Beispiel #1
0
static PetscErrorCode MatIncreaseOverlap_MPISBAIJ_Once(Mat C,PetscInt is_max,IS is[])
{
  Mat_MPISBAIJ  *c = (Mat_MPISBAIJ*)C->data;
  PetscErrorCode ierr;
  PetscMPIInt    size,rank,tag1,tag2,*len_s,nrqr,nrqs,*id_r1,*len_r1,flag,len;
  const PetscInt *idx_i;
  PetscInt       idx,isz,col,*n,*data1,**data1_start,*data2,*data2_i,*data,*data_i,
                 Mbs,i,j,k,*odata1,*odata2,
                 proc_id,**odata2_ptr,*ctable=0,*btable,len_max,len_est;
  PetscInt       proc_end=0,*iwork,len_unused,nodata2;
  PetscInt       ois_max; /* max no of is[] in each of processor */
  char           *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;
  comm = ((PetscObject)C)->comm;
  size = c->size;
  rank = c->rank;
  Mbs  = c->Mbs;

  ierr = PetscObjectGetNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
  ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);

  /* 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);CHKERRQ(ierr);
  ierr = PetscMalloc2(len,PetscBT,&table,(Mbs/PETSC_BITS_PER_BYTE+1)*len,char,&t_p);CHKERRQ(ierr);
  for (i=0; i<len; i++) {
    table[i]  = t_p  + (Mbs/PETSC_BITS_PER_BYTE+1)*i; 
  }

  ierr = MPI_Allreduce(&is_max,&ois_max,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
  
  /* 1. Send this processor's is[] to other processors */
  /*---------------------------------------------------*/
  /* allocate spaces */
  ierr = PetscMalloc(is_max*sizeof(PetscInt),&n);CHKERRQ(ierr);
  len = 0;
  for (i=0; i<is_max; i++) {
    ierr = ISGetLocalSize(is[i],&n[i]);CHKERRQ(ierr);
    len += n[i]; 
  }
  if (!len) { 
    is_max = 0;
  } else {
    len += 1 + is_max; /* max length of data1 for one processor */
  }

 
  ierr = PetscMalloc((size*len+1)*sizeof(PetscInt),&data1);CHKERRQ(ierr);
  ierr = PetscMalloc(size*sizeof(PetscInt*),&data1_start);CHKERRQ(ierr);
  for (i=0; i<size; i++) data1_start[i] = data1 + i*len;

  ierr = PetscMalloc4(size,PetscInt,&len_s,size,PetscInt,&btable,size,PetscInt,&iwork,size+1,PetscInt,&Bowners);CHKERRQ(ierr);

  /* gather c->garray from all processors */
  ierr = ISCreateGeneral(comm,Bnbs,c->garray,&garray_local);CHKERRQ(ierr);
  ierr = ISAllGather(garray_local, &garray_gl);CHKERRQ(ierr);
  ierr = ISDestroy(garray_local);CHKERRQ(ierr);
  ierr = MPI_Allgather(&Bnbs,1,MPIU_INT,Bowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
  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) */
    ierr = PetscMalloc(Mbs*sizeof(PetscInt),&ctable);CHKERRQ(ierr);
    for (proc_id=0,j=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 */
    ierr = ISGetIndices(garray_gl,&idx_i);
    for (i=0; i<size; i++){
      table_i = table[i]; 
      ierr    = PetscBTMemzero(Mbs,table_i);CHKERRQ(ierr);
      for (j = Bowners[i]; j<Bowners[i+1]; j++){ /* go through B cols of proc[i]*/
        ierr = PetscBTSet(table_i,idx_i[j]);CHKERRQ(ierr);
      }
    }
    ierr = ISRestoreIndices(garray_gl,&idx_i);CHKERRQ(ierr);
  }  /* if (is_max) */
  ierr = ISDestroy(garray_gl);CHKERRQ(ierr); 

  /* evaluate communication - mesg to who, length, and buffer space */
  for (i=0; i<size; i++) len_s[i] = 0;
  
  /* header of data1 */
  for (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++) { 
    ierr = ISGetIndices(is[i],&idx_i);CHKERRQ(ierr); 
    for (j=0; j<n[i]; j++){
      idx = idx_i[j];
      *data1_start[rank] = idx; data1_start[rank]++; /* for local proccessing */
      proc_end = ctable[idx];
      for (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 (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] ;
    } 
    ierr = ISRestoreIndices(is[i],&idx_i);CHKERRQ(ierr);
  } 

