TestTetCollection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: TestTetCollection.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,
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/// The above copyright notice and this permission notice shall be included
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// DEALINGS IN THE SOFTWARE.
//
// Description:
//
///////////////////////////////////////////////////////////////////////////////
 
#include <Collections/Collection.h>
#include <Collections/CollectionOptimisation.h>
#include <LocalRegions/TetExp.h>
#include <SpatialDomains/MeshGraph.h>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/test/unit_test.hpp>
 
namespace Nektar::TetCollectionTests
{
SpatialDomains::SegGeomUniquePtr CreateSegGeom(unsigned int id,
                                               SpatialDomains::PointGeom *v0,
                                               SpatialDomains::PointGeom *v1)
{
    std::array<SpatialDomains::PointGeom *, 2> vertices = {v0, v1};
    SpatialDomains::SegGeomUniquePtr result(
        new SpatialDomains::SegGeom(id, 3, vertices));
    return result;
}
 
SpatialDomains::TetGeomUniquePtr CreateTet(
    std::array<SpatialDomains::PointGeom *, 4> v,
    std::array<SpatialDomains::SegGeomUniquePtr, 6> &segVec,
    std::array<SpatialDomains::TriGeomUniquePtr, 4> &faceVec)
{
    std::array<std::array<int, 2>, 6> edgeVerts = {
        {{{0, 1}}, {{1, 2}}, {{0, 2}}, {{0, 3}}, {{1, 3}}, {{2, 3}}}};
    std::array<std::array<int, 3>, 4> faceEdges = {
        {{{0, 1, 2}}, {{0, 4, 3}}, {{1, 5, 4}}, {{2, 5, 3}}}};
 
    // Create segments from vertices
    for (int i = 0; i < 6; ++i)
    {
        segVec[i] = CreateSegGeom(i, v[edgeVerts[i][0]], v[edgeVerts[i][1]]);
    }
 
    // Create faces from edges
    std::array<SpatialDomains::TriGeom *, 4> faces;
    for (int i = 0; i < 4; ++i)
    {
        std::array<SpatialDomains::SegGeom *, 3> face;
        for (int j = 0; j < 3; ++j)
        {
            face[j] = segVec[faceEdges[i][j]].get();
        }
        faceVec[i] = SpatialDomains::TriGeomUniquePtr(
            new SpatialDomains::TriGeom(i, face));
        faces[i] = faceVec[i].get();
    }
 
    SpatialDomains::TetGeomUniquePtr tetGeom(
        new SpatialDomains::TetGeom(0, faces));
    return tetGeom;
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_IterPerExp_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1; // make values distinct
    }
    Array<OneD, NekDouble> phys1(Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(Exp->GetTotPoints());
 
    Exp->BwdTrans(coeffs, phys1);
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_IterPerExp_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.5, -1.5, -1.5));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 6,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(nelmts * Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1;
    }
    Array<OneD, NekDouble> phys1(nelmts * Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(nelmts * Exp->GetTotPoints());
 
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->BwdTrans(coeffs + i * Exp->GetNcoeffs(),
                      tmp = phys1 + i * Exp->GetTotPoints());
    }
 
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_IterPerExp_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffs1(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffs1);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_IterPerExp_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(6,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
    // const Nektar::LibUtilities::BasisKey
    // basisKeyDir2(basisTypeDir2,5,triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nelmts * nq), tmp;
    Array<OneD, NekDouble> coeffs1(nelmts * Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(nelmts * Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->IProductWRTBase(phys, coeffs1);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, &phys[0], 1, &phys[i * nq], 1);
        Exp->IProductWRTBase(phys + i * nq,
                             tmp = coeffs1 + i * Exp->GetNcoeffs());
    }
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-4;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        // clamp values below 1e-14 to zero
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_StdMat_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1; // make values distinct
    }
    Array<OneD, NekDouble> phys1(Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(Exp->GetTotPoints());
 
    Exp->BwdTrans(coeffs, phys1);
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_StdMat_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.5, -1.5, -1.5));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(nelmts * Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1;
    }
    Array<OneD, NekDouble> phys1(nelmts * Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(nelmts * Exp->GetTotPoints());
 
