KokkosBatched::Getrs¶

Defined in header: KokkosBatched_Getrs.hpp

template <typename ArgTrans, typename ArgAlgo>
struct SerialGetrs {
  template <typename AViewType, typename PivViewType, typename BViewType>
  KOKKOS_INLINE_FUNCTION
  static int
  invoke(const AViewType& A,
         const PivViewType& piv,
         const BViewType& b);
};

The Getrs function solves a system of linear equations with a general N-by-N matrix A using the LU factorization computed by Getrf. The function can solve the following systems:

\(A \cdot X = B\) (Trans::NoTranspose)
\(A^T \cdot X = B\) (Trans::Transpose)

where A is a general square matrix that has been factorized using LU decomposition, and B is a matrix with one or more right-hand sides.

Parameters¶

A:: Input matrix view containing the LU factorization from Getrf
piv:: Input view containing the pivot indices from Getrf
b:: Input/output view containing right-hand sides on input and solutions on output

Type Requirements¶

ArgTrans must be one of the following:
- KokkosBatched::Trans::NoTranspose to solve \(A \cdot X = B\)
- KokkosBatched::Trans::Transpose to solve \(A^T \cdot X = B\)
ArgAlgo must specify the algorithm to be used
AViewType must be a rank-2 view containing the matrix with LU factorization
PivViewType must be a rank-1 view containing the pivot indices
BViewType must be a rank-1 view for a single right-hand side, or a rank-2 view for multiple right-hand sides
All views must be accessible in the execution space

Examples¶

#include <Kokkos_Core.hpp>
#include <KokkosBatched_Getrf.hpp>
#include <KokkosBatched_Getrs.hpp>

using execution_space = Kokkos::DefaultExecutionSpace;
using memory_space = execution_space::memory_space;

// Scalar type to use
using scalar_type = double;

int main(int argc, char* argv[]) {
  Kokkos::initialize(argc, argv);
  {
    // Matrix dimensions
    int n = 10;      // Matrix dimension
    int nrhs = 2;    // Number of right-hand sides

    // Create matrix, pivot vector, and right-hand sides
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, memory_space> A("A", n, n);
    Kokkos::View<int*, memory_space> piv("piv", n);
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, memory_space> B("B", n, nrhs);

    // Initialize matrix on host
    auto A_host = Kokkos::create_mirror_view(A);

    // Create a diagonally dominant matrix for stability
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (i == j) {
          // Diagonal - make it dominant
          A_host(i, j) = n + 1.0;
        } else {
          // Off-diagonal
          A_host(i, j) = 1.0;
        }
      }
    }

    // Initialize right-hand sides on host
    auto B_host = Kokkos::create_mirror_view(B);
    for (int j = 0; j < nrhs; ++j) {
      for (int i = 0; i < n; ++i) {
        B_host(i, j) = 1.0 + i + j*n;
      }
    }

    // Save a copy of the original matrix and right-hand sides for verification
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, memory_space> A_orig("A_orig", n, n);
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, memory_space> B_orig("B_orig", n, nrhs);

    auto A_orig_host = Kokkos::create_mirror_view(A_orig);
    auto B_orig_host = Kokkos::create_mirror_view(B_orig);

    Kokkos::deep_copy(A_orig_host, A_host);
    Kokkos::deep_copy(B_orig_host, B_host);

    // Copy initialized data to device
    Kokkos::deep_copy(A, A_host);
    Kokkos::deep_copy(B, B_host);
    Kokkos::deep_copy(A_orig, A_orig_host);
    Kokkos::deep_copy(B_orig, B_orig_host);

    // Perform LU factorization
    Kokkos::parallel_for(1, KOKKOS_LAMBDA(const int i) {
      KokkosBatched::SerialGetrf<KokkosBatched::Algo::Getrf::Unblocked>::invoke(A, piv);
    });

    // Solve the linear system
    Kokkos::parallel_for(1, KOKKOS_LAMBDA(const int i) {
      KokkosBatched::SerialGetrs<KokkosBatched::Trans::NoTranspose,
                                KokkosBatched::Algo::Getrs::Unblocked>::invoke(A, piv, B);
    });

    // Copy results back to host
    Kokkos::deep_copy(B_host, B);