  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++) { 
    ierr = ISDestroy(is[i]);CHKERRQ(ierr); 
  }
  ierr = PetscFree(n);CHKERRQ(ierr);
  ierr = PetscFree(ctable);CHKERRQ(ierr);

  /* Determine the number of messages to expect, their lengths, from from-ids */
  ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&nrqr);CHKERRQ(ierr);
  ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,len_s,&id_r1,&len_r1);CHKERRQ(ierr); 
  
  /*  Now  post the sends */
  ierr = PetscMalloc2(size,MPI_Request,&s_waits1,size,MPI_Request,&s_waits2);CHKERRQ(ierr);
  k = 0;
  for (proc_id=0; proc_id<size; proc_id++){  /* send data1 to processor [proc_id] */
    if (len_s[proc_id]){
      ierr = MPI_Isend(data1_start[proc_id],len_s[proc_id],MPIU_INT,proc_id,tag1,comm,s_waits1+k);CHKERRQ(ierr);
      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];
  }
  ierr = PetscFree(len_r1);CHKERRQ(ierr);
  ierr = PetscFree(id_r1);CHKERRQ(ierr);

  for (proc_id=0; proc_id<size; proc_id++)
    len_s[proc_id] = iwork[proc_id] = 0;
  
  ierr = PetscMalloc((len+1)*sizeof(PetscInt),&odata1);CHKERRQ(ierr);
  ierr = PetscMalloc(size*sizeof(PetscInt**),&odata2_ptr);CHKERRQ(ierr); 
  ierr = PetscBTCreate(Mbs,otable);CHKERRQ(ierr);

  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 */
  ierr = PetscMalloc((len_est+1)*sizeof(PetscInt),&odata2);CHKERRQ(ierr);
  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){
    /* Receive messages */
    ierr = MPI_Iprobe(MPI_ANY_SOURCE,tag1,comm,&flag,&r_status);CHKERRQ(ierr);
    if (flag){ 
      ierr = MPI_Get_count(&r_status,MPIU_INT,&len);CHKERRQ(ierr); 
      proc_id = r_status.MPI_SOURCE;
      ierr = MPI_Irecv(odata1,len,MPIU_INT,proc_id,r_status.MPI_TAG,comm,&r_req);CHKERRQ(ierr);
      ierr = MPI_Wait(&r_req,&r_status);CHKERRQ(ierr);

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

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

      /* Send messages back */
      ierr = MPI_Isend(odata2,len,MPIU_INT,proc_id,tag2,comm,s_waits2+k);CHKERRQ(ierr);
      k++;
      odata2     += len;
      len_unused -= len;
      len_s[proc_id] = len; /* num of messages sending back to [proc_id] by this proc */
    } 
  } 
  ierr = PetscFree(odata1);CHKERRQ(ierr); 
  ierr = PetscBTDestroy(otable);CHKERRQ(ierr); 

  /* 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 */
    ierr = PetscMalloc((len_est+1)*sizeof(PetscInt),&odata2);CHKERRQ(ierr);
    odata2_ptr[++nodata2] = odata2;
    len_unused = len_est;
  }

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

  /* 4. Receive work done on other processors, then merge */
  /*------------------------------------------------------*/
  /* get max number of messages that this processor expects to recv */
  ierr = MPI_Allreduce(len_s,iwork,size,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
  ierr = PetscMalloc((iwork[rank]+1)*sizeof(PetscInt),&data2);CHKERRQ(ierr);
  ierr = PetscFree4(len_s,btable,iwork,Bowners);CHKERRQ(ierr);

  k = 0;
  while (k < nrqs){
    /* Receive messages */
    ierr = MPI_Iprobe(MPI_ANY_SOURCE,tag2,comm,&flag,&r_status);
    if (flag){
      ierr = MPI_Get_count(&r_status,MPIU_INT,&len);CHKERRQ(ierr);
      proc_id = r_status.MPI_SOURCE;
      ierr = MPI_Irecv(data2,len,MPIU_INT,proc_id,r_status.MPI_TAG,comm,&r_req);CHKERRQ(ierr);
      ierr = MPI_Wait(&r_req,&r_status);CHKERRQ(ierr);
      if (len > 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++;
    } 
  } 
  ierr = PetscFree(data2);CHKERRQ(ierr);
  ierr = PetscFree2(table,t_p);CHKERRQ(ierr);

