
static char help[] = "Extract submatrices using unsorted indices. For SEQSBAIJ either sort both rows and columns, or sort none.\n\n";
/*
   Take a 4x4 grid and form a 5-point stencil graph Laplacian over it.
   Partition the grid into two subdomains by splitting into two in the j-direction (slowest varying).
   Impose an overlap of 1 and order the subdomains with the j-direction varying fastest.
   Extract the subdomain submatrices, one per rank.
*/
/* Results:
    Sequential:
    - seqaij:   will error out, if rows or columns are unsorted
    - seqbaij:  will extract submatrices correctly even for unsorted row or column indices
    - seqsbaij: will extract submatrices correctly even for unsorted row and column indices (both must be sorted or not);
                CANNOT automatically report inversions, because MatGetRow is not available.
    MPI:
    - mpiaij:   will error out, if columns are unsorted
    - mpibaij:  will error out, if columns are unsorted.
    - mpisbaij: will error out, if columns are unsorted; even with unsorted rows will produce correct submatrices;
                CANNOT automatically report inversions, because MatGetRow is not available.
*/

#include <petscmat.h>
#include <petscis.h>

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **args)
{
  Mat            A, *S;
  IS             rowis[2], colis[2];
  PetscInt       n,N,i,j,k,l,nsub,Jlow[2] = {0,1}, *jlow, Jhigh[2] = {3,4}, *jhigh, row, col, *subindices, ncols;
  const PetscInt *cols;
  PetscScalar    v;
  PetscMPIInt    rank, size, p, inversions, total_inversions;
  PetscBool      sort_rows, sort_cols, show_inversions;
  PetscErrorCode ierr;
  PetscInitialize(&argc,&args,(char*)0,help);

  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size>2) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG, "A uniprocessor or two-processor example only.\n");

  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  if (size > 1) {
    n = 8; N = 16;
  } else {
    n = 16; N = 16;
  }
  ierr = MatSetSizes(A,n,n,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSetUp(A);CHKERRQ(ierr);

  /* Don't care if the entries are set multiple times by different procs. */
  for (i=0; i<4; ++i) {
    for (j = 0; j<4; ++j) {
      row = j*4+i;
      v   = -1.0;
      if (i>0) {
        col =  row-1; ierr = MatSetValues(A,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
      }
      if (i<3) {
        col = row+1; ierr = MatSetValues(A,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
      }
      if (j>0) {
        col = row-4; ierr = MatSetValues(A,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
      }
      if (j<3) {
        col = row+4; ierr = MatSetValues(A,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
      }
      v    = 4.0;
      ierr = MatSetValues(A,1,&row,1,&row,&v,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD, "Original matrix\n");CHKERRQ(ierr);
  ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);

  if (size > 1) {
    nsub = 1; /* one subdomain per rank */
  }
  else {
    nsub = 2; /* both subdomains on rank 0 */
  }
  if (rank) {
    jlow = Jlow+1; jhigh = Jhigh+1;
  }
  else {
    jlow = Jlow; jhigh = Jhigh;
  }
  sort_rows = PETSC_FALSE;
  ierr      = PetscOptionsGetBool(NULL,NULL, "-sort_rows", &sort_rows, NULL);CHKERRQ(ierr);
  sort_cols = PETSC_FALSE;
  ierr      = PetscOptionsGetBool(NULL,NULL, "-sort_cols", &sort_cols, NULL);CHKERRQ(ierr);
  for (l = 0; l < nsub; ++l) {
    ierr = PetscMalloc1(12, &subindices);CHKERRQ(ierr);
    k    = 0;
    for (i = 0; i < 4; ++i) {
      for (j = jlow[l]; j < jhigh[l]; ++j) {
        subindices[k] = j*4+i;
        k++;
      }
    }
    ierr = ISCreateGeneral(PETSC_COMM_SELF, 12, subindices, PETSC_OWN_POINTER, rowis+l);CHKERRQ(ierr);
    if ((sort_rows && !sort_cols) || (!sort_rows && sort_cols)) {
      ierr = ISDuplicate(rowis[l],colis+l);CHKERRQ(ierr);
    } else {
      ierr = PetscObjectReference((PetscObject)rowis[l]);CHKERRQ(ierr);
      colis[l] = rowis[l];
    }
    if (sort_rows) {
      ierr = ISSort(rowis[l]);CHKERRQ(ierr);
    }
    if (sort_cols) {
      ierr = ISSort(colis[l]);CHKERRQ(ierr);
    }
  }
  ierr = PetscMalloc1(nsub, &S);CHKERRQ(ierr);
  ierr = MatGetSubMatrices(A,nsub,rowis,colis,MAT_INITIAL_MATRIX, &S);CHKERRQ(ierr);

  show_inversions = PETSC_FALSE;

  ierr = PetscOptionsGetBool(NULL,NULL, "-show_inversions", &show_inversions, NULL);CHKERRQ(ierr);

  inversions = 0;
  for (p = 0; p < size; ++p) {
    if (p == rank) {
      ierr = PetscPrintf(PETSC_COMM_SELF, "[%D:%D]: Number of subdomains: %D:\n", rank, size, nsub);CHKERRQ(ierr);
      for (l = 0; l < nsub; ++l) {
        PetscInt i0, i1;
        ierr = PetscPrintf(PETSC_COMM_SELF, "[%D:%D]: Subdomain row IS %D:\n", rank, size, l);CHKERRQ(ierr);
        ierr = ISView(rowis[l],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
        ierr = PetscPrintf(PETSC_COMM_SELF, "[%D:%D]: Subdomain col IS %D:\n", rank, size, l);CHKERRQ(ierr);
        ierr = ISView(colis[l],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
        ierr = PetscPrintf(PETSC_COMM_SELF, "[%D:%D]: Submatrix %D:\n", rank, size, l);CHKERRQ(ierr);
        ierr = MatView(S[l],PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
        if (show_inversions) {
          ierr = MatGetOwnershipRange(S[l], &i0,&i1);CHKERRQ(ierr);
          for (i = i0; i < i1; ++i) {
            ierr = MatGetRow(S[l], i, &ncols, &cols, NULL);CHKERRQ(ierr);
            for (j = 1; j < ncols; ++j) {
              if (cols[j] < cols[j-1]) {
                ierr = PetscPrintf(PETSC_COMM_SELF, "***Inversion in row %D: col[%D] = %D < %D = col[%D]\n", i, j, cols[j], cols[j-1], j-1);CHKERRQ(ierr);
                inversions++;
              }
            }
            ierr = MatRestoreRow(S[l], i, &ncols, &cols, NULL);CHKERRQ(ierr);
          }
        }
      }
    }
    ierr = MPI_Barrier(PETSC_COMM_WORLD);CHKERRQ(ierr);
  }
  if (show_inversions) {
    ierr = MPI_Reduce(&inversions,&total_inversions,1,MPIU_INT, MPI_SUM,0,PETSC_COMM_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD, "*Total inversions: %D\n", total_inversions);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  for (l = 0; l < nsub; ++l) {
    ierr = MatDestroy(&(S[l]));CHKERRQ(ierr);
    ierr = ISDestroy(&(rowis[l]));CHKERRQ(ierr);
    ierr = ISDestroy(&(colis[l]));CHKERRQ(ierr);
  }
  ierr = PetscFree(S);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return 0;
}
