xref: /petsc/src/mat/impls/baij/mpi/baijov.c (revision 2235c4e21094f57f73a5851b0c05b8ecf6dffc6d)

/*
   Routines to compute overlapping regions of a parallel MPI matrix
  and to find submatrices that were shared across processors.
*/
#include <../src/mat/impls/baij/mpi/mpibaij.h>
#include <petscbt.h>

static PetscErrorCode MatIncreaseOverlap_MPIBAIJ_Local(Mat, PetscInt, PetscBT *, PetscInt *, PetscInt **);
static PetscErrorCode MatIncreaseOverlap_MPIBAIJ_Receive(Mat, PetscInt, PetscInt **, PetscInt **, PetscInt *);

PetscErrorCode MatIncreaseOverlap_MPIBAIJ(Mat C, PetscInt imax, IS is[], PetscInt ov)
{
  PetscInt        i, N = C->cmap->N, bs = C->rmap->bs, n;
  const PetscInt *idx;
  IS             *is_new;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(imax, &is_new));
  /* Convert the indices into block format */
  PetscCall(ISCompressIndicesGeneral(N, C->rmap->n, bs, imax, is, is_new));
  PetscCheck(ov >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap specified");
  for (i = 0; i < ov; ++i) PetscCall(MatIncreaseOverlap_MPIBAIJ_Once(C, imax, is_new));
  for (i = 0; i < imax; i++) {
    PetscCall(ISDestroy(&is[i]));
    PetscCall(ISGetLocalSize(is_new[i], &n));
    PetscCall(ISGetIndices(is_new[i], &idx));
    PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)is_new[i]), bs, n, idx, PETSC_COPY_VALUES, &is[i]));
    PetscCall(ISDestroy(&is_new[i]));
  }
  PetscCall(PetscFree(is_new));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Sample message format:
  If a processor A wants processor B to process some elements corresponding
  to index sets is[1], is[5]
  mesg [0] = 2   (no of index sets in the mesg)
  -----------
  mesg [1] = 1 => is[1]
  mesg [2] = sizeof(is[1]);
  -----------
  mesg [5] = 5  => is[5]
  mesg [6] = sizeof(is[5]);
  -----------
  mesg [7]
  mesg [n]  data(is[1])
  -----------
  mesg[n+1]
  mesg[m]  data(is[5])
  -----------

  Notes:
  nrqs - no of requests sent (or to be sent out)
  nrqr - no of requests received (which have to be or which have been processed)
*/
PetscErrorCode MatIncreaseOverlap_MPIBAIJ_Once(Mat C, PetscInt imax, IS is[])
{
  Mat_MPIBAIJ     *c = (Mat_MPIBAIJ *)C->data;
  const PetscInt **idx, *idx_i;
  PetscInt        *n, *w3, *w4, **data, len;
  PetscMPIInt      size, rank, tag1, tag2, *w2, *w1, nrqs, nrqr, *pa;
  PetscInt         Mbs, **rbuf, row, msz, **outdat, **ptr;
  PetscInt        *ctr, *tmp, *isz, *isz1, **xdata, **rbuf2, *d_p;
  PetscMPIInt     *onodes1, *olengths1, *onodes2, *olengths2, proc = -1;
  PetscBT         *table;
  MPI_Comm         comm, *iscomms;
  MPI_Request     *s_waits1, *r_waits1, *s_waits2, *r_waits2;
  PetscByte       *t_p;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
  size = c->size;
  rank = c->rank;
  Mbs  = c->Mbs;

  PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag1));
  PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag2));

  PetscCall(PetscMalloc2(imax, (PetscInt ***)&idx, imax, &n));

  for (PetscInt i = 0; i < imax; i++) {
    PetscCall(ISGetIndices(is[i], &idx[i]));
    PetscCall(ISGetLocalSize(is[i], &n[i]));
  }

  /* evaluate communication - mesg to who,length of mesg, and buffer space
     required. Based on this, buffers are allocated, and data copied into them*/
  PetscCall(PetscCalloc4(size, &w1, size, &w2, size, &w3, size, &w4));
  for (PetscInt i = 0; i < imax; i++) {
    PetscCall(PetscArrayzero(w4, size)); /* initialise work vector*/
    idx_i = idx[i];
    len   = n[i];
    for (PetscInt j = 0; j < len; j++) {
      row = idx_i[j];
      PetscCheck(row >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Index set cannot have negative entries");
      PetscCall(PetscLayoutFindOwner(C->rmap, row * C->rmap->bs, &proc));
      w4[proc]++;
    }
    for (PetscMPIInt j = 0; j < size; j++) {
      if (w4[j]) {
        w1[j] += w4[j];
        w3[j]++;
      }
    }
  }

  nrqs     = 0; /* no of outgoing messages */
  msz      = 0; /* total mesg length (for all proc */
  w1[rank] = 0; /* no mesg sent to itself */
  w3[rank] = 0;
  for (PetscMPIInt i = 0; i < size; i++) {
    if (w1[i]) {
      w2[i] = 1;
      nrqs++;
    } /* there exists a message to proc i */
  }
  /* pa - is list of processors to communicate with */
  PetscCall(PetscMalloc1(nrqs, &pa));
  for (PetscMPIInt i = 0, j = 0; i < size; i++) {
    if (w1[i]) {
      pa[j] = i;
      j++;
    }
  }

  /* Each message would have a header = 1 + 2*(no of IS) + data */
  for (PetscMPIInt i = 0; i < nrqs; i++) {
    PetscMPIInt j = pa[i];
    w1[j] += w2[j] + 2 * w3[j];
    msz += w1[j];
  }

  /* Determine the number of messages to expect, their lengths, from from-ids */
  PetscCall(PetscGatherNumberOfMessages(comm, w2, w1, &nrqr));
  PetscCall(PetscGatherMessageLengths(comm, nrqs, nrqr, w1, &onodes1, &olengths1));

  /* Now post the Irecvs corresponding to these messages */
  PetscCall(PetscPostIrecvInt(comm, tag1, nrqr, onodes1, olengths1, &rbuf, &r_waits1));

  /* Allocate Memory for outgoing messages */
  PetscCall(PetscMalloc4(size, &outdat, size, &ptr, msz, &tmp, size, &ctr));
  PetscCall(PetscArrayzero(outdat, size));
  PetscCall(PetscArrayzero(ptr, size));
  {
    PetscInt *iptr = tmp, ict = 0;
    for (PetscMPIInt i = 0; i < nrqs; i++) {
      PetscMPIInt j = pa[i];
      iptr += ict;
      outdat[j] = iptr;
      ict       = w1[j];
    }
  }

  /* Form the outgoing messages */
  /*plug in the headers*/
  for (PetscMPIInt i = 0; i < nrqs; i++) {
    PetscMPIInt j = pa[i];
    outdat[j][0]  = 0;
    PetscCall(PetscArrayzero(outdat[j] + 1, 2 * w3[j]));
    ptr[j] = outdat[j] + 2 * w3[j] + 1;
  }

  /* Memory for doing local proc's work*/
  {
    PetscCall(PetscCalloc5(imax, &table, imax, &data, imax, &isz, Mbs * imax, &d_p, (Mbs / PETSC_BITS_PER_BYTE + 1) * imax, &t_p));

    for (PetscInt i = 0; i < imax; i++) {
      table[i] = t_p + (Mbs / PETSC_BITS_PER_BYTE + 1) * i;
      data[i]  = d_p + (Mbs)*i;
    }
  }

  /* Parse the IS and update local tables and the outgoing buf with the data*/
  {
    PetscInt n_i, *data_i, isz_i, *outdat_j, ctr_j, k;
    PetscBT  table_i;

    for (PetscInt i = 0; i < imax; i++) {
      PetscCall(PetscArrayzero(ctr, size));
      n_i     = n[i];
      table_i = table[i];
      idx_i   = idx[i];
      data_i  = data[i];
      isz_i   = isz[i];
      for (PetscInt j = 0; j < n_i; j++) { /* parse the indices of each IS */
        row = idx_i[j];
        PetscCall(PetscLayoutFindOwner(C->rmap, row * C->rmap->bs, &proc));
        if (proc != rank) { /* copy to the outgoing buffer */
          ctr[proc]++;
          *ptr[proc] = row;
          ptr[proc]++;
        } else { /* Update the local table */
          if (!PetscBTLookupSet(table_i, row)) data_i[isz_i++] = row;
        }
      }
      /* Update the headers for the current IS */
      for (PetscMPIInt j = 0; j < size; j++) { /* Can Optimise this loop by using pa[] */
        if ((ctr_j = ctr[j])) {
          outdat_j            = outdat[j];
          k                   = ++outdat_j[0];
          outdat_j[2 * k]     = ctr_j;
          outdat_j[2 * k - 1] = i;
        }
      }
      isz[i] = isz_i;
    }
  }