  /* phase 1 sends are complete */
  ierr = PetscMalloc(size*sizeof(MPI_Status),&s_status);CHKERRQ(ierr);
  if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status);CHKERRQ(ierr);}
  ierr = PetscFree(data1);CHKERRQ(ierr); 
       
  /* phase 2 sends are complete */
  if (nrqr){ierr = MPI_Waitall(nrqr,s_waits2,s_status);CHKERRQ(ierr);}
  ierr = PetscFree2(s_waits1,s_waits2);CHKERRQ(ierr);
  ierr = PetscFree(s_status);CHKERRQ(ierr); 

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

  PetscFunctionReturn(0);
}
Beispiel #2
0
static PetscErrorCode MatStashScatterBegin_Ref(Mat mat,MatStash *stash,PetscInt *owners)
{
  PetscInt           *owner,*startv,*starti,tag1=stash->tag1,tag2=stash->tag2,bs2;
  PetscInt           size=stash->size,nsends;
  PetscErrorCode     ierr;
  PetscInt           count,*sindices,**rindices,i,j,idx,lastidx,l;
  PetscScalar        **rvalues,*svalues;
  MPI_Comm           comm = stash->comm;
  MPI_Request        *send_waits,*recv_waits,*recv_waits1,*recv_waits2;
  PetscMPIInt        *sizes,*nlengths,nreceives;
  PetscInt           *sp_idx,*sp_idy;
  PetscScalar        *sp_val;
  PetscMatStashSpace space,space_next;

  PetscFunctionBegin;
  {                             /* make sure all processors are either in INSERTMODE or ADDMODE */
    InsertMode addv;
    ierr = MPIU_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
    if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
    mat->insertmode = addv; /* in case this processor had no cache */
  }

  bs2 = stash->bs*stash->bs;

  /*  first count number of contributors to each processor */
  ierr = PetscCalloc1(size,&sizes);CHKERRQ(ierr);
  ierr = PetscCalloc1(size,&nlengths);CHKERRQ(ierr);
  ierr = PetscMalloc1(stash->n+1,&owner);CHKERRQ(ierr);

  i       = j    = 0;
  lastidx = -1;
  space   = stash->space_head;
  while (space) {
    space_next = space->next;
    sp_idx     = space->idx;
    for (l=0; l<space->local_used; l++) {
      /* if indices are NOT locally sorted, need to start search at the beginning */
      if (lastidx > (idx = sp_idx[l])) j = 0;
      lastidx = idx;
      for (; j<size; j++) {
        if (idx >= owners[j] && idx < owners[j+1]) {
          nlengths[j]++; owner[i] = j; break;
        }
      }
      i++;
    }
    space = space_next;
  }
  /* Now check what procs get messages - and compute nsends. */
  for (i=0, nsends=0; i<size; i++) {
    if (nlengths[i]) {
      sizes[i] = 1; nsends++;
    }
  }

  {PetscMPIInt *onodes,*olengths;
   /* Determine the number of messages to expect, their lengths, from from-ids */
   ierr = PetscGatherNumberOfMessages(comm,sizes,nlengths,&nreceives);CHKERRQ(ierr);
   ierr = PetscGatherMessageLengths(comm,nsends,nreceives,nlengths,&onodes,&olengths);CHKERRQ(ierr);
   /* since clubbing row,col - lengths are multiplied by 2 */
   for (i=0; i<nreceives; i++) olengths[i] *=2;
   ierr = PetscPostIrecvInt(comm,tag1,nreceives,onodes,olengths,&rindices,&recv_waits1);CHKERRQ(ierr);
   /* values are size 'bs2' lengths (and remove earlier factor 2 */
   for (i=0; i<nreceives; i++) olengths[i] = olengths[i]*bs2/2;
   ierr = PetscPostIrecvScalar(comm,tag2,nreceives,onodes,olengths,&rvalues,&recv_waits2);CHKERRQ(ierr);
   ierr = PetscFree(onodes);CHKERRQ(ierr);
   ierr = PetscFree(olengths);CHKERRQ(ierr);}

