Amesos2_Cholmod_def.hpp

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#ifndef AMESOS2_CHOLMOD_DEF_HPP
#define AMESOS2_CHOLMOD_DEF_HPP

#include <Teuchos_Tuple.hpp>
#include <Teuchos_ParameterList.hpp>
#include <Teuchos_StandardParameterEntryValidators.hpp>

#include "Amesos2_SolverCore_def.hpp"
#include "Amesos2_Cholmod_decl.hpp"

#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
#include "KokkosSparse_sptrsv_cholmod.hpp"
#endif

namespace Amesos2 {


template <class Matrix, class Vector>
Cholmod<Matrix,Vector>::Cholmod(
  Teuchos::RCP<const Matrix> A,
  Teuchos::RCP<Vector>       X,
  Teuchos::RCP<const Vector> B )
  : SolverCore<Amesos2::Cholmod,Matrix,Vector>(A, X, B)
  , firstsolve(true)
  , skip_symfact(false)
  , map()
  , is_contiguous_(true) // default is set by params
  , use_triangular_solves_(false) // default is set by params
  , use_cholmod_int_type_(false) // if true we use CHOLMOD_INT (no GPU support)
{
  data_.L = NULL;
  data_.Y = NULL;
  data_.E = NULL;

  data_.c.supernodal = CHOLMOD_AUTO;
  data_.c.quick_return_if_not_posdef = 1;
}


template <class Matrix, class Vector>
Cholmod<Matrix,Vector>::~Cholmod( )
{
  if(use_cholmod_int_type_) {
    cholmod_free_factor(&(data_.L), &(data_.c));
    cholmod_free_dense(&(data_.Y), &data_.c);
    cholmod_free_dense(&(data_.E), &data_.c);
    cholmod_finish(&(data_.c));
  }
  else {
    // useful to check if GPU is being used, but very verbose
    // cholmod_l_gpu_stats(&(data_.c));
    cholmod_l_free_factor(&(data_.L), &(data_.c));
    cholmod_l_free_dense(&(data_.Y), &data_.c);
    cholmod_l_free_dense(&(data_.E), &data_.c);
    cholmod_l_finish(&(data_.c));
  }
}

template<class Matrix, class Vector>
int
Cholmod<Matrix,Vector>::preOrdering_impl()
{
#ifdef HAVE_AMESOS2_TIMERS
  Teuchos::TimeMonitor preOrderTimer(this->timers_.preOrderTime_);
#endif

  int info = 0;

  if(use_cholmod_int_type_) {
    data_.L = cholmod_analyze(&data_.A, &(data_.c));
  }
  else {
    data_.L = cholmod_l_analyze(&data_.A, &(data_.c));
  }

  info = data_.c.status;
  skip_symfact = true;

  /* All processes should have the same error code */
  Teuchos::broadcast(*(this->matrixA_->getComm()), 0, &info);
  
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
    std::runtime_error,
    "Amesos2 cholmod_l_analyze failure in Cholmod preOrdering_impl");

  return(0);
}


template <class Matrix, class Vector>
int
Cholmod<Matrix,Vector>::symbolicFactorization_impl()
{
  int info = 0;

  if(!skip_symfact) {
#ifdef HAVE_AMESOS2_TIMERS
    Teuchos::TimeMonitor symFactTimer(this->timers_.symFactTime_);
#endif

    if(use_cholmod_int_type_) {
      cholmod_resymbol (&data_.A, NULL, 0, true, data_.L, &(data_.c));
    }
    else {
      cholmod_l_resymbol (&data_.A, NULL, 0, true, data_.L, &(data_.c));
    }

    info = data_.c.status;
  } else {
    /*
     * Symbolic factorization has already occured in preOrdering_impl,
     * but if the user calls this routine directly later, we need to
     * redo the symbolic factorization.
     */
    skip_symfact = false;
  }

  /* All processes should have the same error code */
  Teuchos::broadcast(*(this->matrixA_->getComm()), 0, &info);
  
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
    std::runtime_error,
    "Amesos2 cholmod_l_resymbol failure in Cholmod symbolicFactorization_impl");

  if(use_triangular_solves_) {
    triangular_solve_symbolic();
  }

  return(0);
}


template <class Matrix, class Vector>
int
Cholmod<Matrix,Vector>::numericFactorization_impl()
{
  int info = 0;

