Intrepid2_OrientationToolsDefCoeffMatrix_HGRAD.hpp

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#ifndef __INTREPID2_ORIENTATIONTOOLS_DEF_COEFF_MATRIX_HGRAD_HPP__
#define __INTREPID2_ORIENTATIONTOOLS_DEF_COEFF_MATRIX_HGRAD_HPP__

// disable clang warnings
#if defined (__clang__) && !defined (__INTEL_COMPILER)
#pragma clang system_header
#endif

namespace Intrepid2 {

namespace Impl {
namespace Debug {

#ifdef HAVE_INTREPID2_DEBUG
template<typename subcellBasisType,
typename cellBasisType>
inline
void
check_getCoeffMatrix_HGRAD(const subcellBasisType& subcellBasis,
    const cellBasisType& cellBasis,
    const ordinal_type subcellId,
    const ordinal_type subcellOrt) {

  // populate points on a subcell and map to subcell
  const shards::CellTopology cellTopo = cellBasis.getBaseCellTopology();
  const shards::CellTopology subcellTopo = subcellBasis.getBaseCellTopology();

  const ordinal_type cellDim = cellTopo.getDimension();
  const ordinal_type subcellDim = subcellTopo.getDimension();

  INTREPID2_TEST_FOR_EXCEPTION( subcellDim > cellDim,
      std::logic_error,
      ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
      "cellDim cannot be smaller than subcellDim.");

  INTREPID2_TEST_FOR_EXCEPTION( subcellDim > 2,
      std::logic_error,
      ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
      "subCellDim cannot be larger than 2.");

  const auto subcellBaseKey = subcellTopo.getBaseKey();

  INTREPID2_TEST_FOR_EXCEPTION( subcellBaseKey != shards::Line<>::key &&
      subcellBaseKey != shards::Quadrilateral<>::key &&
      subcellBaseKey != shards::Triangle<>::key,
      std::logic_error,
      ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
      "subcellBasis must have line, quad, or triangle topology.");


  //
  // Function space
  //

  {
    const bool cellBasisIsHGRAD = cellBasis.getFunctionSpace() == FUNCTION_SPACE_HGRAD;
    const bool subcellBasisIsHGRAD = subcellBasis.getFunctionSpace() == FUNCTION_SPACE_HGRAD;
    if (cellBasisIsHGRAD) {
      INTREPID2_TEST_FOR_EXCEPTION( !subcellBasisIsHGRAD,
          std::logic_error,
          ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
          "subcellBasis function space is not consistent to cellBasis.");
    }

    INTREPID2_TEST_FOR_EXCEPTION( subcellBasis.getDegree() != cellBasis.getDegree(),
        std::logic_error,
        ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
        "subcellBasis has a different polynomial degree from cellBasis' degree.");
  }
}
#endif
} // Debug namespace

template<typename OutputViewType,
typename subcellBasisHostType,
typename cellBasisHostType>
inline
void
OrientationTools::
getCoeffMatrix_HGRAD(OutputViewType &output, 
                     const subcellBasisHostType& subcellBasis, 
                     const cellBasisHostType& cellBasis, 
                     const ordinal_type subcellId,
                     const ordinal_type subcellOrt,
                     const bool inverse) {

#ifdef HAVE_INTREPID2_DEBUG
  Debug::check_getCoeffMatrix_HGRAD(subcellBasis,cellBasis,subcellId,subcellOrt);
#endif

  using host_device_type = typename Kokkos::HostSpace::device_type;
  using value_type = typename OutputViewType::non_const_value_type;

  //
  // Topology
  //

  const shards::CellTopology cellTopo = cellBasis.getBaseCellTopology();
  const shards::CellTopology subcellTopo = subcellBasis.getBaseCellTopology();
  const ordinal_type cellDim = cellTopo.getDimension();
  const ordinal_type subcellDim = subcellTopo.getDimension();
  const auto subcellBaseKey = subcellTopo.getBaseKey();
  const ordinal_type numCellBasis = cellBasis.getCardinality();
  const ordinal_type numSubcellBasis = subcellBasis.getCardinality();
  const ordinal_type ndofSubcell = cellBasis.getDofCount(subcellDim,subcellId);

  //
  // Reference points
  //

  // Reference points \xi_j on the subcell
  Kokkos::DynRankView<value_type,host_device_type> refPtsSubcell("refPtsSubcell", ndofSubcell, subcellDim);
  auto latticeSize=PointTools::getLatticeSize(subcellTopo, subcellBasis.getDegree(), 1);

  INTREPID2_TEST_FOR_EXCEPTION( latticeSize != ndofSubcell,
      std::logic_error,
      ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): " \
      "Lattice size should be equal to the number of subcell internal DoFs");
  PointTools::getLattice(refPtsSubcell, subcellTopo, subcellBasis.getDegree(), 1, POINTTYPE_WARPBLEND);

