xref: /petsc/src/mat/tests/ex226.c (revision 732aec7a18f2199fb53bb9a2f3aef439a834ce31)

static char help[] = "Benchmark for MatMatMult() of AIJ matrices using different 2d finite-difference stencils.\n\n";

#include <petscmat.h>

/* Converts 3d grid coordinates (i,j,k) for a grid of size m \times n to global indexing. Pass k = 0 for a 2d grid. */
PetscInt global_index(PetscInt i, PetscInt j, PetscInt k, PetscInt m, PetscInt n)
{
  return i + j * m + k * m * n;
}

int main(int argc, char **argv)
{
  Mat           A, B, C, PtAP, PtAP_copy, PtAP_squared;
  PetscInt      i, M, N, Istart, Iend, n = 7, j, J, Ii, m = 8, k, o = 1;
  PetscScalar   v;
  PetscBool     equal = PETSC_FALSE, mat_view = PETSC_FALSE;
  char          stencil[PETSC_MAX_PATH_LEN];
  PetscLogStage fullMatMatMultStage;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-o", &o, NULL));
  PetscCall(PetscOptionsHasName(NULL, NULL, "-result_view", &mat_view));
  PetscCall(PetscOptionsGetString(NULL, NULL, "-stencil", stencil, sizeof(stencil), NULL));

  /* Create a aij matrix A */
  M = N = m * n * o;
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, M, N));
  PetscCall(MatSetType(A, MATAIJ));
  PetscCall(MatSetFromOptions(A));

  /* Consistency checks */
  PetscCheck(o >= 1 && m > 1 && n >= 1, PETSC_COMM_WORLD, PETSC_ERR_USER, "Dimensions need to be larger than zero!");