#ifdef HAVE_AMESOS2_DEBUG
  TEUCHOS_TEST_FOR_EXCEPTION(data_.A.ncol != Teuchos::as<size_t>(this->globalNumCols_),
    std::runtime_error,
    "Error in converting to cholmod_sparse: wrong number of global columns." );
  TEUCHOS_TEST_FOR_EXCEPTION(data_.A.nrow != Teuchos::as<size_t>(this->globalNumRows_),
    std::runtime_error,
    "Error in converting to cholmod_sparse: wrong number of global rows." );
#endif

#ifdef HAVE_AMESOS2_TIMERS
  Teuchos::TimeMonitor numFactTimer(this->timers_.numFactTime_);
#endif

#ifdef HAVE_AMESOS2_VERBOSE_DEBUG
  // Add print out of views here - need host conversion first
#endif

  if(use_cholmod_int_type_) {
    cholmod_factorize(&data_.A, data_.L, &(data_.c));
  }
  else {
    cholmod_l_factorize(&data_.A, data_.L, &(data_.c));
  }

  info = data_.c.status;

  /* All processes should have the same error code */
  Teuchos::broadcast(*(this->matrixA_->getComm()), 0, &info);

  TEUCHOS_TEST_FOR_EXCEPTION(info == CHOLMOD_OUT_OF_MEMORY,
    std::runtime_error,
    "Amesos2 cholmod_l_factorize error code: CHOLMOD_OUT_OF_MEMORY");

  TEUCHOS_TEST_FOR_EXCEPTION(info == CHOLMOD_NOT_POSDEF,
    std::runtime_error,
    "Amesos2 cholmod_l_factorize error code: CHOLMOD_NOT_POSDEF.");

  TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
    std::runtime_error,
    "Amesos2 cholmod_l_factorize error code:" << info);

  if(use_triangular_solves_) {
    triangular_solve_numeric();
  }

  return(info);
}


template <class Matrix, class Vector>
int
Cholmod<Matrix,Vector>::solve_impl(const Teuchos::Ptr<MultiVecAdapter<Vector> >       X,
                                   const Teuchos::Ptr<const MultiVecAdapter<Vector> > B) const
{
  const global_size_type ld_rhs = X->getGlobalLength();
  const size_t nrhs = X->getGlobalNumVectors();

  bool bDidAssignX;
  {                             // Get values from RHS B
#ifdef HAVE_AMESOS2_TIMERS
    Teuchos::TimeMonitor mvConvTimer(this->timers_.vecConvTime_);
    Teuchos::TimeMonitor redistTimer( this->timers_.vecRedistTime_ );
#endif

    // In general we may want to write directly to the x space without a copy.
    // So we 'get' x which may be a direct view assignment to the MV.
    const bool initialize_data = true;
    const bool do_not_initialize_data = false;
    if(use_triangular_solves_) { // to device
#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
      Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
          device_solve_array_t>::do_get(initialize_data, B, device_bValues_,
              Teuchos::as<size_t>(ld_rhs),
              (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
              this->rowIndexBase_);
        bDidAssignX = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
          device_solve_array_t>::do_get(do_not_initialize_data, X, device_xValues_,
              Teuchos::as<size_t>(ld_rhs),
              (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
              this->rowIndexBase_);
#endif
    }
    else { // to host
      Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
          host_solve_array_t>::do_get(initialize_data, B, host_bValues_,
              Teuchos::as<size_t>(ld_rhs),
              (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
              this->rowIndexBase_);
        bDidAssignX = Util::get_1d_copy_helper_kokkos_view<MultiVecAdapter<Vector>,
          host_solve_array_t>::do_get(do_not_initialize_data, X, host_xValues_,
              Teuchos::as<size_t>(ld_rhs),
              (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
              this->rowIndexBase_);
    }
  }

  int ierr = 0; // returned error code

#ifdef HAVE_AMESOS2_TIMERS
  Teuchos::TimeMonitor solveTimer(this->timers_.solveTime_);
#endif

  if(use_triangular_solves_) {
    triangular_solve();
  }
  else {
    function_map::cholmod_init_dense(Teuchos::as<long>(this->globalNumRows_),
      Teuchos::as<int>(nrhs), Teuchos::as<int>(ld_rhs), host_bValues_.data(), &data_.b);
    function_map::cholmod_init_dense(Teuchos::as<long>(this->globalNumRows_),
      Teuchos::as<int>(nrhs), Teuchos::as<int>(ld_rhs), host_xValues_.data(), &data_.x);

    cholmod_dense *xtemp = &(data_.x);
    if(use_cholmod_int_type_) {
      cholmod_solve2(CHOLMOD_A, data_.L, &data_.b, NULL,
        &(xtemp), NULL, &data_.Y, &data_.E, &data_.c);
    }
    else {
      cholmod_l_solve2(CHOLMOD_A, data_.L, &data_.b, NULL,
        &(xtemp), NULL, &data_.Y, &data_.E, &data_.c);
    }
  }

  ierr = data_.c.status;