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->BwdTrans(coeffs + i * Exp->GetNcoeffs(),
                      tmp = phys1 + i * Exp->GetTotPoints());
    }
 
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_SumFac_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1; // make values distinct
    }
    Array<OneD, NekDouble> phys1(Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(Exp->GetTotPoints());
 
    Exp->BwdTrans(coeffs, phys1);
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_SumFac_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.5, -1.5, -1.5));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(nelmts * Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1;
    }
    Array<OneD, NekDouble> phys1(nelmts * Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(nelmts * Exp->GetTotPoints());
 
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->BwdTrans(coeffs + i * Exp->GetNcoeffs(),
                      tmp = phys1 + i * Exp->GetTotPoints());
    }
 
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_SumFac_MultiElmt_VariableP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.5, -1.5, -1.5));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(6,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 6,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 1;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(nelmts * Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1;
    }
    Array<OneD, NekDouble> phys1(nelmts * Exp->GetTotPoints());
    Array<OneD, NekDouble> phys2(nelmts * Exp->GetTotPoints());
 
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->BwdTrans(coeffs + i * Exp->GetNcoeffs(),
                      tmp = phys1 + i * Exp->GetTotPoints());
    }
 
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < phys1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(phys1[i], phys2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_MatrixFree_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eBwdTrans] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1; // make values distinct
    }
    Array<OneD, NekDouble> physRef(Exp->GetTotPoints());
    Array<OneD, NekDouble> phys(Exp->GetTotPoints());
 
    Exp->BwdTrans(coeffs, physRef);
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < physRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(physRef[i], phys[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetBwdTrans_MatrixFree_UniformP_OverInt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 8;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eBwdTrans] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eBwdTrans);
 
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs(), 1.0), tmp;
    for (int i = 0; i < coeffs.size(); ++i)
    {
        coeffs[i] = i + 1; // make values distinct
    }
    Array<OneD, NekDouble> physRef(Exp->GetTotPoints());
    Array<OneD, NekDouble> phys(Exp->GetTotPoints());
 
    Exp->BwdTrans(coeffs, physRef);
    c.ApplyOperator(Collections::eBwdTrans, coeffs, phys);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < physRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(physRef[i], phys[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_StdMat_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffs1(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffs1);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_StdMat_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nelmts * nq), tmp;
    Array<OneD, NekDouble> coeffs1(nelmts * Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(nelmts * Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->IProductWRTBase(phys, coeffs1);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, &phys[0], 1, &phys[i * nq], 1);
        Exp->IProductWRTBase(phys + i * nq,
                             tmp = coeffs1 + i * Exp->GetNcoeffs());
    }
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-4;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        // clamp values below 1e-14 to zero
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_SumFac_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffs1(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffs1);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_SumFac_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    // const Nektar::LibUtilities::BasisKey
    // basisKeyDir2(basisTypeDir2,6,triPointsKeyDir2);
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nelmts * nq), tmp;
    Array<OneD, NekDouble> coeffs1(nelmts * Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs2(nelmts * Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->IProductWRTBase(phys, coeffs1);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, &phys[0], 1, &phys[i * nq], 1);
        Exp->IProductWRTBase(phys + i * nq,
                             tmp = coeffs1 + i * Exp->GetNcoeffs());
    }
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs2);
 