  /*  Now  post the sends */
  PetscCall(PetscMalloc1(nrqs, &s_waits1));
  for (PetscMPIInt i = 0; i < nrqs; ++i) {
    PetscMPIInt j = pa[i];
    PetscCallMPI(MPIU_Isend(outdat[j], w1[j], MPIU_INT, j, tag1, comm, s_waits1 + i));
  }

  /* No longer need the original indices*/
  for (PetscInt i = 0; i < imax; ++i) PetscCall(ISRestoreIndices(is[i], idx + i));
  PetscCall(PetscFree2(*(PetscInt ***)&idx, n));

  PetscCall(PetscMalloc1(imax, &iscomms));
  for (PetscInt i = 0; i < imax; ++i) {
    PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)is[i]), &iscomms[i], NULL));
    PetscCall(ISDestroy(&is[i]));
  }

  /* Do Local work*/
  PetscCall(MatIncreaseOverlap_MPIBAIJ_Local(C, imax, table, isz, data));

  /* Receive messages*/
  PetscCallMPI(MPI_Waitall(nrqr, r_waits1, MPI_STATUSES_IGNORE));
  PetscCallMPI(MPI_Waitall(nrqs, s_waits1, MPI_STATUSES_IGNORE));

  /* Phase 1 sends are complete - deallocate buffers */
  PetscCall(PetscFree4(outdat, ptr, tmp, ctr));
  PetscCall(PetscFree4(w1, w2, w3, w4));

  PetscCall(PetscMalloc1(nrqr, &xdata));
  PetscCall(PetscMalloc1(nrqr, &isz1));
  PetscCall(MatIncreaseOverlap_MPIBAIJ_Receive(C, nrqr, rbuf, xdata, isz1));
  if (rbuf) {
    PetscCall(PetscFree(rbuf[0]));
    PetscCall(PetscFree(rbuf));
  }

  /* Send the data back*/
  /* Do a global reduction to know the buffer space req for incoming messages*/
  {
    PetscMPIInt *rw1;

    PetscCall(PetscCalloc1(size, &rw1));
    for (PetscMPIInt i = 0; i < nrqr; ++i) {
      proc = onodes1[i];
      PetscCall(PetscMPIIntCast(isz1[i], &rw1[proc]));
    }

    /* Determine the number of messages to expect, their lengths, from from-ids */
    PetscCall(PetscGatherMessageLengths(comm, nrqr, nrqs, rw1, &onodes2, &olengths2));
    PetscCall(PetscFree(rw1));
  }
  /* Now post the Irecvs corresponding to these messages */
  PetscCall(PetscPostIrecvInt(comm, tag2, nrqs, onodes2, olengths2, &rbuf2, &r_waits2));

  /*  Now  post the sends */
  PetscCall(PetscMalloc1(nrqr, &s_waits2));
  for (PetscMPIInt i = 0; i < nrqr; ++i) {
    PetscMPIInt j = onodes1[i];
    PetscCallMPI(MPIU_Isend(xdata[i], isz1[i], MPIU_INT, j, tag2, comm, s_waits2 + i));
  }

  PetscCall(PetscFree(onodes1));
  PetscCall(PetscFree(olengths1));

  /* receive work done on other processors*/
  {
    PetscMPIInt idex;
    PetscInt    is_no, ct1, max, *rbuf2_i, isz_i, *data_i, jmax;
    PetscBT     table_i;

    for (PetscMPIInt i = 0; i < nrqs; ++i) {
      PetscCallMPI(MPI_Waitany(nrqs, r_waits2, &idex, MPI_STATUS_IGNORE));
      /* Process the message*/
      rbuf2_i = rbuf2[idex];
      ct1     = 2 * rbuf2_i[0] + 1;
      jmax    = rbuf2[idex][0];
      for (PetscInt j = 1; j <= jmax; j++) {
        max     = rbuf2_i[2 * j];
        is_no   = rbuf2_i[2 * j - 1];
        isz_i   = isz[is_no];
        data_i  = data[is_no];
        table_i = table[is_no];
        for (PetscInt k = 0; k < max; k++, ct1++) {
          row = rbuf2_i[ct1];
          if (!PetscBTLookupSet(table_i, row)) data_i[isz_i++] = row;
        }
        isz[is_no] = isz_i;
      }
    }
    PetscCallMPI(MPI_Waitall(nrqr, s_waits2, MPI_STATUSES_IGNORE));
  }

  for (PetscInt i = 0; i < imax; ++i) {
    PetscCall(ISCreateGeneral(iscomms[i], isz[i], data[i], PETSC_COPY_VALUES, is + i));
    PetscCall(PetscCommDestroy(&iscomms[i]));
  }

  PetscCall(PetscFree(iscomms));
  PetscCall(PetscFree(onodes2));
  PetscCall(PetscFree(olengths2));

  PetscCall(PetscFree(pa));
  if (rbuf2) {
    PetscCall(PetscFree(rbuf2[0]));
    PetscCall(PetscFree(rbuf2));
  }
  PetscCall(PetscFree(s_waits1));
  PetscCall(PetscFree(r_waits1));
  PetscCall(PetscFree(s_waits2));
  PetscCall(PetscFree(r_waits2));
  PetscCall(PetscFree5(table, data, isz, d_p, t_p));
  if (xdata) {
    PetscCall(PetscFree(xdata[0]));
    PetscCall(PetscFree(xdata));
  }
  PetscCall(PetscFree(isz1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   MatIncreaseOverlap_MPIBAIJ_Local - Called by MatincreaseOverlap, to do
       the work on the local processor.

     Inputs:
      C      - MAT_MPIBAIJ;
      imax - total no of index sets processed at a time;
      table  - an array of char - size = Mbs bits.

     Output:
      isz    - array containing the count of the solution elements corresponding
               to each index set;
      data   - pointer to the solutions
*/
static PetscErrorCode MatIncreaseOverlap_MPIBAIJ_Local(Mat C, PetscInt imax, PetscBT *table, PetscInt *isz, PetscInt **data)
{
  Mat_MPIBAIJ *c = (Mat_MPIBAIJ *)C->data;
  Mat          A = c->A, B = c->B;
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)B->data;
  PetscInt     start, end, val, max, rstart, cstart, *ai, *aj;
  PetscInt    *bi, *bj, *garray, i, j, k, row, *data_i, isz_i;
  PetscBT      table_i;

  PetscFunctionBegin;
  rstart = c->rstartbs;
  cstart = c->cstartbs;
  ai     = a->i;
  aj     = a->j;
  bi     = b->i;
  bj     = b->j;
  garray = c->garray;

  for (i = 0; i < imax; i++) {
    data_i  = data[i];
    table_i = table[i];
    isz_i   = isz[i];
    for (j = 0, max = isz[i]; j < max; j++) {
      row   = data_i[j] - rstart;
      start = ai[row];
      end   = ai[row + 1];
      for (k = start; k < end; k++) { /* Amat */
        val = aj[k] + cstart;
        if (!PetscBTLookupSet(table_i, val)) data_i[isz_i++] = val;
      }
      start = bi[row];
      end   = bi[row + 1];
      for (k = start; k < end; k++) { /* Bmat */
        val = garray[bj[k]];
        if (!PetscBTLookupSet(table_i, val)) data_i[isz_i++] = val;
      }
    }
    isz[i] = isz_i;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
      MatIncreaseOverlap_MPIBAIJ_Receive - Process the received messages,
         and return the output

         Input:
           C    - the matrix
           nrqr - no of messages being processed.
           rbuf - an array of pointers to the received requests

         Output:
           xdata - array of messages to be sent back
           isz1  - size of each message

  For better efficiency perhaps we should malloc separately each xdata[i],
then if a remalloc is required we need only copy the data for that one row
rather than all previous rows as it is now where a single large chunk of
memory is used.