  /* All processes should have the same error code */
  Teuchos::broadcast(*(this->getComm()), 0, &ierr);

  TEUCHOS_TEST_FOR_EXCEPTION(ierr == -2, std::runtime_error, "Ran out of memory" );

  /* Update X's global values */

  // if bDidAssignX, then we solved straight to the adapter's X memory space without
  // requiring additional memory allocation, so the x data is already in place.
  if(!bDidAssignX) {
#ifdef HAVE_AMESOS2_TIMERS
    Teuchos::TimeMonitor redistTimer(this->timers_.vecRedistTime_);
#endif

    if(use_triangular_solves_) { // to device
#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
      Util::put_1d_data_helper_kokkos_view<
        MultiVecAdapter<Vector>,device_solve_array_t>::do_put(X, device_xValues_,
            Teuchos::as<size_t>(ld_rhs),
            (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
            this->rowIndexBase_);
#endif
    }
    else { // to host
      Util::put_1d_data_helper_kokkos_view<
        MultiVecAdapter<Vector>,host_solve_array_t>::do_put(X, host_xValues_,
            Teuchos::as<size_t>(ld_rhs),
            (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
            this->rowIndexBase_);
    }
  }

  return(ierr);
}


template <class Matrix, class Vector>
bool
Cholmod<Matrix,Vector>::matrixShapeOK_impl() const
{
  return( this->matrixA_->getGlobalNumRows() == this->matrixA_->getGlobalNumCols() );
}


template <class Matrix, class Vector>
void
Cholmod<Matrix,Vector>::setParameters_impl(const Teuchos::RCP<Teuchos::ParameterList> & parameterList )
{
  // Note that the ordering is very important here. We must do this sequence:
  //  (1) Read parameter for use_cholmod_int_type
  //  (2) Call cholmod_start or cholmod_l_start
  //  (3) Set additional data_.c values
  use_cholmod_int_type_ = parameterList->get<bool>("CholmodInt", false);

  if(use_cholmod_int_type_) {
    data_.c.itype = CHOLMOD_INT;
    cholmod_start(&data_.c);
  }
  else {
    data_.c.itype = CHOLMOD_LONG;
    cholmod_l_start(&data_.c); // long form required for CUDA
  }

  using Teuchos::RCP;
  using Teuchos::getIntegralValue;
  using Teuchos::ParameterEntryValidator;

  RCP<const Teuchos::ParameterList> valid_params = getValidParameters_impl();

  is_contiguous_ = parameterList->get<bool>("IsContiguous", true);
  use_triangular_solves_ = parameterList->get<bool>("Enable_KokkosKernels_TriangularSolves", false);

  if(use_triangular_solves_) {
#if not defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) || not defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
    TEUCHOS_TEST_FOR_EXCEPTION(true, std::runtime_error,
      "Calling for triangular solves but KokkosKernels_ENABLE_SUPERNODAL_SPTRSV and KokkosKernels_ENABLE_TPL_CHOLMOD not configured." );
#endif
  }

  data_.c.dbound = parameterList->get<double>("dbound", 0.0);
  data_.c.prefer_upper = (parameterList->get<bool>("PreferUpper", true)) ? 1 : 0;
  data_.c.print = parameterList->get<int>("print", 3);
  data_.c.nmethods = parameterList->get<int>("nmethods", 0); // tries AMD and may try METIS if necessary and available

  // useGPU = 1 means use GPU if possible - note this must be set after cholmod_l_start
  // since cholmod_l_start sets it to the default value of -1.
  // Setting to -1 means GPU is only used if env variable CHOLMOD_USE_GPU is set to 1.
#ifdef KOKKOS_ENABLE_CUDA
  const int default_gpu_setting = 1; // use gpu by default
#else
  // If building Trilinos with Cuda off, Cholmod can stil use GPU and the solver will still work.
  // But that is likely not what was expected/wanted. If you do still want it, set the param to 1.
  const int default_gpu_setting = 0; // use gpu by default
#endif

  data_.c.useGPU = parameterList->get<int>("useGPU", default_gpu_setting);

