xref: /petsc/src/mat/impls/sbaij/mpi/sbaijov.c (revision 2235c4e21094f57f73a5851b0c05b8ecf6dffc6d)

/*
   Routines to compute overlapping regions of a parallel MPI matrix.
   Used for finding submatrices that were shared across processors.
*/
#include <../src/mat/impls/sbaij/mpi/mpisbaij.h>
#include <petscbt.h>

static PetscErrorCode MatIncreaseOverlap_MPISBAIJ_Once(Mat, PetscInt, IS *);
static PetscErrorCode MatIncreaseOverlap_MPISBAIJ_Local(Mat, PetscInt *, PetscInt, PetscInt *, PetscBT *);

PetscErrorCode MatIncreaseOverlap_MPISBAIJ(Mat C, PetscInt is_max, IS is[], PetscInt ov)
{
  PetscInt        i, N = C->cmap->N, bs = C->rmap->bs, M = C->rmap->N, Mbs = M / bs, *nidx, isz, iov;
  IS             *is_new, *is_row;
  Mat            *submats;
  Mat_MPISBAIJ   *c = (Mat_MPISBAIJ *)C->data;
  Mat_SeqSBAIJ   *asub_i;
  PetscBT         table;
  PetscInt       *ai, brow, nz, nis, l, nmax, nstages, max_no, pos;
  const PetscInt *idx;
  PetscBool       flg;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(is_max, &is_new));
  /* Convert the indices into block format */
  PetscCall(ISCompressIndicesGeneral(N, C->rmap->n, bs, is_max, is, is_new));
  PetscCheck(ov >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap specified");

  /*  previous non-scalable implementation  */
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsHasName(NULL, NULL, "-IncreaseOverlap_old", &flg));
  if (flg) { /* previous non-scalable implementation */
    printf("use previous non-scalable implementation...\n");
    for (i = 0; i < ov; ++i) PetscCall(MatIncreaseOverlap_MPISBAIJ_Once(C, is_max, is_new));
  } else { /* implementation using modified BAIJ routines */

    PetscCall(PetscMalloc1(Mbs + 1, &nidx));
    PetscCall(PetscBTCreate(Mbs, &table)); /* for column search */

    /* Create is_row */
    PetscCall(PetscMalloc1(is_max, &is_row));
    PetscCall(ISCreateStride(PETSC_COMM_SELF, Mbs, 0, 1, &is_row[0]));

    for (i = 1; i < is_max; i++) is_row[i] = is_row[0]; /* reuse is_row[0] */

    /* Allocate memory to hold all the submatrices - Modified from MatCreateSubMatrices_MPIBAIJ() */
    PetscCall(PetscMalloc1(is_max + 1, &submats));

    /* Determine the number of stages through which submatrices are done */
    nmax = 20 * 1000000 / (c->Nbs * sizeof(PetscInt));
    if (!nmax) nmax = 1;
    nstages = is_max / nmax + ((is_max % nmax) ? 1 : 0);

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

    {
      const PetscObject obj = (PetscObject)c->A;
      size_t            new_len, cur_len, max_len;

      PetscCall(PetscStrlen(MATSEQBAIJ, &new_len));
      PetscCall(PetscStrlen(MATSEQSBAIJ, &cur_len));
      max_len = PetscMax(cur_len, new_len) + 1;
      PetscCall(PetscRealloc(max_len * sizeof(*obj->type_name), &obj->type_name));
      /* The resulting submatrices should be BAIJ, not SBAIJ, hence we change this value to
         trigger that */
      for (iov = 0; iov < ov; ++iov) {
        /* 1) Get submats for column search */
        PetscCall(PetscStrncpy(obj->type_name, MATSEQBAIJ, max_len));
        for (i = 0, pos = 0; i < nstages; i++) {
          if (pos + nmax <= is_max) max_no = nmax;
          else if (pos == is_max) max_no = 0;
          else max_no = is_max - pos;
          c->ijonly = PETSC_TRUE; /* only matrix data structures are requested */

          PetscCall(MatCreateSubMatrices_MPIBAIJ_local(C, max_no, is_row + pos, is_new + pos, MAT_INITIAL_MATRIX, submats + pos, PETSC_TRUE));
          pos += max_no;
        }
        PetscCall(PetscStrncpy(obj->type_name, MATSEQSBAIJ, max_len));