    double epsilon = 1.0e-4;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        // clamp values below 1e-14 to zero
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_MatrixFree_UniformP_Undeformed)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eIProductWRTBase] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffsRef(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffsRef);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTBase_MatrixFree_UniformP_Deformed)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -2.0, -3.0, -4.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eIProductWRTBase] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffsRef(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffsRef);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(
    TestTetIProductWRTBase_MatrixFree_UniformP_Deformed_OverInt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -2.0, -3.0, -4.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 8;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eIProductWRTBase] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTBase);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> phys(nq);
    Array<OneD, NekDouble> coeffsRef(Exp->GetNcoeffs());
    Array<OneD, NekDouble> coeffs(Exp->GetNcoeffs());
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->IProductWRTBase(phys, coeffsRef);
    c.ApplyOperator(Collections::eIProductWRTBase, phys, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_IterPerExp_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nq);
    Array<OneD, NekDouble> diff2(3 * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->PhysDeriv(phys, diff1, tmp = diff1 + nq, tmp1 = diff1 + 2 * nq);
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2, tmp = diff2 + nq,
                    tmp2 = diff2 + 2 * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_IterPerExp_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 6,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nelmts * nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nelmts * nq);
    Array<OneD, NekDouble> diff2(3 * nelmts * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->PhysDeriv(phys, diff1, tmp1 = diff1 + (nelmts)*nq,
                   tmp2 = diff1 + (2 * nelmts) * nq);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys, 1, tmp = phys + i * nq, 1);
        Exp->PhysDeriv(phys, tmp = diff1 + i * nq,
                       tmp1 = diff1 + (nelmts + i) * nq,
                       tmp2 = diff1 + (2 * nelmts + i) * nq);
    }
 
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2,
                    tmp = diff2 + nelmts * nq, tmp2 = diff2 + 2 * nelmts * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_StdMat_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nq);
    Array<OneD, NekDouble> diff2(3 * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->PhysDeriv(phys, diff1, tmp = diff1 + nq, tmp1 = diff1 + 2 * nq);
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2, tmp = diff2 + nq,
                    tmp2 = diff2 + 2 * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_StdMat_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 6,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nelmts * nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nelmts * nq);
    Array<OneD, NekDouble> diff2(3 * nelmts * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->PhysDeriv(phys, diff1, tmp1 = diff1 + (nelmts)*nq,
                   tmp2 = diff1 + (2 * nelmts) * nq);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys, 1, tmp = phys + i * nq, 1);
        Exp->PhysDeriv(phys, tmp = diff1 + i * nq,
                       tmp1 = diff1 + (nelmts + i) * nq,
                       tmp2 = diff1 + (2 * nelmts + i) * nq);
    }
 
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2,
                    tmp = diff2 + nelmts * nq, tmp2 = diff2 + 2 * nelmts * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_SumFac_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nq);
    Array<OneD, NekDouble> diff2(3 * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->PhysDeriv(phys, diff1, tmp = diff1 + nq, tmp1 = diff1 + 2 * nq);
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2, tmp = diff2 + nq,
                    tmp2 = diff2 + 2 * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_SumFac_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(7,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 6,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nelmts * nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diff1(3 * nelmts * nq);
    Array<OneD, NekDouble> diff2(3 * nelmts * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
    Exp->PhysDeriv(phys, diff1, tmp1 = diff1 + (nelmts)*nq,
                   tmp2 = diff1 + (2 * nelmts) * nq);
 
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys, 1, tmp = phys + i * nq, 1);
        Exp->PhysDeriv(phys, tmp = diff1 + i * nq,
                       tmp1 = diff1 + (nelmts + i) * nq,
                       tmp2 = diff1 + (2 * nelmts + i) * nq);
    }
 
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff2,
                    tmp = diff2 + nelmts * nq, tmp2 = diff2 + 2 * nelmts * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diff1.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diff1[i], diff2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysDeriv_MatrixFree_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::ePhysDeriv] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::ePhysDeriv);
 
    const int nq = Exp->GetTotPoints();
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq), tmp, tmp1, tmp2;
    Array<OneD, NekDouble> diffRef(3 * nq);
    Array<OneD, NekDouble> diff(3 * nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
    }
 
    Exp->PhysDeriv(phys, diffRef, tmp = diffRef + nq, tmp1 = diffRef + 2 * nq);
    c.ApplyOperator(Collections::ePhysDeriv, phys, diff, tmp = diff + nq,
                    tmp2 = diff + 2 * nq);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < diffRef.size(); ++i)
    {
        BOOST_CHECK_CLOSE(diffRef[i], diff[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_IterPerExp_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nq);
    Array<OneD, NekDouble> phys2(nq);
    Array<OneD, NekDouble> phys3(nq);
    Array<OneD, NekDouble> coeffs1(nm);
    Array<OneD, NekDouble> coeffs2(nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
 
