ExpListHomogeneous2D.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File ExpListHomogeneous2D.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: An ExpList which is homogeneous in 2-directions
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <LibUtilities/Foundations/ManagerAccess.h> // for PointsManager, etc
#include <LocalRegions/Expansion.h>
#include <MultiRegions/ExpListHomogeneous2D.h>
#include <StdRegions/StdQuadExp.h>
#include <StdRegions/StdSegExp.h>
 
using namespace std;
 
namespace Nektar
{
namespace MultiRegions
{
// Forward declaration for typedefs
ExpListHomogeneous2D::ExpListHomogeneous2D(const ExpansionType type)
    : ExpList(type), m_homogeneousBasis_y(LibUtilities::NullBasisSharedPtr),
      m_homogeneousBasis_z(LibUtilities::NullBasisSharedPtr), m_lhom_y(1),
      m_lhom_z(1), m_homogeneous2DBlockMat(
                       MemoryManager<Homo2DBlockMatrixMap>::AllocateSharedPtr())
{
}
 
ExpListHomogeneous2D::ExpListHomogeneous2D(
    const ExpansionType type,
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const LibUtilities::BasisKey &HomoBasis_y,
    const LibUtilities::BasisKey &HomoBasis_z, const NekDouble lhom_y,
    const NekDouble lhom_z, const bool useFFT, const bool dealiasing)
    : ExpList(type), m_useFFT(useFFT), m_lhom_y(lhom_y), m_lhom_z(lhom_z),
      m_homogeneous2DBlockMat(
          MemoryManager<Homo2DBlockMatrixMap>::AllocateSharedPtr()),
      m_dealiasing(dealiasing)
{
    m_session = pSession;
    m_comm    = pSession->GetComm();
 
    ASSERTL2(HomoBasis_y != LibUtilities::NullBasisKey,
             "Homogeneous Basis in y direction is a null basis");
    ASSERTL2(HomoBasis_z != LibUtilities::NullBasisKey,
             "Homogeneous Basis in z direction is a null basis");
 
    m_homogeneousBasis_y = LibUtilities::BasisManager()[HomoBasis_y];
    m_homogeneousBasis_z = LibUtilities::BasisManager()[HomoBasis_z];
 
    m_transposition =
        MemoryManager<LibUtilities::Transposition>::AllocateSharedPtr(
            HomoBasis_y, HomoBasis_z, m_comm->GetColumnComm());
 
    m_Ycomm = m_comm->GetColumnComm()->GetRowComm();
    m_Zcomm = m_comm->GetColumnComm()->GetRowComm();
 
    m_ny = m_homogeneousBasis_y->GetNumPoints() / m_Ycomm->GetSize();
    m_nz = m_homogeneousBasis_z->GetNumPoints() / m_Zcomm->GetSize();
 
    m_lines = Array<OneD, ExpListSharedPtr>(m_ny * m_nz);
 
    if (m_useFFT)
    {
        m_FFT_y =
            LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW", m_ny);
        m_FFT_z =
            LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW", m_nz);
    }
 
    if (m_dealiasing)
    {
        ASSERTL0(m_comm->GetColumnComm()->GetSize() == 1,
                 "Remove dealiasing if you want to run in parallel");
        SetPaddingBase();
    }
}
 
/**
 * @param   In          ExpListHomogeneous2D object to copy.
 */
ExpListHomogeneous2D::ExpListHomogeneous2D(const ExpListHomogeneous2D &In)
    : ExpList(In, false), m_useFFT(In.m_useFFT), m_FFT_y(In.m_FFT_y),
      m_FFT_z(In.m_FFT_z), m_transposition(In.m_transposition),
      m_Ycomm(In.m_Ycomm), m_Zcomm(In.m_Ycomm),
      m_homogeneousBasis_y(In.m_homogeneousBasis_y),
      m_homogeneousBasis_z(In.m_homogeneousBasis_z), m_lhom_y(In.m_lhom_y),
      m_lhom_z(In.m_lhom_z),
      m_homogeneous2DBlockMat(In.m_homogeneous2DBlockMat), m_ny(In.m_ny),
      m_nz(In.m_nz), m_dealiasing(In.m_dealiasing), m_padsize_y(In.m_padsize_y),
      m_padsize_z(In.m_padsize_z), MatFwdPAD(In.MatFwdPAD),
      MatBwdPAD(In.MatBwdPAD)
{
    m_lines = Array<OneD, ExpListSharedPtr>(In.m_lines.size());
}
 
ExpListHomogeneous2D::ExpListHomogeneous2D(
    const ExpListHomogeneous2D &In, const std::vector<unsigned int> &eIDs)
    : ExpList(In, eIDs, false), m_useFFT(In.m_useFFT), m_FFT_y(In.m_FFT_y),
      m_FFT_z(In.m_FFT_z), m_transposition(In.m_transposition),
      m_Ycomm(In.m_Ycomm), m_Zcomm(In.m_Ycomm),
      m_homogeneousBasis_y(In.m_homogeneousBasis_y),
      m_homogeneousBasis_z(In.m_homogeneousBasis_z), m_lhom_y(In.m_lhom_y),
      m_lhom_z(In.m_lhom_z),
      m_homogeneous2DBlockMat(
          MemoryManager<Homo2DBlockMatrixMap>::AllocateSharedPtr()),
      m_ny(In.m_ny), m_nz(In.m_nz), m_dealiasing(In.m_dealiasing),
      m_padsize_y(In.m_padsize_y), m_padsize_z(In.m_padsize_z),
      MatFwdPAD(In.MatFwdPAD), MatBwdPAD(In.MatBwdPAD)
{
    m_lines = Array<OneD, ExpListSharedPtr>(In.m_lines.size());
}
 