  /* do sends:
      1) starts[i] gives the starting index in svalues for stuff going to
         the ith processor
  */
  ierr = PetscMalloc2(bs2*stash->n,&svalues,2*(stash->n+1),&sindices);CHKERRQ(ierr);
  ierr = PetscMalloc1(2*nsends,&send_waits);CHKERRQ(ierr);
  ierr = PetscMalloc2(size,&startv,size,&starti);CHKERRQ(ierr);
  /* use 2 sends the first with all_a, the next with all_i and all_j */
  startv[0] = 0; starti[0] = 0;
  for (i=1; i<size; i++) {
    startv[i] = startv[i-1] + nlengths[i-1];
    starti[i] = starti[i-1] + 2*nlengths[i-1];
  }

  i     = 0;
  space = stash->space_head;
  while (space) {
    space_next = space->next;
    sp_idx     = space->idx;
    sp_idy     = space->idy;
    sp_val     = space->val;
    for (l=0; l<space->local_used; l++) {
      j = owner[i];
      if (bs2 == 1) {
        svalues[startv[j]] = sp_val[l];
      } else {
        PetscInt    k;
        PetscScalar *buf1,*buf2;
        buf1 = svalues+bs2*startv[j];
        buf2 = space->val + bs2*l;
        for (k=0; k<bs2; k++) buf1[k] = buf2[k];
      }
      sindices[starti[j]]             = sp_idx[l];
      sindices[starti[j]+nlengths[j]] = sp_idy[l];
      startv[j]++;
      starti[j]++;
      i++;
    }
    space = space_next;
  }
  startv[0] = 0;
  for (i=1; i<size; i++) startv[i] = startv[i-1] + nlengths[i-1];

  for (i=0,count=0; i<size; i++) {
    if (sizes[i]) {
      ierr = MPI_Isend(sindices+2*startv[i],2*nlengths[i],MPIU_INT,i,tag1,comm,send_waits+count++);CHKERRQ(ierr);
      ierr = MPI_Isend(svalues+bs2*startv[i],bs2*nlengths[i],MPIU_SCALAR,i,tag2,comm,send_waits+count++);CHKERRQ(ierr);
    }
  }
#if defined(PETSC_USE_INFO)
  ierr = PetscInfo1(NULL,"No of messages: %d \n",nsends);CHKERRQ(ierr);
  for (i=0; i<size; i++) {
    if (sizes[i]) {
      ierr = PetscInfo2(NULL,"Mesg_to: %d: size: %d bytes\n",i,nlengths[i]*(bs2*sizeof(PetscScalar)+2*sizeof(PetscInt)));CHKERRQ(ierr);
    }
  }
#endif
  ierr = PetscFree(nlengths);CHKERRQ(ierr);
  ierr = PetscFree(owner);CHKERRQ(ierr);
  ierr = PetscFree2(startv,starti);CHKERRQ(ierr);
  ierr = PetscFree(sizes);CHKERRQ(ierr);

  /* recv_waits need to be contiguous for MatStashScatterGetMesg_Private() */
  ierr = PetscMalloc1(2*nreceives,&recv_waits);CHKERRQ(ierr);

  for (i=0; i<nreceives; i++) {
    recv_waits[2*i]   = recv_waits1[i];
    recv_waits[2*i+1] = recv_waits2[i];
  }
  stash->recv_waits = recv_waits;

  ierr = PetscFree(recv_waits1);CHKERRQ(ierr);
  ierr = PetscFree(recv_waits2);CHKERRQ(ierr);

  stash->svalues         = svalues;
  stash->sindices        = sindices;
  stash->rvalues         = rvalues;
  stash->rindices        = rindices;
  stash->send_waits      = send_waits;
  stash->nsends          = nsends;
  stash->nrecvs          = nreceives;
  stash->reproduce_count = 0;
  PetscFunctionReturn(0);
}
Beispiel #3
0
static PetscErrorCode PCSetUp_Redistribute(PC pc)
{
  PC_Redistribute   *red = (PC_Redistribute*)pc->data;
  PetscErrorCode    ierr;
  MPI_Comm          comm;
  PetscInt          rstart,rend,i,nz,cnt,*rows,ncnt,dcnt,*drows;
  PetscLayout       map,nmap;
  PetscMPIInt       size,imdex,tag,n;
  PetscInt          *source = PETSC_NULL;
  PetscMPIInt       *nprocs = PETSC_NULL,nrecvs;
  PetscInt          j,nsends;
  PetscInt          *owner = PETSC_NULL,*starts = PETSC_NULL,count,slen;
  PetscInt          *rvalues,*svalues,recvtotal;
  PetscMPIInt       *onodes1,*olengths1;
  MPI_Request       *send_waits = PETSC_NULL,*recv_waits = PETSC_NULL;
  MPI_Status        recv_status,*send_status;
  Vec               tvec,diag;
  Mat               tmat;
  const PetscScalar *d;