    // Standard routines
    Exp->IProductWRTDerivBase(0, phys1, coeffs1);
    Exp->IProductWRTDerivBase(1, phys2, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
    Exp->IProductWRTDerivBase(2, phys3, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_IterPerExp_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(6,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
    // const Nektar::LibUtilities::BasisKey
    // basisKeyDir2(basisTypeDir2,5,triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 1;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nelmts * nq), tmp;
    Array<OneD, NekDouble> phys2(nelmts * nq);
    Array<OneD, NekDouble> phys3(nelmts * nq);
    Array<OneD, NekDouble> coeffs1(nelmts * nm);
    Array<OneD, NekDouble> coeffs2(nelmts * nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys1, 1, tmp = phys1 + i * nq, 1);
        Vmath::Vcopy(nq, phys2, 1, tmp = phys2 + i * nq, 1);
        Vmath::Vcopy(nq, phys3, 1, tmp = phys3 + i * nq, 1);
    }
 
    // Standard routines
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->IProductWRTDerivBase(0, phys1 + i * nq, tmp = coeffs1 + i * nm);
        Exp->IProductWRTDerivBase(1, phys2 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
        Exp->IProductWRTDerivBase(2, phys3 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
    }
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_StdMat_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nq);
    Array<OneD, NekDouble> phys2(nq);
    Array<OneD, NekDouble> phys3(nq);
    Array<OneD, NekDouble> coeffs1(nm);
    Array<OneD, NekDouble> coeffs2(nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
 
    // Standard routines
    Exp->IProductWRTDerivBase(0, phys1, coeffs1);
    Exp->IProductWRTDerivBase(1, phys2, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
    Exp->IProductWRTDerivBase(2, phys3, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_StdMat_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(6,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
    // const Nektar::LibUtilities::BasisKey
    // basisKeyDir2(basisTypeDir2,5,triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 1;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nelmts * nq), tmp;
    Array<OneD, NekDouble> phys2(nelmts * nq);
    Array<OneD, NekDouble> phys3(nelmts * nq);
    Array<OneD, NekDouble> coeffs1(nelmts * nm);
    Array<OneD, NekDouble> coeffs2(nelmts * nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys1, 1, tmp = phys1 + i * nq, 1);
        Vmath::Vcopy(nq, phys2, 1, tmp = phys2 + i * nq, 1);
        Vmath::Vcopy(nq, phys3, 1, tmp = phys3 + i * nq, 1);
    }
 
    // Standard routines
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->IProductWRTDerivBase(0, phys1 + i * nq, tmp = coeffs1 + i * nm);
        Exp->IProductWRTDerivBase(1, phys2 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
        Exp->IProductWRTDerivBase(2, phys3 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
    }
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_SumFac_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(4,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(4,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 4,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nq);
    Array<OneD, NekDouble> phys2(nq);
    Array<OneD, NekDouble> phys3(nq);
    Array<OneD, NekDouble> coeffs1(nm);
    Array<OneD, NekDouble> coeffs2(nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
 
    // Standard routines
    Exp->IProductWRTDerivBase(0, phys1, coeffs1);
    Exp->IProductWRTDerivBase(1, phys2, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
    Exp->IProductWRTDerivBase(2, phys3, coeffs2);
    Vmath::Vadd(nm, coeffs1, 1, coeffs2, 1, coeffs1, 1);
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-7;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_SumFac_VariableP_MultiElmt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(5,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, 4,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(6,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, 4,
                                                      triPointsKeyDir2);
    // const Nektar::LibUtilities::BasisKey
    // basisKeyDir2(basisTypeDir2,5,triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(9,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, 8,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 1;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eSumFac);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nelmts * nq), tmp;
    Array<OneD, NekDouble> phys2(nelmts * nq);
    Array<OneD, NekDouble> phys3(nelmts * nq);
    Array<OneD, NekDouble> coeffs1(nelmts * nm);
    Array<OneD, NekDouble> coeffs2(nelmts * nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
    for (int i = 1; i < nelmts; ++i)
    {
        Vmath::Vcopy(nq, phys1, 1, tmp = phys1 + i * nq, 1);
        Vmath::Vcopy(nq, phys2, 1, tmp = phys2 + i * nq, 1);
        Vmath::Vcopy(nq, phys3, 1, tmp = phys3 + i * nq, 1);
    }
 