  /************ 2D stencils ***************/
  PetscCall(PetscStrcmp(stencil, "2d5point", &equal));
  if (equal) { /* 5-point stencil, 2D */
    PetscCall(MatMPIAIJSetPreallocation(A, 5, NULL, 5, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 5, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 4.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "2d9point", &equal));
  if (equal) { /* 9-point stencil, 2D */
    PetscCall(MatMPIAIJSetPreallocation(A, 9, NULL, 9, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 9, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 0 && j > 0) {
        J = global_index(i - 1, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && j > 0) {
        J = global_index(i + 1, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && j < n - 1) {
        J = global_index(i + 1, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 0 && j < n - 1) {
        J = global_index(i - 1, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 8.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "2d9point2", &equal));
  if (equal) { /* 9-point Cartesian stencil (width 2 per coordinate), 2D */
    PetscCall(MatMPIAIJSetPreallocation(A, 9, NULL, 9, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 9, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 1) {
        J = global_index(i - 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 2) {
        J = global_index(i + 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 1) {
        J = global_index(i, j - 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 2) {
        J = global_index(i, j + 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 8.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "2d13point", &equal));
  if (equal) { /* 13-point Cartesian stencil (width 3 per coordinate), 2D */
    PetscCall(MatMPIAIJSetPreallocation(A, 13, NULL, 13, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 13, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 1) {
        J = global_index(i - 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 2) {
        J = global_index(i - 3, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 2) {
        J = global_index(i + 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 3) {
        J = global_index(i + 3, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 1) {
        J = global_index(i, j - 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 2) {
        J = global_index(i, j - 3, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 2) {
        J = global_index(i, j + 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 3) {
        J = global_index(i, j + 3, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 12.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  /************ 3D stencils ***************/
  PetscCall(PetscStrcmp(stencil, "3d7point", &equal));
  if (equal) { /* 7-point stencil, 3D */
    PetscCall(MatMPIAIJSetPreallocation(A, 7, NULL, 7, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 7, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k > 0) {
        J = global_index(i, j, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k < o - 1) {
        J = global_index(i, j, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 6.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "3d13point", &equal));
  if (equal) { /* 13-point stencil, 3D */
    PetscCall(MatMPIAIJSetPreallocation(A, 13, NULL, 13, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 13, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 1) {
        J = global_index(i - 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 2) {
        J = global_index(i + 2, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 1) {
        J = global_index(i, j - 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 2) {
        J = global_index(i, j + 2, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k > 0) {
        J = global_index(i, j, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k > 1) {
        J = global_index(i, j, k - 2, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k < o - 1) {
        J = global_index(i, j, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k < o - 2) {
        J = global_index(i, j, k + 2, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 12.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "3d19point", &equal));
  if (equal) { /* 19-point stencil, 3D */
    PetscCall(MatMPIAIJSetPreallocation(A, 19, NULL, 19, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 19, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      /* one hop */
      if (i > 0) {
        J = global_index(i - 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1) {
        J = global_index(i + 1, j, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0) {
        J = global_index(i, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1) {
        J = global_index(i, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k > 0) {
        J = global_index(i, j, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (k < o - 1) {
        J = global_index(i, j, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      /* two hops */
      if (i > 0 && j > 0) {
        J = global_index(i - 1, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 0 && k > 0) {
        J = global_index(i - 1, j, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 0 && j < n - 1) {
        J = global_index(i - 1, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i > 0 && k < o - 1) {
        J = global_index(i - 1, j, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && j > 0) {
        J = global_index(i + 1, j - 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && k > 0) {
        J = global_index(i + 1, j, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && j < n - 1) {
        J = global_index(i + 1, j + 1, k, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (i < m - 1 && k < o - 1) {
        J = global_index(i + 1, j, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0 && k > 0) {
        J = global_index(i, j - 1, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j > 0 && k < o - 1) {
        J = global_index(i, j - 1, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1 && k > 0) {
        J = global_index(i, j + 1, k - 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      if (j < n - 1 && k < o - 1) {
        J = global_index(i, j + 1, k + 1, m, n);
        PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      }
      v = 18.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(PetscStrcmp(stencil, "3d27point", &equal));
  if (equal) { /* 27-point stencil, 3D */
    PetscCall(MatMPIAIJSetPreallocation(A, 27, NULL, 27, NULL));
    PetscCall(MatSeqAIJSetPreallocation(A, 27, NULL));
    PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
    for (Ii = Istart; Ii < Iend; Ii++) {
      v = -1.0;
      k = Ii / (m * n);
      j = (Ii - k * m * n) / m;
      i = (Ii - k * m * n - j * m);
      if (k > 0) {
        if (j > 0) {
          if (i > 0) {
            J = global_index(i - 1, j - 1, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j - 1, k - 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j - 1, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        {
          if (i > 0) {
            J = global_index(i - 1, j, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j, k - 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        if (j < n - 1) {
          if (i > 0) {
            J = global_index(i - 1, j + 1, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j + 1, k - 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j + 1, k - 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
      }
      {
        if (j > 0) {
          if (i > 0) {
            J = global_index(i - 1, j - 1, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j - 1, k, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j - 1, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        {
          if (i > 0) {
            J = global_index(i - 1, j, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j, k, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        if (j < n - 1) {
          if (i > 0) {
            J = global_index(i - 1, j + 1, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j + 1, k, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j + 1, k, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
      }
      if (k < o - 1) {
        if (j > 0) {
          if (i > 0) {
            J = global_index(i - 1, j - 1, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j - 1, k + 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j - 1, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        {
          if (i > 0) {
            J = global_index(i - 1, j, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j, k + 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
        if (j < n - 1) {
          if (i > 0) {
            J = global_index(i - 1, j + 1, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
          J = global_index(i, j + 1, k + 1, m, n);
          PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          if (i < m - 1) {
            J = global_index(i + 1, j + 1, k + 1, m, n);
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES));
          }
        }
      }
      v = 26.0;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

  /* Copy A into B in order to have a more representative benchmark (A*A has more cache hits than A*B) */
  PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &B));

  PetscCall(PetscLogStageRegister("Full MatMatMult", &fullMatMatMultStage));

  /* Test C = A*B */
  PetscCall(PetscLogStagePush(fullMatMatMultStage));
  PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &C));

  /* Test PtAP_squared = PtAP(C,C)*PtAP(C,C)  */
  PetscCall(MatPtAP(C, C, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &PtAP));
  PetscCall(MatDuplicate(PtAP, MAT_COPY_VALUES, &PtAP_copy));
  PetscCall(MatMatMult(PtAP, PtAP_copy, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &PtAP_squared));

  PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(MatView(PtAP_squared, PETSC_VIEWER_STDOUT_WORLD));

  PetscCall(MatDestroy(&PtAP_squared));
  PetscCall(MatDestroy(&PtAP_copy));
  PetscCall(MatDestroy(&PtAP));
  PetscCall(MatDestroy(&C));
  PetscCall(MatDestroy(&B));
  PetscCall(MatDestroy(&A));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

 test:
      suffix: 1
      nsize: 1
      args: -m 8 -n 8 -stencil 2d5point -matmatmult_via sorted

 test:
       suffix: 2
       nsize: 1
       args: -m 5 -n 5 -o 5 -stencil 3d27point -matmatmult_via rowmerge

 test:
      suffix: 3
      nsize: 4
      args: -m 6 -n 6 -stencil 2d5point -matmatmult_via seqmpi

TEST*/