  PetscFunctionBegin;
  if (pc->setupcalled) {
    ierr = KSPGetOperators(red->ksp,PETSC_NULL,&tmat,PETSC_NULL);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pc->pmat,red->is,red->is,MAT_REUSE_MATRIX,&tmat);CHKERRQ(ierr);
    ierr = KSPSetOperators(red->ksp,tmat,tmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  } else {
    PetscInt NN;

    ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
    ierr = PetscObjectGetNewTag((PetscObject)pc,&tag);CHKERRQ(ierr);

    /* count non-diagonal rows on process */
    ierr = MatGetOwnershipRange(pc->mat,&rstart,&rend);CHKERRQ(ierr);
    cnt  = 0;
    for (i=rstart; i<rend; i++) {
      ierr = MatGetRow(pc->mat,i,&nz,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
      if (nz > 1) cnt++;
      ierr = MatRestoreRow(pc->mat,i,&nz,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
    }
    ierr = PetscMalloc(cnt*sizeof(PetscInt),&rows);CHKERRQ(ierr);
    ierr = PetscMalloc((rend - rstart - cnt)*sizeof(PetscInt),&drows);CHKERRQ(ierr);

    /* list non-diagonal rows on process */
    cnt  = 0; dcnt = 0;
    for (i=rstart; i<rend; i++) {
      ierr = MatGetRow(pc->mat,i,&nz,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
      if (nz > 1) rows[cnt++] = i;
      else drows[dcnt++] = i - rstart;
      ierr = MatRestoreRow(pc->mat,i,&nz,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
    }

    /* create PetscLayout for non-diagonal rows on each process */
    ierr = PetscLayoutCreate(comm,&map);CHKERRQ(ierr);
    ierr = PetscLayoutSetLocalSize(map,cnt);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(map,1);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(map);CHKERRQ(ierr);
    rstart = map->rstart;
    rend   = map->rend;

    /* create PetscLayout for load-balanced non-diagonal rows on each process */
    ierr = PetscLayoutCreate(comm,&nmap);CHKERRQ(ierr);
    ierr = MPI_Allreduce(&cnt,&ncnt,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
    ierr = PetscLayoutSetSize(nmap,ncnt);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(nmap,1);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(nmap);CHKERRQ(ierr);

    ierr = MatGetSize(pc->pmat,&NN,PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscInfo2(pc,"Number of diagonal rows eliminated %d, percentage eliminated %g\n",NN-ncnt,((PetscReal)(NN-ncnt))/((PetscReal)(NN)));CHKERRQ(ierr);
    /*
        this code is taken from VecScatterCreate_PtoS()
        Determines what rows need to be moved where to
        load balance the non-diagonal rows
    */
    /*  count number of contributors to each processor */
    ierr = PetscMalloc2(size,PetscMPIInt,&nprocs,cnt,PetscInt,&owner);CHKERRQ(ierr);
    ierr = PetscMemzero(nprocs,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
    j      = 0;
    nsends = 0;
    for (i=rstart; i<rend; i++) {
      if (i < nmap->range[j]) j = 0;
      for (; j<size; j++) {
        if (i < nmap->range[j+1]) {
          if (!nprocs[j]++) nsends++;
          owner[i-rstart] = j;
          break;
        }
      }
    }
    /* inform other processors of number of messages and max length*/
    ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,nprocs,&nrecvs);CHKERRQ(ierr);
    ierr = PetscGatherMessageLengths(comm,nsends,nrecvs,nprocs,&onodes1,&olengths1);CHKERRQ(ierr);
    ierr = PetscSortMPIIntWithArray(nrecvs,onodes1,olengths1);CHKERRQ(ierr);
    recvtotal = 0; for (i=0; i<nrecvs; i++) recvtotal += olengths1[i];