/**
 * Destructor
 */
ExpListHomogeneous2D::~ExpListHomogeneous2D()
{
}
 
void ExpListHomogeneous2D::v_HomogeneousFwdTrans(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, bool Shuff, bool UnShuff)
{
    // Forwards trans
    Homogeneous2DTrans(inarray, outarray, true, Shuff, UnShuff);
}
 
void ExpListHomogeneous2D::v_HomogeneousBwdTrans(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, bool Shuff, bool UnShuff)
{
    // Backwards trans
    Homogeneous2DTrans(inarray, outarray, false, Shuff, UnShuff);
}
 
void ExpListHomogeneous2D::v_DealiasedProd(
    const Array<OneD, NekDouble> &inarray1,
    const Array<OneD, NekDouble> &inarray2, Array<OneD, NekDouble> &outarray)
{
    int npoints = outarray.size(); // number of total physical points
    int nlines =
        m_lines.size(); // number of lines == number of Fourier modes = number
                        // of Fourier coeff = number of points per slab
    int nslabs = npoints /
                 nlines; // number of slabs = numebr of physical points per line
 
    Array<OneD, NekDouble> V1(npoints);
    Array<OneD, NekDouble> V2(npoints);
    Array<OneD, NekDouble> V1V2(npoints);
    Array<OneD, NekDouble> ShufV1(npoints);
    Array<OneD, NekDouble> ShufV2(npoints);
    Array<OneD, NekDouble> ShufV1V2(npoints);
 
    if (m_WaveSpace)
    {
        V1 = inarray1;
        V2 = inarray2;
    }
    else
    {
        HomogeneousFwdTrans(inarray1, V1);
        HomogeneousFwdTrans(inarray2, V2);
    }
 
    m_transposition->Transpose(V1, ShufV1, false, LibUtilities::eXtoYZ);
    m_transposition->Transpose(V2, ShufV2, false, LibUtilities::eXtoYZ);
 
    Array<OneD, NekDouble> PadV1_slab_coeff(m_padsize_y * m_padsize_z, 0.0);
    Array<OneD, NekDouble> PadV2_slab_coeff(m_padsize_y * m_padsize_z, 0.0);
    Array<OneD, NekDouble> PadRe_slab_coeff(m_padsize_y * m_padsize_z, 0.0);
 
    Array<OneD, NekDouble> PadV1_slab_phys(m_padsize_y * m_padsize_z, 0.0);
    Array<OneD, NekDouble> PadV2_slab_phys(m_padsize_y * m_padsize_z, 0.0);
    Array<OneD, NekDouble> PadRe_slab_phys(m_padsize_y * m_padsize_z, 0.0);
 
    NekVector<NekDouble> PadIN_V1(m_padsize_y * m_padsize_z, PadV1_slab_coeff,
                                  eWrapper);
    NekVector<NekDouble> PadOUT_V1(m_padsize_y * m_padsize_z, PadV1_slab_phys,
                                   eWrapper);
 
    NekVector<NekDouble> PadIN_V2(m_padsize_y * m_padsize_z, PadV2_slab_coeff,
                                  eWrapper);
    NekVector<NekDouble> PadOUT_V2(m_padsize_y * m_padsize_z, PadV2_slab_phys,
                                   eWrapper);
 
    NekVector<NekDouble> PadIN_Re(m_padsize_y * m_padsize_z, PadRe_slab_phys,
                                  eWrapper);
    NekVector<NekDouble> PadOUT_Re(m_padsize_y * m_padsize_z, PadRe_slab_coeff,
                                   eWrapper);
 
    // Looping on the slabs
    for (int j = 0; j < nslabs; j++)
    {
        // Copying the j-th slab of size N*M into a bigger slab of lenght 2*N*M
        // We are in Fourier space
        for (int i = 0; i < m_nz; i++)
        {
            Vmath::Vcopy(m_ny, &(ShufV1[i * m_ny + j * nlines]), 1,
                         &(PadV1_slab_coeff[i * 2 * m_ny]), 1);
            Vmath::Vcopy(m_ny, &(ShufV2[i * m_ny + j * nlines]), 1,
                         &(PadV2_slab_coeff[i * 2 * m_ny]), 1);
        }
 
        // Moving to physical space using the padded system
        PadOUT_V1 = (*MatBwdPAD) * PadIN_V1;
        PadOUT_V2 = (*MatBwdPAD) * PadIN_V2;
 