  // map the points into the parent, cell accounting for orientation
  Kokkos::DynRankView<value_type,host_device_type> refPtsCell("refPtsCell", ndofSubcell, cellDim);
  // refPtsCell = F_s (\eta_o (refPtsSubcell))
  if(cellDim == subcellDim) //the cell is a side of dimension 1 or 2.
    mapToModifiedReference(refPtsCell,refPtsSubcell,subcellBaseKey,subcellOrt);
  else {
    auto subcellParam = Intrepid2::RefSubcellParametrization<host_device_type>::get(subcellDim, cellTopo.getKey());
    mapSubcellCoordsToRefCell(refPtsCell,refPtsSubcell, subcellParam, subcellBaseKey, subcellId, subcellOrt);
  }

  //
  // Bases evaluation on the reference points
  //

  // cellBasisValues = \psi_k(F_s (\eta_o (\xi_j)))
  Kokkos::DynRankView<value_type,host_device_type> cellBasisValues("cellBasisValues", numCellBasis, ndofSubcell);

  // subcellBasisValues = \phi_i (\xi_j)
  Kokkos::DynRankView<value_type,host_device_type> subcellBasisValues("subcellBasisValues", numSubcellBasis, ndofSubcell);

  cellBasis.getValues(cellBasisValues, refPtsCell, OPERATOR_VALUE);
  subcellBasis.getValues(subcellBasisValues, refPtsSubcell, OPERATOR_VALUE);

  //
  // Compute Psi_jk = \psi_k(F_s (\eta_o (\xi_j))) and Phi_ji = \phi_i (\xi_j),
  // and solve
  // Psi A^T = Phi
  //

  // construct Psi and Phi  matrices.  LAPACK wants left layout
  Kokkos::DynRankView<value_type,Kokkos::LayoutLeft,host_device_type>
    PsiMat("PsiMat", ndofSubcell, ndofSubcell),
    PhiMat("PhiMat", ndofSubcell, ndofSubcell),
    RefMat,
    OrtMat;
  
  auto cellTagToOrdinal = cellBasis.getAllDofOrdinal();
  auto subcellTagToOrdinal = subcellBasis.getAllDofOrdinal();

  for (ordinal_type i=0;i<ndofSubcell;++i) {
    const ordinal_type ic = cellTagToOrdinal(subcellDim, subcellId, i);
    const ordinal_type isc = subcellTagToOrdinal(subcellDim, 0, i);
    for (ordinal_type j=0;j<ndofSubcell;++j) {
      PsiMat(j, i) = cellBasisValues(ic,j);
      PhiMat(j, i) = subcellBasisValues(isc,j);
    }
  }

  RefMat = inverse ? PhiMat : PsiMat;
  OrtMat = inverse ? PsiMat : PhiMat;

  // Solve the system
  {
    Teuchos::LAPACK<ordinal_type,value_type> lapack;
    ordinal_type info = 0;

    Kokkos::DynRankView<ordinal_type,Kokkos::LayoutLeft,host_device_type> pivVec("pivVec", ndofSubcell);
    lapack.GESV(ndofSubcell, ndofSubcell,
                RefMat.data(),
                RefMat.stride_1(),
                pivVec.data(),
                OrtMat.data(),
                OrtMat.stride_1(),
                &info);
    
    if (info) {
      std::stringstream ss;
      ss << ">>> ERROR (Intrepid::OrientationTools::getCoeffMatrix_HGRAD): "
         << "LAPACK return with error code: "
         << info;
      INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error, ss.str().c_str() );
    }
    
    //After solving the system w/ LAPACK, Phi contains A^T
    
    // transpose B and clean up numerical noise (for permutation matrices)
    const double eps = tolerence();
    for (ordinal_type i=0;i<ndofSubcell;++i) {
      auto intmatii = std::round(OrtMat(i,i));
      OrtMat(i,i) = (std::abs(OrtMat(i,i) - intmatii) < eps) ? intmatii : OrtMat(i,i);
      for (ordinal_type j=i+1;j<ndofSubcell;++j) {
        auto matij = OrtMat(i,j);

        auto intmatji = std::round(OrtMat(j,i));
        OrtMat(i,j) = (std::abs(OrtMat(j,i) - intmatji) < eps) ? intmatji : OrtMat(j,i);

        auto intmatij = std::round(matij);
        OrtMat(j,i) = (std::abs(matij - intmatij) < eps) ? intmatij : matij;
      }
    }

  }

  // Print A Matrix
  /*
  {
    std::cout  << "|";
    for (ordinal_type i=0;i<ndofSubcell;++i) {
      for (ordinal_type j=0;j<ndofSubcell;++j) {
        std::cout << OrtMat(i,j) << " ";
      }
      std::cout  << "| ";
    }
    std::cout <<std::endl;
  }
  */

  {
    // move the data to original device memory
    const Kokkos::pair<ordinal_type,ordinal_type> range(0, ndofSubcell);
    auto suboutput = Kokkos::subview(output, range, range);
    auto tmp = Kokkos::create_mirror_view_and_copy(typename OutputViewType::device_type::memory_space(), OrtMat);
    Kokkos::deep_copy(suboutput, tmp);
  }
}
}

}
#endif