    // Standard routines
    for (int i = 0; i < nelmts; ++i)
    {
        Exp->IProductWRTDerivBase(0, phys1 + i * nq, tmp = coeffs1 + i * nm);
        Exp->IProductWRTDerivBase(1, phys2 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
        Exp->IProductWRTDerivBase(2, phys3 + i * nq, tmp = coeffs2 + i * nm);
        Vmath::Vadd(nm, coeffs1 + i * nm, 1, coeffs2 + i * nm, 1,
                    tmp = coeffs1 + i * nm, 1);
    }
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs2);
 
    double epsilon = 1.0e-7;
    for (int i = 0; i < coeffs1.size(); ++i)
    {
        coeffs1[i] = (fabs(coeffs1[i]) < 1e-14) ? 0.0 : coeffs1[i];
        coeffs2[i] = (fabs(coeffs2[i]) < 1e-14) ? 0.0 : coeffs2[i];
        BOOST_CHECK_CLOSE(coeffs1[i], coeffs2[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetHelmholtz_IterPerExp_UniformP_ConstVarDiff)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda]   = 1.5;
    factors[StdRegions::eFactorCoeffD00] = 1.25;
    factors[StdRegions::eFactorCoeffD01] = 0.25;
    factors[StdRegions::eFactorCoeffD11] = 1.25;
    factors[StdRegions::eFactorCoeffD02] = 0.25;
    factors[StdRegions::eFactorCoeffD12] = 0.25;
    factors[StdRegions::eFactorCoeffD22] = 1.25;
 
    c.Initialise(Collections::eHelmholtz, factors);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eHelmholtz, Exp->DetShapeType(),
                                  *Exp, factors);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eHelmholtz, coeffsIn, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetHelmholtz_MatrixFree_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.5;
 
    c.Initialise(Collections::eHelmholtz, factors);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eHelmholtz, Exp->DetShapeType(),
                                  *Exp, factors);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eHelmholtz, coeffsIn, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetHelmholtz_MatrixFree_Deformed_OverInt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -2.0, -3.0, -4.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 8;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.5;
 
    c.Initialise(Collections::eHelmholtz, factors);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eHelmholtz, Exp->DetShapeType(),
                                  *Exp, factors);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eHelmholtz, coeffsIn, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetIProductWRTDerivBase_MatrixFree_UniformP_Undeformed)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -2.0, -3.0, -4.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eStdMat);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    // ... only one op at the time ...
    impTypes[Collections::eIProductWRTDerivBase] = Collections::eMatrixFree;
    Collections::Collection c(CollExp, impTypes);
    c.Initialise(Collections::eIProductWRTDerivBase);
 
    const int nq = Exp->GetTotPoints();
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> phys1(nq);
    Array<OneD, NekDouble> phys2(nq);
    Array<OneD, NekDouble> phys3(nq);
    Array<OneD, NekDouble> coeffsRef(nm);
    Array<OneD, NekDouble> coeffs(nm);
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys1[i] = sin(xc[i]) * cos(yc[i]) * sin(zc[i]);
        phys2[i] = cos(xc[i]) * sin(yc[i]) * cos(zc[i]);
        phys3[i] = cos(xc[i]) * sin(yc[i]) * sin(zc[i]);
    }
 
