aij/mpi/mpiaij.c

#ifndef lint
static char vcid[] = "$Id: mpiaij.c,v 1.20 1995/03/27 22:58:06 bsmith Exp curfman $";
#endif

#include "mpiaij.h"
#include "vec/vecimpl.h"
#include "inline/spops.h"

#define CHUNCKSIZE   100
/*
   This is a simple minded stash. Do a linear search to determine if
 in stash, if not add to end.
*/
static int StashValues(Stash *stash,int row,int n, int *idxn,
                       Scalar *values,InsertMode addv)
{
  int    i,j,N = stash->n,found,*n_idx, *n_idy;
  Scalar val,*n_array;

  for ( i=0; i<n; i++ ) {
    found = 0;
    val = *values++;
    for ( j=0; j<N; j++ ) {
      if ( stash->idx[j] == row && stash->idy[j] == idxn[i]) {
        /* found a match */
        if (addv == AddValues) stash->array[j] += val;
        else stash->array[j] = val;
        found = 1;
        break;
      }
    }
    if (!found) { /* not found so add to end */
      if ( stash->n == stash->nmax ) {
        /* allocate a larger stash */
        n_array = (Scalar *) MALLOC( (stash->nmax + CHUNCKSIZE)*(
                                     2*sizeof(int) + sizeof(Scalar)));
        CHKPTR(n_array);
        n_idx = (int *) (n_array + stash->nmax + CHUNCKSIZE);
        n_idy = (int *) (n_idx + stash->nmax + CHUNCKSIZE);
        MEMCPY(n_array,stash->array,stash->nmax*sizeof(Scalar));
        MEMCPY(n_idx,stash->idx,stash->nmax*sizeof(int));
        MEMCPY(n_idy,stash->idy,stash->nmax*sizeof(int));
        if (stash->array) FREE(stash->array);
        stash->array = n_array; stash->idx = n_idx; stash->idy = n_idy;
        stash->nmax += CHUNCKSIZE;
      }
      stash->array[stash->n]   = val;
      stash->idx[stash->n]     = row;
      stash->idy[stash->n++]   = idxn[i];
    }
  }
  return 0;
}

/* local utility routine that creates a mapping from the global column
number to the local number in the off-diagonal part of the local
storage of the matrix.  This is done in a non scable way since the
length of colmap equals the global matrix length.
*/
static int CreateColmap(Mat mat)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
  Mat_AIJ    *B = (Mat_AIJ*) aij->B->data;
  int        n = B->n,i;
  aij->colmap = (int *) MALLOC( aij->N*sizeof(int) ); CHKPTR(aij->colmap);
  MEMSET(aij->colmap,0,aij->N*sizeof(int));
  for ( i=0; i<n; i++ ) aij->colmap[aij->garray[i]] = i+1;
  return 0;
}

static int MatInsertValues_MPIAIJ(Mat mat,int m,int *idxm,int n,
                            int *idxn,Scalar *v,InsertMode addv)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
  int        ierr,i,j, rstart = aij->rstart, rend = aij->rend;
  int        cstart = aij->cstart, cend = aij->cend,row,col;

  if (aij->insertmode != NotSetValues && aij->insertmode != addv) {
    SETERR(1,"You cannot mix inserts and adds");
  }
  aij->insertmode = addv;
  for ( i=0; i<m; i++ ) {
    if (idxm[i] < 0) SETERR(1,"Negative row index");
    if (idxm[i] >= aij->M) SETERR(1,"Row index too large");
    if (idxm[i] >= rstart && idxm[i] < rend) {
      row = idxm[i] - rstart;
      for ( j=0; j<n; j++ ) {
        if (idxn[j] < 0) SETERR(1,"Negative column index");
        if (idxn[j] >= aij->N) SETERR(1,"Column index too large");
        if (idxn[j] >= cstart && idxn[j] < cend){
          col = idxn[j] - cstart;
          ierr = MatSetValues(aij->A,1,&row,1,&col,v+i*n+j,addv);CHKERR(ierr);
        }
        else {
          if (aij->assembled) {
            if (!aij->colmap) {ierr = CreateColmap(mat); CHKERR(ierr);}
            col = aij->colmap[idxn[j]] - 1;
            if (col < 0) {
              SETERR(1,"Cannot insert new off diagonal block nonzero in\
                     already\
                     assembled matrix. Contact petsc-maint@mcs.anl.gov\
                     if your need this feature");
            }
          }
          else col = idxn[j];
          ierr = MatSetValues(aij->B,1,&row,1,&col,v+i*n+j,addv);CHKERR(ierr);
        }
      }
    }
    else {
      ierr = StashValues(&aij->stash,idxm[i],n,idxn,v+i*n,addv);CHKERR(ierr);
    }
  }
  return 0;
}

/*
    the assembly code is alot like the code for vectors, we should
    sometime derive a single assembly code that can be used for
    either case.
*/

static int MatBeginAssemble_MPIAIJ(Mat mat)
{
  Mat_MPIAIJ  *aij = (Mat_MPIAIJ *) mat->data;
  MPI_Comm    comm = mat->comm;
  int         numtids = aij->numtids, *owners = aij->rowners;
  int         mytid = aij->mytid;
  MPI_Request *send_waits,*recv_waits;
  int         *nprocs,i,j,idx,*procs,nsends,nreceives,nmax,*work;
  int         tag = 50, *owner,*starts,count;
  InsertMode  addv;
  Scalar      *rvalues,*svalues;

  /* make sure all processors are either in INSERTMODE or ADDMODE */
  MPI_Allreduce((void *) &aij->insertmode,(void *) &addv,1,MPI_INT,
                MPI_BOR,comm);
  if (addv == (AddValues|InsertValues)) {
    SETERR(1,"Some processors have inserted while others have added");
  }
  aij->insertmode = addv; /* in case this processor had no cache */