#ifdef KOKKOS_ENABLE_CUDA
  TEUCHOS_TEST_FOR_EXCEPTION(data_.c.useGPU != 0 && use_cholmod_int_type_, std::runtime_error,
    "Amesos2 Cholmod solver must not use GPU (parameter useGPU = 0) if CholmodInt is turned on because Cholmod only supports GPU with long." );
#endif

  bool bSuperNodal = parameterList->get<bool>("SuperNodal", false);
  data_.c.supernodal = bSuperNodal ? CHOLMOD_SUPERNODAL : CHOLMOD_AUTO;
}


template <class Matrix, class Vector>
Teuchos::RCP<const Teuchos::ParameterList>
Cholmod<Matrix,Vector>::getValidParameters_impl() const
{
  using std::string;
  using Teuchos::tuple;
  using Teuchos::ParameterList;
  using Teuchos::EnhancedNumberValidator;
  using Teuchos::setStringToIntegralParameter;
  using Teuchos::stringToIntegralParameterEntryValidator;

  static Teuchos::RCP<const Teuchos::ParameterList> valid_params;

  if( is_null(valid_params) ){
    Teuchos::RCP<Teuchos::ParameterList> pl = Teuchos::parameterList();


    Teuchos::RCP<EnhancedNumberValidator<int> > print_validator
      = Teuchos::rcp( new EnhancedNumberValidator<int>(0,5));

    Teuchos::RCP<EnhancedNumberValidator<int> > nmethods_validator
      = Teuchos::rcp( new EnhancedNumberValidator<int>(0,9));

    pl->set("nmethods", 0, "Specifies the number of different ordering methods to try", nmethods_validator);

    pl->set("print", 3, "Specifies the verbosity of the print statements", print_validator);

    pl->set("dbound", 0.0,
            "Specifies the smallest absolute value on the diagonal D for the LDL factorization");

    pl->set("PreferUpper", true,
            "Specifies whether the matrix will be " 
            "stored in upper triangular form.");

    pl->set("useGPU", -1, "1: Use GPU is 1, 0: Do not use GPU, -1: ENV CHOLMOD_USE_GPU set GPU usage.");

    pl->set("Enable_KokkosKernels_TriangularSolves", false, "Whether to use triangular solves.");

    pl->set("CholmodInt", false, "Whether to use cholmod in int form");

    pl->set("IsContiguous", true, "Whether GIDs contiguous");

    pl->set("SuperNodal", false, "Whether to use super nodal");

    valid_params = pl;
  }

  return valid_params;
}


template <class Matrix, class Vector>
bool
Cholmod<Matrix,Vector>::loadA_impl(EPhase current_phase)
{
#ifdef HAVE_AMESOS2_TIMERS
  Teuchos::TimeMonitor convTimer(this->timers_.mtxConvTime_);
#endif

  // Only the root image needs storage allocated
  Kokkos::resize(host_nzvals_view_, this->globalNumNonZeros_);
  if(use_cholmod_int_type_) {
    Kokkos::resize(host_rows_int_view_, this->globalNumNonZeros_);
    Kokkos::resize(host_col_ptr_int_view_, this->globalNumRows_ + 1);
  }
  else {
    Kokkos::resize(host_rows_long_view_, this->globalNumNonZeros_);
    Kokkos::resize(host_col_ptr_long_view_, this->globalNumRows_ + 1);
  }

  {
#ifdef HAVE_AMESOS2_TIMERS
    Teuchos::TimeMonitor mtxRedistTimer( this->timers_.mtxRedistTime_ );
#endif

    TEUCHOS_TEST_FOR_EXCEPTION(this->rowIndexBase_ != this->columnIndexBase_,
              std::runtime_error,
              "Row and column maps have different indexbase ");

    if(use_cholmod_int_type_) {
      int nnz_ret = 0;
      Util::get_ccs_helper_kokkos_view<
        MatrixAdapter<Matrix>,host_value_type_array,host_ordinal_int_type_array,
          host_size_int_type_array>::do_get(this->matrixA_.ptr(),
            host_nzvals_view_, host_rows_int_view_,
            host_col_ptr_int_view_, nnz_ret,
            (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
            ARBITRARY,
            this->rowIndexBase_);

      TEUCHOS_TEST_FOR_EXCEPTION(nnz_ret != Teuchos::as<long>(this->globalNumNonZeros_),
               std::runtime_error,
               "Did not get the expected number of non-zero vals");
    }
    else {
      long nnz_ret = 0;