        // Perfroming the vectors multiplication in physical
        // space on the padded system
        Vmath::Vmul(m_padsize_y * m_padsize_z, PadV1_slab_phys, 1,
                    PadV2_slab_phys, 1, PadRe_slab_phys, 1);
 
        // Moving back the result (V1*V2)_phys in Fourier
        // space, padded system
        PadOUT_Re = (*MatFwdPAD) * PadIN_Re;
 
        // Copying the first half of the padded pencil in the
        // full vector (Fourier space)
        for (int i = 0; i < m_nz; i++)
        {
            Vmath::Vcopy(m_ny, &(PadRe_slab_coeff[i * 2 * m_ny]), 1,
                         &(ShufV1V2[i * m_ny + j * nlines]), 1);
        }
    }
 
    if (m_WaveSpace)
    {
        m_transposition->Transpose(ShufV1V2, outarray, false,
                                   LibUtilities::eYZtoX);
    }
    else
    {
        m_transposition->Transpose(ShufV1V2, V1V2, false, LibUtilities::eYZtoX);
 
        // Moving the results in physical space for the output
        HomogeneousBwdTrans(V1V2, outarray);
    }
}
 
void ExpListHomogeneous2D::v_DealiasedDotProd(
    const Array<OneD, Array<OneD, NekDouble>> &inarray1,
    const Array<OneD, Array<OneD, NekDouble>> &inarray2,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    // TODO Proper implementation of this
    int ndim = inarray1.size();
    ASSERTL1(inarray2.size() % ndim == 0,
             "Wrong dimensions for DealiasedDotProd.");
    int nvec = inarray2.size() % ndim;
    int npts = inarray1[0].size();
 
    Array<OneD, NekDouble> out(npts);
    for (int i = 0; i < nvec; i++)
    {
        Vmath::Zero(npts, outarray[i], 1);
        for (int j = 0; j < ndim; j++)
        {
            DealiasedProd(inarray1[j], inarray2[i * ndim + j], out);
            Vmath::Vadd(npts, outarray[i], 1, out, 1, outarray[i], 1);
        }
    }
}
 
void ExpListHomogeneous2D::v_FwdTrans(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int cnt = 0, cnt1 = 0;
    Array<OneD, NekDouble> tmparray;
    int nlines = m_lines.size();
 
    for (int n = 0; n < nlines; ++n)
    {
        m_lines[n]->FwdTrans(inarray + cnt, tmparray = outarray + cnt1);
        cnt += m_lines[n]->GetTotPoints();
        cnt1 += m_lines[n]->GetNcoeffs();
    }
    if (!m_WaveSpace)
    {
        HomogeneousFwdTrans(outarray, outarray);
    }
}
 
void ExpListHomogeneous2D::v_FwdTransLocalElmt(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int cnt = 0, cnt1 = 0;
    Array<OneD, NekDouble> tmparray;
    int nlines = m_lines.size();
 
    for (int n = 0; n < nlines; ++n)
    {
        m_lines[n]->FwdTransLocalElmt(inarray + cnt,
                                      tmparray = outarray + cnt1);
 
        cnt += m_lines[n]->GetTotPoints();
        cnt1 += m_lines[n]->GetNcoeffs();
    }
    if (!m_WaveSpace)
    {
        HomogeneousFwdTrans(outarray, outarray);
    }
}
 
void ExpListHomogeneous2D::v_BwdTrans(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int cnt = 0, cnt1 = 0;
    Array<OneD, NekDouble> tmparray;
    int nlines = m_lines.size();
 
    for (int n = 0; n < nlines; ++n)
    {
        m_lines[n]->BwdTrans(inarray + cnt, tmparray = outarray + cnt1);
        cnt += m_lines[n]->GetNcoeffs();
        cnt1 += m_lines[n]->GetTotPoints();
    }
    if (!m_WaveSpace)
    {
        HomogeneousBwdTrans(outarray, outarray);
    }
}
 
void ExpListHomogeneous2D::v_IProductWRTBase(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int cnt = 0, cnt1 = 0;
    Array<OneD, NekDouble> tmparray;
    int nlines = m_lines.size();
 
    for (int n = 0; n < nlines; ++n)
    {
        m_lines[n]->IProductWRTBase(inarray + cnt, tmparray = outarray + cnt1);
 
        cnt += m_lines[n]->GetNcoeffs();
        cnt1 += m_lines[n]->GetTotPoints();
    }
}
 
void ExpListHomogeneous2D::Homogeneous2DTrans(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, bool IsForwards, bool Shuff, bool UnShuff)
{
    boost::ignore_unused(Shuff, UnShuff);
 
    if (m_useFFT)
    {
 
        int n = m_lines.size(); // number of Fourier points in the Fourier
                                // directions (x-z grid)
        int s = inarray.size(); // number of total points = n. of Fourier points
                                // * n. of points per line
        int p =
            s /
            n; // number of points per line = n of Fourier transform required
 