  /*  first count number of contributors to each processor */
  nprocs = (int *) MALLOC( 2*numtids*sizeof(int) ); CHKPTR(nprocs);
  MEMSET(nprocs,0,2*numtids*sizeof(int)); procs = nprocs + numtids;
  owner = (int *) MALLOC( (aij->stash.n+1)*sizeof(int) ); CHKPTR(owner);
  for ( i=0; i<aij->stash.n; i++ ) {
    idx = aij->stash.idx[i];
    for ( j=0; j<numtids; j++ ) {
      if (idx >= owners[j] && idx < owners[j+1]) {
        nprocs[j]++; procs[j] = 1; owner[i] = j; break;
      }
    }
  }
  nsends = 0;  for ( i=0; i<numtids; i++ ) { nsends += procs[i];}

  /* inform other processors of number of messages and max length*/
  work = (int *) MALLOC( numtids*sizeof(int) ); CHKPTR(work);
  MPI_Allreduce((void *) procs,(void *) work,numtids,MPI_INT,MPI_SUM,comm);
  nreceives = work[mytid];
  MPI_Allreduce((void *) nprocs,(void *) work,numtids,MPI_INT,MPI_MAX,comm);
  nmax = work[mytid];
  FREE(work);

  /* post receives:
       1) each message will consist of ordered pairs
     (global index,value) we store the global index as a double
     to simplify the message passing.
       2) since we don't know how long each individual message is we
     allocate the largest needed buffer for each receive. Potentially
     this is a lot of wasted space.


       This could be done better.
  */
  rvalues = (Scalar *) MALLOC(3*(nreceives+1)*(nmax+1)*sizeof(Scalar));
  CHKPTR(rvalues);
  recv_waits = (MPI_Request *) MALLOC((nreceives+1)*sizeof(MPI_Request));
  CHKPTR(recv_waits);
  for ( i=0; i<nreceives; i++ ) {
    MPI_Irecv((void *)(rvalues+3*nmax*i),3*nmax,MPI_SCALAR,MPI_ANY_SOURCE,tag,
              comm,recv_waits+i);
  }

  /* do sends:
      1) starts[i] gives the starting index in svalues for stuff going to
         the ith processor
  */
  svalues = (Scalar *) MALLOC( 3*(aij->stash.n+1)*sizeof(Scalar) );
  CHKPTR(svalues);
  send_waits = (MPI_Request *) MALLOC( (nsends+1)*sizeof(MPI_Request));
  CHKPTR(send_waits);
  starts = (int *) MALLOC( numtids*sizeof(int) ); CHKPTR(starts);
  starts[0] = 0;
  for ( i=1; i<numtids; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
  for ( i=0; i<aij->stash.n; i++ ) {
    svalues[3*starts[owner[i]]]       = (Scalar)  aij->stash.idx[i];
    svalues[3*starts[owner[i]]+1]     = (Scalar)  aij->stash.idy[i];
    svalues[3*(starts[owner[i]]++)+2] =  aij->stash.array[i];
  }
  FREE(owner);
  starts[0] = 0;
  for ( i=1; i<numtids; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
  count = 0;
  for ( i=0; i<numtids; i++ ) {
    if (procs[i]) {
      MPI_Isend((void*)(svalues+3*starts[i]),3*nprocs[i],MPI_SCALAR,i,tag,
                comm,send_waits+count++);
    }
  }
  FREE(starts); FREE(nprocs);

  /* Free cache space */
  aij->stash.nmax = aij->stash.n = 0;
  if (aij->stash.array){ FREE(aij->stash.array); aij->stash.array = 0;}

  aij->svalues    = svalues;       aij->rvalues = rvalues;
  aij->nsends     = nsends;         aij->nrecvs = nreceives;
  aij->send_waits = send_waits; aij->recv_waits = recv_waits;
  aij->rmax       = nmax;

  return 0;
}
extern int MatSetUpMultiply_MPIAIJ(Mat);

static int MatEndAssemble_MPIAIJ(Mat mat)
{
  int        ierr;
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;

  MPI_Status  *send_status,recv_status;
  int         imdex,nrecvs = aij->nrecvs, count = nrecvs, i, n;
  int         row,col;
  Scalar      *values,val;
  InsertMode  addv = aij->insertmode;

  /*  wait on receives */
  while (count) {
    MPI_Waitany(nrecvs,aij->recv_waits,&imdex,&recv_status);
    /* unpack receives into our local space */
    values = aij->rvalues + 3*imdex*aij->rmax;
    MPI_Get_count(&recv_status,MPI_SCALAR,&n);
    n = n/3;
    for ( i=0; i<n; i++ ) {
      row = (int) PETSCREAL(values[3*i]) - aij->rstart;
      col = (int) PETSCREAL(values[3*i+1]);
      val = values[3*i+2];
      if (col >= aij->cstart && col < aij->cend) {
          col -= aij->cstart;
        MatSetValues(aij->A,1,&row,1,&col,&val,addv);
      }
      else {
        if (aij->assembled) {
          if (!aij->colmap) {ierr = CreateColmap(mat); CHKERR(ierr);}
          col = aij->colmap[col] - 1;
          if (col < 0) {
            SETERR(1,"Cannot insert new off diagonal block nonzero in\
                     already\
                     assembled matrix. Contact petsc-maint@mcs.anl.gov\
                     if your need this feature");
          }
        }
        MatSetValues(aij->B,1,&row,1,&col,&val,addv);
      }
    }
    count--;
  }
  FREE(aij->recv_waits); FREE(aij->rvalues);

