xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 8aeee837e39241f7ecf3a62c74b9dd3234a177b2)

#include "src/mat/impls/aij/mpi/mpiaij.h"
#include "src/inline/spops.h"

/*
  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.  When PETSC_USE_CTABLE is used this is scalable at
a slightly higher hash table cost; without it it is not scalable (each processor
has an order N integer array but is fast to acess.
*/
#undef __FUNCT__
#define __FUNCT__ "CreateColmap_MPIAIJ_Private"
PetscErrorCode CreateColmap_MPIAIJ_Private(Mat mat)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode ierr;
  int        n = aij->B->n,i;

  PetscFunctionBegin;
#if defined (PETSC_USE_CTABLE)
  ierr = PetscTableCreate(n,&aij->colmap);CHKERRQ(ierr);
  for (i=0; i<n; i++){
    ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1);CHKERRQ(ierr);
  }
#else
  ierr = PetscMalloc((mat->N+1)*sizeof(int),&aij->colmap);CHKERRQ(ierr);
  PetscLogObjectMemory(mat,mat->N*sizeof(int));
  ierr = PetscMemzero(aij->colmap,mat->N*sizeof(int));CHKERRQ(ierr);
  for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
#endif
  PetscFunctionReturn(0);
}

#define CHUNKSIZE   15
#define MatSetValues_SeqAIJ_A_Private(row,col,value,addv) \
{ \
 \
    rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
    rmax = aimax[row]; nrow = ailen[row];  \
    col1 = col - shift; \
     \
    low = 0; high = nrow; \
    while (high-low > 5) { \
      t = (low+high)/2; \
      if (rp[t] > col) high = t; \
      else             low  = t; \
    } \
      for (_i=low; _i<high; _i++) { \
        if (rp[_i] > col1) break; \
        if (rp[_i] == col1) { \
          if (addv == ADD_VALUES) ap[_i] += value;   \
          else                  ap[_i] = value; \
          goto a_noinsert; \
        } \
      }  \
      if (nonew == 1) goto a_noinsert; \
      else if (nonew == -1) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) into matrix", row, col); \
      if (nrow >= rmax) { \
        /* there is no extra room in row, therefore enlarge */ \
        int    new_nz = ai[am] + CHUNKSIZE,len,*new_i,*new_j; \
        PetscScalar *new_a; \
 \
        if (nonew == -2) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) in the matrix", row, col); \
 \
        /* malloc new storage space */ \
        len     = new_nz*(sizeof(int)+sizeof(PetscScalar))+(am+1)*sizeof(int); \
        ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
        new_j   = (int*)(new_a + new_nz); \
        new_i   = new_j + new_nz; \
 \
        /* copy over old data into new slots */ \
        for (ii=0; ii<row+1; ii++) {new_i[ii] = ai[ii];} \
        for (ii=row+1; ii<am+1; ii++) {new_i[ii] = ai[ii]+CHUNKSIZE;} \
        ierr = PetscMemcpy(new_j,aj,(ai[row]+nrow+shift)*sizeof(int));CHKERRQ(ierr); \
        len = (new_nz - CHUNKSIZE - ai[row] - nrow - shift); \
        ierr = PetscMemcpy(new_j+ai[row]+shift+nrow+CHUNKSIZE,aj+ai[row]+shift+nrow, \
                                                           len*sizeof(int));CHKERRQ(ierr); \
        ierr = PetscMemcpy(new_a,aa,(ai[row]+nrow+shift)*sizeof(PetscScalar));CHKERRQ(ierr); \
        ierr = PetscMemcpy(new_a+ai[row]+shift+nrow+CHUNKSIZE,aa+ai[row]+shift+nrow, \
                                                           len*sizeof(PetscScalar));CHKERRQ(ierr);  \
        /* free up old matrix storage */ \
 \
        ierr = PetscFree(a->a);CHKERRQ(ierr);  \
        if (!a->singlemalloc) { \
           ierr = PetscFree(a->i);CHKERRQ(ierr); \
           ierr = PetscFree(a->j);CHKERRQ(ierr); \
        } \
        aa = a->a = new_a; ai = a->i = new_i; aj = a->j = new_j;  \
        a->singlemalloc = PETSC_TRUE; \
 \
        rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
        rmax = aimax[row] = aimax[row] + CHUNKSIZE; \
        PetscLogObjectMemory(A,CHUNKSIZE*(sizeof(int) + sizeof(PetscScalar))); \
        a->maxnz += CHUNKSIZE; \
        a->reallocs++; \
      } \
      N = nrow++ - 1; a->nz++; \
      /* shift up all the later entries in this row */ \
      for (ii=N; ii>=_i; ii--) { \
        rp[ii+1] = rp[ii]; \
        ap[ii+1] = ap[ii]; \
      } \
      rp[_i] = col1;  \
      ap[_i] = value;  \
      a_noinsert: ; \
      ailen[row] = nrow; \
}

