KokkosSparse::sptrsv_solve¶
Defined in header KokkosSparse_sptrsv.hpp
template <typename ExecutionSpace, typename KernelHandle, typename lno_row_view_t_, typename lno_nnz_view_t_,
typename scalar_nnz_view_t_, class BType, class XType>
void sptrsv_solve(ExecutionSpace &space, KernelHandle *handle, lno_row_view_t_ rowmap, lno_nnz_view_t_ entries,
scalar_nnz_view_t_ values, BType b, XType x);
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);
Compute the solution of a triangular system of linear equations
where \(A\) is the input triangular matrix, \(b\) is the input right-hand-side vector, and \(x\) is the output solution vector.
Compute the solution of a triangular system of linear equations, optionally attempts to use cuSPARSE when available and types are a match.
Same as 1. but uses the resources of the default execution space instance associated with KernelHandle::HandleExecSpace.
Parameters¶
- space:
execution space instance describing the resources available to run the kernels.
- handle:
an instance of
KokkosKernels::KokkosKernelsHandlefrom which an sptrsv_handle will be used to extract control parameters.- rowmap:
row map of the input matrix \(A\).
- entries:
column indices of the input matrix \(A\).
- values:
values associated with the entries of the input matrix \(A\).
- b:
input right-hand-side vector \(b\) of the triangular linear system to solve.
- x:
output solution vector \(x\) of the triangular linear system to solve
Type Requirements¶
The types of the input views representing the CrsMatrix must be consistent with the types defined by the KernelsHandle and with each others:
std::is_same_v<ExecutionSpace, typename KernelHandle::HandleExecSpace> == truestd::is_same_v<typename lno_row_view_t_::non_const_value_type, typename KernelHandle::size_type> == truestd::is_same_v<typename lno_nnz_view_t_::non_const_value_type, typename KernelHandle::nnz_lno_t> == truestd::is_same_v<typename scalar_nnz_view_t_::value_type, typename KernelHandle::nnz_scalar_t> == truestd::is_same_v<typename lno_row_view_t_::device_type, typename lno_nnz_view_t_::device_type> == truestd::is_same_v<typename lno_row_view_t_::device_type, typename scalar_nnz_view_t_::device_type> == true
BType and XType must both be Kokkos Views of rank 1 with execution spaces consistent with the handle and XType must store non-const values
std::is_same_v<typename BType::device_type::execution_space, typename KernelHandle::SPTRSVHandleType::execution_space> == truestd::is_same_v<typename BType::device_type, typename XType::device_type> == truestd::is_same_v<typename XType::value_type, typename XType::non_const_value_type> == true
Note
We should update the static assertions on device_type and instead use the Kokkos::SpaceAccessibility<exec_space, mem_space>::accessible to check that the views store data in memory spaces that are accessible from the execution space of the handle. Technically multiple memory spaces are fine, for instance A might be in Kokkos::CudaSpace while x and b are in Kokkos::CudaUVMSpace.
We should also check that the view of the matrix are actual Kokkos::View…
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();
}