xref: /petsc/src/mat/impls/adj/mpi/mpiadj.c (revision d8a51d2aac522cef49bfbd84fd4cf473dc3fa6ee)

/*
    Defines the basic matrix operations for the ADJ adjacency list matrix data-structure.
*/
#include <../src/mat/impls/adj/mpi/mpiadj.h> /*I "petscmat.h" I*/
#include <petscsf.h>

/*
  The interface should be easy to use for both MatCreateSubMatrix (parallel sub-matrix) and MatCreateSubMatrices (sequential sub-matrices)
*/
static PetscErrorCode MatCreateSubMatrix_MPIAdj_data(Mat adj, IS irows, IS icols, PetscInt **sadj_xadj, PetscInt **sadj_adjncy, PetscInt **sadj_values)
{
  PetscInt        nlrows_is, icols_n, i, j, nroots, nleaves, rlocalindex, *ncols_send, *ncols_recv;
  PetscInt        nlrows_mat, *adjncy_recv, Ncols_recv, Ncols_send, *xadj_recv, *values_recv;
  PetscInt       *ncols_recv_offsets, loc, rnclos, *sadjncy, *sxadj, *svalues;
  const PetscInt *irows_indices, *icols_indices, *xadj, *adjncy;
  PetscMPIInt     owner;
  Mat_MPIAdj     *a = (Mat_MPIAdj *)adj->data;
  PetscLayout     rmap;
  MPI_Comm        comm;
  PetscSF         sf;
  PetscSFNode    *iremote;
  PetscBool       done;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)adj, &comm));
  PetscCall(MatGetLayouts(adj, &rmap, NULL));
  PetscCall(ISGetLocalSize(irows, &nlrows_is));
  PetscCall(ISGetIndices(irows, &irows_indices));
  PetscCall(PetscMalloc1(nlrows_is, &iremote));
  /* construct sf graph*/
  nleaves = nlrows_is;
  for (i = 0; i < nlrows_is; i++) {
    owner       = -1;
    rlocalindex = -1;
    PetscCall(PetscLayoutFindOwnerIndex(rmap, irows_indices[i], &owner, &rlocalindex));
    iremote[i].rank  = owner;
    iremote[i].index = rlocalindex;
  }
  PetscCall(MatGetRowIJ(adj, 0, PETSC_FALSE, PETSC_FALSE, &nlrows_mat, &xadj, &adjncy, &done));
  PetscCall(PetscCalloc4(nlrows_mat, &ncols_send, nlrows_is, &xadj_recv, nlrows_is + 1, &ncols_recv_offsets, nlrows_is, &ncols_recv));
  nroots = nlrows_mat;
  for (i = 0; i < nlrows_mat; i++) ncols_send[i] = xadj[i + 1] - xadj[i];
  PetscCall(PetscSFCreate(comm, &sf));
  PetscCall(PetscSFSetGraph(sf, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
  PetscCall(PetscSFSetType(sf, PETSCSFBASIC));
  PetscCall(PetscSFSetFromOptions(sf));
  PetscCall(PetscSFBcastBegin(sf, MPIU_INT, ncols_send, ncols_recv, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sf, MPIU_INT, ncols_send, ncols_recv, MPI_REPLACE));
  PetscCall(PetscSFBcastBegin(sf, MPIU_INT, xadj, xadj_recv, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sf, MPIU_INT, xadj, xadj_recv, MPI_REPLACE));
  PetscCall(PetscSFDestroy(&sf));
  Ncols_recv = 0;
  for (i = 0; i < nlrows_is; i++) {
    Ncols_recv += ncols_recv[i];
    ncols_recv_offsets[i + 1] = ncols_recv[i] + ncols_recv_offsets[i];
  }
  Ncols_send = 0;
  for (i = 0; i < nlrows_mat; i++) Ncols_send += ncols_send[i];
  PetscCall(PetscCalloc1(Ncols_recv, &iremote));
  PetscCall(PetscCalloc1(Ncols_recv, &adjncy_recv));
  nleaves    = Ncols_recv;
  Ncols_recv = 0;
  for (i = 0; i < nlrows_is; i++) {
    PetscCall(PetscLayoutFindOwner(rmap, irows_indices[i], &owner));
    for (j = 0; j < ncols_recv[i]; j++) {
      iremote[Ncols_recv].rank    = owner;
      iremote[Ncols_recv++].index = xadj_recv[i] + j;
    }
  }
  PetscCall(ISRestoreIndices(irows, &irows_indices));
  /*if we need to deal with edge weights ???*/
  if (a->useedgeweights) PetscCall(PetscCalloc1(Ncols_recv, &values_recv));
  nroots = Ncols_send;
  PetscCall(PetscSFCreate(comm, &sf));
  PetscCall(PetscSFSetGraph(sf, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
  PetscCall(PetscSFSetType(sf, PETSCSFBASIC));
  PetscCall(PetscSFSetFromOptions(sf));
  PetscCall(PetscSFBcastBegin(sf, MPIU_INT, adjncy, adjncy_recv, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sf, MPIU_INT, adjncy, adjncy_recv, MPI_REPLACE));
  if (a->useedgeweights) {
    PetscCall(PetscSFBcastBegin(sf, MPIU_INT, a->values, values_recv, MPI_REPLACE));
    PetscCall(PetscSFBcastEnd(sf, MPIU_INT, a->values, values_recv, MPI_REPLACE));
  }
  PetscCall(PetscSFDestroy(&sf));
  PetscCall(MatRestoreRowIJ(adj, 0, PETSC_FALSE, PETSC_FALSE, &nlrows_mat, &xadj, &adjncy, &done));
  PetscCall(ISGetLocalSize(icols, &icols_n));
  PetscCall(ISGetIndices(icols, &icols_indices));
  rnclos = 0;
  for (i = 0; i < nlrows_is; i++) {
    for (j = ncols_recv_offsets[i]; j < ncols_recv_offsets[i + 1]; j++) {
      PetscCall(PetscFindInt(adjncy_recv[j], icols_n, icols_indices, &loc));
      if (loc < 0) {
        adjncy_recv[j] = -1;
        if (a->useedgeweights) values_recv[j] = -1;
        ncols_recv[i]--;
      } else {
        rnclos++;
      }
    }
  }
  PetscCall(ISRestoreIndices(icols, &icols_indices));
  PetscCall(PetscCalloc1(rnclos, &sadjncy));
  if (a->useedgeweights) PetscCall(PetscCalloc1(rnclos, &svalues));
  PetscCall(PetscCalloc1(nlrows_is + 1, &sxadj));
  rnclos = 0;
  for (i = 0; i < nlrows_is; i++) {
    for (j = ncols_recv_offsets[i]; j < ncols_recv_offsets[i + 1]; j++) {
      if (adjncy_recv[j] < 0) continue;
      sadjncy[rnclos] = adjncy_recv[j];
      if (a->useedgeweights) svalues[rnclos] = values_recv[j];
      rnclos++;
    }
  }
  for (i = 0; i < nlrows_is; i++) sxadj[i + 1] = sxadj[i] + ncols_recv[i];
  if (sadj_xadj) {
    *sadj_xadj = sxadj;
  } else PetscCall(PetscFree(sxadj));
  if (sadj_adjncy) {
    *sadj_adjncy = sadjncy;
  } else PetscCall(PetscFree(sadjncy));
  if (sadj_values) {
    if (a->useedgeweights) *sadj_values = svalues;
    else *sadj_values = NULL;
  } else {
    if (a->useedgeweights) PetscCall(PetscFree(svalues));
  }
  PetscCall(PetscFree4(ncols_send, xadj_recv, ncols_recv_offsets, ncols_recv));
  PetscCall(PetscFree(adjncy_recv));
  if (a->useedgeweights) PetscCall(PetscFree(values_recv));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatrices_MPIAdj_Private(Mat mat, PetscInt n, const IS irow[], const IS icol[], PetscBool subcomm, MatReuse scall, Mat *submat[])
{
  PetscInt        i, irow_n, icol_n, *sxadj, *sadjncy, *svalues;
  PetscInt       *indices, nindx, j, k, loc;
  PetscMPIInt     issame;
  const PetscInt *irow_indices, *icol_indices;
  MPI_Comm        scomm_row, scomm_col, scomm_mat;