      Util::get_ccs_helper_kokkos_view<
        MatrixAdapter<Matrix>,host_value_type_array,host_ordinal_long_type_array,
          host_size_long_type_array>::do_get(this->matrixA_.ptr(),
            host_nzvals_view_, host_rows_long_view_,
            host_col_ptr_long_view_, nnz_ret,
            (is_contiguous_ == true) ? ROOTED : CONTIGUOUS_AND_ROOTED,
            ARBITRARY,
            this->rowIndexBase_);

      TEUCHOS_TEST_FOR_EXCEPTION(nnz_ret != Teuchos::as<long>(this->globalNumNonZeros_),
               std::runtime_error,
               "Did not get the expected number of non-zero vals");
    }
  }

  if(use_cholmod_int_type_) {
    function_map::cholmod_init_sparse(Teuchos::as<size_t>(this->globalNumRows_),
            Teuchos::as<size_t>(this->globalNumCols_),
            Teuchos::as<size_t>(this->globalNumNonZeros_),
            0,
            host_col_ptr_int_view_.data(),
            host_nzvals_view_.data(),
            host_rows_int_view_.data(),
            &(data_.A),
            CHOLMOD_INT);
  }
  else {
    function_map::cholmod_init_sparse(Teuchos::as<size_t>(this->globalNumRows_),
            Teuchos::as<size_t>(this->globalNumCols_),
            Teuchos::as<size_t>(this->globalNumNonZeros_),
            0,
            host_col_ptr_long_view_.data(),
            host_nzvals_view_.data(),
            host_rows_long_view_.data(),
            &(data_.A),
            CHOLMOD_LONG);
  }

  TEUCHOS_TEST_FOR_EXCEPTION(data_.A.stype == 0, std::runtime_error,
    "CHOLMOD loadA_impl loaded matrix but it is not symmetric.");

  return true;
}


template <class Matrix, class Vector>
void
Cholmod<Matrix,Vector>::triangular_solve_symbolic()
{
#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
  // Create handles for U and U^T solves
  if(use_cholmod_int_type_) {
    device_int_khL_.create_sptrsv_handle(
      KokkosSparse::Experimental::SPTRSVAlgorithm::SUPERNODAL_ETREE, data_.L->n, true);
    device_int_khU_.create_sptrsv_handle(
      KokkosSparse::Experimental::SPTRSVAlgorithm::SUPERNODAL_ETREE, data_.L->n, false);
  }
  else {
    device_long_khL_.create_sptrsv_handle(
      KokkosSparse::Experimental::SPTRSVAlgorithm::SUPERNODAL_ETREE, data_.L->n, true);
    device_long_khU_.create_sptrsv_handle(
      KokkosSparse::Experimental::SPTRSVAlgorithm::SUPERNODAL_ETREE, data_.L->n, false);
  }

  // extract etree and iperm from CHOLMOD
  Kokkos::resize(host_trsv_etree_, data_.L->nsuper);
  if(use_cholmod_int_type_) {
    int *int_etree = static_cast<int*>(data_.c.Iwork) + 2 * data_.L->n;
    for (size_t i = 0 ; i < data_.L->nsuper; ++i) {
      host_trsv_etree_(i) = int_etree[i];
    }
  }
  else {
    long *long_etree = static_cast<long*>(data_.c.Iwork) + 2 * data_.L->n;
    for (size_t i = 0 ; i < data_.L->nsuper; ++i) { // convert long to int array for trsv API
      host_trsv_etree_(i) = static_cast<int>(long_etree[i]);
    }
  }

  // set etree
  if(use_cholmod_int_type_) {
    device_int_khL_.set_sptrsv_etree(host_trsv_etree_.data());
    device_int_khU_.set_sptrsv_etree(host_trsv_etree_.data());
  }
  else {
    device_long_khL_.set_sptrsv_etree(host_trsv_etree_.data());
    device_long_khU_.set_sptrsv_etree(host_trsv_etree_.data());
  }

  size_t ld_rhs = this->matrixA_->getGlobalNumRows();
  Kokkos::resize(host_trsv_perm_, ld_rhs);
  if(use_cholmod_int_type_) {
    int *int_iperm = static_cast<int*>(data_.L->Perm);
    for (size_t i = 0; i < ld_rhs; i++) {
      host_trsv_perm_(int_iperm[i]) = i;
    }
  }
  else {
    long *long_iperm = static_cast<long*>(data_.L->Perm);
    for (size_t i = 0; i < ld_rhs; i++) {
      host_trsv_perm_(long_iperm[i]) = i;
    }
  }
  deep_copy_or_assign_view(device_trsv_perm_, host_trsv_perm_); // will use device to permute