*/
static PetscErrorCode MatIncreaseOverlap_MPIBAIJ_Receive(Mat C, PetscInt nrqr, PetscInt **rbuf, PetscInt **xdata, PetscInt *isz1)
{
  Mat_MPIBAIJ *c = (Mat_MPIBAIJ *)C->data;
  Mat          A = c->A, B = c->B;
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)B->data;
  PetscInt     rstart, cstart, *ai, *aj, *bi, *bj, *garray, i, j, k;
  PetscInt     row, total_sz, ct, ct1, ct2, ct3, mem_estimate, oct2, l, start, end;
  PetscInt     val, max1, max2, Mbs, no_malloc = 0, *tmp, new_estimate, ctr;
  PetscInt    *rbuf_i, kmax, rbuf_0;
  PetscBT      xtable;

  PetscFunctionBegin;
  Mbs    = c->Mbs;
  rstart = c->rstartbs;
  cstart = c->cstartbs;
  ai     = a->i;
  aj     = a->j;
  bi     = b->i;
  bj     = b->j;
  garray = c->garray;

  for (i = 0, ct = 0, total_sz = 0; i < nrqr; ++i) {
    rbuf_i = rbuf[i];
    rbuf_0 = rbuf_i[0];
    ct += rbuf_0;
    for (j = 1; j <= rbuf_0; j++) total_sz += rbuf_i[2 * j];
  }

  if (c->Mbs) max1 = ct * (a->nz + b->nz) / c->Mbs;
  else max1 = 1;
  mem_estimate = 3 * ((total_sz > max1 ? total_sz : max1) + 1);
  if (nrqr) {
    PetscCall(PetscMalloc1(mem_estimate, &xdata[0]));
    ++no_malloc;
  }
  PetscCall(PetscBTCreate(Mbs, &xtable));
  PetscCall(PetscArrayzero(isz1, nrqr));

  ct3 = 0;
  for (i = 0; i < nrqr; i++) { /* for easch mesg from proc i */
    rbuf_i = rbuf[i];
    rbuf_0 = rbuf_i[0];
    ct1    = 2 * rbuf_0 + 1;
    ct2    = ct1;
    ct3 += ct1;
    for (j = 1; j <= rbuf_0; j++) { /* for each IS from proc i*/
      PetscCall(PetscBTMemzero(Mbs, xtable));
      oct2 = ct2;
      kmax = rbuf_i[2 * j];
      for (k = 0; k < kmax; k++, ct1++) {
        row = rbuf_i[ct1];
        if (!PetscBTLookupSet(xtable, row)) {
          if (!(ct3 < mem_estimate)) {
            new_estimate = (PetscInt)(1.5 * mem_estimate) + 1;
            PetscCall(PetscMalloc1(new_estimate, &tmp));
            PetscCall(PetscArraycpy(tmp, xdata[0], mem_estimate));
            PetscCall(PetscFree(xdata[0]));
            xdata[0]     = tmp;
            mem_estimate = new_estimate;
            ++no_malloc;
            for (ctr = 1; ctr <= i; ctr++) xdata[ctr] = xdata[ctr - 1] + isz1[ctr - 1];
          }
          xdata[i][ct2++] = row;
          ct3++;
        }
      }
      for (k = oct2, max2 = ct2; k < max2; k++) {
        row   = xdata[i][k] - rstart;
        start = ai[row];
        end   = ai[row + 1];
        for (l = start; l < end; l++) {
          val = aj[l] + cstart;
          if (!PetscBTLookupSet(xtable, val)) {
            if (!(ct3 < mem_estimate)) {
              new_estimate = (PetscInt)(1.5 * mem_estimate) + 1;
              PetscCall(PetscMalloc1(new_estimate, &tmp));
              PetscCall(PetscArraycpy(tmp, xdata[0], mem_estimate));
              PetscCall(PetscFree(xdata[0]));
              xdata[0]     = tmp;
              mem_estimate = new_estimate;
              ++no_malloc;
              for (ctr = 1; ctr <= i; ctr++) xdata[ctr] = xdata[ctr - 1] + isz1[ctr - 1];
            }
            xdata[i][ct2++] = val;
            ct3++;
          }
        }
        start = bi[row];
        end   = bi[row + 1];
        for (l = start; l < end; l++) {
          val = garray[bj[l]];
          if (!PetscBTLookupSet(xtable, val)) {
            if (!(ct3 < mem_estimate)) {
              new_estimate = (PetscInt)(1.5 * mem_estimate) + 1;
              PetscCall(PetscMalloc1(new_estimate, &tmp));
              PetscCall(PetscArraycpy(tmp, xdata[0], mem_estimate));
              PetscCall(PetscFree(xdata[0]));
              xdata[0]     = tmp;
              mem_estimate = new_estimate;
              ++no_malloc;
              for (ctr = 1; ctr <= i; ctr++) xdata[ctr] = xdata[ctr - 1] + isz1[ctr - 1];
            }
            xdata[i][ct2++] = val;
            ct3++;
          }
        }
      }
      /* Update the header*/
      xdata[i][2 * j]     = ct2 - oct2; /* Undo the vector isz1 and use only a var*/
      xdata[i][2 * j - 1] = rbuf_i[2 * j - 1];
    }
    xdata[i][0] = rbuf_0;
    if (i + 1 < nrqr) xdata[i + 1] = xdata[i] + ct2;
    isz1[i] = ct2; /* size of each message */
  }
  PetscCall(PetscBTDestroy(&xtable));
  PetscCall(PetscInfo(C, "Allocated %" PetscInt_FMT " bytes, required %" PetscInt_FMT ", no of mallocs = %" PetscInt_FMT "\n", mem_estimate, ct3, no_malloc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatCreateSubMatrices_MPIBAIJ(Mat C, PetscInt ismax, const IS isrow[], const IS iscol[], MatReuse scall, Mat *submat[])
{
  IS          *isrow_block, *iscol_block;
  Mat_MPIBAIJ *c = (Mat_MPIBAIJ *)C->data;
  PetscInt     nmax, nstages, i, pos, max_no, N = C->cmap->N, bs = C->rmap->bs;
  Mat_SeqBAIJ *subc;
  Mat_SubSppt *smat;
  PetscBool    sym = PETSC_FALSE, flg[2];

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)C, MATMPISBAIJ, flg));
  if (flg[0]) {
    if (isrow == iscol) sym = PETSC_TRUE;
    else {
      flg[0] = flg[1] = PETSC_TRUE;
      for (i = 0; i < ismax; i++) {
        if (isrow[i] != iscol[i]) flg[0] = PETSC_FALSE;
        PetscCall(ISGetLocalSize(iscol[0], &nmax));
        if (nmax == C->cmap->N && flg[1]) PetscCall(ISIdentity(iscol[0], flg + 1));
      }
      sym = (PetscBool)(flg[0] || flg[1]);
    }
  }
  /* The compression and expansion should be avoided. Doesn't point
     out errors, might change the indices, hence buggey */
  PetscCall(PetscMalloc2(ismax, &isrow_block, ismax, &iscol_block));
  PetscCall(ISCompressIndicesGeneral(C->rmap->N, C->rmap->n, bs, ismax, isrow, isrow_block));
  if (isrow == iscol) {
    for (i = 0; i < ismax; i++) {
      iscol_block[i] = isrow_block[i];
      PetscCall(PetscObjectReference((PetscObject)iscol_block[i]));
    }
  } else PetscCall(ISCompressIndicesGeneral(N, C->cmap->n, bs, ismax, iscol, iscol_block));

  /* Determine the number of stages through which submatrices are done */
  if (!C->cmap->N) nmax = 20 * 1000000 / sizeof(PetscInt);
  else nmax = 20 * 1000000 / (c->Nbs * sizeof(PetscInt));
  if (!nmax) nmax = 1;

  if (scall == MAT_INITIAL_MATRIX) {
    nstages = ismax / nmax + ((ismax % nmax) ? 1 : 0); /* local nstages */

    /* Make sure every processor loops through the nstages */
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &nstages, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)C)));

    /* Allocate memory to hold all the submatrices and dummy submatrices */
    PetscCall(PetscCalloc1(ismax + nstages, submat));
  } else { /* MAT_REUSE_MATRIX */
    if (ismax) {
      subc = (Mat_SeqBAIJ *)((*submat)[0]->data);
      smat = subc->submatis1;
    } else { /* (*submat)[0] is a dummy matrix */
      smat = (Mat_SubSppt *)(*submat)[0]->data;
    }
    PetscCheck(smat, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "MatCreateSubMatrices(...,MAT_REUSE_MATRIX,...) requires submat");
    nstages = smat->nstages;
  }

  for (i = 0, pos = 0; i < nstages; i++) {
    if (pos + nmax <= ismax) max_no = nmax;
    else if (pos >= ismax) max_no = 0;
    else max_no = ismax - pos;