    // Standard routines
    Exp->IProductWRTDerivBase(0, phys1, coeffsRef);
    Exp->IProductWRTDerivBase(1, phys2, coeffs);
    Vmath::Vadd(nm, coeffsRef, 1, coeffs, 1, coeffsRef, 1);
    Exp->IProductWRTDerivBase(2, phys3, coeffs);
    Vmath::Vadd(nm, coeffsRef, 1, coeffs, 1, coeffsRef, 1);
 
    c.ApplyOperator(Collections::eIProductWRTDerivBase, phys1, phys2, phys3,
                    coeffs);
 
    double epsilon = 1.0e-7;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetHelmholtz_MatrixFree_UniformP_ConstVarDiff)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda]   = 1.5;
    factors[StdRegions::eFactorCoeffD00] = 1.25;
    factors[StdRegions::eFactorCoeffD01] = 0.25;
    factors[StdRegions::eFactorCoeffD11] = 1.25;
    factors[StdRegions::eFactorCoeffD02] = 0.25;
    factors[StdRegions::eFactorCoeffD12] = 0.25;
    factors[StdRegions::eFactorCoeffD22] = 1.25;
 
    c.Initialise(Collections::eHelmholtz, factors);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eHelmholtz, Exp->DetShapeType(),
                                  *Exp, factors);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eHelmholtz, coeffsIn, coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysInterp1D_NoCollections_UniformP)
{
 
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eNoCollection);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
 
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorConst] = 1.5;
    c.Initialise(Collections::ePhysInterp1DScaled, factors);
 
    const int nq = Exp->GetTotPoints();
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = pow(xc[i], 3) + pow(yc[i], 3) + pow(zc[i], 3);
    }
 
    const int nq1 = c.GetOutputSize(Collections::ePhysInterp1DScaled);
    Array<OneD, NekDouble> xc1(nq1);
    Array<OneD, NekDouble> yc1(nq1);
    Array<OneD, NekDouble> zc1(nq1);
    Array<OneD, NekDouble> phys1(nq1);
 
    c.ApplyOperator(Collections::ePhysInterp1DScaled, xc, xc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, yc, yc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, zc, zc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, phys, phys1);
 
    double epsilon = 1.0e-8;
    // since solution is a polynomial should be able to compare soln directly
    for (int i = 0; i < nq1; ++i)
    {
        NekDouble exact = pow(xc1[i], 3) + pow(yc1[i], 3) + pow(zc1[i], 3);
        phys1[i]        = (fabs(phys1[i]) < 1e-14) ? 0.0 : phys1[i];
        exact           = (fabs(exact) < 1e-14) ? 0.0 : exact;
        BOOST_CHECK_CLOSE(phys1[i], exact, epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(TestTetPhysInterp1D_MatrixFree_UniformP)
{
 
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    CollExp.push_back(Exp);
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 3,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
 
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorConst] = 1.5;
    c.Initialise(Collections::ePhysInterp1DScaled, factors);
 
    const int nq = Exp->GetTotPoints();
 
    Array<OneD, NekDouble> xc(nq), yc(nq), zc(nq);
    Array<OneD, NekDouble> phys(nq);
 
    Exp->GetCoords(xc, yc, zc);
 
    for (int i = 0; i < nq; ++i)
    {
        phys[i] = pow(xc[i], 3) + pow(yc[i], 3) + pow(zc[i], 3);
    }
 
    const int nq1 = c.GetOutputSize(Collections::ePhysInterp1DScaled);
    Array<OneD, NekDouble> xc1(nq1);
    Array<OneD, NekDouble> yc1(nq1);
    Array<OneD, NekDouble> zc1(nq1);
    Array<OneD, NekDouble> phys1(nq1);
 
    c.ApplyOperator(Collections::ePhysInterp1DScaled, xc, xc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, yc, yc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, zc, zc1);
    c.ApplyOperator(Collections::ePhysInterp1DScaled, phys, phys1);
 
    double epsilon = 1.0e-8;
    // since solution is a polynomial should be able to compare soln directly
    for (int i = 0; i < nq1; ++i)
    {
        NekDouble exact = pow(xc1[i], 3) + pow(yc1[i], 3) + pow(zc1[i], 3);
        phys1[i]        = (fabs(phys1[i]) < 1e-14) ? 0.0 : phys1[i];
        exact           = (fabs(exact) < 1e-14) ? 0.0 : exact;
        BOOST_CHECK_CLOSE(phys1[i], exact, epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(
    TestTetLinearAdvectionDiffusionReaction_IterPerExp_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eIterPerExp);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.5;
 
    c.Initialise(Collections::eLinearAdvectionDiffusionReaction, factors);
 