  /* wait on sends */
  if (aij->nsends) {
    send_status = (MPI_Status *) MALLOC( aij->nsends*sizeof(MPI_Status) );
    CHKPTR(send_status);
    MPI_Waitall(aij->nsends,aij->send_waits,send_status);
    FREE(send_status);
  }
  FREE(aij->send_waits); FREE(aij->svalues);

  aij->insertmode = NotSetValues;
  ierr = MatBeginAssembly(aij->A); CHKERR(ierr);
  ierr = MatEndAssembly(aij->A); CHKERR(ierr);

  if (!aij->assembled) {
    ierr = MatSetUpMultiply_MPIAIJ(mat); CHKERR(ierr);
  }
  ierr = MatBeginAssembly(aij->B); CHKERR(ierr);
  ierr = MatEndAssembly(aij->B); CHKERR(ierr);

  aij->assembled = 1;
  return 0;
}

static int MatZero_MPIAIJ(Mat A)
{
  Mat_MPIAIJ *l = (Mat_MPIAIJ *) A->data;

  MatZeroEntries(l->A); MatZeroEntries(l->B);
  return 0;
}

/* again this uses the same basic stratagy as in the assembly and
   scatter create routines, we should try to do it systemamatically
   if we can figure out the proper level of generality. */

/* the code does not do the diagonal entries correctly unless the
   matrix is square and the column and row owerships are identical.
   This is a BUG. The only way to fix it seems to be to access
   aij->A and aij->B directly and not through the MatZeroRows()
   routine.
*/
static int MatZeroRows_MPIAIJ(Mat A,IS is,Scalar *diag)
{
  Mat_MPIAIJ     *l = (Mat_MPIAIJ *) A->data;
  int            i,ierr,N, *rows,*owners = l->rowners,numtids = l->numtids;
  int            *procs,*nprocs,j,found,idx,nsends,*work;
  int            nmax,*svalues,*starts,*owner,nrecvs,mytid = l->mytid;
  int            *rvalues,tag = 67,count,base,slen,n,*source;
  int            *lens,imdex,*lrows,*values;
  MPI_Comm       comm = A->comm;
  MPI_Request    *send_waits,*recv_waits;
  MPI_Status     recv_status,*send_status;
  IS             istmp;

  if (!l->assembled) SETERR(1,"MatZeroRows_MPIAIJ: must assemble matrix first");
  ierr = ISGetLocalSize(is,&N); CHKERR(ierr);
  ierr = ISGetIndices(is,&rows); CHKERR(ierr);

  /*  first count number of contributors to each processor */
  nprocs = (int *) MALLOC( 2*numtids*sizeof(int) ); CHKPTR(nprocs);
  MEMSET(nprocs,0,2*numtids*sizeof(int)); procs = nprocs + numtids;
  owner = (int *) MALLOC((N+1)*sizeof(int)); CHKPTR(owner); /* see note*/
  for ( i=0; i<N; i++ ) {
    idx = rows[i];
    found = 0;
    for ( j=0; j<numtids; j++ ) {
      if (idx >= owners[j] && idx < owners[j+1]) {
        nprocs[j]++; procs[j] = 1; owner[i] = j; found = 1; break;
      }
    }
    if (!found) SETERR(1,"Imdex out of range");
  }
  nsends = 0;  for ( i=0; i<numtids; i++ ) { nsends += procs[i];}

  /* inform other processors of number of messages and max length*/
  work = (int *) MALLOC( numtids*sizeof(int) ); CHKPTR(work);
  MPI_Allreduce((void *) procs,(void *) work,numtids,MPI_INT,MPI_SUM,comm);
  nrecvs = work[mytid];
  MPI_Allreduce((void *) nprocs,(void *) work,numtids,MPI_INT,MPI_MAX,comm);
  nmax = work[mytid];
  FREE(work);

  /* post receives:   */
  rvalues = (int *) MALLOC((nrecvs+1)*(nmax+1)*sizeof(int)); /*see note */
  CHKPTR(rvalues);
  recv_waits = (MPI_Request *) MALLOC((nrecvs+1)*sizeof(MPI_Request));
  CHKPTR(recv_waits);
  for ( i=0; i<nrecvs; i++ ) {
    MPI_Irecv((void *)(rvalues+nmax*i),nmax,MPI_INT,MPI_ANY_SOURCE,tag,
              comm,recv_waits+i);
  }

  /* do sends:
      1) starts[i] gives the starting index in svalues for stuff going to
         the ith processor
  */
  svalues = (int *) MALLOC( (N+1)*sizeof(int) ); CHKPTR(svalues);
  send_waits = (MPI_Request *) MALLOC( (nsends+1)*sizeof(MPI_Request));
  CHKPTR(send_waits);
  starts = (int *) MALLOC( (numtids+1)*sizeof(int) ); CHKPTR(starts);
  starts[0] = 0;
  for ( i=1; i<numtids; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
  for ( i=0; i<N; i++ ) {
    svalues[starts[owner[i]]++] = rows[i];
  }
  ISRestoreIndices(is,&rows);

  starts[0] = 0;
  for ( i=1; i<numtids+1; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
  count = 0;
  for ( i=0; i<numtids; i++ ) {
    if (procs[i]) {
      MPI_Isend((void*)(svalues+starts[i]),nprocs[i],MPI_INT,i,tag,
                comm,send_waits+count++);
    }
  }
  FREE(starts);

  base = owners[mytid];

  /*  wait on receives */
  lens = (int *) MALLOC( 2*(nrecvs+1)*sizeof(int) ); CHKPTR(lens);
  source = lens + nrecvs;
  count = nrecvs; slen = 0;
  while (count) {
    MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);
    /* unpack receives into our local space */
    MPI_Get_count(&recv_status,MPI_INT,&n);
    source[imdex]  = recv_status.MPI_SOURCE;
    lens[imdex]  = n;
    slen += n;
    count--;
  }
  FREE(recv_waits);

  /* move the data into the send scatter */
  lrows = (int *) MALLOC( slen*sizeof(int) ); CHKPTR(lrows);
  count = 0;
  for ( i=0; i<nrecvs; i++ ) {
    values = rvalues + i*nmax;
    for ( j=0; j<lens[i]; j++ ) {
      lrows[count++] = values[j] - base;
    }
  }
  FREE(rvalues); FREE(lens);
  FREE(owner); FREE(nprocs);