    PetscCall(MatCreateSubMatrices_MPIBAIJ_local(C, max_no, isrow_block + pos, iscol_block + pos, scall, *submat + pos, sym));
    if (!max_no) {
      if (scall == MAT_INITIAL_MATRIX) { /* submat[pos] is a dummy matrix */
        smat          = (Mat_SubSppt *)(*submat)[pos]->data;
        smat->nstages = nstages;
      }
      pos++; /* advance to next dummy matrix if any */
    } else pos += max_no;
  }

  if (scall == MAT_INITIAL_MATRIX && ismax) {
    /* save nstages for reuse */
    subc          = (Mat_SeqBAIJ *)((*submat)[0]->data);
    smat          = subc->submatis1;
    smat->nstages = nstages;
  }

  for (i = 0; i < ismax; i++) {
    PetscCall(ISDestroy(&isrow_block[i]));
    PetscCall(ISDestroy(&iscol_block[i]));
  }
  PetscCall(PetscFree2(isrow_block, iscol_block));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* This code is used for BAIJ and SBAIJ matrices (unfortunate dependency) */
PetscErrorCode MatCreateSubMatrices_MPIBAIJ_local(Mat C, PetscInt ismax, const IS isrow[], const IS iscol[], MatReuse scall, Mat *submats, PetscBool sym)
{
  Mat_MPIBAIJ     *c = (Mat_MPIBAIJ *)C->data;
  Mat              A = c->A;
  Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)c->B->data, *subc;
  const PetscInt **icol, **irow;
  PetscInt        *nrow, *ncol, start;
  PetscMPIInt     *pa, **row2proc, *row2proc_i, proc = -1;
  PetscMPIInt      rank, size, tag0, tag2, tag3, tag4, *w1, *w2, *w3, *w4, nrqr, nrqs = 0, *req_source1 = NULL, *req_source2;
  PetscInt       **sbuf1, **sbuf2, *sbuf2_i, ct1, ct2, **rbuf1, row;
  PetscInt         msz, **ptr = NULL, *req_size = NULL, *ctr = NULL, *tmp = NULL, tcol;
  PetscInt       **rbuf3 = NULL, **sbuf_aj, **rbuf2 = NULL, max1, max2;
  PetscInt       **lens, is_no, ncols, *cols, mat_i, *mat_j, tmp2, jmax;
#if defined(PETSC_USE_CTABLE)
  PetscHMapI *cmap, cmap_i = NULL, *rmap, rmap_i;
#else
  PetscInt **cmap, *cmap_i = NULL, **rmap, *rmap_i;
#endif
  const PetscInt *irow_i, *icol_i;
  PetscInt        ctr_j, *sbuf1_j, *sbuf_aj_i, *rbuf1_i, kmax, *lens_i, jcnt;
  MPI_Request    *s_waits1, *r_waits1, *s_waits2, *r_waits2, *r_waits3;
  MPI_Request    *r_waits4, *s_waits3, *s_waits4;
  MPI_Comm        comm;
  PetscScalar   **rbuf4, *rbuf4_i = NULL, **sbuf_aa, *vals, *mat_a = NULL, *imat_a = NULL, *sbuf_aa_i;
  PetscMPIInt    *onodes1, *olengths1, end;
  PetscInt       *imat_ilen, *imat_j, *imat_i;
  Mat_SubSppt    *smat_i;
  PetscBool      *issorted, colflag, iscsorted = PETSC_TRUE;
  PetscInt       *sbuf1_i, *rbuf2_i, *rbuf3_i, ilen;
  PetscInt        bs = C->rmap->bs, bs2 = c->bs2, rstart = c->rstartbs;
  PetscBool       ijonly = c->ijonly; /* private flag indicates only matrix data structures are requested */
  PetscInt        nzA, nzB, *a_i = a->i, *b_i = b->i, *a_j = a->j, *b_j = b->j, ctmp, imark, *cworkA, *cworkB;
  PetscScalar    *vworkA = NULL, *vworkB = NULL, *a_a = a->a, *b_a = b->a;
  PetscInt        cstart = c->cstartbs, *bmap = c->garray;
  PetscBool      *allrows, *allcolumns;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
  size = c->size;
  rank = c->rank;

  PetscCall(PetscMalloc5(ismax, &row2proc, ismax, &cmap, ismax, &rmap, ismax + 1, &allcolumns, ismax, &allrows));
  PetscCall(PetscMalloc5(ismax, (PetscInt ***)&irow, ismax, (PetscInt ***)&icol, ismax, &nrow, ismax, &ncol, ismax, &issorted));

  for (PetscInt i = 0; i < ismax; i++) {
    PetscCall(ISSorted(iscol[i], &issorted[i]));
    if (!issorted[i]) iscsorted = issorted[i]; /* columns are not sorted! */
    PetscCall(ISSorted(isrow[i], &issorted[i]));

    /* Check for special case: allcolumns */
    PetscCall(ISIdentity(iscol[i], &colflag));
    PetscCall(ISGetLocalSize(iscol[i], &ncol[i]));

    if (colflag && ncol[i] == c->Nbs) {
      allcolumns[i] = PETSC_TRUE;
      icol[i]       = NULL;
    } else {
      allcolumns[i] = PETSC_FALSE;
      PetscCall(ISGetIndices(iscol[i], &icol[i]));
    }

    /* Check for special case: allrows */
    PetscCall(ISIdentity(isrow[i], &colflag));
    PetscCall(ISGetLocalSize(isrow[i], &nrow[i]));
    if (colflag && nrow[i] == c->Mbs) {
      allrows[i] = PETSC_TRUE;
      irow[i]    = NULL;
    } else {
      allrows[i] = PETSC_FALSE;
      PetscCall(ISGetIndices(isrow[i], &irow[i]));
    }
  }

  if (scall == MAT_REUSE_MATRIX) {
    /* Assumes new rows are same length as the old rows */
    for (PetscInt i = 0; i < ismax; i++) {
      subc = (Mat_SeqBAIJ *)submats[i]->data;

      PetscCheck(subc->mbs == nrow[i] && subc->nbs == ncol[i], PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong size");

      /* Initial matrix as if empty */
      PetscCall(PetscArrayzero(subc->ilen, subc->mbs));

      /* Initial matrix as if empty */
      submats[i]->factortype = C->factortype;

      smat_i = subc->submatis1;

      nrqs        = smat_i->nrqs;
      nrqr        = smat_i->nrqr;
      rbuf1       = smat_i->rbuf1;
      rbuf2       = smat_i->rbuf2;
      rbuf3       = smat_i->rbuf3;
      req_source2 = smat_i->req_source2;

      sbuf1 = smat_i->sbuf1;
      sbuf2 = smat_i->sbuf2;
      ptr   = smat_i->ptr;
      tmp   = smat_i->tmp;
      ctr   = smat_i->ctr;

      pa          = smat_i->pa;
      req_size    = smat_i->req_size;
      req_source1 = smat_i->req_source1;

      allcolumns[i] = smat_i->allcolumns;
      allrows[i]    = smat_i->allrows;
      row2proc[i]   = smat_i->row2proc;
      rmap[i]       = smat_i->rmap;
      cmap[i]       = smat_i->cmap;
    }

    if (!ismax) { /* Get dummy submatrices and retrieve struct submatis1 */
      PetscCheck(submats[0], PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "submats are null, cannot reuse");
      smat_i = (Mat_SubSppt *)submats[0]->data;

      nrqs        = smat_i->nrqs;
      nrqr        = smat_i->nrqr;
      rbuf1       = smat_i->rbuf1;
      rbuf2       = smat_i->rbuf2;
      rbuf3       = smat_i->rbuf3;
      req_source2 = smat_i->req_source2;

      sbuf1 = smat_i->sbuf1;
      sbuf2 = smat_i->sbuf2;
      ptr   = smat_i->ptr;
      tmp   = smat_i->tmp;
      ctr   = smat_i->ctr;

      pa          = smat_i->pa;
      req_size    = smat_i->req_size;
      req_source1 = smat_i->req_source1;

      allcolumns[0] = PETSC_FALSE;
    }
  } else { /* scall == MAT_INITIAL_MATRIX */
    /* Get some new tags to keep the communication clean */
    PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag2));
    PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag3));

    /* evaluate communication - mesg to who, length of mesg, and buffer space
     required. Based on this, buffers are allocated, and data copied into them*/
    PetscCall(PetscCalloc4(size, &w1, size, &w2, size, &w3, size, &w4)); /* mesg size, initialize work vectors */

    for (PetscInt i = 0; i < ismax; i++) {
      jmax   = nrow[i];
      irow_i = irow[i];

