SPARSE 2::sptrsv

KokkosSparse::sptrsv()

Header File: KokkosSparse_sptrsv.hpp

Usage: KokkosSparse::Experimental::sptrsv_symbolic(handle, rowmap, entries, values);

Usage: KokkosSparse::Experimental::sptrsv_solve(handle, rowmap, entries, values, b, x);

Perform sparse triangular solve of linear system with triangular matrix stored in compressed row sparse ("Crs") format.

• Note: This capability is in the Experimental namespace, which indicates the interface is subject to change.

Interface

  template <typename KernelHandle,
            typename lno_row_view_t_,
            typename lno_nnz_view_t_,
            typename scalar_nnz_view_t_>
  void sptrsv_symbolic(KernelHandle *handle, 
                       lno_row_view_t_ rowmap,
                       lno_nnz_view_t_ entries,
                       scalar_nnz_view_t_ values);

  template <typename KernelHandle,
            typename lno_row_view_t_,
            typename lno_nnz_view_t_,
            typename scalar_nnz_view_t_,
            class BType,
            class XType>
  void sptrsv_solve(KernelHandle *handle, 
                    lno_row_view_t_ rowmap,
                    lno_nnz_view_t_ entries,
                    scalar_nnz_view_t_ values,
                    BType b,
                    XType x);
      

Parameters:

sptrsv_symbolic

• KernelHandle
• lno_row_view_t: a rank-1 Kokkos::View of input matrix row map
• lno_nnz_view_t: a rank-1 Kokkos::View of input matrix entries
• scalar_nnz_view_t: a rank-1 Kokkos::View of input matrix values.

sptrsv_solve

• KernelHandle
• lno_row_view_t: a rank-1 Kokkos::View of input matrix row map
• lno_nnz_view_t: a rank-1 Kokkos::View of input matrix entries
• scalar_nnz_view_t: a rank-1 Kokkos::View of input matrix values.
• BType: a rank-1 Kokkos::View of vector values.
• XType: a rank-1 Kokkos::View of vector values.

Requirements:

• Creation of a KernelHandle
• All Views must have rank 1
• lno_row_view_t::non_const_value_type must match KernelHandle::size_type
• lno_nnz_view_t::non_const_value_type must match KernelHandle::nnz_lno_t
• scalar_nnz_view_t::value_type must match KernelHandle::nnz_scalar_t
• XType::value_type must be non-const
• KernelHandle and Views have same execution spaces, all Views have same device types

Example

#include <Kokkos_Core.hpp>
#include <KokkosSparse_CrsMatrix.hpp>
#include <KokkosSparse_sptrsv.hpp>
#include <KokkosKernels_IOUtils.hpp>
#include <KokkosKernels_SparseUtils.hpp>

int main(int argc, char* argv[]) {

  using namespace KokkosSparse;
  using namespace KokkosSparse::Experimental;
  using namespace KokkosKernels;
  using namespace KokkosKernels::Impl;
  using namespace KokkosKernels::Experimental;
  
   Kokkos::initialize();
   {
     using scalar_t  = double;
     using lno_t     = int;
     using size_type = int;
     using device = typename Kokkos::DefaultExecutionSpace::device_type;

     using RowMapType  = Kokkos::View< size_type*, device >;
     using EntriesType = Kokkos::View< lno_t*, device >;
     using ValuesType  = Kokkos::View< scalar_t*, device >;

     using KernelHandle = KokkosKernels::Experimental::KokkosKernelsHandle <size_type, lno_t, scalar_t,
           typename device::execution_space, typename device::memory_space, typename device::memory_space>;

     scalar_t ZERO = scalar_t(0);
     scalar_t ONE = scalar_t(1);

     const size_type nrows = 5;
     const size_type nnz   = 10;

     // Upper triangular solve: x = U \ b
     {
       RowMapType  row_map("row_map", nrows+1);
       EntriesType entries("entries", nnz);
       ValuesType  values("values", nnz);

       auto hrow_map = Kokkos::create_mirror_view(row_map);
       auto hentries = Kokkos::create_mirror_view(entries);
       auto hvalues  = Kokkos::create_mirror_view(values);