        /* 2) Row search */
        PetscCall(MatIncreaseOverlap_MPIBAIJ_Once(C, is_max, is_new));

        /* 3) Column search */
        for (i = 0; i < is_max; i++) {
          asub_i = (Mat_SeqSBAIJ *)submats[i]->data;
          ai     = asub_i->i;

          /* put is_new obtained from MatIncreaseOverlap_MPIBAIJ() to table */
          PetscCall(PetscBTMemzero(Mbs, table));

          PetscCall(ISGetIndices(is_new[i], &idx));
          PetscCall(ISGetLocalSize(is_new[i], &nis));
          for (l = 0; l < nis; l++) {
            PetscCall(PetscBTSet(table, idx[l]));
            nidx[l] = idx[l];
          }
          isz = nis;

          /* add column entries to table */
          for (brow = 0; brow < Mbs; brow++) {
            nz = ai[brow + 1] - ai[brow];
            if (nz) {
              if (!PetscBTLookupSet(table, brow)) nidx[isz++] = brow;
            }
          }
          PetscCall(ISRestoreIndices(is_new[i], &idx));
          PetscCall(ISDestroy(&is_new[i]));

          /* create updated is_new */
          PetscCall(ISCreateGeneral(PETSC_COMM_SELF, isz, nidx, PETSC_COPY_VALUES, is_new + i));
        }

        /* Free tmp spaces */
        for (i = 0; i < is_max; i++) PetscCall(MatDestroy(&submats[i]));
      }

      PetscCall(PetscBTDestroy(&table));
      PetscCall(PetscFree(submats));
      PetscCall(ISDestroy(&is_row[0]));
      PetscCall(PetscFree(is_row));
      PetscCall(PetscFree(nidx));
    }
  }
  for (i = 0; i < is_max; i++) {
    PetscCall(ISDestroy(&is[i]));
    PetscCall(ISGetLocalSize(is_new[i], &nis));
    PetscCall(ISGetIndices(is_new[i], &idx));
    PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)is_new[i]), bs, nis, idx, PETSC_COPY_VALUES, &is[i]));
    PetscCall(ISDestroy(&is_new[i]));
  }
  PetscCall(PetscFree(is_new));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef enum {
  MINE,
  OTHER
} WhoseOwner;
/*  data1, odata1 and odata2 are packed in the format (for communication):
       data[0]          = is_max, no of is
       data[1]          = size of is[0]
        ...
       data[is_max]     = size of is[is_max-1]
       data[is_max + 1] = data(is[0])
        ...
       data[is_max+1+sum(size of is[k]), k=0,...,i-1] = data(is[i])
        ...
   data2 is packed in the format (for creating output is[]):
       data[0]          = is_max, no of is
       data[1]          = size of is[0]
        ...
       data[is_max]     = size of is[is_max-1]
       data[is_max + 1] = data(is[0])
        ...
       data[is_max + 1 + Mbs*i) = data(is[i])
        ...
*/
static PetscErrorCode MatIncreaseOverlap_MPISBAIJ_Once(Mat C, PetscInt is_max, IS is[])
{
  Mat_MPISBAIJ   *c        = (Mat_MPISBAIJ *)C->data;
  PetscMPIInt     proc_end = 0, size, rank, tag1, tag2, *len_s, nrqr, nrqs, *id_r1, *len_r1, flag, *iwork;
  const PetscInt *idx_i;
  PetscInt        idx, isz, col, *n, *data1, **data1_start, *data2, *data2_i, *data, *data_i, len;
  PetscInt        Mbs, i, j, k, *odata1, *odata2;
  PetscInt      **odata2_ptr, *ctable = NULL, *btable, len_max, len_est;
  PetscInt        len_unused, nodata2;
  PetscInt        ois_max; /* max no of is[] in each of processor */
  PetscByte      *t_p;
  MPI_Comm        comm;
  MPI_Request    *s_waits1, *s_waits2, r_req;
  MPI_Status     *s_status, r_status;
  PetscBT        *table; /* mark indices of this processor's is[] */
  PetscBT         table_i;
  PetscBT         otable; /* mark indices of other processors' is[] */
  PetscInt        bs = C->rmap->bs, Bn = c->B->cmap->n, Bnbs = Bn / bs, *Bowners;
  IS              garray_local, garray_gl;

  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));