        Array<OneD, NekDouble> fft_in(s);
        Array<OneD, NekDouble> fft_out(s);
 
        m_transposition->Transpose(inarray, fft_in, false,
                                   LibUtilities::eXtoYZ);
 
        if (IsForwards)
        {
            for (int i = 0; i < (p * m_nz); i++)
            {
                m_FFT_y->FFTFwdTrans(m_tmpIN  = fft_in + i * m_ny,
                                     m_tmpOUT = fft_out + i * m_ny);
            }
        }
        else
        {
            for (int i = 0; i < (p * m_nz); i++)
            {
                m_FFT_y->FFTBwdTrans(m_tmpIN  = fft_in + i * m_ny,
                                     m_tmpOUT = fft_out + i * m_ny);
            }
        }
 
        m_transposition->Transpose(fft_out, fft_in, false,
                                   LibUtilities::eYZtoZY);
 
        if (IsForwards)
        {
            for (int i = 0; i < (p * m_ny); i++)
            {
                m_FFT_z->FFTFwdTrans(m_tmpIN  = fft_in + i * m_nz,
                                     m_tmpOUT = fft_out + i * m_nz);
            }
        }
        else
        {
            for (int i = 0; i < (p * m_ny); i++)
            {
                m_FFT_z->FFTBwdTrans(m_tmpIN  = fft_in + i * m_nz,
                                     m_tmpOUT = fft_out + i * m_nz);
            }
        }
 
        // TODO: required ZYtoX routine
        m_transposition->Transpose(fft_out, fft_in, false,
                                   LibUtilities::eZYtoYZ);
 
        m_transposition->Transpose(fft_in, outarray, false,
                                   LibUtilities::eYZtoX);
    }
    else
    {
        DNekBlkMatSharedPtr blkmatY;
        DNekBlkMatSharedPtr blkmatZ;
 
        if (inarray.size() == m_npoints) // transform phys space
        {
            if (IsForwards)
            {
                blkmatY = GetHomogeneous2DBlockMatrix(eForwardsPhysSpaceY1D);
                blkmatZ = GetHomogeneous2DBlockMatrix(eForwardsPhysSpaceZ1D);
            }
            else
            {
                blkmatY = GetHomogeneous2DBlockMatrix(eBackwardsPhysSpaceY1D);
                blkmatZ = GetHomogeneous2DBlockMatrix(eBackwardsPhysSpaceZ1D);
            }
        }
        else
        {
            if (IsForwards)
            {
                blkmatY = GetHomogeneous2DBlockMatrix(eForwardsCoeffSpaceY1D);
                blkmatZ = GetHomogeneous2DBlockMatrix(eForwardsCoeffSpaceZ1D);
            }
            else
            {
                blkmatY = GetHomogeneous2DBlockMatrix(eBackwardsCoeffSpaceY1D);
                blkmatZ = GetHomogeneous2DBlockMatrix(eBackwardsCoeffSpaceZ1D);
            }
        }
 
        int nrowsY = blkmatY->GetRows();
        int ncolsY = blkmatY->GetColumns();
 
        Array<OneD, NekDouble> sortedinarrayY(ncolsY);
        Array<OneD, NekDouble> sortedoutarrayY(nrowsY);
 
        int nrowsZ = blkmatZ->GetRows();
        int ncolsZ = blkmatZ->GetColumns();
 
        Array<OneD, NekDouble> sortedinarrayZ(ncolsZ);
        Array<OneD, NekDouble> sortedoutarrayZ(nrowsZ);
 
        NekVector<NekDouble> inY(ncolsY, sortedinarrayY, eWrapper);
        NekVector<NekDouble> outY(nrowsY, sortedoutarrayY, eWrapper);
 
        NekVector<NekDouble> inZ(ncolsZ, sortedinarrayZ, eWrapper);
        NekVector<NekDouble> outZ(nrowsZ, sortedoutarrayZ, eWrapper);
 
        m_transposition->Transpose(inarray, sortedinarrayY, !IsForwards,
                                   LibUtilities::eXtoYZ);
 
        outY = (*blkmatY) * inY;
 
        m_transposition->Transpose(sortedoutarrayY, sortedinarrayZ, false,
                                   LibUtilities::eYZtoZY);
 
        outZ = (*blkmatZ) * inZ;
 
        m_transposition->Transpose(sortedoutarrayZ, sortedoutarrayY, false,
                                   LibUtilities::eZYtoYZ);
 
        m_transposition->Transpose(sortedoutarrayY, outarray, false,
                                   LibUtilities::eYZtoX);
    }
}
 
DNekBlkMatSharedPtr ExpListHomogeneous2D::GetHomogeneous2DBlockMatrix(
    Homogeneous2DMatType mattype) const
{
    auto matrixIter = m_homogeneous2DBlockMat->find(mattype);
 
    if (matrixIter == m_homogeneous2DBlockMat->end())
    {
        return ((*m_homogeneous2DBlockMat)[mattype] =
                    GenHomogeneous2DBlockMatrix(mattype));
    }
    else
    {
        return matrixIter->second;
    }
}
 
DNekBlkMatSharedPtr ExpListHomogeneous2D::GenHomogeneous2DBlockMatrix(
    Homogeneous2DMatType mattype) const
{
    int i;
    int n_exp = 0;
 
    DNekMatSharedPtr loc_mat;
    DNekBlkMatSharedPtr BlkMatrix;
 