      PetscCall(PetscMalloc1(jmax, &row2proc_i));
      row2proc[i] = row2proc_i;

      if (issorted[i]) proc = 0;
      for (PetscInt j = 0; j < jmax; j++) {
        if (!issorted[i]) proc = 0;
        if (allrows[i]) row = j;
        else row = irow_i[j];

        while (row >= c->rangebs[proc + 1]) proc++;
        w4[proc]++;
        row2proc_i[j] = proc; /* map row index to proc */
      }
      for (PetscMPIInt j = 0; j < size; j++) {
        if (w4[j]) {
          w1[j] += w4[j];
          w3[j]++;
          w4[j] = 0;
        }
      }
    }

    nrqs     = 0; /* no of outgoing messages */
    msz      = 0; /* total mesg length (for all procs) */
    w1[rank] = 0; /* no mesg sent to self */
    w3[rank] = 0;
    for (PetscMPIInt i = 0; i < size; i++) {
      if (w1[i]) {
        w2[i] = 1;
        nrqs++;
      } /* there exists a message to proc i */
    }
    PetscCall(PetscMalloc1(nrqs, &pa)); /*(proc -array)*/
    for (PetscMPIInt i = 0, j = 0; i < size; i++) {
      if (w1[i]) pa[j++] = i;
    }

    /* Each message would have a header = 1 + 2*(no of IS) + data */
    for (PetscMPIInt i = 0; i < nrqs; i++) {
      PetscMPIInt j = pa[i];
      w1[j] += w2[j] + 2 * w3[j];
      msz += w1[j];
    }
    PetscCall(PetscInfo(0, "Number of outgoing messages %d Total message length %" PetscInt_FMT "\n", nrqs, msz));

    /* Determine the number of messages to expect, their lengths, from from-ids */
    PetscCall(PetscGatherNumberOfMessages(comm, w2, w1, &nrqr));
    PetscCall(PetscGatherMessageLengths(comm, nrqs, nrqr, w1, &onodes1, &olengths1));

    /* Now post the Irecvs corresponding to these messages */
    PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag0));
    PetscCall(PetscPostIrecvInt(comm, tag0, nrqr, onodes1, olengths1, &rbuf1, &r_waits1));

    /* Allocate Memory for outgoing messages */
    PetscCall(PetscMalloc4(size, &sbuf1, size, &ptr, 2 * msz, &tmp, size, &ctr));
    PetscCall(PetscArrayzero(sbuf1, size));
    PetscCall(PetscArrayzero(ptr, size));

    {
      PetscInt   *iptr = tmp;
      PetscMPIInt k    = 0;
      for (PetscMPIInt i = 0; i < nrqs; i++) {
        PetscMPIInt j = pa[i];
        iptr += k;
        sbuf1[j] = iptr;
        k        = w1[j];
      }
    }

    /* Form the outgoing messages. Initialize the header space */
    for (PetscMPIInt i = 0; i < nrqs; i++) {
      PetscMPIInt j = pa[i];

      sbuf1[j][0] = 0;
      PetscCall(PetscArrayzero(sbuf1[j] + 1, 2 * w3[j]));
      ptr[j] = sbuf1[j] + 2 * w3[j] + 1;
    }

    /* Parse the isrow and copy data into outbuf */
    for (PetscInt i = 0; i < ismax; i++) {
      row2proc_i = row2proc[i];
      PetscCall(PetscArrayzero(ctr, size));
      irow_i = irow[i];
      jmax   = nrow[i];
      for (PetscInt j = 0; j < jmax; j++) { /* parse the indices of each IS */
        proc = row2proc_i[j];
        if (allrows[i]) row = j;
        else row = irow_i[j];

        if (proc != rank) { /* copy to the outgoing buf*/
          ctr[proc]++;
          *ptr[proc] = row;
          ptr[proc]++;
        }
      }
      /* Update the headers for the current IS */
      for (PetscMPIInt j = 0; j < size; j++) { /* Can Optimise this loop too */
        if ((ctr_j = ctr[j])) {
          PetscInt k;

          sbuf1_j            = sbuf1[j];
          k                  = ++sbuf1_j[0];
          sbuf1_j[2 * k]     = ctr_j;
          sbuf1_j[2 * k - 1] = i;
        }
      }
    }

    /*  Now  post the sends */
    PetscCall(PetscMalloc1(nrqs, &s_waits1));
    for (PetscMPIInt i = 0; i < nrqs; ++i) {
      PetscMPIInt j = pa[i];
      PetscCallMPI(MPIU_Isend(sbuf1[j], w1[j], MPIU_INT, j, tag0, comm, s_waits1 + i));
    }

    /* Post Receives to capture the buffer size */
    PetscCall(PetscMalloc1(nrqs, &r_waits2));
    PetscCall(PetscMalloc3(nrqs, &req_source2, nrqs, &rbuf2, nrqs, &rbuf3));
    if (nrqs) rbuf2[0] = tmp + msz;
    for (PetscMPIInt i = 1; i < nrqs; ++i) rbuf2[i] = rbuf2[i - 1] + w1[pa[i - 1]];
    for (PetscMPIInt i = 0; i < nrqs; ++i) {
      PetscMPIInt j = pa[i];
      PetscCallMPI(MPIU_Irecv(rbuf2[i], w1[j], MPIU_INT, j, tag2, comm, r_waits2 + i));
    }

    /* Send to other procs the buf size they should allocate */
    /* Receive messages*/
    PetscCall(PetscMalloc1(nrqr, &s_waits2));
    PetscCall(PetscMalloc3(nrqr, &sbuf2, nrqr, &req_size, nrqr, &req_source1));

    PetscCallMPI(MPI_Waitall(nrqr, r_waits1, MPI_STATUSES_IGNORE));
    for (PetscMPIInt i = 0; i < nrqr; ++i) {
      req_size[i] = 0;
      rbuf1_i     = rbuf1[i];
      start       = 2 * rbuf1_i[0] + 1;
      end         = olengths1[i];
      PetscCall(PetscMalloc1(end, &sbuf2[i]));
      sbuf2_i = sbuf2[i];
      for (PetscInt j = start; j < end; j++) {
        row        = rbuf1_i[j] - rstart;
        ncols      = a_i[row + 1] - a_i[row] + b_i[row + 1] - b_i[row];
        sbuf2_i[j] = ncols;
        req_size[i] += ncols;
      }
      req_source1[i] = onodes1[i];
      /* form the header */
      sbuf2_i[0] = req_size[i];
      for (PetscInt j = 1; j < start; j++) sbuf2_i[j] = rbuf1_i[j];

      PetscCallMPI(MPIU_Isend(sbuf2_i, end, MPIU_INT, req_source1[i], tag2, comm, s_waits2 + i));
    }
    PetscCall(PetscFree(onodes1));
    PetscCall(PetscFree(olengths1));

    PetscCall(PetscFree(r_waits1));
    PetscCall(PetscFree4(w1, w2, w3, w4));

    /* Receive messages*/
    PetscCall(PetscMalloc1(nrqs, &r_waits3));

    PetscCallMPI(MPI_Waitall(nrqs, r_waits2, MPI_STATUSES_IGNORE));
    for (PetscMPIInt i = 0; i < nrqs; ++i) {
      PetscCall(PetscMalloc1(rbuf2[i][0], &rbuf3[i]));
      req_source2[i] = pa[i];
      PetscCallMPI(MPIU_Irecv(rbuf3[i], rbuf2[i][0], MPIU_INT, req_source2[i], tag3, comm, r_waits3 + i));
    }
    PetscCall(PetscFree(r_waits2));

    /* Wait on sends1 and sends2 */
    PetscCallMPI(MPI_Waitall(nrqs, s_waits1, MPI_STATUSES_IGNORE));
    PetscCallMPI(MPI_Waitall(nrqr, s_waits2, MPI_STATUSES_IGNORE));
    PetscCall(PetscFree(s_waits1));
    PetscCall(PetscFree(s_waits2));

    /* Now allocate sending buffers for a->j, and send them off */
    PetscCall(PetscMalloc1(nrqr, &sbuf_aj));
    jcnt = 0;
    for (PetscMPIInt i = 0; i < nrqr; i++) jcnt += req_size[i];
    if (nrqr) PetscCall(PetscMalloc1(jcnt, &sbuf_aj[0]));
    for (PetscMPIInt i = 1; i < nrqr; i++) sbuf_aj[i] = sbuf_aj[i - 1] + req_size[i - 1];