  /* create tables used in
     step 1: table[i] - mark c->garray of proc [i]
     step 3: table[i] - mark indices of is[i] when whose=MINE
             table[0] - mark incideces of is[] when whose=OTHER */
  len = PetscMax(is_max, size);
  PetscCall(PetscMalloc2(len, &table, (Mbs / PETSC_BITS_PER_BYTE + 1) * len, &t_p));
  for (i = 0; i < len; i++) table[i] = t_p + (Mbs / PETSC_BITS_PER_BYTE + 1) * i;

  PetscCallMPI(MPIU_Allreduce(&is_max, &ois_max, 1, MPIU_INT, MPI_MAX, comm));

  /* 1. Send this processor's is[] to other processors */
  /* allocate spaces */
  PetscCall(PetscMalloc1(is_max, &n));
  len = 0;
  for (i = 0; i < is_max; i++) {
    PetscCall(ISGetLocalSize(is[i], &n[i]));
    len += n[i];
  }
  if (!len) {
    is_max = 0;
  } else {
    len += 1 + is_max; /* max length of data1 for one processor */
  }

  PetscCall(PetscMalloc1(size * len + 1, &data1));
  PetscCall(PetscMalloc1(size, &data1_start));
  for (i = 0; i < size; i++) data1_start[i] = data1 + i * len;

  PetscCall(PetscMalloc4(size, &len_s, size, &btable, size, &iwork, size + 1, &Bowners));

  /* gather c->garray from all processors */
  PetscCall(ISCreateGeneral(comm, Bnbs, c->garray, PETSC_COPY_VALUES, &garray_local));
  PetscCall(ISAllGather(garray_local, &garray_gl));
  PetscCall(ISDestroy(&garray_local));
  PetscCallMPI(MPI_Allgather(&Bnbs, 1, MPIU_INT, Bowners + 1, 1, MPIU_INT, comm));

  Bowners[0] = 0;
  for (i = 0; i < size; i++) Bowners[i + 1] += Bowners[i];

  if (is_max) {
    /* hash table ctable which maps c->row to proc_id) */
    PetscCall(PetscMalloc1(Mbs, &ctable));
    j = 0;
    for (PetscMPIInt proc_id = 0; proc_id < size; proc_id++) {
      for (; j < C->rmap->range[proc_id + 1] / bs; j++) ctable[j] = proc_id;
    }

    /* hash tables marking c->garray */
    PetscCall(ISGetIndices(garray_gl, &idx_i));
    for (i = 0; i < size; i++) {
      table_i = table[i];
      PetscCall(PetscBTMemzero(Mbs, table_i));
      for (j = Bowners[i]; j < Bowners[i + 1]; j++) { /* go through B cols of proc[i]*/
        PetscCall(PetscBTSet(table_i, idx_i[j]));
      }
    }
    PetscCall(ISRestoreIndices(garray_gl, &idx_i));
  } /* if (is_max) */
  PetscCall(ISDestroy(&garray_gl));

  /* evaluate communication - mesg to who, length, and buffer space */
  for (i = 0; i < size; i++) len_s[i] = 0;

  /* header of data1 */
  for (PetscMPIInt proc_id = 0; proc_id < size; proc_id++) {
    iwork[proc_id]        = 0;
    *data1_start[proc_id] = is_max;
    data1_start[proc_id]++;
    for (j = 0; j < is_max; j++) {
      if (proc_id == rank) {
        *data1_start[proc_id] = n[j];
      } else {
        *data1_start[proc_id] = 0;
      }
      data1_start[proc_id]++;
    }
  }

  for (i = 0; i < is_max; i++) {
    PetscCall(ISGetIndices(is[i], &idx_i));
    for (j = 0; j < n[i]; j++) {
      idx                = idx_i[j];
      *data1_start[rank] = idx;
      data1_start[rank]++; /* for local processing */
      PetscCall(PetscMPIIntCast(ctable[idx], &proc_end));
      for (PetscMPIInt proc_id = 0; proc_id <= proc_end; proc_id++) {            /* for others to process */
        if (proc_id == rank) continue;                                           /* done before this loop */
        if (proc_id < proc_end && !PetscBTLookup(table[proc_id], idx)) continue; /* no need for sending idx to [proc_id] */
        *data1_start[proc_id] = idx;
        data1_start[proc_id]++;
        len_s[proc_id]++;
      }
    }
    /* update header data */
    for (PetscMPIInt proc_id = 0; proc_id < size; proc_id++) {
      if (proc_id == rank) continue;
      *(data1 + proc_id * len + 1 + i) = len_s[proc_id] - iwork[proc_id];
      iwork[proc_id]                   = len_s[proc_id];
    }
    PetscCall(ISRestoreIndices(is[i], &idx_i));
  }