    LibUtilities::BasisSharedPtr Basis;
 
    int NumPoints  = 0;
    int NumModes   = 0;
    int NumPencils = 0;
 
    if ((mattype == eForwardsCoeffSpaceY1D) ||
        (mattype == eBackwardsCoeffSpaceY1D) ||
        (mattype == eForwardsPhysSpaceY1D) ||
        (mattype == eBackwardsPhysSpaceY1D))
    {
        Basis      = m_homogeneousBasis_y;
        NumPoints  = m_homogeneousBasis_y->GetNumModes();
        NumModes   = m_homogeneousBasis_y->GetNumPoints();
        NumPencils = m_homogeneousBasis_z->GetNumPoints();
    }
    else
    {
        Basis      = m_homogeneousBasis_z;
        NumPoints  = m_homogeneousBasis_z->GetNumModes();
        NumModes   = m_homogeneousBasis_z->GetNumPoints();
        NumPencils = m_homogeneousBasis_y->GetNumPoints();
    }
 
    if ((mattype == eForwardsCoeffSpaceY1D) ||
        (mattype == eForwardsCoeffSpaceZ1D) ||
        (mattype == eBackwardsCoeffSpaceY1D) ||
        (mattype == eBackwardsCoeffSpaceZ1D))
    {
        n_exp = m_lines[0]->GetNcoeffs();
    }
    else
    {
        n_exp = m_lines[0]->GetTotPoints(); // will operatore on m_phys
    }
 
    Array<OneD, unsigned int> nrows(n_exp);
    Array<OneD, unsigned int> ncols(n_exp);
 
    if ((mattype == eForwardsCoeffSpaceY1D) ||
        (mattype == eForwardsPhysSpaceY1D) ||
        (mattype == eForwardsCoeffSpaceZ1D) ||
        (mattype == eForwardsPhysSpaceZ1D))
    {
        nrows = Array<OneD, unsigned int>(n_exp * NumPencils, NumModes);
        ncols = Array<OneD, unsigned int>(n_exp * NumPencils, NumPoints);
    }
    else
    {
        nrows = Array<OneD, unsigned int>(n_exp * NumPencils, NumPoints);
        ncols = Array<OneD, unsigned int>(n_exp * NumPencils, NumModes);
    }
 
    MatrixStorage blkmatStorage = eDIAGONAL;
    BlkMatrix = MemoryManager<DNekBlkMat>::AllocateSharedPtr(nrows, ncols,
                                                             blkmatStorage);
 
    StdRegions::StdSegExp StdSeg(Basis->GetBasisKey());
 
    if ((mattype == eForwardsCoeffSpaceY1D) ||
        (mattype == eForwardsPhysSpaceY1D) ||
        (mattype == eForwardsCoeffSpaceZ1D) ||
        (mattype == eForwardsPhysSpaceZ1D))
    {
        StdRegions::StdMatrixKey matkey(StdRegions::eFwdTrans,
                                        StdSeg.DetShapeType(), StdSeg);
 
        loc_mat = StdSeg.GetStdMatrix(matkey);
    }
    else
    {
        StdRegions::StdMatrixKey matkey(StdRegions::eBwdTrans,
                                        StdSeg.DetShapeType(), StdSeg);
 
        loc_mat = StdSeg.GetStdMatrix(matkey);
    }
 
    // set up array of block matrices.
    for (i = 0; i < (n_exp * NumPencils); ++i)
    {
        BlkMatrix->SetBlock(i, i, loc_mat);
    }
 
    return BlkMatrix;
}
 
std::vector<LibUtilities::FieldDefinitionsSharedPtr> ExpListHomogeneous2D::
    v_GetFieldDefinitions()
{
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> returnval;
    // Set up Homogeneous length details.
    Array<OneD, LibUtilities::BasisSharedPtr> HomoBasis(2);
    HomoBasis[0] = m_homogeneousBasis_y;
    HomoBasis[1] = m_homogeneousBasis_z;
 
    std::vector<NekDouble> HomoLen(2);
    HomoLen[0] = m_lhom_y;
    HomoLen[1] = m_lhom_z;
 
    int nhom_modes_y = m_homogeneousBasis_y->GetNumModes();
    int nhom_modes_z = m_homogeneousBasis_z->GetNumModes();
 
    std::vector<unsigned int> sIDs = LibUtilities::NullUnsignedIntVector;
 
    std::vector<unsigned int> yIDs;
    std::vector<unsigned int> zIDs;
 
    for (int n = 0; n < nhom_modes_z; ++n)
    {
        for (int m = 0; m < nhom_modes_y; ++m)
        {
            zIDs.push_back(n);
            yIDs.push_back(m);
        }
    }
 
    m_lines[0]->GeneralGetFieldDefinitions(returnval, 2, HomoBasis, HomoLen,
                                           false, sIDs, zIDs, yIDs);
    return returnval;
}
 
void ExpListHomogeneous2D::v_GetFieldDefinitions(
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> &fielddef)
{
    // Set up Homogeneous length details.
    Array<OneD, LibUtilities::BasisSharedPtr> HomoBasis(2);
    HomoBasis[0] = m_homogeneousBasis_y;
    HomoBasis[1] = m_homogeneousBasis_z;
    std::vector<NekDouble> HomoLen(2);
    HomoLen[0] = m_lhom_y;
    HomoLen[1] = m_lhom_z;
 