  /* actually zap the local rows */
  ierr = ISCreateSequential(slen,lrows,&istmp); CHKERR(ierr);  FREE(lrows);
  ierr = MatZeroRows(l->A,istmp,diag); CHKERR(ierr);
  ierr = MatZeroRows(l->B,istmp,0); CHKERR(ierr);
  ierr = ISDestroy(istmp); CHKERR(ierr);

  /* wait on sends */
  if (nsends) {
    send_status = (MPI_Status *) MALLOC( nsends*sizeof(MPI_Status) );
    CHKPTR(send_status);
    MPI_Waitall(nsends,send_waits,send_status);
    FREE(send_status);
  }
  FREE(send_waits); FREE(svalues);


  return 0;
}

static int MatMult_MPIAIJ(Mat aijin,Vec xx,Vec yy)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) aijin->data;
  int        ierr;
  if (!aij->assembled) SETERR(1,"MatMult_MPIAIJ: must assemble matrix first");
  ierr = VecScatterBegin(xx,0,aij->lvec,0,InsertValues,ScatterAll,aij->Mvctx);
  CHKERR(ierr);
  ierr = MatMult(aij->A,xx,yy); CHKERR(ierr);
  ierr = VecScatterEnd(xx,0,aij->lvec,0,InsertValues,ScatterAll,aij->Mvctx);
  CHKERR(ierr);
  ierr = MatMultAdd(aij->B,aij->lvec,yy,yy); CHKERR(ierr);
  return 0;
}

static int MatMultAdd_MPIAIJ(Mat aijin,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) aijin->data;
  int        ierr;
  if (!aij->assembled) SETERR(1,"MatMult_MPIAIJ: must assemble matrix first");
  ierr = VecScatterBegin(xx,0,aij->lvec,0,InsertValues,ScatterAll,aij->Mvctx);
  CHKERR(ierr);
  ierr = MatMultAdd(aij->A,xx,yy,zz); CHKERR(ierr);
  ierr = VecScatterEnd(xx,0,aij->lvec,0,InsertValues,ScatterAll,aij->Mvctx);
  CHKERR(ierr);
  ierr = MatMultAdd(aij->B,aij->lvec,zz,zz); CHKERR(ierr);
  return 0;
}

static int MatMultTrans_MPIAIJ(Mat aijin,Vec xx,Vec yy)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) aijin->data;
  int        ierr;

  if (!aij->assembled)
    SETERR(1,"MatMulTrans_MPIAIJ: must assemble matrix first");
  /* do nondiagonal part */
  ierr = MatMultTrans(aij->B,xx,aij->lvec); CHKERR(ierr);
  /* send it on its way */
  ierr = VecScatterBegin(aij->lvec,0,yy,0,AddValues,
                         ScatterAll|ScatterReverse,aij->Mvctx); CHKERR(ierr);
  /* do local part */
  ierr = MatMultTrans(aij->A,xx,yy); CHKERR(ierr);
  /* receive remote parts: note this assumes the values are not actually */
  /* inserted in yy until the next line, which is true for my implementation*/
  /* but is not perhaps always true. */
  ierr = VecScatterEnd(aij->lvec,0,yy,0,AddValues,ScatterAll|ScatterReverse,
                         aij->Mvctx); CHKERR(ierr);
  return 0;
}

static int MatMultTransAdd_MPIAIJ(Mat aijin,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) aijin->data;
  int        ierr;

  if (!aij->assembled)
    SETERR(1,"MatMulTransAdd_MPIAIJ: must assemble matrix first");
  /* do nondiagonal part */
  ierr = MatMultTrans(aij->B,xx,aij->lvec); CHKERR(ierr);
  /* send it on its way */
  ierr = VecScatterBegin(aij->lvec,0,zz,0,AddValues,
                         ScatterAll|ScatterReverse,aij->Mvctx); CHKERR(ierr);
  /* do local part */
  ierr = MatMultTransAdd(aij->A,xx,yy,zz); CHKERR(ierr);
  /* receive remote parts: note this assumes the values are not actually */
  /* inserted in yy until the next line, which is true for my implementation*/
  /* but is not perhaps always true. */
  ierr = VecScatterEnd(aij->lvec,0,zz,0,AddValues,ScatterAll|ScatterReverse,
                         aij->Mvctx); CHKERR(ierr);
  return 0;
}

/*
  This only works correctly for square matrices where the subblock A->A is the
   diagonal block
*/
static int MatGetDiag_MPIAIJ(Mat Ain,Vec v)
{
  Mat_MPIAIJ *A = (Mat_MPIAIJ *) Ain->data;
  if (!A->assembled) SETERR(1,"MatGetDiag_MPIAIJ: must assemble matrix first");
  return MatGetDiagonal(A->A,v);
}

static int MatDestroy_MPIAIJ(PetscObject obj)
{
  Mat        mat = (Mat) obj;
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
  int        ierr;
#if defined(PETSC_LOG)
  PLogObjectState(obj,"Rows %d Cols %d",aij->M,aij->N);
#endif
  FREE(aij->rowners);
  ierr = MatDestroy(aij->A); CHKERR(ierr);
  ierr = MatDestroy(aij->B); CHKERR(ierr);
  if (aij->colmap) FREE(aij->colmap);
  if (aij->garray) FREE(aij->garray);
  if (aij->lvec) VecDestroy(aij->lvec);
  if (aij->Mvctx) VecScatterCtxDestroy(aij->Mvctx);
  FREE(aij);
  PLogObjectDestroy(mat);
  PETSCHEADERDESTROY(mat);
  return 0;
}

static int MatView_MPIAIJ(PetscObject obj,Viewer viewer)
{
  Mat        mat = (Mat) obj;
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
  int        ierr;
  PetscObject vobj = (PetscObject) viewer;