       // Fill rowmap, entries, of Crs graph for simple example matrix, values set to ones

       //  [ [1 0 1 0 0]
       //    [0 1 0 0 1]
       //    [0 0 1 1 1]
       //    [0 0 0 1 1]
       //    [0 0 0 0 1] ];

       hrow_map(0) = 0;
       hrow_map(1) = 2;
       hrow_map(2) = 4;
       hrow_map(3) = 7;
       hrow_map(4) = 9;
       hrow_map(5) = 10;

       hentries(0) = 0;
       hentries(1) = 2;
       hentries(2) = 1;
       hentries(3) = 4;
       hentries(4) = 2;
       hentries(5) = 3;
       hentries(6) = 4;
       hentries(7) = 3;
       hentries(8) = 4;
       hentries(9) = 4;

       Kokkos::deep_copy(row_map, hrow_map);
       Kokkos::deep_copy(entries, hentries);

       Kokkos::deep_copy(values, ONE);


       // Create the x and b vectors

       // Solution to find
       ValuesType x("x", nrows);

       ValuesType b("b", nrows);
       Kokkos::deep_copy(b, ONE);

       // Create sptrsv kernel handle
       KernelHandle kh;
       bool is_lower_tri = false;
       kh.create_sptrsv_handle(SPTRSVAlgorithm::SEQLVLSCHD_TP1, nrows, is_lower_tri);

       sptrsv_symbolic(&kh, row_map, entries, values);
       Kokkos::fence();

       sptrsv_solve(&kh, row_map, entries, values, b, x);
       Kokkos::fence();
       kh.destroy_sptrsv_handle();
     }


     // Lower triangular solve: x = L \ b
     {
       RowMapType  row_map("row_map", nrows+1);
       EntriesType entries("entries", nnz);
       ValuesType  values("values", nnz);

       auto hrow_map = Kokkos::create_mirror_view(row_map);
       auto hentries = Kokkos::create_mirror_view(entries);
       auto hvalues  = Kokkos::create_mirror_view(values);

       // Fill rowmap, entries, of Crs graph for simple example matrix, values set to ones

       //  [ [1 0 0 0 0]
       //    [0 1 0 0 0]
       //    [1 0 1 0 0]
       //    [0 0 1 1 0]
       //    [1 1 1 1 1] ];

       hrow_map(0) = 0;
       hrow_map(1) = 1;
       hrow_map(2) = 2;
       hrow_map(3) = 4;
       hrow_map(4) = 6;
       hrow_map(5) = 10;

       hentries(0) = 0;
       hentries(1) = 1;
       hentries(2) = 0;
       hentries(3) = 2;
       hentries(4) = 2;
       hentries(5) = 3;
       hentries(6) = 1;
       hentries(7) = 2;
       hentries(8) = 3;
       hentries(9) = 4;

       Kokkos::deep_copy(row_map, hrow_map);
       Kokkos::deep_copy(entries, hentries);

       Kokkos::deep_copy(values, ONE);


       // Create the x and b vectors

       // Solution to find
       ValuesType x("x", nrows);

       ValuesType b("b", nrows);
       Kokkos::deep_copy(b, ONE);

       // Create sptrsv kernel handle
       KernelHandle kh;
       bool is_lower_tri = true;
       kh.create_sptrsv_handle(SPTRSVAlgorithm::SEQLVLSCHD_TP1, nrows, is_lower_tri);

       sptrsv_symbolic(&kh, row_map, entries, values);
       Kokkos::fence();

       sptrsv_solve(&kh, row_map, entries, values, b, x);
       Kokkos::fence();
       kh.destroy_sptrsv_handle();
     }

   }
   Kokkos::finalize();
}

TPL support

When the CuSPARSE TPL is enabled at configuration the algorithm is available as an option for sptrsv. Set the solver to use CuSPARSE during handle creation with the option SPTRSVAlgorithm::SPTRSV_CUSPARSE