  nrqs = 0;
  nrqr = 0;
  for (i = 0; i < size; i++) {
    data1_start[i] = data1 + i * len;
    if (len_s[i]) {
      nrqs++;
      len_s[i] += 1 + is_max; /* add no. of header msg */
    }
  }

  for (i = 0; i < is_max; i++) PetscCall(ISDestroy(&is[i]));
  PetscCall(PetscFree(n));
  PetscCall(PetscFree(ctable));

  /* Determine the number of messages to expect, their lengths, from from-ids */
  PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrqr));
  PetscCall(PetscGatherMessageLengths(comm, nrqs, nrqr, len_s, &id_r1, &len_r1));

  /*  Now  post the sends */
  PetscCall(PetscMalloc2(size, &s_waits1, size, &s_waits2));
  k = 0;
  for (PetscMPIInt proc_id = 0; proc_id < size; proc_id++) { /* send data1 to processor [proc_id] */
    if (len_s[proc_id]) {
      PetscCallMPI(MPIU_Isend(data1_start[proc_id], len_s[proc_id], MPIU_INT, proc_id, tag1, comm, s_waits1 + k));
      k++;
    }
  }

  /* 2. Receive other's is[] and process. Then send back */
  len = 0;
  for (i = 0; i < nrqr; i++) {
    if (len_r1[i] > len) len = len_r1[i];
  }
  PetscCall(PetscFree(len_r1));
  PetscCall(PetscFree(id_r1));

  for (PetscMPIInt proc_id = 0; proc_id < size; proc_id++) len_s[proc_id] = iwork[proc_id] = 0;

  PetscCall(PetscMalloc1(len + 1, &odata1));
  PetscCall(PetscMalloc1(size, &odata2_ptr));
  PetscCall(PetscBTCreate(Mbs, &otable));

  len_max = ois_max * (Mbs + 1); /* max space storing all is[] for each receive */
  len_est = 2 * len_max;         /* estimated space of storing is[] for all receiving messages */
  PetscCall(PetscMalloc1(len_est + 1, &odata2));
  nodata2 = 0; /* nodata2+1: num of PetscMalloc(,&odata2_ptr[]) called */

  odata2_ptr[nodata2] = odata2;

  len_unused = len_est; /* unused space in the array odata2_ptr[nodata2]-- needs to be >= len_max  */

  k = 0;
  while (k < nrqr) {
    PetscMPIInt ilen;

    /* Receive messages */
    PetscCallMPI(MPI_Iprobe(MPI_ANY_SOURCE, tag1, comm, &flag, &r_status));
    if (flag) {
      PetscMPIInt proc_id;

      PetscCallMPI(MPI_Get_count(&r_status, MPIU_INT, &ilen));
      proc_id = r_status.MPI_SOURCE;
      PetscCallMPI(MPIU_Irecv(odata1, ilen, MPIU_INT, proc_id, r_status.MPI_TAG, comm, &r_req));
      PetscCallMPI(MPI_Wait(&r_req, &r_status));

      /*  Process messages */
      /*  make sure there is enough unused space in odata2 array */
      if (len_unused < len_max) { /* allocate more space for odata2 */
        PetscCall(PetscMalloc1(len_est + 1, &odata2));
        odata2_ptr[++nodata2] = odata2;
        len_unused            = len_est;
      }

      PetscCall(MatIncreaseOverlap_MPISBAIJ_Local(C, odata1, OTHER, odata2, &otable));
      len = 1 + odata2[0];
      for (i = 0; i < odata2[0]; i++) len += odata2[1 + i];

      /* Send messages back */
      PetscCallMPI(MPIU_Isend(odata2, len, MPIU_INT, proc_id, tag2, comm, s_waits2 + k));
      k++;
      odata2 += len;
      len_unused -= len;
      PetscCall(PetscMPIIntCast(len, &len_s[proc_id])); /* length of message sending back to proc_id */
    }
  }
  PetscCall(PetscFree(odata1));
  PetscCall(PetscBTDestroy(&otable));