  PetscFunctionBegin;
  nindx = 0;
  /*
   * Estimate a maximum number for allocating memory
   */
  for (i = 0; i < n; i++) {
    PetscCall(ISGetLocalSize(irow[i], &irow_n));
    PetscCall(ISGetLocalSize(icol[i], &icol_n));
    nindx = nindx > (irow_n + icol_n) ? nindx : (irow_n + icol_n);
  }
  PetscCall(PetscMalloc1(nindx, &indices));
  /* construct a submat */
  //  if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscMalloc1(n,submat));

  for (i = 0; i < n; i++) {
    if (subcomm) {
      PetscCall(PetscObjectGetComm((PetscObject)irow[i], &scomm_row));
      PetscCall(PetscObjectGetComm((PetscObject)icol[i], &scomm_col));
      PetscCallMPI(MPI_Comm_compare(scomm_row, scomm_col, &issame));
      PetscCheck(issame == MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "row index set must have the same comm as the col index set");
      PetscCallMPI(MPI_Comm_compare(scomm_row, PETSC_COMM_SELF, &issame));
      PetscCheck(issame != MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, " can not use PETSC_COMM_SELF as comm when extracting a parallel submatrix");
    } else {
      scomm_row = PETSC_COMM_SELF;
    }
    /*get sub-matrix data*/
    sxadj   = NULL;
    sadjncy = NULL;
    svalues = NULL;
    PetscCall(MatCreateSubMatrix_MPIAdj_data(mat, irow[i], icol[i], &sxadj, &sadjncy, &svalues));
    PetscCall(ISGetLocalSize(irow[i], &irow_n));
    PetscCall(ISGetLocalSize(icol[i], &icol_n));
    PetscCall(ISGetIndices(irow[i], &irow_indices));
    PetscCall(PetscArraycpy(indices, irow_indices, irow_n));
    PetscCall(ISRestoreIndices(irow[i], &irow_indices));
    PetscCall(ISGetIndices(icol[i], &icol_indices));
    PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(indices, irow_n), icol_indices, icol_n));
    PetscCall(ISRestoreIndices(icol[i], &icol_indices));
    nindx = irow_n + icol_n;
    PetscCall(PetscSortRemoveDupsInt(&nindx, indices));
    /* renumber columns */
    for (j = 0; j < irow_n; j++) {
      for (k = sxadj[j]; k < sxadj[j + 1]; k++) {
        PetscCall(PetscFindInt(sadjncy[k], nindx, indices, &loc));
        PetscCheck(loc >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "can not find col %" PetscInt_FMT, sadjncy[k]);
        sadjncy[k] = loc;
      }
    }
    if (scall == MAT_INITIAL_MATRIX) {
      PetscCall(MatCreateMPIAdj(scomm_row, irow_n, icol_n, sxadj, sadjncy, svalues, submat[i]));
    } else {
      Mat         sadj = *(submat[i]);
      Mat_MPIAdj *sa   = (Mat_MPIAdj *)((sadj)->data);
      PetscCall(PetscObjectGetComm((PetscObject)sadj, &scomm_mat));
      PetscCallMPI(MPI_Comm_compare(scomm_row, scomm_mat, &issame));
      PetscCheck(issame == MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "submatrix  must have the same comm as the col index set");
      PetscCall(PetscArraycpy(sa->i, sxadj, irow_n + 1));
      PetscCall(PetscArraycpy(sa->j, sadjncy, sxadj[irow_n]));
      if (svalues) PetscCall(PetscArraycpy(sa->values, svalues, sxadj[irow_n]));
      PetscCall(PetscFree(sxadj));
      PetscCall(PetscFree(sadjncy));
      PetscCall(PetscFree(svalues));
    }
  }
  PetscCall(PetscFree(indices));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatricesMPI_MPIAdj(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
{
  /*get sub-matrices across a sub communicator */
  PetscFunctionBegin;
  PetscCall(MatCreateSubMatrices_MPIAdj_Private(mat, n, irow, icol, PETSC_TRUE, scall, submat));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatrices_MPIAdj(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
{
  PetscFunctionBegin;
  /*get sub-matrices based on PETSC_COMM_SELF */
  PetscCall(MatCreateSubMatrices_MPIAdj_Private(mat, n, irow, icol, PETSC_FALSE, scall, submat));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatView_MPIAdj_ASCII(Mat A, PetscViewer viewer)
{
  Mat_MPIAdj       *a = (Mat_MPIAdj *)A->data;
  PetscInt          i, j, m = A->rmap->n;
