aij/mpi/mpiaij.c

#ifndef lint
static char vcid[] = "$Id: mpiaij.c,v 1.7 1995/03/06 04:04:51 bsmith Exp bsmith $";
#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;
}

static int MatiAIJInsertValues(Mat mat,int m,int *idxm,int n,
                            int *idxn,Scalar *v,InsertMode addv)
{
  Matimpiaij *aij = (Matimpiaij *) 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) {
            SETERR(1,"Cannot insert off diagonal block in already\
                     assembled matrix. Contact petsc-maint@mcs.anl.gov\
                     if your need this feature");
          }
          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 MatiAIJBeginAssemble(Mat mat)
{
  Matimpiaij  *aij = (Matimpiaij *) 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 MPIAIJSetUpMultiply(Mat);

static int MatiAIJEndAssemble(Mat mat)
{
  int        ierr;
  Matimpiaij *aij = (Matimpiaij *) 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) {
          SETERR(1,"Cannot insert off diagonal block 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) {
    /* this is because the present implimentation doesn't support
     inserting values off the diagonal block.*/
    return 0;
  }

  ierr = MPIAIJSetUpMultiply(mat); CHKERR(ierr);
  ierr = MatBeginAssembly(aij->B); CHKERR(ierr);
  ierr = MatEndAssembly(aij->B); CHKERR(ierr);

  aij->assembled = 1;
  return 0;
}

static int MatiZero(Mat A)
{
  Matimpiaij *l = (Matimpiaij *) 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 MatiZerorows(Mat A,IS is,Scalar *diag)
{
  Matimpiaij     *l = (Matimpiaij *) 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,"MatiZerorows: must assmble 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 MatiAIJMult(Mat aijin,Vec xx,Vec yy)
{
  Matimpiaij *aij = (Matimpiaij *) aijin->data;
  int        ierr;
  if (!aij->assembled) SETERR(1,"MatiAIJMul: must assmble 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 MatiAIJMultadd(Mat aijin,Vec xx,Vec yy,Vec zz)
{
  Matimpiaij *aij = (Matimpiaij *) aijin->data;
  int        ierr;
  if (!aij->assembled) SETERR(1,"MatiAIJMul: must assmble 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 MatiAIJMultTrans(Mat aijin,Vec xx,Vec yy)
{
  Matimpiaij *aij = (Matimpiaij *) aijin->data;
  int        ierr;

  if (!aij->assembled) SETERR(1,"MatiAIJMulTrans: must assmble 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 MatiAIJMultTransadd(Mat aijin,Vec xx,Vec yy,Vec zz)
{
  Matimpiaij *aij = (Matimpiaij *) aijin->data;
  int        ierr;

  if (!aij->assembled) SETERR(1,"MatiAIJMulTrans: must assmble 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 MatiAIJgetdiag(Mat Ain,Vec v)
{
  Matimpiaij *A = (Matimpiaij *) Ain->data;
  if (!A->assembled) SETERR(1,"MatiAIJgetdiag: must assmble matrix first");
  return MatGetDiagonal(A->A,v);
}

static int MatiAIJdestroy(PetscObject obj)
{
  Mat        mat = (Mat) obj;
  Matimpiaij *aij = (Matimpiaij *) mat->data;
  int        ierr;
  FREE(aij->rowners);
  ierr = MatDestroy(aij->A); CHKERR(ierr);
  ierr = MatDestroy(aij->B); CHKERR(ierr);
  FREE(aij); FREE(mat);
  if (aij->lvec) VecDestroy(aij->lvec);
  if (aij->Mvctx) VecScatterCtxDestroy(aij->Mvctx);
  return 0;
}

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

  if (!aij->assembled) SETERR(1,"MatiAIJMulTrans: must assmble matrix first");
  MPE_Seq_begin(mat->comm,1);
    printf("[%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,0); CHKERR(ierr);
    ierr = MatView(aij->B,0); CHKERR(ierr);
    fflush(stdout);
  MPE_Seq_end(mat->comm,1);
  return 0;
}

extern int MatiAIJmarkdiag(Matiaij  *);
/*
    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 MatiAIJrelax(Mat matin,Vec bb,double omega,int flag,double shift,
                        int its,Vec xx)
{
  Matimpiaij *mat = (Matimpiaij *) matin->data;
  Mat        AA = mat->A, BB = mat->B;
  Matiaij    *A = (Matiaij *) AA->data, *B = (Matiaij *)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,"MatiAIJRelax: must assmble 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 = MatiAIJmarkdiag(A))) return ierr;}
  diag = A->diag;
  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 MatiAIJinsopt(Mat aijin,int op)
{
  Matimpiaij *aij = (Matimpiaij *) 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 MatiAIJsize(Mat matin,int *m,int *n)
{
  Matimpiaij *mat = (Matimpiaij *) matin->data;
  *m = mat->M; *n = mat->N;
  return 0;
}

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

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

static int MatiCopy(Mat,Mat *);

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps = {MatiAIJInsertValues,
       0, 0,
       MatiAIJMult,MatiAIJMultadd,MatiAIJMultTrans,MatiAIJMultTransadd,
       0,0,0,0,
       0,0,
       MatiAIJrelax,
       0,
       0,0,0,
       MatiCopy,
       MatiAIJgetdiag,0,0,
       MatiAIJBeginAssemble,MatiAIJEndAssemble,
       0,
       MatiAIJinsopt,MatiZero,MatiZerorows,0,
       0,0,0,0,
       MatiAIJsize,MatiAIJlocalsize,MatiAIJrange };


/*@

      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;
  Matimpiaij   *aij;
  int          ierr, i,sum[2],work[2];
  *newmat         = 0;
  CREATEHEADER(mat,_Mat);
  mat->data       = (void *) (aij = NEW(Matimpiaij)); CHKPTR(aij);
  mat->cookie     = MAT_COOKIE;
  mat->ops        = &MatOps;
  mat->destroy    = MatiAIJdestroy;
  mat->view       = MatiView;
  mat->type       = MATAIJMPI;
  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);
  ierr = MatCreateSequentialAIJ(m,N,o_nz,o_nnz,&aij->B); CHKERR(ierr);

  /* 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);

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

  *newmat = mat;
  return 0;
}

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

  if (!oldmat->assembled) SETERR(1,"Cannot copy unassembled matrix");
  CREATEHEADER(mat,_Mat);
  mat->data       = (void *) (aij = NEW(Matimpiaij)); CHKPTR(aij);
  mat->cookie     = MAT_COOKIE;
  mat->ops        = &MatOps;
  mat->destroy    = MatiAIJdestroy;
  mat->view       = MatiView;
  mat->type       = MATAIJMPI;
  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;
  mat->comm       = matin->comm;

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