  if (!viewer) { /* so that viewers may be used from debuggers */
    viewer = STDOUT_VIEWER; vobj = (PetscObject) viewer;
  }
  if (!aij->assembled) SETERR(1,"MatView_MPIAIJ: must assemble matrix first");
  if (vobj->cookie == VIEWER_COOKIE) {
    FILE *fd = ViewerFileGetPointer(viewer);
    if (vobj->type == FILE_VIEWER) {
      MPE_Seq_begin(mat->comm,1);
      fprintf(fd,"[%d] rows %d starts %d ends %d cols %d starts %d ends %d\n",
             aij->mytid,aij->m,aij->rstart,aij->rend,aij->n,aij->cstart,
             aij->cend);
      ierr = MatView(aij->A,viewer); CHKERR(ierr);
      ierr = MatView(aij->B,viewer); CHKERR(ierr);
      fflush(fd);
      MPE_Seq_end(mat->comm,1);
    }
    else if (vobj->type == FILES_VIEWER) {
      int numtids = aij->numtids, mytid = aij->mytid;
      if (numtids == 1) {
        ierr = MatView(aij->A,viewer); CHKERR(ierr);
      }
      else {
        /* assemble the entire matrix onto first processor. */
        Mat     A;
        Mat_AIJ *Aaij;
        int     M = aij->M, N = aij->N,m,*ai,*aj,row,*cols,i,*ct;
        Scalar  *a;
        if (!mytid) {
          ierr = MatCreateMPIAIJ(mat->comm,M,N,M,N,0,0,0,0,&A);
        }
        else {
          ierr = MatCreateMPIAIJ(mat->comm,0,0,M,N,0,0,0,0,&A);
        }
        CHKERR(ierr);

        /* copy over the A part */
        Aaij = (Mat_AIJ*) aij->A->data;
        m = Aaij->m; ai = Aaij->i; aj = Aaij->j; a = Aaij->a;
        row = aij->rstart;
        for ( i=0; i<ai[m]; i++ ) {aj[i] += aij->cstart - 1;}
        for ( i=0; i<m; i++ ) {
          ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,InsertValues);
          CHKERR(ierr);
          row++; a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
        }
        aj = Aaij->j;
        for ( i=0; i<ai[m]; i++ ) {aj[i] -= aij->cstart - 1;}

        /* copy over the B part */
        Aaij = (Mat_AIJ*) aij->B->data;
        m = Aaij->m;  ai = Aaij->i; aj = Aaij->j; a = Aaij->a;
        row = aij->rstart;
        ct = cols = (int *) MALLOC( (ai[m]+1)*sizeof(int) ); CHKPTR(cols);
        for ( i=0; i<ai[m]; i++ ) {cols[i] = aij->garray[aj[i]-1];}
        for ( i=0; i<m; i++ ) {
          ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,InsertValues);
          CHKERR(ierr);
          row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
        }
        FREE(ct);

        ierr = MatBeginAssembly(A); CHKERR(ierr);
        ierr = MatEndAssembly(A); CHKERR(ierr);
        if (!mytid) {
          ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,viewer); CHKERR(ierr);
        }
        ierr = MatDestroy(A); CHKERR(ierr);
      }
    }
  }
  return 0;
}

extern int MatMarkDiag_AIJ(Mat_AIJ  *);
/*
    This has to provide several versions.

     1) per sequential
     2) a) use only local smoothing updating outer values only once.
        b) local smoothing updating outer values each inner iteration
     3) color updating out values betwen colors.
*/
static int MatRelax_MPIAIJ(Mat matin,Vec bb,double omega,int flag,double shift,
                        int its,Vec xx)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
  Mat        AA = mat->A, BB = mat->B;
  Mat_AIJ    *A = (Mat_AIJ *) AA->data, *B = (Mat_AIJ *)BB->data;
  Scalar     zero = 0.0,*b,*x,*xs,*ls,d,*v,sum,scale,*t,*ts;
  int        ierr,*idx, *diag;
  int        n = mat->n, m = mat->m, i;
  Vec        tt;

  if (!mat->assembled) SETERR(1,"MatRelax_MPIAIJ: must assemble matrix first");

  VecGetArray(xx,&x); VecGetArray(bb,&b); VecGetArray(mat->lvec,&ls);
  xs = x -1; /* shift by one for index start of 1 */
  ls--;
  if (!A->diag) {if ((ierr = MatMarkDiag_AIJ(A))) return ierr;}
  diag = A->diag;
  if (flag == SOR_APPLY_UPPER || flag == SOR_APPLY_LOWER) {
    SETERR(1,"That option not yet support for parallel AIJ matrices");
  }
  if (flag & SOR_EISENSTAT) {
    /* Let  A = L + U + D; where L is lower trianglar,
    U is upper triangular, E is diagonal; This routine applies

            (L + E)^{-1} A (U + E)^{-1}

    to a vector efficiently using Eisenstat's trick. This is for
    the case of SSOR preconditioner, so E is D/omega where omega
    is the relaxation factor.
    */
    ierr = VecCreate(xx,&tt); CHKERR(ierr);
    VecGetArray(tt,&t);
    scale = (2.0/omega) - 1.0;
    /*  x = (E + U)^{-1} b */
    VecSet(&zero,mat->lvec);
    ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                              mat->Mvctx); CHKERR(ierr);
    for ( i=m-1; i>-1; i-- ) {
      n    = A->i[i+1] - diag[i] - 1;
      idx  = A->j + diag[i];
      v    = A->a + diag[i];
      sum  = b[i];
      SPARSEDENSEMDOT(sum,xs,v,idx,n);
      d    = shift + A->a[diag[i]-1];
      n    = B->i[i+1] - B->i[i];
      idx  = B->j + B->i[i] - 1;
      v    = B->a + B->i[i] - 1;
      SPARSEDENSEMDOT(sum,ls,v,idx,n);
      x[i] = omega*(sum/d);
    }
    ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                            mat->Mvctx); CHKERR(ierr);