  const char       *name;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetName((PetscObject)A, &name));
  PetscCall(PetscViewerGetFormat(viewer, &format));
  if (format == PETSC_VIEWER_ASCII_INFO) {
    PetscFunctionReturn(PETSC_SUCCESS);
  } else {
    PetscCheck(format != PETSC_VIEWER_ASCII_MATLAB, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MATLAB format not supported");
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
    PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    for (i = 0; i < m; i++) {
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "row %" PetscInt_FMT ":", i + A->rmap->rstart));
      for (j = a->i[i]; j < a->i[i + 1]; j++) {
        if (a->values) {
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " (%" PetscInt_FMT ", %" PetscInt_FMT ") ", a->j[j], a->values[j]));
        } else {
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %" PetscInt_FMT " ", a->j[j]));
        }
      }
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
    PetscCall(PetscViewerFlush(viewer));
    PetscCall(PetscViewerASCIIPopSynchronized(viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatView_MPIAdj(Mat A, PetscViewer viewer)
{
  PetscBool iascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) PetscCall(MatView_MPIAdj_ASCII(A, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDestroy_MPIAdj(Mat mat)
{
  Mat_MPIAdj *a = (Mat_MPIAdj *)mat->data;

  PetscFunctionBegin;
  PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT, mat->rmap->n, mat->cmap->n, a->nz));
  PetscCall(PetscFree(a->diag));
  if (a->freeaij) {
    if (a->freeaijwithfree) {
      if (a->i) free(a->i);
      if (a->j) free(a->j);
    } else {
      PetscCall(PetscFree(a->i));
      PetscCall(PetscFree(a->j));
      PetscCall(PetscFree(a->values));
    }
  }
  PetscCall(PetscFree(a->rowvalues));
  PetscCall(PetscFree(mat->data));
  PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAdjSetPreallocation_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAdjCreateNonemptySubcommMat_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAdjToSeq_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAdjToSeqRankZero_C", NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetOption_MPIAdj(Mat A, MatOption op, PetscBool flg)
{
  Mat_MPIAdj *a = (Mat_MPIAdj *)A->data;

  PetscFunctionBegin;
  switch (op) {
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SPD:
    a->symmetric = flg;
    break;
  case MAT_SYMMETRY_ETERNAL:
  case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
  case MAT_SPD_ETERNAL:
    break;
  default:
    PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRow_MPIAdj(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  Mat_MPIAdj *a = (Mat_MPIAdj *)A->data;

  PetscFunctionBegin;
  row -= A->rmap->rstart;
  PetscCheck(row >= 0 && row < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row out of range");
  *nz = a->i[row + 1] - a->i[row];
  if (v) {
    PetscInt j;
    if (a->rowvalues_alloc < *nz) {
      PetscCall(PetscFree(a->rowvalues));
      a->rowvalues_alloc = PetscMax(a->rowvalues_alloc * 2, *nz);
      PetscCall(PetscMalloc1(a->rowvalues_alloc, &a->rowvalues));
    }
    for (j = 0; j < *nz; j++) a->rowvalues[j] = a->values ? a->values[a->i[row] + j] : 1.0;
    *v = (*nz) ? a->rowvalues : NULL;
  }
  if (idx) *idx = (*nz) ? a->j + a->i[row] : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRestoreRow_MPIAdj(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatEqual_MPIAdj(Mat A, Mat B, PetscBool *flg)
{
  Mat_MPIAdj *a = (Mat_MPIAdj *)A->data, *b = (Mat_MPIAdj *)B->data;
  PetscBool   flag;

  PetscFunctionBegin;
  /* If the  matrix dimensions are not equal,or no of nonzeros */
  if ((A->rmap->n != B->rmap->n) || (a->nz != b->nz)) flag = PETSC_FALSE;

  /* if the a->i are the same */
  PetscCall(PetscArraycmp(a->i, b->i, A->rmap->n + 1, &flag));

  /* if a->j are the same */
  PetscCall(PetscMemcmp(a->j, b->j, (a->nz) * sizeof(PetscInt), &flag));