    /* post receives:  rvalues - rows I will own; count - nu */
    ierr = PetscMalloc3(recvtotal,PetscInt,&rvalues,nrecvs,PetscInt,&source,nrecvs,MPI_Request,&recv_waits);CHKERRQ(ierr);
    count  = 0;
    for (i=0; i<nrecvs; i++) {
      ierr  = MPI_Irecv((rvalues+count),olengths1[i],MPIU_INT,onodes1[i],tag,comm,recv_waits+i);CHKERRQ(ierr);
      count += olengths1[i];
    }

    /* do sends:
       1) starts[i] gives the starting index in svalues for stuff going to
       the ith processor
    */
    ierr = PetscMalloc3(cnt,PetscInt,&svalues,nsends,MPI_Request,&send_waits,size,PetscInt,&starts);CHKERRQ(ierr);
    starts[0]  = 0;
    for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[i-1];}
    for (i=0; i<cnt; i++) {
      svalues[starts[owner[i]]++] = rows[i];
    }
    for (i=0; i<cnt; i++) rows[i] = rows[i] - rstart;
    red->drows = drows;
    red->dcnt  = dcnt;
    ierr = PetscFree(rows);CHKERRQ(ierr);

    starts[0] = 0;
    for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[i-1];}
    count = 0;
    for (i=0; i<size; i++) {
      if (nprocs[i]) {
        ierr = MPI_Isend(svalues+starts[i],nprocs[i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
      }
    }

    /*  wait on receives */
    count  = nrecvs;
    slen   = 0;
    while (count) {
      ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
      /* unpack receives into our local space */
      ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
      slen += n;
      count--;
    }
    if (slen != recvtotal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Total message lengths %D not expected %D",slen,recvtotal);

    ierr = ISCreateGeneral(comm,slen,rvalues,PETSC_COPY_VALUES,&red->is);CHKERRQ(ierr);

    /* free up all work space */
    ierr = PetscFree(olengths1);CHKERRQ(ierr);
    ierr = PetscFree(onodes1);CHKERRQ(ierr);
    ierr = PetscFree3(rvalues,source,recv_waits);CHKERRQ(ierr);
    ierr = PetscFree2(nprocs,owner);CHKERRQ(ierr);
    if (nsends) {   /* wait on sends */
      ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
      ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
      ierr = PetscFree(send_status);CHKERRQ(ierr);
    }
    ierr = PetscFree3(svalues,send_waits,starts);CHKERRQ(ierr);
    ierr = PetscLayoutDestroy(&map);CHKERRQ(ierr);
    ierr = PetscLayoutDestroy(&nmap);CHKERRQ(ierr);

    ierr = VecCreateMPI(comm,slen,PETSC_DETERMINE,&red->b);CHKERRQ(ierr);
    ierr = VecDuplicate(red->b,&red->x);CHKERRQ(ierr);
    ierr = MatGetVecs(pc->pmat,&tvec,PETSC_NULL);CHKERRQ(ierr);
    ierr = VecScatterCreate(tvec,red->is,red->b,PETSC_NULL,&red->scatter);CHKERRQ(ierr);
    ierr = VecDestroy(&tvec);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pc->pmat,red->is,red->is,MAT_INITIAL_MATRIX,&tmat);CHKERRQ(ierr);
    ierr = KSPSetOperators(red->ksp,tmat,tmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
    ierr = MatDestroy(&tmat);CHKERRQ(ierr);
  }

  /* get diagonal portion of matrix */
  ierr = PetscMalloc(red->dcnt*sizeof(PetscScalar),&red->diag);CHKERRQ(ierr);
  ierr = MatGetVecs(pc->pmat,&diag,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatGetDiagonal(pc->pmat,diag);CHKERRQ(ierr);
  ierr = VecGetArrayRead(diag,&d);CHKERRQ(ierr);
  for (i=0; i<red->dcnt; i++) {
    red->diag[i] = 1.0/d[red->drows[i]];
  }
  ierr = VecRestoreArrayRead(diag,&d);CHKERRQ(ierr);
  ierr = VecDestroy(&diag);CHKERRQ(ierr);
  ierr = KSPSetUp(red->ksp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}