    /*  t = b - (2*E - D)x */
    v = A->a;
    for ( i=0; i<m; i++ ) { t[i] = b[i] - scale*(v[*diag++ - 1])*x[i]; }

    /*  t = (E + L)^{-1}t */
    ts = t - 1; /* shifted by one for index start of a or mat->j*/
    diag = A->diag;
    VecSet(&zero,mat->lvec);
    ierr = VecPipelineBegin(tt,0,mat->lvec,0,InsertValues,PipelineDown,
                                                 mat->Mvctx); CHKERR(ierr);
    for ( i=0; i<m; i++ ) {
      n    = diag[i] - A->i[i];
      idx  = A->j + A->i[i] - 1;
      v    = A->a + A->i[i] - 1;
      sum  = t[i];
      SPARSEDENSEMDOT(sum,ts,v,idx,n);
      d    = shift + A->a[diag[i]-1];
      n    = B->i[i+1] - B->i[i];
      idx  = B->j + B->i[i] - 1;
      v    = B->a + B->i[i] - 1;
      SPARSEDENSEMDOT(sum,ls,v,idx,n);
      t[i] = omega*(sum/d);
    }
    ierr = VecPipelineEnd(tt,0,mat->lvec,0,InsertValues,PipelineDown,
                                                    mat->Mvctx); CHKERR(ierr);
    /*  x = x + t */
    for ( i=0; i<m; i++ ) { x[i] += t[i]; }
    VecDestroy(tt);
    return 0;
  }


  if ((flag & SOR_SYMMETRIC_SWEEP) == SOR_SYMMETRIC_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      VecSet(&zero,mat->lvec); VecSet(&zero,xx);
    }
    else {
      ierr=VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterUp,mat->Mvctx);
      CHKERR(ierr);
      ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterUp,mat->Mvctx);
      CHKERR(ierr);
    }
    while (its--) {
      /* go down through the rows */
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=0; i<m; i++ ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                            mat->Mvctx); CHKERR(ierr);
      /* come up through the rows */
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=m-1; i>-1; i-- ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                            mat->Mvctx); CHKERR(ierr);
    }
  }
  else if (flag & SOR_FORWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      VecSet(&zero,mat->lvec);
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=0; i<m; i++ ) {
        n    = diag[i] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = omega*(sum/d);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                            mat->Mvctx); CHKERR(ierr);
      its--;
    }
    while (its--) {
      ierr=VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterUp,mat->Mvctx);
      CHKERR(ierr);
      ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterUp,mat->Mvctx);
      CHKERR(ierr);
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=0; i<m; i++ ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineDown,
                            mat->Mvctx); CHKERR(ierr);
    }
  }
  else if (flag & SOR_BACKWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      VecSet(&zero,mat->lvec);
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=m-1; i>-1; i-- ) {
        n    = A->i[i+1] - diag[i] - 1;
        idx  = A->j + diag[i];
        v    = A->a + diag[i];
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = omega*(sum/d);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                            mat->Mvctx); CHKERR(ierr);
      its--;
    }
    while (its--) {
      ierr = VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterDown,
                            mat->Mvctx); CHKERR(ierr);
      ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterDown,
                            mat->Mvctx); CHKERR(ierr);
      ierr = VecPipelineBegin(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                              mat->Mvctx); CHKERR(ierr);
      for ( i=m-1; i>-1; i-- ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
      ierr = VecPipelineEnd(xx,0,mat->lvec,0,InsertValues,PipelineUp,
                            mat->Mvctx); CHKERR(ierr);
    }
  }
  else if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      return MatRelax(mat->A,bb,omega,flag,shift,its,xx);
    }
    ierr=VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterAll,mat->Mvctx);
    CHKERR(ierr);
    ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterAll,mat->Mvctx);
    CHKERR(ierr);
    while (its--) {
      /* go down through the rows */
      for ( i=0; i<m; i++ ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
      /* come up through the rows */
      for ( i=m-1; i>-1; i-- ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
    }
  }
  else if (flag & SOR_LOCAL_FORWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      return MatRelax(mat->A,bb,omega,flag,shift,its,xx);
    }
    ierr=VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterAll,mat->Mvctx);
    CHKERR(ierr);
    ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterAll,mat->Mvctx);
    CHKERR(ierr);
    while (its--) {
      for ( i=0; i<m; i++ ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
    }
  }
  else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      return MatRelax(mat->A,bb,omega,flag,shift,its,xx);
    }
    ierr = VecScatterBegin(xx,0,mat->lvec,0,InsertValues,ScatterAll,
                            mat->Mvctx); CHKERR(ierr);
    ierr = VecScatterEnd(xx,0,mat->lvec,0,InsertValues,ScatterAll,
                            mat->Mvctx); CHKERR(ierr);
    while (its--) {
      for ( i=m-1; i>-1; i-- ) {
        n    = A->i[i+1] - A->i[i];
        idx  = A->j + A->i[i] - 1;
        v    = A->a + A->i[i] - 1;
        sum  = b[i];
        SPARSEDENSEMDOT(sum,xs,v,idx,n);
        d    = shift + A->a[diag[i]-1];
        n    = B->i[i+1] - B->i[i];
        idx  = B->j + B->i[i] - 1;
        v    = B->a + B->i[i] - 1;
        SPARSEDENSEMDOT(sum,ls,v,idx,n);
        x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
      }
    }
  }
  return 0;
}
static int MatInsOpt_MPIAIJ(Mat aijin,int op)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *) aijin->data;

  if      (op == NO_NEW_NONZERO_LOCATIONS)  {
    MatSetOption(aij->A,op);
    MatSetOption(aij->B,op);
  }
  else if (op == YES_NEW_NONZERO_LOCATIONS) {
    MatSetOption(aij->A,op);
    MatSetOption(aij->B,op);
  }
  else if (op == COLUMN_ORIENTED) SETERR(1,"Column oriented not supported");
  return 0;
}