  PetscCall(MPIU_Allreduce(&flag, flg, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetRowIJ_MPIAdj(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *m, const PetscInt *inia[], const PetscInt *inja[], PetscBool *done)
{
  PetscInt    i;
  Mat_MPIAdj *a  = (Mat_MPIAdj *)A->data;
  PetscInt  **ia = (PetscInt **)inia, **ja = (PetscInt **)inja;

  PetscFunctionBegin;
  *m    = A->rmap->n;
  *ia   = a->i;
  *ja   = a->j;
  *done = PETSC_TRUE;
  if (oshift) {
    for (i = 0; i < (*ia)[*m]; i++) (*ja)[i]++;
    for (i = 0; i <= (*m); i++) (*ia)[i]++;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatRestoreRowIJ_MPIAdj(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *m, const PetscInt *inia[], const PetscInt *inja[], PetscBool *done)
{
  PetscInt    i;
  Mat_MPIAdj *a  = (Mat_MPIAdj *)A->data;
  PetscInt  **ia = (PetscInt **)inia, **ja = (PetscInt **)inja;

  PetscFunctionBegin;
  PetscCheck(!ia || a->i == *ia, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "ia passed back is not one obtained with MatGetRowIJ()");
  PetscCheck(!ja || a->j == *ja, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "ja passed back is not one obtained with MatGetRowIJ()");
  if (oshift) {
    PetscCheck(ia, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "If oshift then you must passed in inia[] argument");
    PetscCheck(ja, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "If oshift then you must passed in inja[] argument");
    for (i = 0; i <= (*m); i++) (*ia)[i]--;
    for (i = 0; i < (*ia)[*m]; i++) (*ja)[i]--;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatConvertFrom_MPIAdj(Mat A, MatType type, MatReuse reuse, Mat *newmat)
{
  Mat                B;
  PetscInt           i, m, N, nzeros = 0, *ia, *ja, len, rstart, cnt, j, *a;
  const PetscInt    *rj;
  const PetscScalar *ra;
  MPI_Comm           comm;

  PetscFunctionBegin;
  PetscCall(MatGetSize(A, NULL, &N));
  PetscCall(MatGetLocalSize(A, &m, NULL));
  PetscCall(MatGetOwnershipRange(A, &rstart, NULL));

  /* count the number of nonzeros per row */
  for (i = 0; i < m; i++) {
    PetscCall(MatGetRow(A, i + rstart, &len, &rj, NULL));
    for (j = 0; j < len; j++) {
      if (rj[j] == i + rstart) {
        len--;
        break;
      } /* don't count diagonal */
    }
    nzeros += len;
    PetscCall(MatRestoreRow(A, i + rstart, &len, &rj, NULL));
  }

  /* malloc space for nonzeros */
  PetscCall(PetscMalloc1(nzeros + 1, &a));
  PetscCall(PetscMalloc1(N + 1, &ia));
  PetscCall(PetscMalloc1(nzeros + 1, &ja));

  nzeros = 0;
  ia[0]  = 0;
  for (i = 0; i < m; i++) {
    PetscCall(MatGetRow(A, i + rstart, &len, &rj, &ra));
    cnt = 0;
    for (j = 0; j < len; j++) {
      if (rj[j] != i + rstart) { /* if not diagonal */
        a[nzeros + cnt]    = (PetscInt)PetscAbsScalar(ra[j]);
        ja[nzeros + cnt++] = rj[j];
      }
    }
    PetscCall(MatRestoreRow(A, i + rstart, &len, &rj, &ra));
    nzeros += cnt;
    ia[i + 1] = nzeros;
  }

  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCall(MatCreate(comm, &B));
  PetscCall(MatSetSizes(B, m, PETSC_DETERMINE, PETSC_DETERMINE, N));
  PetscCall(MatSetType(B, type));
  PetscCall(MatMPIAdjSetPreallocation(B, ia, ja, a));

  if (reuse == MAT_INPLACE_MATRIX) {
    PetscCall(MatHeaderReplace(A, &B));
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValues_MPIAdj(Mat A, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode im)
{
  Mat_MPIAdj *adj = (Mat_MPIAdj *)A->data;
  PetscInt    rStart, rEnd, cStart, cEnd;

  PetscFunctionBegin;
  PetscCheck(!adj->i, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is already assembled, cannot change its values");
  PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd));
  PetscCall(MatGetOwnershipRangeColumn(A, &cStart, &cEnd));
  if (!adj->ht) {
    PetscCall(PetscHSetIJCreate(&adj->ht));
    PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)A), 1, &A->stash));
    PetscCall(PetscLayoutSetUp(A->rmap));
    PetscCall(PetscLayoutSetUp(A->cmap));
  }
  for (PetscInt r = 0; r < m; ++r) {
    PetscHashIJKey key;

    key.i = rows[r];
    if (key.i < 0) continue;
    if ((key.i < rStart) || (key.i >= rEnd)) {
      PetscCall(MatStashValuesRow_Private(&A->stash, key.i, n, cols, values, PETSC_FALSE));
    } else {
      for (PetscInt c = 0; c < n; ++c) {
        key.j = cols[c];
        if (key.j < 0 || key.i == key.j) continue;
        PetscCall(PetscHSetIJAdd(adj->ht, key));
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyBegin_MPIAdj(Mat A, MatAssemblyType type)
{
  PetscInt    nstash, reallocs;
  Mat_MPIAdj *adj = (Mat_MPIAdj *)A->data;