    int nhom_modes_y = m_homogeneousBasis_y->GetNumModes();
    int nhom_modes_z = m_homogeneousBasis_z->GetNumModes();
 
    std::vector<unsigned int> sIDs = LibUtilities::NullUnsignedIntVector;
 
    std::vector<unsigned int> yIDs;
    std::vector<unsigned int> zIDs;
 
    for (int n = 0; n < nhom_modes_z; ++n)
    {
        for (int m = 0; m < nhom_modes_y; ++m)
        {
            zIDs.push_back(n);
            yIDs.push_back(m);
        }
    }
 
    // enforce NumHomoDir == 1 by direct call
    m_lines[0]->GeneralGetFieldDefinitions(fielddef, 2, HomoBasis, HomoLen,
                                           false, sIDs, zIDs, yIDs);
}
 
void ExpListHomogeneous2D::v_AppendFieldData(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata, Array<OneD, NekDouble> &coeffs)
{
    int i, k;
 
    int NumMod_y = m_homogeneousBasis_y->GetNumModes();
    int NumMod_z = m_homogeneousBasis_z->GetNumModes();
 
    int ncoeffs_per_line = m_lines[0]->GetNcoeffs();
 
    // Determine mapping from element ids to location in
    // expansion list
    map<int, int> ElmtID_to_ExpID;
    for (i = 0; i < m_lines[0]->GetExpSize(); ++i)
    {
        ElmtID_to_ExpID[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
    }
 
    for (i = 0; i < fielddef->m_elementIDs.size(); ++i)
    {
        int eid     = ElmtID_to_ExpID[fielddef->m_elementIDs[i]];
        int datalen = (*m_exp)[eid]->GetNcoeffs();
 
        for (k = 0; k < (NumMod_y * NumMod_z); ++k)
        {
            fielddata.insert(
                fielddata.end(),
                &coeffs[m_coeff_offset[eid] + k * ncoeffs_per_line],
                &coeffs[m_coeff_offset[eid] + k * ncoeffs_per_line] + datalen);
        }
    }
}
 
void ExpListHomogeneous2D::v_AppendFieldData(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata)
{
    v_AppendFieldData(fielddef, fielddata, m_coeffs);
}
 
// Extract the data in fielddata into the m_coeff list
void ExpListHomogeneous2D::v_ExtractDataToCoeffs(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata, std::string &field,
    Array<OneD, NekDouble> &coeffs)
{
    int i, k;
    int offset           = 0;
    int datalen          = fielddata.size() / fielddef->m_fields.size();
    int ncoeffs_per_line = m_lines[0]->GetNcoeffs();
    int NumMod_y         = m_homogeneousBasis_y->GetNumModes();
    int NumMod_z         = m_homogeneousBasis_z->GetNumModes();
 
    // Find data location according to field definition
    for (i = 0; i < fielddef->m_fields.size(); ++i)
    {
        if (fielddef->m_fields[i] == field)
        {
            break;
        }
        offset += datalen;
    }
 
    ASSERTL0(i != fielddef->m_fields.size(), "Field not found in data file");
 
    // Determine mapping from element ids to location in
    // expansion list
    map<int, int> ElmtID_to_ExpID;
    for (i = 0; i < m_lines[0]->GetExpSize(); ++i)
    {
        ElmtID_to_ExpID[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
    }
 
    for (i = 0; i < fielddef->m_elementIDs.size(); ++i)
    {
        int eid     = ElmtID_to_ExpID[fielddef->m_elementIDs[i]];
        int datalen = (*m_exp)[eid]->GetNcoeffs();
 
        for (k = 0; k < (NumMod_y * NumMod_z); ++k)
        {
            Vmath::Vcopy(datalen, &fielddata[offset], 1,
                         &coeffs[m_coeff_offset[eid] + k * ncoeffs_per_line],
                         1);
            offset += datalen;
        }
    }
}
 
void ExpListHomogeneous2D::v_WriteVtkPieceData(std::ostream &outfile,
                                               int expansion, std::string var)
{
    int i;
    int nq               = (*m_exp)[expansion]->GetTotPoints();
    int npoints_per_line = m_lines[0]->GetTotPoints();
 
    // printing the fields of that zone
    outfile << "        <DataArray type=\"Float64\" Name=\"" << var << "\">"
            << endl;
    outfile << "          ";
    for (int n = 0; n < m_lines.size(); ++n)
    {
        const Array<OneD, NekDouble> phys =
            m_phys + m_phys_offset[expansion] + n * npoints_per_line;
        for (i = 0; i < nq; ++i)
        {
            outfile << (fabs(phys[i]) < NekConstants::kNekZeroTol ? 0 : phys[i])
                    << " ";
        }
    }
    outfile << endl;
    outfile << "        </DataArray>" << endl;
}
 
void ExpListHomogeneous2D::v_PhysDeriv(
    const Array<OneD, const NekDouble> &inarray, Array<OneD, NekDouble> &out_d0,
    Array<OneD, NekDouble> &out_d1, Array<OneD, NekDouble> &out_d2)
 
