static char help[] = "Test MatMatMult(), MatTranspose(), MatTransposeMatMult() for Dense and Elemental matrices.\n\n";
/*
 Example:
   mpiexec -n <np> ./ex104 -mat_type elemental
*/

#include <petscmat.h>

int main(int argc, char **argv)
{
  Mat             A, B, C, D;
  PetscInt        i, M = 10, N = 5, j, nrows, ncols, am, an, rstart, rend;
  PetscRandom     r;
  PetscBool       equal, Aiselemental;
  PetscBool       columns_on_one_rank = PETSC_FALSE;
  PetscReal       fill                = 1.0;
  IS              isrows, iscols;
  const PetscInt *rows, *cols;
  PetscScalar    *v, rval;
  PetscBool       Test_MatMatMult = PETSC_TRUE;
  PetscMPIInt     size, rank;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

  PetscCall(PetscOptionsGetInt(NULL, NULL, "-M", &M, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &N, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-columns_on_one_rank", &columns_on_one_rank, NULL));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  if (!columns_on_one_rank) {
    PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, M, N));
  } else {
    PetscCall(MatSetSizes(A, PETSC_DECIDE, rank == 0 ? N : 0, M, N));
  }
  PetscCall(MatSetType(A, MATDENSE));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));
  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &r));
  PetscCall(PetscRandomSetFromOptions(r));

  /* Set local matrix entries */
  PetscCall(MatGetOwnershipIS(A, &isrows, &iscols));
  PetscCall(ISGetLocalSize(isrows, &nrows));
  PetscCall(ISGetIndices(isrows, &rows));
  PetscCall(ISGetLocalSize(iscols, &ncols));
  PetscCall(ISGetIndices(iscols, &cols));
  PetscCall(PetscMalloc1(nrows * ncols, &v));
  for (i = 0; i < nrows; i++) {
    for (j = 0; j < ncols; j++) {
      PetscCall(PetscRandomGetValue(r, &rval));
      v[i * ncols + j] = rval;
    }
  }
  PetscCall(MatSetValues(A, nrows, rows, ncols, cols, v, INSERT_VALUES));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscCall(ISRestoreIndices(isrows, &rows));
  PetscCall(ISRestoreIndices(iscols, &cols));
  PetscCall(ISDestroy(&isrows));
  PetscCall(ISDestroy(&iscols));
  PetscCall(PetscRandomDestroy(&r));

  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATELEMENTAL, &Aiselemental));

  /* Test MatCreateTranspose() and MatTranspose() */
  PetscCall(MatCreateTranspose(A, &C));
  PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &B)); /* B = A^T */
  PetscCall(MatMultEqual(C, B, 10, &equal));
  PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A^T*x != (x^T*A)^T");
  PetscCall(MatDestroy(&B));

  PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &B));
  if (!Aiselemental) {
    PetscCall(MatTranspose(B, MAT_INPLACE_MATRIX, &B));
    PetscCall(MatMultEqual(C, B, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "C*x != B*x");
  }
  PetscCall(MatDestroy(&B));

  /* Test B = C*A for matrix type transpose and seqdense */
  if (size == 1 && !Aiselemental) {
    PetscCall(MatScale(C, -1.0));
    PetscCall(MatMatMult(C, A, MAT_INITIAL_MATRIX, fill, &B));
    PetscCall(MatScale(C, -1.0));
    PetscCall(MatScale(B, -1.0));
    PetscCall(MatMatMultEqual(C, A, B, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "B != C*A for matrix type transpose and seqdense");
    PetscCall(MatDestroy(&B));
  }
  PetscCall(MatDestroy(&C));

  /* Test MatMatMult() */
  if (Test_MatMatMult) {
    PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &B));        /* B = A^T */
    PetscCall(MatMatMult(B, A, MAT_INITIAL_MATRIX, fill, &C)); /* C = B*A = A^T*A */
    PetscCall(MatMatMult(B, A, MAT_REUSE_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(B, A, C, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "B*A*x != C*x");

    /* Test MatDuplicate for matrix product */
    PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &D));

    PetscCall(MatDestroy(&D));
    PetscCall(MatDestroy(&C));
    PetscCall(MatDestroy(&B));
  }

  /* Test MatTransposeMatMult() */
  if (!Aiselemental) {
    Mat E;

    PetscCall(MatTransposeMatMult(A, A, MAT_INITIAL_MATRIX, fill, &D)); /* D = A^T*A */
    PetscCall(MatTransposeMatMult(A, A, MAT_REUSE_MATRIX, fill, &D));
    PetscCall(MatTransposeMatMultEqual(A, A, D, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "D*x != A^T*A*x");