  PetscFunctionBegin;
  if (!adj->ht) {
    PetscCall(PetscHSetIJCreate(&adj->ht));
    PetscCall(PetscLayoutSetUp(A->rmap));
    PetscCall(PetscLayoutSetUp(A->cmap));
  }
  PetscCall(MatStashScatterBegin_Private(A, &A->stash, A->rmap->range));
  PetscCall(MatStashGetInfo_Private(&A->stash, &nstash, &reallocs));
  PetscCall(PetscInfo(A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyEnd_MPIAdj(Mat A, MatAssemblyType type)
{
  PetscScalar   *val;
  PetscInt      *row, *col, m, rstart, *rowstarts;
  PetscInt       i, j, ncols, flg, nz;
  PetscMPIInt    n;
  Mat_MPIAdj    *adj = (Mat_MPIAdj *)A->data;
  PetscHashIter  hi;
  PetscHashIJKey key;
  PetscHSetIJ    ht = adj->ht;

  PetscFunctionBegin;
  while (1) {
    PetscCall(MatStashScatterGetMesg_Private(&A->stash, &n, &row, &col, &val, &flg));
    if (!flg) break;

    for (i = 0; i < n;) {
      /* Identify the consecutive vals belonging to the same row */
      for (j = i, rstart = row[j]; j < n; j++) {
        if (row[j] != rstart) break;
      }
      if (j < n) ncols = j - i;
      else ncols = n - i;
      /* Set all these values with a single function call */
      PetscCall(MatSetValues_MPIAdj(A, 1, row + i, ncols, col + i, val + i, INSERT_VALUES));
      i = j;
    }
  }
  PetscCall(MatStashScatterEnd_Private(&A->stash));
  PetscCall(MatStashDestroy_Private(&A->stash));

  PetscCall(MatGetLocalSize(A, &m, NULL));
  PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
  PetscCall(PetscCalloc1(m + 1, &rowstarts));
  PetscHashIterBegin(ht, hi);
  for (; !PetscHashIterAtEnd(ht, hi);) {
    PetscHashIterGetKey(ht, hi, key);
    rowstarts[key.i - rstart + 1]++;
    PetscHashIterNext(ht, hi);
  }
  for (i = 1; i < m + 1; i++) rowstarts[i] = rowstarts[i - 1] + rowstarts[i];

  PetscCall(PetscHSetIJGetSize(ht, &nz));
  PetscCall(PetscMalloc1(nz, &col));
  PetscHashIterBegin(ht, hi);
  for (; !PetscHashIterAtEnd(ht, hi);) {
    PetscHashIterGetKey(ht, hi, key);
    col[rowstarts[key.i - rstart]++] = key.j;
    PetscHashIterNext(ht, hi);
  }
  PetscCall(PetscHSetIJDestroy(&ht));
  for (i = m; i > 0; i--) rowstarts[i] = rowstarts[i - 1];
  rowstarts[0] = 0;

  for (PetscInt i = 0; i < m; i++) PetscCall(PetscSortInt(rowstarts[i + 1] - rowstarts[i], &col[rowstarts[i]]));

  adj->i       = rowstarts;
  adj->j       = col;
  adj->nz      = rowstarts[m];
  adj->freeaij = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static struct _MatOps MatOps_Values = {MatSetValues_MPIAdj,
                                       MatGetRow_MPIAdj,
                                       MatRestoreRow_MPIAdj,
                                       NULL,
                                       /* 4*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*10*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*15*/ NULL,
                                       MatEqual_MPIAdj,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*20*/ MatAssemblyBegin_MPIAdj,
                                       MatAssemblyEnd_MPIAdj,
                                       MatSetOption_MPIAdj,
                                       NULL,
                                       /*24*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*29*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*34*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*39*/ NULL,
                                       MatCreateSubMatrices_MPIAdj,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*44*/ NULL,
                                       NULL,
                                       MatShift_Basic,
                                       NULL,
                                       NULL,
                                       /*49*/ NULL,
                                       MatGetRowIJ_MPIAdj,
                                       MatRestoreRowIJ_MPIAdj,
                                       NULL,
                                       NULL,
                                       /*54*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*59*/ NULL,
                                       MatDestroy_MPIAdj,
                                       MatView_MPIAdj,
                                       MatConvertFrom_MPIAdj,
                                       NULL,
                                       /*64*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*69*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*74*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*79*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*84*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*89*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*94*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*99*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*104*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*109*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*114*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*119*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*124*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatCreateSubMatricesMPI_MPIAdj,
                                       /*129*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*134*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*139*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*144*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       /*150*/ NULL,
                                       NULL,
                                       NULL};

static PetscErrorCode MatMPIAdjSetPreallocation_MPIAdj(Mat B, PetscInt *i, PetscInt *j, PetscInt *values)
{
  Mat_MPIAdj *b = (Mat_MPIAdj *)B->data;
  PetscBool   useedgeweights;

  PetscFunctionBegin;
  PetscCall(PetscLayoutSetUp(B->rmap));
  PetscCall(PetscLayoutSetUp(B->cmap));
  if (values) useedgeweights = PETSC_TRUE;
  else useedgeweights = PETSC_FALSE;
  /* Make everybody knows if they are using edge weights or not */
  PetscCall(MPIU_Allreduce((int *)&useedgeweights, (int *)&b->useedgeweights, 1, MPI_INT, MPI_MAX, PetscObjectComm((PetscObject)B)));

  if (PetscDefined(USE_DEBUG)) {
    PetscInt ii;

    PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "First i[] index must be zero, instead it is %" PetscInt_FMT, i[0]);
    for (ii = 1; ii < B->rmap->n; ii++) {
      PetscCheck(i[ii] >= 0 && i[ii] >= i[ii - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i[%" PetscInt_FMT "]=%" PetscInt_FMT " index is out of range: i[%" PetscInt_FMT "]=%" PetscInt_FMT, ii, i[ii], ii - 1, i[ii - 1]);
    }
    for (ii = 0; ii < i[B->rmap->n]; ii++) PetscCheck(j[ii] >= 0 && j[ii] < B->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index %" PetscInt_FMT " out of range %" PetscInt_FMT, ii, j[ii]);
  }
  b->j      = j;
  b->i      = i;
  b->values = values;

  b->nz        = i[B->rmap->n];
  b->diag      = NULL;
  b->symmetric = PETSC_FALSE;
  b->freeaij   = PETSC_TRUE;

  B->ops->assemblybegin = NULL;
  B->ops->assemblyend   = NULL;
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatStashDestroy_Private(&B->stash));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMPIAdjCreateNonemptySubcommMat_MPIAdj(Mat A, Mat *B)
{
  Mat_MPIAdj     *a = (Mat_MPIAdj *)A->data;
  const PetscInt *ranges;
  MPI_Comm        acomm, bcomm;
  MPI_Group       agroup, bgroup;
  PetscMPIInt     i, rank, size, nranks, *ranks;

  PetscFunctionBegin;
  *B = NULL;
  PetscCall(PetscObjectGetComm((PetscObject)A, &acomm));
  PetscCallMPI(MPI_Comm_size(acomm, &size));
  PetscCallMPI(MPI_Comm_size(acomm, &rank));
  PetscCall(MatGetOwnershipRanges(A, &ranges));
  for (i = 0, nranks = 0; i < size; i++) {
    if (ranges[i + 1] - ranges[i] > 0) nranks++;
  }
  if (nranks == size) { /* All ranks have a positive number of rows, so we do not need to create a subcomm; */
    PetscCall(PetscObjectReference((PetscObject)A));
    *B = A;
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(PetscMalloc1(nranks, &ranks));
  for (i = 0, nranks = 0; i < size; i++) {
    if (ranges[i + 1] - ranges[i] > 0) ranks[nranks++] = i;
  }
  PetscCallMPI(MPI_Comm_group(acomm, &agroup));
  PetscCallMPI(MPI_Group_incl(agroup, nranks, ranks, &bgroup));
  PetscCall(PetscFree(ranks));
  PetscCallMPI(MPI_Comm_create(acomm, bgroup, &bcomm));
  PetscCallMPI(MPI_Group_free(&agroup));
  PetscCallMPI(MPI_Group_free(&bgroup));
  if (bcomm != MPI_COMM_NULL) {
    PetscInt    m, N;
    Mat_MPIAdj *b;
    PetscCall(MatGetLocalSize(A, &m, NULL));
    PetscCall(MatGetSize(A, NULL, &N));
    PetscCall(MatCreateMPIAdj(bcomm, m, N, a->i, a->j, a->values, B));
    b          = (Mat_MPIAdj *)(*B)->data;
    b->freeaij = PETSC_FALSE;
    PetscCallMPI(MPI_Comm_free(&bcomm));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMPIAdjToSeq_MPIAdj(Mat A, Mat *B)
{
  PetscInt    M, N, *II, *J, NZ, nz, m, nzstart, i;
  PetscInt   *Values = NULL;
  Mat_MPIAdj *adj    = (Mat_MPIAdj *)A->data;
  PetscMPIInt mnz, mm, *allnz, *allm, size, *dispnz, *dispm;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  PetscCall(MatGetSize(A, &M, &N));
  PetscCall(MatGetLocalSize(A, &m, NULL));
  nz = adj->nz;
  PetscCheck(adj->i[m] == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nz %" PetscInt_FMT " not correct i[m] %" PetscInt_FMT, nz, adj->i[m]);
  PetscCall(MPIU_Allreduce(&nz, &NZ, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)A)));

  PetscCall(PetscMPIIntCast(nz, &mnz));
  PetscCall(PetscMalloc2(size, &allnz, size, &dispnz));
  PetscCallMPI(MPI_Allgather(&mnz, 1, MPI_INT, allnz, 1, MPI_INT, PetscObjectComm((PetscObject)A)));
  dispnz[0] = 0;
  for (i = 1; i < size; i++) dispnz[i] = dispnz[i - 1] + allnz[i - 1];
  if (adj->values) {
    PetscCall(PetscMalloc1(NZ, &Values));
    PetscCallMPI(MPI_Allgatherv(adj->values, mnz, MPIU_INT, Values, allnz, dispnz, MPIU_INT, PetscObjectComm((PetscObject)A)));
  }
  PetscCall(PetscMalloc1(NZ, &J));
  PetscCallMPI(MPI_Allgatherv(adj->j, mnz, MPIU_INT, J, allnz, dispnz, MPIU_INT, PetscObjectComm((PetscObject)A)));
  PetscCall(PetscFree2(allnz, dispnz));
  PetscCallMPI(MPI_Scan(&nz, &nzstart, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)A)));
  nzstart -= nz;
  /* shift the i[] values so they will be correct after being received */
  for (i = 0; i < m; i++) adj->i[i] += nzstart;
  PetscCall(PetscMalloc1(M + 1, &II));
  PetscCall(PetscMPIIntCast(m, &mm));
  PetscCall(PetscMalloc2(size, &allm, size, &dispm));
  PetscCallMPI(MPI_Allgather(&mm, 1, MPI_INT, allm, 1, MPI_INT, PetscObjectComm((PetscObject)A)));
  dispm[0] = 0;
  for (i = 1; i < size; i++) dispm[i] = dispm[i - 1] + allm[i - 1];
  PetscCallMPI(MPI_Allgatherv(adj->i, mm, MPIU_INT, II, allm, dispm, MPIU_INT, PetscObjectComm((PetscObject)A)));
  PetscCall(PetscFree2(allm, dispm));
  II[M] = NZ;
  /* shift the i[] values back */
  for (i = 0; i < m; i++) adj->i[i] -= nzstart;
  PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, M, N, II, J, Values, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMPIAdjToSeqRankZero_MPIAdj(Mat A, Mat *B)
{
  PetscInt    M, N, *II, *J, NZ, nz, m, nzstart, i;
  PetscInt   *Values = NULL;
  Mat_MPIAdj *adj    = (Mat_MPIAdj *)A->data;
  PetscMPIInt mnz, mm, *allnz = NULL, *allm, size, *dispnz, *dispm, rank;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
  PetscCall(MatGetSize(A, &M, &N));
  PetscCall(MatGetLocalSize(A, &m, NULL));
  nz = adj->nz;
  PetscCheck(adj->i[m] == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nz %" PetscInt_FMT " not correct i[m] %" PetscInt_FMT, nz, adj->i[m]);
  PetscCall(MPIU_Allreduce(&nz, &NZ, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)A)));