    // Add advection velocities via varcoeffs
    int npoints = Exp->GetTotPoints() * nelmts;
    StdRegions::VarCoeffMap varcoeffs;
    StdRegions::VarCoeffType varcoefftypes[] = {StdRegions::eVarCoeffVelX,
                                                StdRegions::eVarCoeffVelY,
                                                StdRegions::eVarCoeffVelZ};
    for (int i = 0; i < Exp->GetShapeDimension(); i++)
    {
        varcoeffs[varcoefftypes[i]] = Array<OneD, NekDouble>(npoints, 1.0);
    }
    c.UpdateVarcoeffs(Collections::eLinearAdvectionDiffusionReaction,
                      varcoeffs);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eLinearAdvectionDiffusionReaction,
                                  Exp->DetShapeType(), *Exp, factors,
                                  varcoeffs);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eLinearAdvectionDiffusionReaction, coeffsIn,
                    coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(
    TestTetLinearAdvectionDiffusionReaction_MatrixFree_UniformP)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 5;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.5;
 
    c.Initialise(Collections::eLinearAdvectionDiffusionReaction, factors);
 
    // Add advection velocities via varcoeffs
    int npoints = Exp->GetTotPoints() * nelmts;
    StdRegions::VarCoeffMap varcoeffs;
    StdRegions::VarCoeffType varcoefftypes[] = {StdRegions::eVarCoeffVelX,
                                                StdRegions::eVarCoeffVelY,
                                                StdRegions::eVarCoeffVelZ};
    for (int i = 0; i < Exp->GetShapeDimension(); i++)
    {
        varcoeffs[varcoefftypes[i]] = Array<OneD, NekDouble>(npoints, 1.0);
    }
    c.UpdateVarcoeffs(Collections::eLinearAdvectionDiffusionReaction,
                      varcoeffs);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eLinearAdvectionDiffusionReaction,
                                  Exp->DetShapeType(), *Exp, factors,
                                  varcoeffs);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eLinearAdvectionDiffusionReaction, coeffsIn,
                    coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
    }
}
 
BOOST_AUTO_TEST_CASE(
    TestTetLinearAdvectionDiffusionReaction_MatrixFree_Deformed_OverInt)
{
    SpatialDomains::PointGeomUniquePtr v0(
        new SpatialDomains::PointGeom(3u, 0u, -2.0, -3.0, -4.0));
    SpatialDomains::PointGeomUniquePtr v1(
        new SpatialDomains::PointGeom(3u, 1u, 1.0, -1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v2(
        new SpatialDomains::PointGeom(3u, 2u, -1.0, 1.0, -1.0));
    SpatialDomains::PointGeomUniquePtr v3(
        new SpatialDomains::PointGeom(3u, 3u, -1.0, -1.0, 1.0));
 
    std::array<SpatialDomains::PointGeom *, 4> v = {v0.get(), v1.get(),
                                                    v2.get(), v3.get()};
    std::array<SpatialDomains::SegGeomUniquePtr, 6> segVec;
    std::array<SpatialDomains::TriGeomUniquePtr, 4> faceVec;
    SpatialDomains::TetGeomUniquePtr tetGeom = CreateTet(v, segVec, faceVec);
 
    unsigned int numQuadPoints = 8;
    unsigned int numModes      = 4;
 
    Nektar::LibUtilities::PointsType triPointsTypeDir1 =
        Nektar::LibUtilities::eGaussLobattoLegendre;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir1(numQuadPoints,
                                                           triPointsTypeDir1);
    Nektar::LibUtilities::BasisType basisTypeDir1 =
        Nektar::LibUtilities::eModified_A;
    const Nektar::LibUtilities::BasisKey basisKeyDir1(basisTypeDir1, numModes,
                                                      triPointsKeyDir1);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir2 =
        Nektar::LibUtilities::eGaussRadauMAlpha1Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir2(numQuadPoints - 1,
                                                           triPointsTypeDir2);
    Nektar::LibUtilities::BasisType basisTypeDir2 =
        Nektar::LibUtilities::eModified_B;
    const Nektar::LibUtilities::BasisKey basisKeyDir2(basisTypeDir2, numModes,
                                                      triPointsKeyDir2);
 