{
    int nyzlines = m_lines.size(); // number of Fourier points in the Fourier
                                   // directions (nF_pts)
    int npoints = inarray.size();  // number of total points = n. of Fourier
                                   // points * n. of points per line (nT_pts)
    int n_points_line = npoints / nyzlines; // number of points per line
 
    Array<OneD, NekDouble> temparray(npoints);
    Array<OneD, NekDouble> temparray1(npoints);
    Array<OneD, NekDouble> temparray2(npoints);
    Array<OneD, NekDouble> tmp1;
    Array<OneD, NekDouble> tmp2;
    Array<OneD, NekDouble> tmp3;
 
    for (int i = 0; i < nyzlines; i++)
    {
        m_lines[i]->PhysDeriv(tmp1 = inarray + i * n_points_line,
                              tmp2 = out_d0 + i * n_points_line);
    }
 
    if (m_homogeneousBasis_y->GetBasisType() == LibUtilities::eFourier &&
        m_homogeneousBasis_z->GetBasisType() == LibUtilities::eFourier)
    {
        if (m_WaveSpace)
        {
            temparray = inarray;
        }
        else
        {
            HomogeneousFwdTrans(inarray, temparray);
        }
        NekDouble sign = -1.0;
        NekDouble beta;
 
        // along y
        for (int i = 0; i < m_ny; i++)
        {
            beta = -sign * 2 * M_PI * (i / 2) / m_lhom_y;
 
            for (int j = 0; j < m_nz; j++)
            {
                Vmath::Smul(n_points_line, beta,
                            tmp1 = temparray + n_points_line * (i + j * m_ny),
                            1,
                            tmp2 = temparray1 +
                                   n_points_line * ((i - int(sign)) + j * m_ny),
                            1);
            }
 
            sign = -1.0 * sign;
        }
 
        // along z
        sign = -1.0;
        for (int i = 0; i < m_nz; i++)
        {
            beta = -sign * 2 * M_PI * (i / 2) / m_lhom_z;
            Vmath::Smul(
                m_ny * n_points_line, beta,
                tmp1 = temparray + i * m_ny * n_points_line, 1,
                tmp2 = temparray2 + (i - int(sign)) * m_ny * n_points_line, 1);
            sign = -1.0 * sign;
        }
        if (m_WaveSpace)
        {
            out_d1 = temparray1;
            out_d2 = temparray2;
        }
        else
        {
            HomogeneousBwdTrans(temparray1, out_d1);
            HomogeneousBwdTrans(temparray2, out_d2);
        }
    }
    else
    {
        if (m_WaveSpace)
        {
            ASSERTL0(false, "Semi-phyisical time-stepping not implemented yet "
                            "for non-Fourier basis")
        }
        else
        {
            StdRegions::StdQuadExp StdQuad(m_homogeneousBasis_y->GetBasisKey(),
                                           m_homogeneousBasis_z->GetBasisKey());
 
            m_transposition->Transpose(inarray, temparray, false,
                                       LibUtilities::eXtoYZ);
 
            for (int i = 0; i < n_points_line; i++)
            {
                StdQuad.PhysDeriv(tmp1 = temparray + i * nyzlines,
                                  tmp2 = temparray1 + i * nyzlines,
                                  tmp3 = temparray2 + i * nyzlines);
            }
 
            m_transposition->Transpose(temparray1, out_d1, false,
                                       LibUtilities::eYZtoX);
            m_transposition->Transpose(temparray2, out_d2, false,
                                       LibUtilities::eYZtoX);
            Vmath::Smul(npoints, 2.0 / m_lhom_y, out_d1, 1, out_d1, 1);
            Vmath::Smul(npoints, 2.0 / m_lhom_z, out_d2, 1, out_d2, 1);
        }
    }
}
 
void ExpListHomogeneous2D::v_PhysDeriv(
    Direction edir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &out_d)
 
{
    int nyzlines = m_lines.size(); // number of Fourier points in the Fourier
                                   // directions (nF_pts)
    int npoints = inarray.size();  // number of total points = n. of Fourier
                                   // points * n. of points per line (nT_pts)
    int n_points_line = npoints / nyzlines; // number of points per line
    // convert enum into int
    int dir = (int)edir;
 
    Array<OneD, NekDouble> temparray(npoints);
    Array<OneD, NekDouble> temparray1(npoints);
    Array<OneD, NekDouble> temparray2(npoints);
    Array<OneD, NekDouble> tmp1;
    Array<OneD, NekDouble> tmp2;
    Array<OneD, NekDouble> tmp3;
 
    if (dir < 1)
    {
        for (int i = 0; i < nyzlines; i++)
        {
            m_lines[i]->PhysDeriv(tmp1 = inarray + i * n_points_line,
                                  tmp2 = out_d + i * n_points_line);
        }
    }
    else
    {
        if (m_homogeneousBasis_y->GetBasisType() == LibUtilities::eFourier &&
            m_homogeneousBasis_z->GetBasisType() == LibUtilities::eFourier)
        {
            if (m_WaveSpace)
            {
                temparray = inarray;
            }
            else
            {
                HomogeneousFwdTrans(inarray, temparray);
            }
            NekDouble sign = -1.0;
            NekDouble beta;
 
