KokkosLapack::getrf

Defined in header: KokkosLapack_getrf.hpp

template <class ExecutionSpace, class AMatrix, class IpivView, class InfoView>
void getrf(const ExecutionSpace& space, const AMatrix& A, const IpivView& Ipiv, const InfoView& Info);

template <class AMatrix, class IpivView, class InfoView>
void getrf(const AMatrix& A, const IpivView& Ipiv, const InfoView& Info);

\[P*A=L*U\]

where \(A\) is, on input, the matrix storing the linear system of equations and on output, contains the factors L and U in its lower and upper triangular parts. \(Ipiv\) contains the pivots used to construct the row permutation matrix \(P\).

1. Overwrite \(A\) with the \(L\) and \(U\) factors using the resources associated with space.

2. Same as 1. but uses the resources of the default execution space from AMatrix::execution_space.

Parameters

space:

execution space instance.

A:

The input matrix that gets overwritten with the \(L\) and \(U\) factors on output.

Ipiv:

The vector holding the pivots selected during the matrix decomposition.

Info:

A scalar (store in a device view) that holds the return code from Lapack when that library gets called.

Type Requirements

• ExecutionSpace must be a Kokkos execution space

• AMatrix must be a Kokkos View of rank 2 that satisfies

  • Kokkos::SpaceAccessibility<ExecutionSpace, typename AMatrix::memory_space>::accessible

• IpivView must be a Kokkos View of rank 1 that satisfies

  • Kokkos::SpaceAccessibility<ExecutionSpace, typename Tau::memory_space>::accessible

• InfoView must be a Kokkos View of rank 1 that satisfies

  • Kokkos::SpaceAccessibility<ExecutionSpace, typename Info::memory_space>::accessible

Example

// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// SPDX-FileCopyrightText: Copyright Contributors to the Kokkos project

#include <Kokkos_Core.hpp>
#include <KokkosLapack_geqrf.hpp>

int main(void) {
  bool correct = true;
  Kokkos::initialize();
  {
    using execution_space = Kokkos::DefaultExecutionSpace;
    using KAT             = KokkosKernels::ArithTraits<double>;

    Kokkos::View<double**, Kokkos::LayoutLeft> A("A", 3, 3);
    Kokkos::View<double*, Kokkos::LayoutLeft> tau("tau", 3);
    Kokkos::View<int*, Kokkos::LayoutLeft> Info("Info", 1);

    auto h_A = Kokkos::create_mirror_view(A);

    h_A(0, 0) = 12;
    h_A(0, 1) = -51;
    h_A(0, 2) = 4;
    h_A(1, 0) = 6;
    h_A(1, 1) = 167;
    h_A(1, 2) = -68;
    h_A(2, 0) = -4;
    h_A(2, 1) = 24;
    h_A(2, 2) = -41;
    Kokkos::deep_copy(A, h_A);

    execution_space space{};
    KokkosLapack::geqrf(space, A, tau, Info);
    Kokkos::fence();
    Kokkos::deep_copy(h_A, A);

    Kokkos::View<double**, Kokkos::DefaultHostExecutionSpace> analytic("result", 3, 3);
    analytic(0, 0) = -14;
    analytic(0, 1) = -21;
    analytic(0, 2) = 14;
    analytic(1, 0) = 6. / 26;
    analytic(1, 1) = -175;
    analytic(1, 2) = 70;
    analytic(2, 0) = -4. / 26;
    analytic(2, 1) = 1. / 18;
    analytic(2, 2) = -35;

    for (int rowIdx = 0; rowIdx < A.extent_int(0); ++rowIdx) {
      for (int colIdx = 0; colIdx < A.extent_int(1); ++colIdx) {
        if (KAT::abs(h_A(rowIdx, colIdx) - analytic(rowIdx, colIdx)) >
            KAT::abs(analytic(rowIdx, colIdx)) * KAT::epsilon()) {
          std::cout << "h_A(" << rowIdx << ", " << colIdx << ")=" << h_A(rowIdx, colIdx) << ", analytic is "
                    << analytic(rowIdx, colIdx) << std::endl;
          correct = false;
        }
      }
    }
  }
  Kokkos::finalize();

  if (!correct) throw std::runtime_error("KokkosLapack::geqrf is incorrect!");
  return 0;
}

output:

KokkosLapack::getrf() returned correct results!