  /* 3. Do local work on this processor's is[] */
  /* make sure there is enough unused space in odata2(=data) array */
  len_max = is_max * (Mbs + 1); /* max space storing all is[] for this processor */
  if (len_unused < len_max) {   /* allocate more space for odata2 */
    PetscCall(PetscMalloc1(len_est + 1, &odata2));

    odata2_ptr[++nodata2] = odata2;
  }

  data = odata2;
  PetscCall(MatIncreaseOverlap_MPISBAIJ_Local(C, data1_start[rank], MINE, data, table));
  PetscCall(PetscFree(data1_start));

  /* 4. Receive work done on other processors, then merge */
  /* get max number of messages that this processor expects to recv */
  PetscCallMPI(MPIU_Allreduce(len_s, iwork, size, MPI_INT, MPI_MAX, comm));
  PetscCall(PetscMalloc1(iwork[rank] + 1, &data2));
  PetscCall(PetscFree4(len_s, btable, iwork, Bowners));

  k = 0;
  while (k < nrqs) {
    /* Receive messages */
    PetscCallMPI(MPI_Iprobe(MPI_ANY_SOURCE, tag2, comm, &flag, &r_status));
    if (flag) {
      PetscMPIInt proc_id, ilen;
      PetscCallMPI(MPI_Get_count(&r_status, MPIU_INT, &ilen));
      proc_id = r_status.MPI_SOURCE;
      PetscCallMPI(MPIU_Irecv(data2, ilen, MPIU_INT, proc_id, r_status.MPI_TAG, comm, &r_req));
      PetscCallMPI(MPI_Wait(&r_req, &r_status));
      if (ilen > 1 + is_max) { /* Add data2 into data */
        data2_i = data2 + 1 + is_max;
        for (i = 0; i < is_max; i++) {
          table_i = table[i];
          data_i  = data + 1 + is_max + Mbs * i;
          isz     = data[1 + i];
          for (j = 0; j < data2[1 + i]; j++) {
            col = data2_i[j];
            if (!PetscBTLookupSet(table_i, col)) data_i[isz++] = col;
          }
          data[1 + i] = isz;
          if (i < is_max - 1) data2_i += data2[1 + i];
        }
      }
      k++;
    }
  }
  PetscCall(PetscFree(data2));
  PetscCall(PetscFree2(table, t_p));

  /* phase 1 sends are complete */
  PetscCall(PetscMalloc1(size, &s_status));
  if (nrqs) PetscCallMPI(MPI_Waitall(nrqs, s_waits1, s_status));
  PetscCall(PetscFree(data1));

  /* phase 2 sends are complete */
  if (nrqr) PetscCallMPI(MPI_Waitall(nrqr, s_waits2, s_status));
  PetscCall(PetscFree2(s_waits1, s_waits2));
  PetscCall(PetscFree(s_status));

  /* 5. Create new is[] */
  for (i = 0; i < is_max; i++) {
    data_i = data + 1 + is_max + Mbs * i;
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF, data[1 + i], data_i, PETSC_COPY_VALUES, is + i));
  }
  for (k = 0; k <= nodata2; k++) PetscCall(PetscFree(odata2_ptr[k]));
  PetscCall(PetscFree(odata2_ptr));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   MatIncreaseOverlap_MPISBAIJ_Local - Called by MatIncreaseOverlap, to do
       the work on the local processor.

     Inputs:
      C      - MAT_MPISBAIJ;
      data   - holds is[]. See MatIncreaseOverlap_MPISBAIJ_Once() for the format.
      whose  - whose is[] to be processed,
               MINE:  this processor's is[]
               OTHER: other processor's is[]
     Output:
       nidx  - whose = MINE:
                     holds input and newly found indices in the same format as data
               whose = OTHER:
                     only holds the newly found indices
       table - table[i]: mark the indices of is[i], i=0,...,is_max. Used only in the case 'whose=MINE'.
*/
/* Would computation be reduced by swapping the loop 'for each is' and 'for each row'? */
static PetscErrorCode MatIncreaseOverlap_MPISBAIJ_Local(Mat C, PetscInt *data, PetscInt whose, PetscInt *nidx, PetscBT *table)
{
  Mat_MPISBAIJ *c = (Mat_MPISBAIJ *)C->data;
  Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)c->A->data;
  Mat_SeqBAIJ  *b = (Mat_SeqBAIJ *)c->B->data;
  PetscInt      row, mbs, Mbs, *nidx_i, col, col_max, isz, isz0, *ai, *aj, *bi, *bj, *garray, rstart, l;
  PetscInt      a_start, a_end, b_start, b_end, i, j, k, is_max, *idx_i, n;
  PetscBT       table0;  /* mark the indices of input is[] for look up */
  PetscBT       table_i; /* points to i-th table. When whose=OTHER, a single table is used for all is[] */