    // Verify the solution by checking A*X ≈ B_orig
    bool test_passed = true;
    for (int j = 0; j < nrhs; ++j) {
      for (int i = 0; i < n; ++i) {
        scalar_type sum = 0.0;

        // Compute row i of A * column j of X
        for (int k = 0; k < n; ++k) {
          sum += A_orig_host(i, k) * B_host(k, j);
        }

        // Check against original right-hand side
        if (std::abs(sum - B_orig_host(i, j)) > 1e-10) {
          test_passed = false;
          std::cout << "Mismatch at (" << i << ", " << j << "): "
                    << sum << " vs " << B_orig_host(i, j) << std::endl;
        }
      }
    }

    if (test_passed) {
      std::cout << "Getrs test: PASSED" << std::endl;
    } else {
      std::cout << "Getrs test: FAILED" << std::endl;
    }
  }
  Kokkos::finalize();
  return 0;
}

Batched Example¶

#include <Kokkos_Core.hpp>
#include <KokkosBatched_Getrf.hpp>
#include <KokkosBatched_Getrs.hpp>

using execution_space = Kokkos::DefaultExecutionSpace;
using memory_space = execution_space::memory_space;

// Scalar type to use
using scalar_type = double;

int main(int argc, char* argv[]) {
  Kokkos::initialize(argc, argv);
  {
    // Batch and matrix dimensions
    int batch_size = 100; // Number of matrices
    int n = 10;           // Matrix dimension
    int nrhs = 2;         // Number of right-hand sides

    // Create batched views
    Kokkos::View<scalar_type***, Kokkos::LayoutRight, memory_space>
      A("A", batch_size, n, n);
    Kokkos::View<int**, memory_space> piv("piv", batch_size, n);
    Kokkos::View<scalar_type***, Kokkos::LayoutRight, memory_space>
      B("B", batch_size, n, nrhs);

    // Initialize on host
    auto A_host = Kokkos::create_mirror_view(A);
    auto B_host = Kokkos::create_mirror_view(B);

    for (int b = 0; b < batch_size; ++b) {
      // Create a diagonally dominant matrix for stability
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          if (i == j) {
            // Diagonal - make it dominant
            A_host(b, i, j) = n + 1.0 + 0.1 * b;
          } else {
            // Off-diagonal
            A_host(b, i, j) = 1.0 + 0.01 * b;
          }
        }
      }

      // Initialize right-hand sides
      for (int j = 0; j < nrhs; ++j) {
        for (int i = 0; i < n; ++i) {
          B_host(b, i, j) = 1.0 + i + j*n + b*0.1;
        }
      }
    }

    // Copy to device
    Kokkos::deep_copy(A, A_host);
    Kokkos::deep_copy(B, B_host);

    // Save original for verification
    Kokkos::View<scalar_type***, Kokkos::LayoutRight, memory_space>
      A_orig("A_orig", batch_size, n, n);
    Kokkos::View<scalar_type***, Kokkos::LayoutRight, memory_space>
      B_orig("B_orig", batch_size, n, nrhs);

    Kokkos::deep_copy(A_orig, A);
    Kokkos::deep_copy(B_orig, B);

    // Perform batched LU factorization
    Kokkos::parallel_for(batch_size, KOKKOS_LAMBDA(const int b) {
      auto A_b = Kokkos::subview(A, b, Kokkos::ALL(), Kokkos::ALL());
      auto piv_b = Kokkos::subview(piv, b, Kokkos::ALL());

      KokkosBatched::SerialGetrf<KokkosBatched::Algo::Getrf::Unblocked>::invoke(A_b, piv_b);
    });

    // Solve batched linear systems
    Kokkos::parallel_for(batch_size, KOKKOS_LAMBDA(const int b) {
      auto A_b = Kokkos::subview(A, b, Kokkos::ALL(), Kokkos::ALL());
      auto piv_b = Kokkos::subview(piv, b, Kokkos::ALL());
      auto B_b = Kokkos::subview(B, b, Kokkos::ALL(), Kokkos::ALL());

      KokkosBatched::SerialGetrs<KokkosBatched::Trans::NoTranspose,
                                KokkosBatched::Algo::Getrs::Unblocked>::invoke(A_b, piv_b, B_b);
    });

    // Solutions are now in B
    // Each B(b, :, :) contains the solution for the corresponding system
  }
  Kokkos::finalize();
  return 0;
}