,     0.0);
            Array<OneD, NekDouble> tmp, tmp2, tmp3, tmp4;


            const LibUtilities::PointsKey Pkey0 = m_base[0]->GetPointsKey();
            const LibUtilities::PointsKey Pkey1 = m_base[1]->GetPointsKey();
            const LibUtilities::PointsKey Pkey2 = m_base[2]->GetPointsKey();

            LibUtilities::BasisKey bortho0(
                LibUtilities::eOrtho_A,    nmodes0, Pkey0);
            LibUtilities::BasisKey bortho1(
                LibUtilities::eOrtho_A,    nmodes1, Pkey1);
            LibUtilities::BasisKey bortho2(
                LibUtilities::eOrthoPyr_C, nmodes2, Pkey2);

            int cnt = 0;
            int u   = 0;
            int i   = 0;
            StdRegions::StdPyrExpSharedPtr OrthoPyrExp;

            OrthoPyrExp = MemoryManager<StdRegions::StdPyrExp>
                ::AllocateSharedPtr(bortho0, bortho1, bortho2);

            BwdTrans(inarray,phys_tmp);
            OrthoPyrExp->FwdTrans(phys_tmp, coeff);

            // filtering
            for (u = 0; u < numMin; ++u)
            {
                 for (i = 0; i < numMin; ++i)
                 {
                     
                     int maxui = max(u,i);
                     Vmath::Vcopy(numMin - maxui, tmp  = coeff      + cnt, 1,
                                  tmp2 = coeff_tmp1 + cnt, 1);
                     cnt   += nmodes2 - maxui;
                 }

                 for (i = numMin; i < nmodes1; ++i)
                 {
                     int maxui = max(u,i);
                     cnt += numMax - maxui;
                 }
            }

            OrthoPyrExp->BwdTrans(coeff_tmp1, phys_tmp);
            StdPyrExp::FwdTrans(phys_tmp, outarray);
        }
        
    }
}