    PetscCall(PetscMalloc1(nrqr, &s_waits3));
    {
      for (PetscMPIInt i = 0; i < nrqr; i++) {
        rbuf1_i   = rbuf1[i];
        sbuf_aj_i = sbuf_aj[i];
        ct1       = 2 * rbuf1_i[0] + 1;
        ct2       = 0;
        for (PetscInt j = 1, max1 = rbuf1_i[0]; j <= max1; j++) {
          kmax = rbuf1[i][2 * j];
          for (PetscInt k = 0; k < kmax; k++, ct1++) {
            PetscInt l;
            row    = rbuf1_i[ct1] - rstart;
            nzA    = a_i[row + 1] - a_i[row];
            nzB    = b_i[row + 1] - b_i[row];
            ncols  = nzA + nzB;
            cworkA = PetscSafePointerPlusOffset(a_j, a_i[row]);
            cworkB = PetscSafePointerPlusOffset(b_j, b_i[row]);

            /* load the column indices for this row into cols */
            cols = sbuf_aj_i + ct2;
            for (l = 0; l < nzB; l++) {
              if ((ctmp = bmap[cworkB[l]]) < cstart) cols[l] = ctmp;
              else break;
            }
            imark = l;
            for (l = 0; l < nzA; l++) cols[imark + l] = cstart + cworkA[l];
            for (l = imark; l < nzB; l++) cols[nzA + l] = bmap[cworkB[l]];
            ct2 += ncols;
          }
        }
        PetscCallMPI(MPIU_Isend(sbuf_aj_i, req_size[i], MPIU_INT, req_source1[i], tag3, comm, s_waits3 + i));
      }
    }

    /* create col map: global col of C -> local col of submatrices */
#if defined(PETSC_USE_CTABLE)
    for (PetscInt i = 0; i < ismax; i++) {
      if (!allcolumns[i]) {
        PetscCall(PetscHMapICreateWithSize(ncol[i], cmap + i));

        jmax   = ncol[i];
        icol_i = icol[i];
        cmap_i = cmap[i];
        for (PetscInt j = 0; j < jmax; j++) PetscCall(PetscHMapISet(cmap[i], icol_i[j] + 1, j + 1));
      } else cmap[i] = NULL;
    }
#else
    for (PetscInt i = 0; i < ismax; i++) {
      if (!allcolumns[i]) {
        PetscCall(PetscCalloc1(c->Nbs, &cmap[i]));
        jmax   = ncol[i];
        icol_i = icol[i];
        cmap_i = cmap[i];
        for (PetscInt j = 0; j < jmax; j++) cmap_i[icol_i[j]] = j + 1;
      } else cmap[i] = NULL;
    }
#endif

    /* Create lens which is required for MatCreate... */
    jcnt = 0;
    for (PetscInt i = 0; i < ismax; i++) jcnt += nrow[i];
    PetscCall(PetscMalloc1(ismax, &lens));
    if (ismax) PetscCall(PetscCalloc1(jcnt, &lens[0]));
    for (PetscInt i = 1; i < ismax; i++) lens[i] = PetscSafePointerPlusOffset(lens[i - 1], nrow[i - 1]);

    /* Update lens from local data */
    for (PetscInt i = 0; i < ismax; i++) {
      row2proc_i = row2proc[i];
      jmax       = nrow[i];
      if (!allcolumns[i]) cmap_i = cmap[i];
      irow_i = irow[i];
      lens_i = lens[i];
      for (PetscInt j = 0; j < jmax; j++) {
        if (allrows[i]) row = j;
        else row = irow_i[j]; /* global blocked row of C */

        proc = row2proc_i[j];
        if (proc == rank) {
          /* Get indices from matA and then from matB */
#if defined(PETSC_USE_CTABLE)
          PetscInt tt;
#endif
          row    = row - rstart;
          nzA    = a_i[row + 1] - a_i[row];
          nzB    = b_i[row + 1] - b_i[row];
          cworkA = a_j + a_i[row];
          cworkB = PetscSafePointerPlusOffset(b_j, b_i[row]);

          if (!allcolumns[i]) {
#if defined(PETSC_USE_CTABLE)
            for (PetscInt k = 0; k < nzA; k++) {
              PetscCall(PetscHMapIGetWithDefault(cmap_i, cstart + cworkA[k] + 1, 0, &tt));
              if (tt) lens_i[j]++;
            }
            for (PetscInt k = 0; k < nzB; k++) {
              PetscCall(PetscHMapIGetWithDefault(cmap_i, bmap[cworkB[k]] + 1, 0, &tt));
              if (tt) lens_i[j]++;
            }

#else
            for (PetscInt k = 0; k < nzA; k++) {
              if (cmap_i[cstart + cworkA[k]]) lens_i[j]++;
            }
            for (PetscInt k = 0; k < nzB; k++) {
              if (cmap_i[bmap[cworkB[k]]]) lens_i[j]++;
            }
#endif
          } else { /* allcolumns */
            lens_i[j] = nzA + nzB;
          }
        }
      }
    }

    /* Create row map: global row of C -> local row of submatrices */
    for (PetscInt i = 0; i < ismax; i++) {
      if (!allrows[i]) {
#if defined(PETSC_USE_CTABLE)
        PetscCall(PetscHMapICreateWithSize(nrow[i], rmap + i));
        irow_i = irow[i];
        jmax   = nrow[i];
        for (PetscInt j = 0; j < jmax; j++) {
          if (allrows[i]) {
            PetscCall(PetscHMapISet(rmap[i], j + 1, j + 1));
          } else {
            PetscCall(PetscHMapISet(rmap[i], irow_i[j] + 1, j + 1));
          }
        }
#else
        PetscCall(PetscCalloc1(c->Mbs, &rmap[i]));
        rmap_i = rmap[i];
        irow_i = irow[i];
        jmax   = nrow[i];
        for (PetscInt j = 0; j < jmax; j++) {
          if (allrows[i]) rmap_i[j] = j;
          else rmap_i[irow_i[j]] = j;
        }
#endif
      } else rmap[i] = NULL;
    }

    /* Update lens from offproc data */
    {
      PetscInt *rbuf2_i, *rbuf3_i, *sbuf1_i;

      PetscCallMPI(MPI_Waitall(nrqs, r_waits3, MPI_STATUSES_IGNORE));
      for (tmp2 = 0; tmp2 < nrqs; tmp2++) {
        sbuf1_i = sbuf1[pa[tmp2]];
        jmax    = sbuf1_i[0];
        ct1     = 2 * jmax + 1;
        ct2     = 0;
        rbuf2_i = rbuf2[tmp2];
        rbuf3_i = rbuf3[tmp2];
        for (PetscInt j = 1; j <= jmax; j++) {
          is_no  = sbuf1_i[2 * j - 1];
          max1   = sbuf1_i[2 * j];
          lens_i = lens[is_no];
          if (!allcolumns[is_no]) cmap_i = cmap[is_no];
          rmap_i = rmap[is_no];
          for (PetscInt k = 0; k < max1; k++, ct1++) {
            if (allrows[is_no]) {
              row = sbuf1_i[ct1];
            } else {
#if defined(PETSC_USE_CTABLE)
              PetscCall(PetscHMapIGetWithDefault(rmap_i, sbuf1_i[ct1] + 1, 0, &row));
              row--;
              PetscCheck(row >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "row not found in table");
#else
              row = rmap_i[sbuf1_i[ct1]]; /* the val in the new matrix to be */
#endif
            }
            max2 = rbuf2_i[ct1];
            for (PetscInt l = 0; l < max2; l++, ct2++) {
              if (!allcolumns[is_no]) {
#if defined(PETSC_USE_CTABLE)
                PetscCall(PetscHMapIGetWithDefault(cmap_i, rbuf3_i[ct2] + 1, 0, &tcol));
#else
                tcol = cmap_i[rbuf3_i[ct2]];
#endif
                if (tcol) lens_i[row]++;
              } else {         /* allcolumns */
                lens_i[row]++; /* lens_i[row] += max2 ? */
              }
            }
          }
        }
      }
    }
    PetscCall(PetscFree(r_waits3));
    PetscCallMPI(MPI_Waitall(nrqr, s_waits3, MPI_STATUSES_IGNORE));
    PetscCall(PetscFree(s_waits3));