    /* Test MatDuplicate for matrix product */
    PetscCall(MatDuplicate(D, MAT_COPY_VALUES, &C));
    PetscCall(MatDestroy(&C));

    /* Test A*D for fast path when D is on one process */
    PetscCall(MatSetRandom(D, NULL));
    PetscCall(MatMatMult(A, D, MAT_INITIAL_MATRIX, fill, &E));
    PetscCall(MatMatMult(A, D, MAT_REUSE_MATRIX, fill, &E));
    PetscCall(MatMatMultEqual(A, D, E, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "E*x != A*D*x");
    PetscCall(MatDestroy(&E));

    PetscCall(MatDestroy(&D));

    /* Test D*x = A^T*C*A*x, where C is in AIJ format */
    PetscCall(MatGetLocalSize(A, &am, &an));
    PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
    if (size == 1) {
      PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, am, am));
    } else {
      PetscCall(MatSetSizes(C, am, am, PETSC_DECIDE, PETSC_DECIDE));
    }
    PetscCall(MatSetFromOptions(C));
    PetscCall(MatSetUp(C));
    PetscCall(MatGetOwnershipRange(C, &rstart, &rend));
    v[0] = 1.0;
    for (i = rstart; i < rend; i++) PetscCall(MatSetValues(C, 1, &i, 1, &i, v, INSERT_VALUES));
    PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    /* B = C*A, D = A^T*B */
    PetscCall(MatMatMult(C, A, MAT_INITIAL_MATRIX, 1.0, &B));
    PetscCall(MatTransposeMatMult(A, B, MAT_INITIAL_MATRIX, fill, &D));
    PetscCall(MatTransposeMatMultEqual(A, B, D, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "D*x != A^T*B*x");

    PetscCall(MatDestroy(&D));
    PetscCall(MatDestroy(&C));
    PetscCall(MatDestroy(&B));
  }

  /* Test MatMatTransposeMult() */
  if (!Aiselemental) {
    PetscReal diff, scale;
    PetscInt  am, an, aM, aN;

    PetscCall(MatGetLocalSize(A, &am, &an));
    PetscCall(MatGetSize(A, &aM, &aN));
    PetscCall(MatCreateDense(PetscObjectComm((PetscObject)A), PETSC_DECIDE, an, aM + 10, aN, NULL, &B));
    PetscCall(MatSetRandom(B, NULL));
    PetscCall(MatMatTransposeMult(A, B, MAT_INITIAL_MATRIX, fill, &D)); /* D = A*A^T */

    /* Test MatDuplicate for matrix product */
    PetscCall(MatDuplicate(D, MAT_COPY_VALUES, &C));

    PetscCall(MatMatTransposeMult(A, B, MAT_REUSE_MATRIX, fill, &D));
    PetscCall(MatAXPY(C, -1., D, SAME_NONZERO_PATTERN));

    PetscCall(MatNorm(C, NORM_FROBENIUS, &diff));
    PetscCall(MatNorm(D, NORM_FROBENIUS, &scale));
    PetscCheck(diff <= PETSC_SMALL * scale, PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "MatMatTransposeMult() differs between MAT_INITIAL_MATRIX and MAT_REUSE_MATRIX");
    PetscCall(MatDestroy(&C));

    PetscCall(MatMatTransposeMultEqual(A, B, D, 10, &equal));
    PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_PLIB, "D*x != A^T*A*x");
    PetscCall(MatDestroy(&D));
    PetscCall(MatDestroy(&B));
  }

  PetscCall(MatDestroy(&A));
  PetscCall(PetscFree(v));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

    test:
      output_file: output/empty.out

    test:
      suffix: 2
      nsize: 2
      output_file: output/empty.out

    test:
      suffix: 3
      nsize: 4
      output_file: output/empty.out
      args: -M 23 -N 31

    test:
      suffix: 4
      nsize: 4
      output_file: output/empty.out
      args: -M 23 -N 31 -matmattransmult_mpidense_mpidense_via cyclic

    test:
      suffix: 5
      nsize: 4
      output_file: output/empty.out
      args: -M 23 -N 31 -matmattransmult_mpidense_mpidense_via allgatherv

    test:
      suffix: 6
      args: -mat_type elemental
      requires: elemental
      output_file: output/empty.out

    testset:
      nsize: 2
      output_file: output/empty.out
      requires: elemental
      test:
        suffix: 7_dense
        args: -mat_type dense -mat_product_algorithm elemental
      test:
        suffix: 7_elemental
        args: -mat_type elemental

    test:
      suffix: 8
      nsize: 4
      args: -columns_on_one_rank
      output_file: output/empty.out

    test:
      suffix: 9
      nsize: 4
      requires: cuda
      args: -columns_on_one_rank -mat_type densecuda
      output_file: output/empty.out

TEST*/