  PetscFunctionBegin;
  Mbs    = c->Mbs;
  mbs    = a->mbs;
  ai     = a->i;
  aj     = a->j;
  bi     = b->i;
  bj     = b->j;
  garray = c->garray;
  rstart = c->rstartbs;
  is_max = data[0];

  PetscCall(PetscBTCreate(Mbs, &table0));

  nidx[0] = is_max;
  idx_i   = data + is_max + 1;   /* ptr to input is[0] array */
  nidx_i  = nidx + is_max + 1;   /* ptr to output is[0] array */
  for (i = 0; i < is_max; i++) { /* for each is */
    isz = 0;
    n   = data[1 + i]; /* size of input is[i] */

    /* initialize and set table_i(mark idx and nidx) and table0(only mark idx) */
    if (whose == MINE) { /* process this processor's is[] */
      table_i = table[i];
      nidx_i  = nidx + 1 + is_max + Mbs * i;
    } else { /* process other processor's is[] - only use one temp table */
      table_i = table[0];
    }
    PetscCall(PetscBTMemzero(Mbs, table_i));
    PetscCall(PetscBTMemzero(Mbs, table0));
    if (n == 0) {
      nidx[1 + i] = 0; /* size of new is[i] */
      continue;
    }

    isz0    = 0;
    col_max = 0;
    for (j = 0; j < n; j++) {
      col = idx_i[j];
      PetscCheck(col < Mbs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "index col %" PetscInt_FMT " >= Mbs %" PetscInt_FMT, col, Mbs);
      if (!PetscBTLookupSet(table_i, col)) {
        PetscCall(PetscBTSet(table0, col));
        if (whose == MINE) nidx_i[isz0] = col;
        if (col_max < col) col_max = col;
        isz0++;
      }
    }

    if (whose == MINE) isz = isz0;
    k = 0; /* no. of indices from input is[i] that have been examined */
    for (row = 0; row < mbs; row++) {
      a_start = ai[row];
      a_end   = ai[row + 1];
      b_start = bi[row];
      b_end   = bi[row + 1];
      if (PetscBTLookup(table0, row + rstart)) { /* row is on input is[i]:
                                                do row search: collect all col in this row */
        for (l = a_start; l < a_end; l++) {      /* Amat */
          col = aj[l] + rstart;
          if (!PetscBTLookupSet(table_i, col)) nidx_i[isz++] = col;
        }
        for (l = b_start; l < b_end; l++) { /* Bmat */
          col = garray[bj[l]];
          if (!PetscBTLookupSet(table_i, col)) nidx_i[isz++] = col;
        }
        k++;
        if (k >= isz0) break;               /* for (row=0; row<mbs; row++) */
      } else {                              /* row is not on input is[i]:
                  do col search: add row onto nidx_i if there is a col in nidx_i */
        for (l = a_start; l < a_end; l++) { /* Amat */
          col = aj[l] + rstart;
          if (col > col_max) break;
          if (PetscBTLookup(table0, col)) {
            if (!PetscBTLookupSet(table_i, row + rstart)) nidx_i[isz++] = row + rstart;
            break; /* for l = start; l<end ; l++) */
          }
        }
        for (l = b_start; l < b_end; l++) { /* Bmat */
          col = garray[bj[l]];
          if (col > col_max) break;
          if (PetscBTLookup(table0, col)) {
            if (!PetscBTLookupSet(table_i, row + rstart)) nidx_i[isz++] = row + rstart;
            break; /* for l = start; l<end ; l++) */
          }
        }
      }
    }

    if (i < is_max - 1) {
      idx_i += n;    /* ptr to input is[i+1] array */
      nidx_i += isz; /* ptr to output is[i+1] array */
    }
    nidx[1 + i] = isz; /* size of new is[i] */
  } /* for each is */
  PetscCall(PetscBTDestroy(&table0));
  PetscFunctionReturn(PETSC_SUCCESS);
}