    /* Create the submatrices */
    for (PetscInt i = 0; i < ismax; i++) {
      PetscInt bs_tmp;
      if (ijonly) bs_tmp = 1;
      else bs_tmp = bs;

      PetscCall(MatCreate(PETSC_COMM_SELF, submats + i));
      PetscCall(MatSetSizes(submats[i], nrow[i] * bs_tmp, ncol[i] * bs_tmp, PETSC_DETERMINE, PETSC_DETERMINE));

      PetscCall(MatSetType(submats[i], sym ? ((PetscObject)A)->type_name : MATSEQBAIJ));
      PetscCall(MatSeqBAIJSetPreallocation(submats[i], bs_tmp, 0, lens[i]));
      PetscCall(MatSeqSBAIJSetPreallocation(submats[i], bs_tmp, 0, lens[i])); /* this subroutine is used by SBAIJ routines */

      /* create struct Mat_SubSppt and attached it to submat */
      PetscCall(PetscNew(&smat_i));
      subc            = (Mat_SeqBAIJ *)submats[i]->data;
      subc->submatis1 = smat_i;

      smat_i->destroy          = submats[i]->ops->destroy;
      submats[i]->ops->destroy = MatDestroySubMatrix_SeqBAIJ;
      submats[i]->factortype   = C->factortype;

      smat_i->id          = i;
      smat_i->nrqs        = nrqs;
      smat_i->nrqr        = nrqr;
      smat_i->rbuf1       = rbuf1;
      smat_i->rbuf2       = rbuf2;
      smat_i->rbuf3       = rbuf3;
      smat_i->sbuf2       = sbuf2;
      smat_i->req_source2 = req_source2;

      smat_i->sbuf1 = sbuf1;
      smat_i->ptr   = ptr;
      smat_i->tmp   = tmp;
      smat_i->ctr   = ctr;

      smat_i->pa          = pa;
      smat_i->req_size    = req_size;
      smat_i->req_source1 = req_source1;

      smat_i->allcolumns = allcolumns[i];
      smat_i->allrows    = allrows[i];
      smat_i->singleis   = PETSC_FALSE;
      smat_i->row2proc   = row2proc[i];
      smat_i->rmap       = rmap[i];
      smat_i->cmap       = cmap[i];
    }

    if (!ismax) { /* Create dummy submats[0] for reuse struct subc */
      PetscCall(MatCreate(PETSC_COMM_SELF, &submats[0]));
      PetscCall(MatSetSizes(submats[0], 0, 0, PETSC_DETERMINE, PETSC_DETERMINE));
      PetscCall(MatSetType(submats[0], MATDUMMY));

      /* create struct Mat_SubSppt and attached it to submat */
      PetscCall(PetscNew(&smat_i));
      submats[0]->data = (void *)smat_i;

      smat_i->destroy          = submats[0]->ops->destroy;
      submats[0]->ops->destroy = MatDestroySubMatrix_Dummy;
      submats[0]->factortype   = C->factortype;

      smat_i->id          = 0;
      smat_i->nrqs        = nrqs;
      smat_i->nrqr        = nrqr;
      smat_i->rbuf1       = rbuf1;
      smat_i->rbuf2       = rbuf2;
      smat_i->rbuf3       = rbuf3;
      smat_i->sbuf2       = sbuf2;
      smat_i->req_source2 = req_source2;

      smat_i->sbuf1 = sbuf1;
      smat_i->ptr   = ptr;
      smat_i->tmp   = tmp;
      smat_i->ctr   = ctr;

      smat_i->pa          = pa;
      smat_i->req_size    = req_size;
      smat_i->req_source1 = req_source1;

      smat_i->allcolumns = PETSC_FALSE;
      smat_i->singleis   = PETSC_FALSE;
      smat_i->row2proc   = NULL;
      smat_i->rmap       = NULL;
      smat_i->cmap       = NULL;
    }

    if (ismax) PetscCall(PetscFree(lens[0]));
    PetscCall(PetscFree(lens));
    if (sbuf_aj) {
      PetscCall(PetscFree(sbuf_aj[0]));
      PetscCall(PetscFree(sbuf_aj));
    }

  } /* endof scall == MAT_INITIAL_MATRIX */

  /* Post recv matrix values */
  if (!ijonly) {
    PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag4));
    PetscCall(PetscMalloc1(nrqs, &rbuf4));
    PetscCall(PetscMalloc1(nrqs, &r_waits4));
    for (PetscMPIInt i = 0; i < nrqs; ++i) {
      PetscCall(PetscMalloc1(rbuf2[i][0] * bs2, &rbuf4[i]));
      PetscCallMPI(MPIU_Irecv(rbuf4[i], rbuf2[i][0] * bs2, MPIU_SCALAR, req_source2[i], tag4, comm, r_waits4 + i));
    }

    /* Allocate sending buffers for a->a, and send them off */
    PetscCall(PetscMalloc1(nrqr, &sbuf_aa));
    jcnt = 0;
    for (PetscMPIInt i = 0; i < nrqr; i++) jcnt += req_size[i];
    if (nrqr) PetscCall(PetscMalloc1(jcnt * bs2, &sbuf_aa[0]));
    for (PetscMPIInt i = 1; i < nrqr; i++) sbuf_aa[i] = sbuf_aa[i - 1] + req_size[i - 1] * bs2;

    PetscCall(PetscMalloc1(nrqr, &s_waits4));

    for (PetscMPIInt i = 0; i < nrqr; i++) {
      rbuf1_i   = rbuf1[i];
      sbuf_aa_i = sbuf_aa[i];
      ct1       = 2 * rbuf1_i[0] + 1;
      ct2       = 0;
      for (PetscInt j = 1, max1 = rbuf1_i[0]; j <= max1; j++) {
        kmax = rbuf1_i[2 * j];
        for (PetscInt k = 0; k < kmax; k++, ct1++) {
          PetscInt l;

          row    = rbuf1_i[ct1] - rstart;
          nzA    = a_i[row + 1] - a_i[row];
          nzB    = b_i[row + 1] - b_i[row];
          ncols  = nzA + nzB;
          cworkB = PetscSafePointerPlusOffset(b_j, b_i[row]);
          vworkA = PetscSafePointerPlusOffset(a_a, a_i[row] * bs2);
          vworkB = PetscSafePointerPlusOffset(b_a, b_i[row] * bs2);

          /* load the column values for this row into vals*/
          vals = sbuf_aa_i + ct2 * bs2;
          for (l = 0; l < nzB; l++) {
            if ((bmap[cworkB[l]]) < cstart) PetscCall(PetscArraycpy(vals + l * bs2, vworkB + l * bs2, bs2));
            else break;
          }
          imark = l;
          for (l = 0; l < nzA; l++) PetscCall(PetscArraycpy(vals + (imark + l) * bs2, vworkA + l * bs2, bs2));
          for (l = imark; l < nzB; l++) PetscCall(PetscArraycpy(vals + (nzA + l) * bs2, vworkB + l * bs2, bs2));

          ct2 += ncols;
        }
      }
      PetscCallMPI(MPIU_Isend(sbuf_aa_i, req_size[i] * bs2, MPIU_SCALAR, req_source1[i], tag4, comm, s_waits4 + i));
    }
  }

  /* Assemble the matrices */
  /* First assemble the local rows */
  for (PetscInt i = 0; i < ismax; i++) {
    row2proc_i = row2proc[i];
    subc       = (Mat_SeqBAIJ *)submats[i]->data;
    imat_ilen  = subc->ilen;
    imat_j     = subc->j;
    imat_i     = subc->i;
    imat_a     = subc->a;

    if (!allcolumns[i]) cmap_i = cmap[i];
    rmap_i = rmap[i];
    irow_i = irow[i];
    jmax   = nrow[i];
    for (PetscInt j = 0; j < jmax; j++) {
      if (allrows[i]) row = j;
      else row = irow_i[j];
      proc = row2proc_i[j];

      if (proc == rank) {
        row    = row - rstart;
        nzA    = a_i[row + 1] - a_i[row];
        nzB    = b_i[row + 1] - b_i[row];
        cworkA = a_j + a_i[row];
        cworkB = PetscSafePointerPlusOffset(b_j, b_i[row]);
        if (!ijonly) {
          vworkA = a_a + a_i[row] * bs2;
          vworkB = PetscSafePointerPlusOffset(b_a, b_i[row] * bs2);
        }

        if (allrows[i]) {
          row = row + rstart;
        } else {
#if defined(PETSC_USE_CTABLE)
          PetscCall(PetscHMapIGetWithDefault(rmap_i, row + rstart + 1, 0, &row));
          row--;