  PetscCall(PetscMPIIntCast(nz, &mnz));
  if (!rank) PetscCall(PetscMalloc2(size, &allnz, size, &dispnz));
  PetscCallMPI(MPI_Gather(&mnz, 1, MPI_INT, allnz, 1, MPI_INT, 0, PetscObjectComm((PetscObject)A)));
  if (!rank) {
    dispnz[0] = 0;
    for (i = 1; i < size; i++) dispnz[i] = dispnz[i - 1] + allnz[i - 1];
    if (adj->values) {
      PetscCall(PetscMalloc1(NZ, &Values));
      PetscCallMPI(MPI_Gatherv(adj->values, mnz, MPIU_INT, Values, allnz, dispnz, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    }
    PetscCall(PetscMalloc1(NZ, &J));
    PetscCallMPI(MPI_Gatherv(adj->j, mnz, MPIU_INT, J, allnz, dispnz, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    PetscCall(PetscFree2(allnz, dispnz));
  } else {
    if (adj->values) PetscCallMPI(MPI_Gatherv(adj->values, mnz, MPIU_INT, NULL, NULL, NULL, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    PetscCallMPI(MPI_Gatherv(adj->j, mnz, MPIU_INT, NULL, NULL, NULL, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
  }
  PetscCallMPI(MPI_Scan(&nz, &nzstart, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)A)));
  nzstart -= nz;
  /* shift the i[] values so they will be correct after being received */
  for (i = 0; i < m; i++) adj->i[i] += nzstart;
  PetscCall(PetscMPIIntCast(m, &mm));
  if (!rank) {
    PetscCall(PetscMalloc1(M + 1, &II));
    PetscCall(PetscMalloc2(size, &allm, size, &dispm));
    PetscCallMPI(MPI_Gather(&mm, 1, MPI_INT, allm, 1, MPI_INT, 0, PetscObjectComm((PetscObject)A)));
    dispm[0] = 0;
    for (i = 1; i < size; i++) dispm[i] = dispm[i - 1] + allm[i - 1];
    PetscCallMPI(MPI_Gatherv(adj->i, mm, MPIU_INT, II, allm, dispm, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
    PetscCall(PetscFree2(allm, dispm));
    II[M] = NZ;
  } else {
    PetscCallMPI(MPI_Gather(&mm, 1, MPI_INT, NULL, 1, MPI_INT, 0, PetscObjectComm((PetscObject)A)));
    PetscCallMPI(MPI_Gatherv(adj->i, mm, MPIU_INT, NULL, NULL, NULL, MPIU_INT, 0, PetscObjectComm((PetscObject)A)));
  }
  /* shift the i[] values back */
  for (i = 0; i < m; i++) adj->i[i] -= nzstart;
  if (!rank) PetscCall(MatCreateMPIAdj(PETSC_COMM_SELF, M, N, II, J, Values, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatMPIAdjCreateNonemptySubcommMat - create the same `MATMPIADJ` matrix on a subcommunicator containing only processes owning a positive number of rows

  Collective

  Input Parameter:
. A - original `MATMPIADJ` matrix

  Output Parameter:
. B - matrix on subcommunicator, `NULL` on MPI processes that own zero rows of `A`

  Level: developer

  Note:
  The matrix `B` should be destroyed with `MatDestroy()`. The arrays are not copied, so `B` should be destroyed before `A` is destroyed.

  Developer Note:
  This function is mostly useful for internal use by mesh partitioning packages, such as ParMETIS that require that every process owns at least one row.

.seealso: [](ch_matrices), `Mat`, `MATMPIADJ`, `MatCreateMPIAdj()`
@*/
PetscErrorCode MatMPIAdjCreateNonemptySubcommMat(Mat A, Mat *B)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscUseMethod(A, "MatMPIAdjCreateNonemptySubcommMat_C", (Mat, Mat *), (A, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  MATMPIADJ - MATMPIADJ = "mpiadj" - A matrix type to be used for distributed adjacency matrices,
  intended for use constructing orderings and partitionings.

