KokkosBatched::Pttrf

Defined in header: KokkosBatched_Pttrf.hpp

template <typename ArgAlgo>
struct SerialPttrf {
  template <typename DViewType, typename EViewType>
  KOKKOS_INLINE_FUNCTION
  static int
  invoke(const DViewType& d,
         const EViewType& e);
};

The Pttrf function computes the L*D*L^T factorization of a symmetric positive definite tridiagonal matrix A. This operation is equivalent to the LAPACK routine DPTTRF for real matrices or ZPTTRF for complex matrices.

The factorization has the form:

\[A = L \cdot D \cdot L^T\]

where:

• \(L\) is a unit lower bidiagonal matrix with subdiagonals stored in e

• \(D\) is a diagonal matrix with diagonal elements stored in d

Parameters

d:

Input/output view containing diagonal elements of the matrix. On exit, contains the diagonal elements of D.

e:

Input/output view containing subdiagonal elements of the matrix. On exit, contains the subdiagonal elements of L.

Type Requirements

• ArgAlgo must be KokkosBatched::Algo::Pttrf::Unblocked for the unblocked algorithm

• DViewType must be a rank-1 view containing the diagonal elements (length n)

• EViewType must be a rank-1 view containing the subdiagonal elements (length n-1)

• All views must be accessible in the execution space

Examples

#include <Kokkos_Core.hpp>
#include <KokkosBatched_Pttrf.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 dimension
    int n = 10;

    // Create diagonal and off-diagonal vectors
    Kokkos::View<scalar_type*, memory_space> d("d", n);      // Diagonal elements
    Kokkos::View<scalar_type*, memory_space> e("e", n-1);    // Subdiagonal elements

    // Initialize vectors on host
    auto d_host = Kokkos::create_mirror_view(d);
    auto e_host = Kokkos::create_mirror_view(e);

    // Fill with a symmetric positive definite tridiagonal matrix
    // Using a simple model problem (1D Poisson equation discretization)
    for (int i = 0; i < n; ++i) {
      d_host(i) = 2.0;  // Diagonal
    }
    for (int i = 0; i < n-1; ++i) {
      e_host(i) = -1.0; // Subdiagonal
    }

    // Copy to device
    Kokkos::deep_copy(d, d_host);
    Kokkos::deep_copy(e, e_host);

    // Save original values for verification
    Kokkos::View<scalar_type*, memory_space> d_orig("d_orig", n);
    Kokkos::View<scalar_type*, memory_space> e_orig("e_orig", n-1);

    Kokkos::deep_copy(d_orig, d);
    Kokkos::deep_copy(e_orig, e);

    // Compute the factorization
    Kokkos::parallel_for(1, KOKKOS_LAMBDA(const int i) {
      KokkosBatched::SerialPttrf<KokkosBatched::Algo::Pttrf::Unblocked>::invoke(d, e);
    });

    // Copy results back to host
    Kokkos::deep_copy(d_host, d);
    Kokkos::deep_copy(e_host, e);

    // Verify the factorization by reconstructing A = L*D*L^T
    auto d_orig_host = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), d_orig);
    auto e_orig_host = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), e_orig);

    // Create full matrices for verification
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, Kokkos::HostSpace>
      A_orig("A_orig", n, n),
      L("L", n, n),
      D("D", n, n),
      LDLT("LDLT", n, n);

    // Construct original A in full storage
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        A_orig(i, j) = 0.0;
      }
      A_orig(i, i) = d_orig_host(i);
    }

    for (int i = 0; i < n-1; ++i) {
      A_orig(i+1, i) = e_orig_host(i);
      A_orig(i, i+1) = e_orig_host(i); // Symmetric
    }

    // Construct L and D from factorization
    // L is unit lower bidiagonal
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        L(i, j) = 0.0;
        D(i, j) = 0.0;
      }
      L(i, i) = 1.0;     // Unit diagonal
      D(i, i) = d_host(i); // Diagonal matrix D
    }

    for (int i = 0; i < n-1; ++i) {
      L(i+1, i) = e_host(i); // Subdiagonal of L
    }

    // Compute L*D*L^T
    // First, L*D
    Kokkos::View<scalar_type**, Kokkos::LayoutRight, Kokkos::HostSpace> LD("LD", n, n);
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        LD(i, j) = 0.0;
        for (int k = 0; k < n; ++k) {
          LD(i, j) += L(i, k) * D(k, j);
        }
      }
    }

    // Then, (L*D)*L^T
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        LDLT(i, j) = 0.0;
        for (int k = 0; k < n; ++k) {
          LDLT(i, j) += LD(i, k) * L(j, k); // Note: L^T(k,j) = L(j,k)
        }
      }
    }

    // Verify A_orig ≈ LDLT
    bool test_passed = true;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (std::abs(LDLT(i, j) - A_orig(i, j)) > 1e-10) {
          test_passed = false;
          std::cout << "Mismatch at (" << i << ", " << j << "): "
                    << LDLT(i, j) << " vs " << A_orig(i, j) << std::endl;
        }
      }
    }

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

Batched Example

#include <Kokkos_Core.hpp>
#include <KokkosBatched_Pttrf.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 = 50; // Number of matrices
    int n = 10;          // Matrix dimension

    // Create batched views
    Kokkos::View<scalar_type**, memory_space> d("d", batch_size, n);       // Diagonal elements
    Kokkos::View<scalar_type**, memory_space> e("e", batch_size, n-1);     // Subdiagonal elements

    // Initialize on host
    auto d_host = Kokkos::create_mirror_view(d);
    auto e_host = Kokkos::create_mirror_view(e);

    for (int b = 0; b < batch_size; ++b) {
      // Fill with a symmetric positive definite tridiagonal matrix
      // Slightly different for each batch
      for (int i = 0; i < n; ++i) {
        d_host(b, i) = 2.0 + 0.1 * b;  // Diagonal
      }
      for (int i = 0; i < n-1; ++i) {
        e_host(b, i) = -1.0 - 0.01 * b; // Subdiagonal
      }
    }

    // Copy to device
    Kokkos::deep_copy(d, d_host);
    Kokkos::deep_copy(e, e_host);

    // Save original for verification
    Kokkos::View<scalar_type**, memory_space> d_orig("d_orig", batch_size, n);
    Kokkos::View<scalar_type**, memory_space> e_orig("e_orig", batch_size, n-1);

    Kokkos::deep_copy(d_orig, d);
    Kokkos::deep_copy(e_orig, e);

    // Perform batched factorization
    Kokkos::parallel_for(batch_size, KOKKOS_LAMBDA(const int b) {
      auto d_b = Kokkos::subview(d, b, Kokkos::ALL());
      auto e_b = Kokkos::subview(e, b, Kokkos::ALL());

      KokkosBatched::SerialPttrf<KokkosBatched::Algo::Pttrf::Unblocked>::invoke(d_b, e_b);
    });

    // Factorizations are now in d and e
    // Each pair (d(b, :), e(b, :)) contains the factors for matrix b
  }
  Kokkos::finalize();
  return 0;
}