static int MatSize_MPIAIJ(Mat matin,int *m,int *n)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
  *m = mat->M; *n = mat->N;
  return 0;
}

static int MatLocalSize_MPIAIJ(Mat matin,int *m,int *n)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
  *m = mat->m; *n = mat->n;
  return 0;
}

static int MatRange_MPIAIJ(Mat matin,int *m,int *n)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
  *m = mat->rstart; *n = mat->rend;
  return 0;
}

static int MatGetRow_MPIAIJ(Mat matin,int row,int *nz,int **idx,Scalar **v)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
  Scalar     *vworkA, *vworkB, **pvA, **pvB;
  int        i, ierr, *cworkA, *cworkB, **pcA, **pcB, cstart = mat->cstart;
  int        nztot, nzA, nzB, lrow, rstart = mat->rstart, rend = mat->rend;

  if (!mat->assembled)
    SETERR(1,"MatGetRow_MPIAIJ: Must assemble matrix first.");
  if (row < rstart || row >= rend)
    SETERR(1,"MatGetRow_MPIAIJ: Currently you can get only local rows.")
  lrow = row - rstart;

  pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
  if (!v)   {pvA = 0; pvB = 0;}
  if (!idx) {pcA = 0; if (!v) pcB = 0;}
  ierr = MatGetRow(mat->A,lrow,&nzA,pcA,pvA); CHKERR(ierr);
  ierr = MatGetRow(mat->B,lrow,&nzB,pcB,pvB); CHKERR(ierr);
  nztot = nzA + nzB;

  if (v  || idx) {
    if (nztot) {
      /* Sort by increasing column numbers, assuming A and B already sorted */
      int imark, imark2;
      for (i=0; i<nzB; i++) cworkB[i] = mat->garray[cworkB[i]];
      if (v) {
        *v = (Scalar *) MALLOC( (nztot)*sizeof(Scalar) ); CHKPTR(*v);
        for ( i=0; i<nzB; i++ ) {
          if (cworkB[i] < cstart)   (*v)[i] = vworkB[i];
          else break;
        }
        imark = i;
        for ( i=0; i<nzA; i++ )     (*v)[imark+i] = vworkA[i];
        imark2 = imark+nzA;
        for ( i=imark; i<nzB; i++ ) (*v)[imark2+i] = vworkB[i];
      }
      if (idx) {
        *idx = (int *) MALLOC( (nztot)*sizeof(int) ); CHKPTR(*idx);
        for (i=0; i<nzA; i++) cworkA[i] += cstart;
        for ( i=0; i<nzB; i++ ) {
          if (cworkB[i] < cstart)   (*idx)[i] = cworkB[i];
          else break;
        }
        imark = i;
        for ( i=0; i<nzA; i++ )     (*idx)[imark+i] = cworkA[i];
        imark2 = imark+nzA;
        for ( i=imark; i<nzB; i++ ) (*idx)[imark2+i] = cworkB[i];
      }
    }
    else {*idx = 0; *v=0;}
  }
  *nz = nztot;
  ierr = MatRestoreRow(mat->A,lrow,&nzA,pcA,pvA); CHKERR(ierr);
  ierr = MatRestoreRow(mat->B,lrow,&nzB,pcB,pvB); CHKERR(ierr);
  return 0;
}

static int MatRestoreRow_MPIAIJ(Mat mat,int row,int *nz,int **idx,Scalar **v)
{
  if (idx) FREE(*idx);
  if (v) FREE(*v);
  return 0;
}

static int MatCopy_MPIAIJ(Mat,Mat *);
extern int MatConvert_MPIAIJ(Mat,MATTYPE,Mat *);

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps = {MatInsertValues_MPIAIJ,
       MatGetRow_MPIAIJ,MatRestoreRow_MPIAIJ,
       MatMult_MPIAIJ,MatMultAdd_MPIAIJ,
       MatMultTrans_MPIAIJ,MatMultTransAdd_MPIAIJ,
       0,0,0,0,
       0,0,
       MatRelax_MPIAIJ,
       0,
       0,0,0,
       MatCopy_MPIAIJ,
       MatGetDiag_MPIAIJ,0,0,
       MatBeginAssemble_MPIAIJ,MatEndAssemble_MPIAIJ,
       0,
       MatInsOpt_MPIAIJ,MatZero_MPIAIJ,MatZeroRows_MPIAIJ,0,
       0,0,0,0,
       MatSize_MPIAIJ,MatLocalSize_MPIAIJ,MatRange_MPIAIJ,
       0,0,
       0,MatConvert_MPIAIJ };

/*@

      MatCreateMPIAIJ - Creates a sparse parallel matrix
                                 in AIJ format.

  Input Parameters:
.   comm - MPI communicator
.   m,n - number of local rows and columns (or -1 to have calculated)
.   M,N - global rows and columns (or -1 to have calculated)
.   d_nz - total number nonzeros in diagonal portion of matrix
.   d_nzz - number of nonzeros per row in diagonal portion of matrix or null
.           You must leave room for the diagonal entry even if it is zero.
.   o_nz - total number nonzeros in off-diagonal portion of matrix
.   o_nzz - number of nonzeros per row in off-diagonal portion of matrix
.           or null. You must have at least one nonzero per row.

