static char help[] = "Partition a tiny grid using hierarchical partitioning.\n\n";

/*
  Include "petscmat.h" so that we can use matrices.  Note that this file
  automatically includes:
     petscsys.h       - base PETSc routines   petscvec.h - vectors
     petscmat.h - matrices
     petscis.h     - index sets
     petscviewer.h - viewers
*/
#include <petscmat.h>

int main(int argc, char **args)
{
  Mat             A;
  PetscMPIInt     rank, size;
  PetscInt       *ia, *ja;
  MatPartitioning part;
  IS              is, isn, isrows;
  IS              coarseparts, fineparts;
  MPI_Comm        comm;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));
  comm = PETSC_COMM_WORLD;
  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCheck(size == 4, comm, PETSC_ERR_WRONG_MPI_SIZE, "Must run with 4 processors");
  PetscCallMPI(MPI_Comm_rank(comm, &rank));

  PetscCall(PetscMalloc1(5, &ia));
  PetscCall(PetscMalloc1(16, &ja));
  if (rank == 0) {
    ja[0] = 1;
    ja[1] = 4;
    ja[2] = 0;
    ja[3] = 2;
    ja[4] = 5;
    ja[5] = 1;
    ja[6] = 3;
    ja[7] = 6;
    ja[8] = 2;
    ja[9] = 7;
    ia[0] = 0;
    ia[1] = 2;
    ia[2] = 5;
    ia[3] = 8;
    ia[4] = 10;
  } else if (rank == 1) {
    ja[0]  = 0;
    ja[1]  = 5;
    ja[2]  = 8;
    ja[3]  = 1;
    ja[4]  = 4;
    ja[5]  = 6;
    ja[6]  = 9;
    ja[7]  = 2;
    ja[8]  = 5;
    ja[9]  = 7;
    ja[10] = 10;
    ja[11] = 3;
    ja[12] = 6;
    ja[13] = 11;
    ia[0]  = 0;
    ia[1]  = 3;
    ia[2]  = 7;
    ia[3]  = 11;
    ia[4]  = 14;
  } else if (rank == 2) {
    ja[0]  = 4;
    ja[1]  = 9;
    ja[2]  = 12;
    ja[3]  = 5;
    ja[4]  = 8;
    ja[5]  = 10;
    ja[6]  = 13;
    ja[7]  = 6;
    ja[8]  = 9;
    ja[9]  = 11;
    ja[10] = 14;
    ja[11] = 7;
    ja[12] = 10;
    ja[13] = 15;
    ia[0]  = 0;
    ia[1]  = 3;
    ia[2]  = 7;
    ia[3]  = 11;
    ia[4]  = 14;
  } else {
    ja[0] = 8;
    ja[1] = 13;
    ja[2] = 9;
    ja[3] = 12;
    ja[4] = 14;
    ja[5] = 10;
    ja[6] = 13;
    ja[7] = 15;
    ja[8] = 11;
    ja[9] = 14;
    ia[0] = 0;
    ia[1] = 2;
    ia[2] = 5;
    ia[3] = 8;
    ia[4] = 10;
  }
  PetscCall(MatCreateMPIAdj(comm, 4, 16, ia, ja, NULL, &A));
  PetscCall(MatView(A, PETSC_VIEWER_STDOUT_WORLD));
  /*
   Partition the graph of the matrix
  */
  PetscCall(MatPartitioningCreate(comm, &part));
  PetscCall(MatPartitioningSetAdjacency(part, A));
  PetscCall(MatPartitioningSetType(part, MATPARTITIONINGHIERARCH));
  PetscCall(MatPartitioningHierarchicalSetNcoarseparts(part, 2));
  PetscCall(MatPartitioningHierarchicalSetNfineparts(part, 2));
  PetscCall(MatPartitioningSetFromOptions(part));
  /* get new processor owner number of each vertex */
  PetscCall(MatPartitioningApply(part, &is));
  /* coarse parts */
  PetscCall(MatPartitioningHierarchicalGetCoarseparts(part, &coarseparts));
  PetscCall(ISView(coarseparts, PETSC_VIEWER_STDOUT_WORLD));
  /* fine parts */
  PetscCall(MatPartitioningHierarchicalGetFineparts(part, &fineparts));
  PetscCall(ISView(fineparts, PETSC_VIEWER_STDOUT_WORLD));
  /* partitioning */
  PetscCall(ISView(is, PETSC_VIEWER_STDOUT_WORLD));
  /* get new global number of each old global number */
  PetscCall(ISPartitioningToNumbering(is, &isn));
  PetscCall(ISView(isn, PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(ISBuildTwoSided(is, NULL, &isrows));
  PetscCall(ISView(isrows, PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(ISDestroy(&is));
  PetscCall(ISDestroy(&coarseparts));
  PetscCall(ISDestroy(&fineparts));
  PetscCall(ISDestroy(&isrows));
  PetscCall(ISDestroy(&isn));
  PetscCall(MatPartitioningDestroy(&part));
  /*
    Free work space.  All PETSc objects should be destroyed when they
    are no longer needed.
  */
  PetscCall(MatDestroy(&A));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      nsize: 4
      requires: parmetis
      TODO: tests cannot use parmetis because it produces different results on different machines

TEST*/