  // set permutation
  if(use_cholmod_int_type_) {
    device_int_khL_.set_sptrsv_perm(host_trsv_perm_.data());
    device_int_khU_.set_sptrsv_perm(host_trsv_perm_.data());
  }
  else {
    device_long_khL_.set_sptrsv_perm(host_trsv_perm_.data());
    device_long_khU_.set_sptrsv_perm(host_trsv_perm_.data());
  }

  // Do symbolic analysis
  if(use_cholmod_int_type_) {
    KokkosSparse::Experimental::sptrsv_symbolic<int, kernel_handle_int_type>
      (&device_int_khL_, &device_int_khU_, data_.L, &data_.c);
  }
  else {
    KokkosSparse::Experimental::sptrsv_symbolic<long, kernel_handle_long_type>
      (&device_long_khL_, &device_long_khU_, data_.L, &data_.c);
  }
#endif
}


template <class Matrix, class Vector>
void
Cholmod<Matrix,Vector>::triangular_solve_numeric()
{
#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
  // Do numerical compute
  if(use_cholmod_int_type_) {
    KokkosSparse::Experimental::sptrsv_compute<int, kernel_handle_int_type>
      (&device_int_khL_, &device_int_khU_, data_.L, &data_.c);
  }
  else {
    KokkosSparse::Experimental::sptrsv_compute<long, kernel_handle_long_type>
      (&device_long_khL_, &device_long_khU_, data_.L, &data_.c);
  }
#endif // HAVE_AMESOS2_TRIANGULAR_SOLVE
}


template <class Matrix, class Vector>
void
Cholmod<Matrix,Vector>::triangular_solve() const
{
#if defined(KOKKOSKERNELS_ENABLE_SUPERNODAL_SPTRSV) && defined(KOKKOSKERNELS_ENABLE_TPL_CHOLMOD)
  size_t ld_rhs = device_xValues_.extent(0);
  size_t nrhs = device_xValues_.extent(1);

  Kokkos::resize(device_trsv_rhs_, ld_rhs, nrhs);
  Kokkos::resize(device_trsv_sol_, ld_rhs, nrhs);

  // forward pivot
  auto local_device_bValues = device_bValues_;
  auto local_device_trsv_perm = device_trsv_perm_;
  auto local_device_trsv_rhs = device_trsv_rhs_;
  Kokkos::parallel_for(Kokkos::RangePolicy<DeviceExecSpaceType>(0, ld_rhs),
    KOKKOS_LAMBDA(size_t j) {
    for(size_t k = 0; k < nrhs; ++k) {
      local_device_trsv_rhs(local_device_trsv_perm(j),k) = local_device_bValues(j,k);
    }
  });

  for(size_t k = 0; k < nrhs; ++k) { // sptrsv_solve does not batch
    auto sub_sol = Kokkos::subview(device_trsv_sol_, Kokkos::ALL, k);
    auto sub_rhs = Kokkos::subview(device_trsv_rhs_, Kokkos::ALL, k);

    // do L solve= - numeric (only rhs is modified) on the default device/host space
    if(use_cholmod_int_type_) {
      KokkosSparse::Experimental::sptrsv_solve(&device_int_khL_, sub_sol, sub_rhs);
    }
    else {
      KokkosSparse::Experimental::sptrsv_solve(&device_long_khL_, sub_sol, sub_rhs);
    }

    // do L^T solve - numeric (only rhs is modified) on the default device/host space
    if(use_cholmod_int_type_) {
      KokkosSparse::Experimental::sptrsv_solve(&device_int_khU_, sub_rhs, sub_sol);
    }
    else {
      KokkosSparse::Experimental::sptrsv_solve(&device_long_khU_, sub_rhs, sub_sol);
    }

  } // end loop over rhs vectors

  // backward pivot
  auto local_device_xValues = device_xValues_;
  Kokkos::parallel_for(Kokkos::RangePolicy<DeviceExecSpaceType>(0, ld_rhs),
    KOKKOS_LAMBDA(size_t j) {
    for(size_t k = 0; k < nrhs; ++k) {
      local_device_xValues(j,k) = local_device_trsv_rhs(local_device_trsv_perm(j),k);
    }
  });
#endif
}


template<class Matrix, class Vector>
const char* Cholmod<Matrix,Vector>::name = "Cholmod";
  

} // end namespace Amesos2

#endif  // AMESOS2_CHOLMOD_DEF_HPP