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[]) {
   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();
}