    Nektar::LibUtilities::PointsType triPointsTypeDir3 =
        Nektar::LibUtilities::eGaussRadauMAlpha2Beta0;
    const Nektar::LibUtilities::PointsKey triPointsKeyDir3(numQuadPoints - 1,
                                                           triPointsTypeDir3);
    Nektar::LibUtilities::BasisType basisTypeDir3 =
        Nektar::LibUtilities::eModified_C;
    const Nektar::LibUtilities::BasisKey basisKeyDir3(basisTypeDir3, numModes,
                                                      triPointsKeyDir3);
 
    Nektar::LocalRegions::TetExpSharedPtr Exp =
        MemoryManager<Nektar::LocalRegions::TetExp>::AllocateSharedPtr(
            basisKeyDir1, basisKeyDir2, basisKeyDir3, tetGeom.get());
 
    int nelmts = 10;
 
    std::vector<LocalRegions::ExpansionSharedPtr> CollExp;
    for (int i = 0; i < nelmts; ++i)
    {
        CollExp.push_back(Exp);
    }
 
    LibUtilities::SessionReaderSharedPtr dummySession;
    Collections::CollectionOptimisation colOpt(dummySession, 2,
                                               Collections::eMatrixFree);
    Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(Exp);
    Collections::Collection c(CollExp, impTypes);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.5;
 
    c.Initialise(Collections::eLinearAdvectionDiffusionReaction, factors);
 
    // Add advection velocities via varcoeffs
    int npoints = Exp->GetTotPoints() * nelmts;
    StdRegions::VarCoeffMap varcoeffs;
    StdRegions::VarCoeffType varcoefftypes[] = {StdRegions::eVarCoeffVelX,
                                                StdRegions::eVarCoeffVelY,
                                                StdRegions::eVarCoeffVelZ};
    for (int i = 0; i < Exp->GetShapeDimension(); i++)
    {
        varcoeffs[varcoefftypes[i]] = Array<OneD, NekDouble>(npoints, 1.0);
    }
    c.UpdateVarcoeffs(Collections::eLinearAdvectionDiffusionReaction,
                      varcoeffs);
 
    const int nm = Exp->GetNcoeffs();
    Array<OneD, NekDouble> coeffsIn(nelmts * nm);
    Array<OneD, NekDouble> coeffsRef(nelmts * nm);
    Array<OneD, NekDouble> coeffs(nelmts * nm), tmp;
 
    for (int i = 0; i < coeffsIn.size(); ++i)
    {
        coeffsIn[i] = i + 1.0;
    }
 
    StdRegions::StdMatrixKey mkey(StdRegions::eLinearAdvectionDiffusionReaction,
                                  Exp->DetShapeType(), *Exp, factors,
                                  varcoeffs);
 
    for (int i = 0; i < nelmts; ++i)
    {
        // Standard routines
        Exp->GeneralMatrixOp(coeffsIn + i * nm, tmp = coeffsRef + i * nm, mkey);
    }
 
    c.ApplyOperator(Collections::eLinearAdvectionDiffusionReaction, coeffsIn,
                    coeffs);
 
    double epsilon = 1.0e-8;
    for (int i = 0; i < coeffsRef.size(); ++i)
    {
        coeffsRef[i] = (std::abs(coeffsRef[i]) < 1e-14) ? 0.0 : coeffsRef[i];
        coeffs[i]    = (std::abs(coeffs[i]) < 1e-14) ? 0.0 : coeffs[i];
        BOOST_CHECK_CLOSE(coeffsRef[i], coeffs[i], epsilon);
        std::cout << "i = " << i << "\tdiff = " << coeffsRef[i] - coeffs[i]
                  << std::endl;
    }
}
 
} // namespace Nektar::TetCollectionTests