  Level: beginner

  Note:
  You can provide values to the matrix using `MatMPIAdjSetPreallocation()`, `MatCreateMPIAdj()`, or
  by calling `MatSetValues()` and `MatAssemblyBegin()` followed by `MatAssemblyEnd()`

.seealso: [](ch_matrices), `Mat`, `MatCreateMPIAdj()`, `MatMPIAdjSetPreallocation()`, `MatSetValues()`
M*/
PETSC_EXTERN PetscErrorCode MatCreate_MPIAdj(Mat B)
{
  Mat_MPIAdj *b;

  PetscFunctionBegin;
  PetscCall(PetscNew(&b));
  B->data         = (void *)b;
  B->ops[0]       = MatOps_Values;
  B->assembled    = PETSC_FALSE;
  B->preallocated = PETSC_TRUE; /* so that MatSetValues() may be used */

  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAdjSetPreallocation_C", MatMPIAdjSetPreallocation_MPIAdj));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAdjCreateNonemptySubcommMat_C", MatMPIAdjCreateNonemptySubcommMat_MPIAdj));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAdjToSeq_C", MatMPIAdjToSeq_MPIAdj));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAdjToSeqRankZero_C", MatMPIAdjToSeqRankZero_MPIAdj));
  PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIADJ));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatMPIAdjToSeq - Converts an parallel `MATMPIADJ` matrix to complete `MATMPIADJ` on each process (needed by sequential partitioners)

  Logically Collective

  Input Parameter:
. A - the matrix

  Output Parameter:
. B - the same matrix on all processes

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATMPIADJ`, `MatCreate()`, `MatCreateMPIAdj()`, `MatSetValues()`, `MatMPIAdjToSeqRankZero()`
@*/
PetscErrorCode MatMPIAdjToSeq(Mat A, Mat *B)
{
  PetscFunctionBegin;
  PetscUseMethod(A, "MatMPIAdjToSeq_C", (Mat, Mat *), (A, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatMPIAdjToSeqRankZero - Converts an parallel `MATMPIADJ` matrix to complete `MATMPIADJ` on rank zero (needed by sequential partitioners)

  Logically Collective

  Input Parameter:
. A - the matrix

  Output Parameter:
. B - the same matrix on rank zero, not set on other ranks

  Level: intermediate

  Note:
  This routine has the advantage on systems with multiple ranks per node since only one copy of the matrix
  is stored on the first node, instead of the number of ranks copies. This can allow partitioning much larger
  parallel graph sequentially.

.seealso: [](ch_matrices), `Mat`, `MATMPIADJ`, `MatCreate()`, `MatCreateMPIAdj()`, `MatSetValues()`, `MatMPIAdjToSeq()`
@*/
PetscErrorCode MatMPIAdjToSeqRankZero(Mat A, Mat *B)
{
  PetscFunctionBegin;
  PetscUseMethod(A, "MatMPIAdjToSeqRankZero_C", (Mat, Mat *), (A, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatMPIAdjSetPreallocation - Sets the array used for storing the matrix elements

  Logically Collective

  Input Parameters:
+ B      - the matrix
. i      - the indices into `j` for the start of each row
. j      - the column indices for each row (sorted for each row).
           The indices in `i` and `j` start with zero (NOT with one).
- values - [use `NULL` if not provided] edge weights

  Level: intermediate

  Notes:
  The indices in `i` and `j` start with zero (NOT with one).

  You must NOT free the `i`, `values` and `j` arrays yourself. PETSc will free them
  when the matrix is destroyed; you must allocate them with `PetscMalloc()`.

  You should not include the matrix diagonal elements.

  If you already have a matrix, you can create its adjacency matrix by a call
  to `MatConvert()`, specifying a type of `MATMPIADJ`.

  Possible values for `MatSetOption()` - `MAT_STRUCTURALLY_SYMMETRIC`

  Fortran Note:
  From Fortran the indices and values are copied so the array space need not be provided with `PetscMalloc()`.

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateMPIAdj()`, `MatSetValues()`, `MATMPIADJ`
@*/
PetscErrorCode MatMPIAdjSetPreallocation(Mat B, PetscInt *i, PetscInt *j, PetscInt *values)
{
  PetscFunctionBegin;
  PetscTryMethod(B, "MatMPIAdjSetPreallocation_C", (Mat, PetscInt *, PetscInt *, PetscInt *), (B, i, j, values));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatCreateMPIAdj - Creates a sparse matrix representing an adjacency list.
  The matrix need not have numerical values associated with it, it is
  intended for ordering (to reduce bandwidth etc) and partitioning.

  Collective

  Input Parameters:
+ comm   - MPI communicator
. m      - number of local rows
. N      - number of global columns
. i      - the indices into `j` for the start of each row
. j      - the column indices for each row (sorted for each row).
- values - the values, optional, use `NULL` if not provided

  Output Parameter:
. A - the matrix

  Level: intermediate

  Notes:
  The indices in `i` and `j` start with zero (NOT with one).

  You must NOT free the `i`, `values` and `j` arrays yourself. PETSc will free them
  when the matrix is destroyed; you must allocate them with `PetscMalloc()`.

  You should not include the matrix diagonals.

  If you already have a matrix, you can create its adjacency matrix by a call
  to `MatConvert()`, specifying a type of `MATMPIADJ`.

  Possible values for `MatSetOption()` - `MAT_STRUCTURALLY_SYMMETRIC`

  Fortran Note:
  From Fortran the indices and values are copied so the array space need not be provided with `PetscMalloc()`.

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatConvert()`, `MatGetOrdering()`, `MATMPIADJ`, `MatMPIAdjSetPreallocation()`
@*/
PetscErrorCode MatCreateMPIAdj(MPI_Comm comm, PetscInt m, PetscInt N, PetscInt *i, PetscInt *j, PetscInt *values, Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, PETSC_DETERMINE, PETSC_DETERMINE, N));
  PetscCall(MatSetType(*A, MATMPIADJ));
  PetscCall(MatMPIAdjSetPreallocation(*A, i, j, values));
  PetscFunctionReturn(PETSC_SUCCESS);
}