  Output parameters:
.  newmat - the matrix

  Keywords: matrix, aij, compressed row, sparse, parallel
@*/
int MatCreateMPIAIJ(MPI_Comm comm,int m,int n,int M,int N,
                 int d_nz,int *d_nnz, int o_nz,int *o_nnz,Mat *newmat)
{
  Mat          mat;
  Mat_MPIAIJ   *aij;
  int          ierr, i,sum[2],work[2];
  *newmat         = 0;
  PETSCHEADERCREATE(mat,_Mat,MAT_COOKIE,MATMPIAIJ,comm);
  PLogObjectCreate(mat);
  mat->data       = (void *) (aij = NEW(Mat_MPIAIJ)); CHKPTR(aij);
  mat->ops        = &MatOps;
  mat->destroy    = MatDestroy_MPIAIJ;
  mat->view       = MatView_MPIAIJ;
  mat->factor     = 0;
  mat->row        = 0;
  mat->col        = 0;

  mat->comm       = comm;
  aij->insertmode = NotSetValues;
  MPI_Comm_rank(comm,&aij->mytid);
  MPI_Comm_size(comm,&aij->numtids);

  if (M == -1 || N == -1) {
    work[0] = m; work[1] = n;
    MPI_Allreduce((void *) work,(void *) sum,2,MPI_INT,MPI_SUM,comm );
    if (M == -1) M = sum[0];
    if (N == -1) N = sum[1];
  }
  if (m == -1) {m = M/aij->numtids + ((M % aij->numtids) > aij->mytid);}
  if (n == -1) {n = N/aij->numtids + ((N % aij->numtids) > aij->mytid);}
  aij->m       = m;
  aij->n       = n;
  aij->N       = N;
  aij->M       = M;

  /* build local table of row and column ownerships */
  aij->rowners = (int *) MALLOC(2*(aij->numtids+2)*sizeof(int));
  CHKPTR(aij->rowners);
  aij->cowners = aij->rowners + aij->numtids + 1;
  MPI_Allgather(&m,1,MPI_INT,aij->rowners+1,1,MPI_INT,comm);
  aij->rowners[0] = 0;
  for ( i=2; i<=aij->numtids; i++ ) {
    aij->rowners[i] += aij->rowners[i-1];
  }
  aij->rstart = aij->rowners[aij->mytid];
  aij->rend   = aij->rowners[aij->mytid+1];
  MPI_Allgather(&n,1,MPI_INT,aij->cowners+1,1,MPI_INT,comm);
  aij->cowners[0] = 0;
  for ( i=2; i<=aij->numtids; i++ ) {
    aij->cowners[i] += aij->cowners[i-1];
  }
  aij->cstart = aij->cowners[aij->mytid];
  aij->cend   = aij->cowners[aij->mytid+1];


  ierr = MatCreateSequentialAIJ(m,n,d_nz,d_nnz,&aij->A); CHKERR(ierr);
  PLogObjectParent(mat,aij->A);
  ierr = MatCreateSequentialAIJ(m,N,o_nz,o_nnz,&aij->B); CHKERR(ierr);
  PLogObjectParent(mat,aij->B);

  /* build cache for off array entries formed */
  aij->stash.nmax = CHUNCKSIZE; /* completely arbratray number */
  aij->stash.n    = 0;
  aij->stash.array = (Scalar *) MALLOC( aij->stash.nmax*(2*sizeof(int) +
                            sizeof(Scalar))); CHKPTR(aij->stash.array);
  aij->stash.idx = (int *) (aij->stash.array + aij->stash.nmax);
  aij->stash.idy = (int *) (aij->stash.idx + aij->stash.nmax);
  aij->colmap    = 0;
  aij->garray    = 0;

  /* stuff used for matrix vector multiply */
  aij->lvec      = 0;
  aij->Mvctx     = 0;
  aij->assembled = 0;

  *newmat = mat;
  return 0;
}

static int MatCopy_MPIAIJ(Mat matin,Mat *newmat)
{
  Mat        mat;
  Mat_MPIAIJ *aij,*oldmat = (Mat_MPIAIJ *) matin->data;
  int        ierr;
  *newmat      = 0;

  if (!oldmat->assembled) SETERR(1,"Cannot copy unassembled matrix");
  PETSCHEADERCREATE(mat,_Mat,MAT_COOKIE,MATMPIAIJ,matin->comm);
  PLogObjectCreate(mat);
  mat->data       = (void *) (aij = NEW(Mat_MPIAIJ)); CHKPTR(aij);
  mat->ops        = &MatOps;
  mat->destroy    = MatDestroy_MPIAIJ;
  mat->view       = MatView_MPIAIJ;
  mat->factor     = matin->factor;
  mat->row        = 0;
  mat->col        = 0;

  aij->m          = oldmat->m;
  aij->n          = oldmat->n;
  aij->M          = oldmat->M;
  aij->N          = oldmat->N;

  aij->assembled  = 1;
  aij->rstart     = oldmat->rstart;
  aij->rend       = oldmat->rend;
  aij->cstart     = oldmat->cstart;
  aij->cend       = oldmat->cend;
  aij->numtids    = oldmat->numtids;
  aij->mytid      = oldmat->mytid;
  aij->insertmode = NotSetValues;

  aij->rowners    = (int *) MALLOC( (aij->numtids+1)*sizeof(int) );
  CHKPTR(aij->rowners);
  MEMCPY(aij->rowners,oldmat->rowners,(aij->numtids+1)*sizeof(int));
  aij->stash.nmax = 0;
  aij->stash.n    = 0;
  aij->stash.array= 0;
  aij->colmap     = 0;
  aij->garray     = 0;
  mat->comm       = matin->comm;

  ierr =  VecCreate(oldmat->lvec,&aij->lvec); CHKERR(ierr);
  PLogObjectParent(mat,aij->lvec);
  ierr =  VecScatterCtxCopy(oldmat->Mvctx,&aij->Mvctx); CHKERR(ierr);
  PLogObjectParent(mat,aij->Mvctx);
  ierr =  MatCopy(oldmat->A,&aij->A); CHKERR(ierr);
  PLogObjectParent(mat,aij->A);
  ierr =  MatCopy(oldmat->B,&aij->B); CHKERR(ierr);
  PLogObjectParent(mat,aij->B);
  *newmat = mat;
  return 0;
}