          PetscCheck(row >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "row not found in table");
#else
          row = rmap_i[row + rstart];
#endif
        }
        mat_i = imat_i[row];
        if (!ijonly) mat_a = PetscSafePointerPlusOffset(imat_a, mat_i * bs2);
        mat_j = PetscSafePointerPlusOffset(imat_j, mat_i);
        ilen  = imat_ilen[row];

        /* load the column indices for this row into cols*/
        if (!allcolumns[i]) {
          PetscInt l;

          for (l = 0; l < nzB; l++) {
            if ((ctmp = bmap[cworkB[l]]) < cstart) {
#if defined(PETSC_USE_CTABLE)
              PetscCall(PetscHMapIGetWithDefault(cmap_i, ctmp + 1, 0, &tcol));
              if (tcol) {
#else
              if ((tcol = cmap_i[ctmp])) {
#endif
                *mat_j++ = tcol - 1;
                PetscCall(PetscArraycpy(mat_a, vworkB + l * bs2, bs2));
                mat_a += bs2;
                ilen++;
              }
            } else break;
          }
          imark = l;
          for (PetscInt l = 0; l < nzA; l++) {
#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(cmap_i, cstart + cworkA[l] + 1, 0, &tcol));
            if (tcol) {
#else
            if ((tcol = cmap_i[cstart + cworkA[l]])) {
#endif
              *mat_j++ = tcol - 1;
              if (!ijonly) {
                PetscCall(PetscArraycpy(mat_a, vworkA + l * bs2, bs2));
                mat_a += bs2;
              }
              ilen++;
            }
          }
          for (l = imark; l < nzB; l++) {
#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(cmap_i, bmap[cworkB[l]] + 1, 0, &tcol));
            if (tcol) {
#else
            if ((tcol = cmap_i[bmap[cworkB[l]]])) {
#endif
              *mat_j++ = tcol - 1;
              if (!ijonly) {
                PetscCall(PetscArraycpy(mat_a, vworkB + l * bs2, bs2));
                mat_a += bs2;
              }
              ilen++;
            }
          }
        } else { /* allcolumns */
          PetscInt l;
          for (l = 0; l < nzB; l++) {
            if ((ctmp = bmap[cworkB[l]]) < cstart) {
              *mat_j++ = ctmp;
              PetscCall(PetscArraycpy(mat_a, vworkB + l * bs2, bs2));
              mat_a += bs2;
              ilen++;
            } else break;
          }
          imark = l;
          for (l = 0; l < nzA; l++) {
            *mat_j++ = cstart + cworkA[l];
            if (!ijonly) {
              PetscCall(PetscArraycpy(mat_a, vworkA + l * bs2, bs2));
              mat_a += bs2;
            }
            ilen++;
          }
          for (l = imark; l < nzB; l++) {
            *mat_j++ = bmap[cworkB[l]];
            if (!ijonly) {
              PetscCall(PetscArraycpy(mat_a, vworkB + l * bs2, bs2));
              mat_a += bs2;
            }
            ilen++;
          }
        }
        imat_ilen[row] = ilen;
      }
    }
  }

  /* Now assemble the off proc rows */
  if (!ijonly) PetscCallMPI(MPI_Waitall(nrqs, r_waits4, MPI_STATUSES_IGNORE));
  for (tmp2 = 0; tmp2 < nrqs; tmp2++) {
    sbuf1_i = sbuf1[pa[tmp2]];
    jmax    = sbuf1_i[0];
    ct1     = 2 * jmax + 1;
    ct2     = 0;
    rbuf2_i = rbuf2[tmp2];
    rbuf3_i = rbuf3[tmp2];
    if (!ijonly) rbuf4_i = rbuf4[tmp2];
    for (PetscInt j = 1; j <= jmax; j++) {
      is_no  = sbuf1_i[2 * j - 1];
      rmap_i = rmap[is_no];
      if (!allcolumns[is_no]) cmap_i = cmap[is_no];
      subc      = (Mat_SeqBAIJ *)submats[is_no]->data;
      imat_ilen = subc->ilen;
      imat_j    = subc->j;
      imat_i    = subc->i;
      if (!ijonly) imat_a = subc->a;
      max1 = sbuf1_i[2 * j];
      for (PetscInt k = 0; k < max1; k++, ct1++) { /* for each recved block row */
        row = sbuf1_i[ct1];

        if (allrows[is_no]) {
          row = sbuf1_i[ct1];
        } else {
#if defined(PETSC_USE_CTABLE)
          PetscCall(PetscHMapIGetWithDefault(rmap_i, row + 1, 0, &row));
          row--;
          PetscCheck(row >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "row not found in table");
#else
          row = rmap_i[row];
#endif
        }
        ilen  = imat_ilen[row];
        mat_i = imat_i[row];
        if (!ijonly) mat_a = imat_a + mat_i * bs2;
        mat_j = imat_j + mat_i;
        max2  = rbuf2_i[ct1];
        if (!allcolumns[is_no]) {
          for (PetscInt l = 0; l < max2; l++, ct2++) {
#if defined(PETSC_USE_CTABLE)
            PetscCall(PetscHMapIGetWithDefault(cmap_i, rbuf3_i[ct2] + 1, 0, &tcol));
#else
            tcol = cmap_i[rbuf3_i[ct2]];
#endif
            if (tcol) {
              *mat_j++ = tcol - 1;
              if (!ijonly) {
                PetscCall(PetscArraycpy(mat_a, rbuf4_i + ct2 * bs2, bs2));
                mat_a += bs2;
              }
              ilen++;
            }
          }
        } else { /* allcolumns */
          for (PetscInt l = 0; l < max2; l++, ct2++) {
            *mat_j++ = rbuf3_i[ct2]; /* same global column index of C */
            if (!ijonly) {
              PetscCall(PetscArraycpy(mat_a, rbuf4_i + ct2 * bs2, bs2));
              mat_a += bs2;
            }
            ilen++;
          }
        }
        imat_ilen[row] = ilen;
      }
    }
  }

  if (!iscsorted) { /* sort column indices of the rows */
    MatScalar *work;

    PetscCall(PetscMalloc1(bs2, &work));
    for (PetscInt i = 0; i < ismax; i++) {
      subc      = (Mat_SeqBAIJ *)submats[i]->data;
      imat_ilen = subc->ilen;
      imat_j    = subc->j;
      imat_i    = subc->i;
      if (!ijonly) imat_a = subc->a;
      if (allcolumns[i]) continue;

      jmax = nrow[i];
      for (PetscInt j = 0; j < jmax; j++) {
        mat_i = imat_i[j];
        mat_j = imat_j + mat_i;
        ilen  = imat_ilen[j];
        if (ijonly) {
          PetscCall(PetscSortInt(ilen, mat_j));
        } else {
          mat_a = imat_a + mat_i * bs2;
          PetscCall(PetscSortIntWithDataArray(ilen, mat_j, mat_a, bs2 * sizeof(MatScalar), work));
        }
      }
    }
    PetscCall(PetscFree(work));
  }

  if (!ijonly) {
    PetscCall(PetscFree(r_waits4));
    PetscCallMPI(MPI_Waitall(nrqr, s_waits4, MPI_STATUSES_IGNORE));
    PetscCall(PetscFree(s_waits4));
  }

  /* Restore the indices */
  for (PetscInt i = 0; i < ismax; i++) {
    if (!allrows[i]) PetscCall(ISRestoreIndices(isrow[i], irow + i));
    if (!allcolumns[i]) PetscCall(ISRestoreIndices(iscol[i], icol + i));
  }

  for (PetscInt i = 0; i < ismax; i++) {
    PetscCall(MatAssemblyBegin(submats[i], MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(submats[i], MAT_FINAL_ASSEMBLY));
  }

  PetscCall(PetscFree5(*(PetscInt ***)&irow, *(PetscInt ***)&icol, nrow, ncol, issorted));
  PetscCall(PetscFree5(row2proc, cmap, rmap, allcolumns, allrows));

  if (!ijonly) {
    if (sbuf_aa) {
      PetscCall(PetscFree(sbuf_aa[0]));
      PetscCall(PetscFree(sbuf_aa));
    }

    for (PetscMPIInt i = 0; i < nrqs; ++i) PetscCall(PetscFree(rbuf4[i]));
    PetscCall(PetscFree(rbuf4));
  }
  c->ijonly = PETSC_FALSE; /* set back to the default */
  PetscFunctionReturn(PETSC_SUCCESS);
}