            if (dir == 1)
            {
                // along y
                for (int i = 0; i < m_ny; i++)
                {
                    beta = -sign * 2 * M_PI * (i / 2) / m_lhom_y;
 
                    for (int j = 0; j < m_nz; j++)
                    {
                        Vmath::Smul(
                            n_points_line, beta,
                            tmp1 = temparray + n_points_line * (i + j * m_ny),
                            1,
                            tmp2 = temparray1 +
                                   n_points_line * ((i - int(sign)) + j * m_ny),
                            1);
                    }
                    sign = -1.0 * sign;
                }
                if (m_WaveSpace)
                {
                    out_d = temparray1;
                }
                else
                {
                    HomogeneousBwdTrans(temparray1, out_d);
                }
            }
            else
            {
                // along z
                for (int i = 0; i < m_nz; i++)
                {
                    beta = -sign * 2 * M_PI * (i / 2) / m_lhom_z;
                    Vmath::Smul(m_ny * n_points_line, beta,
                                tmp1 = temparray + i * m_ny * n_points_line, 1,
                                tmp2 = temparray2 +
                                       (i - int(sign)) * m_ny * n_points_line,
                                1);
                    sign = -1.0 * sign;
                }
                if (m_WaveSpace)
                {
                    out_d = temparray2;
                }
                else
                {
                    HomogeneousBwdTrans(temparray2, out_d);
                }
            }
        }
        else
        {
            if (m_WaveSpace)
            {
                ASSERTL0(false, "Semi-phyisical time-stepping not implemented "
                                "yet for non-Fourier basis")
            }
            else
            {
                StdRegions::StdQuadExp StdQuad(
                    m_homogeneousBasis_y->GetBasisKey(),
                    m_homogeneousBasis_z->GetBasisKey());
 
                m_transposition->Transpose(inarray, temparray, false,
                                           LibUtilities::eXtoYZ);
 
                for (int i = 0; i < n_points_line; i++)
                {
                    StdQuad.PhysDeriv(tmp1 = temparray + i * nyzlines,
                                      tmp2 = temparray1 + i * nyzlines,
                                      tmp3 = temparray2 + i * nyzlines);
                }
 
                if (dir == 1)
                {
                    m_transposition->Transpose(temparray1, out_d, false,
                                               LibUtilities::eYZtoX);
                    Vmath::Smul(npoints, 2.0 / m_lhom_y, out_d, 1, out_d, 1);
                }
                else
                {
                    m_transposition->Transpose(temparray2, out_d, false,
                                               LibUtilities::eYZtoX);
                    Vmath::Smul(npoints, 2.0 / m_lhom_z, out_d, 1, out_d, 1);
                }
            }
        }
    }
}
 
void ExpListHomogeneous2D::PhysDeriv(
    const Array<OneD, const NekDouble> &inarray, Array<OneD, NekDouble> &out_d0,
    Array<OneD, NekDouble> &out_d1, Array<OneD, NekDouble> &out_d2)
 
{
    v_PhysDeriv(inarray, out_d0, out_d1, out_d2);
}
 
void ExpListHomogeneous2D::PhysDeriv(
    Direction edir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &out_d)
{
    // convert int into enum
    v_PhysDeriv(edir, inarray, out_d);
}
 
void ExpListHomogeneous2D::SetPaddingBase(void)
{
    NekDouble size_y = 1.5 * m_ny;
    NekDouble size_z = 1.5 * m_nz;
    m_padsize_y      = int(size_y);
    m_padsize_z      = int(size_z);
 
    const LibUtilities::PointsKey Ppad_y(m_padsize_y,
                                         LibUtilities::eFourierEvenlySpaced);
    const LibUtilities::BasisKey Bpad_y(LibUtilities::eFourier, m_padsize_y,
                                        Ppad_y);
 
    const LibUtilities::PointsKey Ppad_z(m_padsize_z,
                                         LibUtilities::eFourierEvenlySpaced);
    const LibUtilities::BasisKey Bpad_z(LibUtilities::eFourier, m_padsize_z,
                                        Ppad_z);
 
    m_paddingBasis_y = LibUtilities::BasisManager()[Bpad_y];
    m_paddingBasis_z = LibUtilities::BasisManager()[Bpad_z];
 
    StdRegions::StdQuadExp StdQuad(m_paddingBasis_y->GetBasisKey(),
                                   m_paddingBasis_z->GetBasisKey());
 
    StdRegions::StdMatrixKey matkey1(StdRegions::eFwdTrans,
                                     StdQuad.DetShapeType(), StdQuad);
    StdRegions::StdMatrixKey matkey2(StdRegions::eBwdTrans,
                                     StdQuad.DetShapeType(), StdQuad);
 
    MatFwdPAD = StdQuad.GetStdMatrix(matkey1);
    MatBwdPAD = StdQuad.GetStdMatrix(matkey2);
}
} // namespace MultiRegions
} // namespace Nektar