#define MatSetValues_SeqAIJ_B_Private(row,col,value,addv) \
{ \
 \
    rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
    rmax = bimax[row]; nrow = bilen[row];  \
    col1 = col - shift; \
     \
    low = 0; high = nrow; \
    while (high-low > 5) { \
      t = (low+high)/2; \
      if (rp[t] > col) high = t; \
      else             low  = t; \
    } \
       for (_i=low; _i<high; _i++) { \
        if (rp[_i] > col1) break; \
        if (rp[_i] == col1) { \
          if (addv == ADD_VALUES) ap[_i] += value;   \
          else                  ap[_i] = value; \
          goto b_noinsert; \
        } \
      }  \
      if (nonew == 1) goto b_noinsert; \
      else if (nonew == -1) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) into matrix", row, col); \
      if (nrow >= rmax) { \
        /* there is no extra room in row, therefore enlarge */ \
        int    new_nz = bi[bm] + CHUNKSIZE,len,*new_i,*new_j; \
        PetscScalar *new_a; \
 \
        if (nonew == -2) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) in the matrix", row, col); \
 \
        /* malloc new storage space */ \
        len     = new_nz*(sizeof(int)+sizeof(PetscScalar))+(bm+1)*sizeof(int); \
        ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
        new_j   = (int*)(new_a + new_nz); \
        new_i   = new_j + new_nz; \
 \
        /* copy over old data into new slots */ \
        for (ii=0; ii<row+1; ii++) {new_i[ii] = bi[ii];} \
        for (ii=row+1; ii<bm+1; ii++) {new_i[ii] = bi[ii]+CHUNKSIZE;} \
        ierr = PetscMemcpy(new_j,bj,(bi[row]+nrow+shift)*sizeof(int));CHKERRQ(ierr); \
        len = (new_nz - CHUNKSIZE - bi[row] - nrow - shift); \
        ierr = PetscMemcpy(new_j+bi[row]+shift+nrow+CHUNKSIZE,bj+bi[row]+shift+nrow, \
                                                           len*sizeof(int));CHKERRQ(ierr); \
        ierr = PetscMemcpy(new_a,ba,(bi[row]+nrow+shift)*sizeof(PetscScalar));CHKERRQ(ierr); \
        ierr = PetscMemcpy(new_a+bi[row]+shift+nrow+CHUNKSIZE,ba+bi[row]+shift+nrow, \
                                                           len*sizeof(PetscScalar));CHKERRQ(ierr);  \
        /* free up old matrix storage */ \
 \
        ierr = PetscFree(b->a);CHKERRQ(ierr);  \
        if (!b->singlemalloc) { \
          ierr = PetscFree(b->i);CHKERRQ(ierr); \
          ierr = PetscFree(b->j);CHKERRQ(ierr); \
        } \
        ba = b->a = new_a; bi = b->i = new_i; bj = b->j = new_j;  \
        b->singlemalloc = PETSC_TRUE; \
 \
        rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
        rmax = bimax[row] = bimax[row] + CHUNKSIZE; \
        PetscLogObjectMemory(B,CHUNKSIZE*(sizeof(int) + sizeof(PetscScalar))); \
        b->maxnz += CHUNKSIZE; \
        b->reallocs++; \
      } \
      N = nrow++ - 1; b->nz++; \
      /* shift up all the later entries in this row */ \
      for (ii=N; ii>=_i; ii--) { \
        rp[ii+1] = rp[ii]; \
        ap[ii+1] = ap[ii]; \
      } \
      rp[_i] = col1;  \
      ap[_i] = value;  \
      b_noinsert: ; \
      bilen[row] = nrow; \
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValues_MPIAIJ"
PetscErrorCode MatSetValues_MPIAIJ(Mat mat,int m,const int im[],int n,const int in[],const PetscScalar v[],InsertMode addv)
{
  Mat_MPIAIJ   *aij = (Mat_MPIAIJ*)mat->data;
  PetscScalar  value;
  PetscErrorCode ierr;
  int          i,j,rstart = aij->rstart,rend = aij->rend;
  int          cstart = aij->cstart,cend = aij->cend,row,col;
  PetscTruth   roworiented = aij->roworiented;

  /* Some Variables required in the macro */
  Mat          A = aij->A;
  Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
  int          *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
  PetscScalar  *aa = a->a;
  PetscTruth   ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES))?PETSC_TRUE:PETSC_FALSE);
  Mat          B = aij->B;
  Mat_SeqAIJ   *b = (Mat_SeqAIJ*)B->data;
  int          *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->m,am = aij->A->m;
  PetscScalar  *ba = b->a;

  int          *rp,ii,nrow,_i,rmax,N,col1,low,high,t;
  int          nonew = a->nonew,shift=0;
  PetscScalar  *ap;

  PetscFunctionBegin;
  for (i=0; i<m; i++) {
    if (im[i] < 0) continue;
#if defined(PETSC_USE_BOPT_g)
    if (im[i] >= mat->M) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",im[i],mat->M-1);
#endif
    if (im[i] >= rstart && im[i] < rend) {
      row = im[i] - rstart;
      for (j=0; j<n; j++) {
        if (in[j] >= cstart && in[j] < cend){
          col = in[j] - cstart;
          if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
          if (ignorezeroentries && value == 0.0) continue;
          MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
          /* ierr = MatSetValues_SeqAIJ(aij->A,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
        } else if (in[j] < 0) continue;
#if defined(PETSC_USE_BOPT_g)
        else if (in[j] >= mat->N) {SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",in[j],mat->N-1);}
#endif
        else {
          if (mat->was_assembled) {
            if (!aij->colmap) {
              ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
            }
#if defined (PETSC_USE_CTABLE)
            ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
	    col--;
#else
            col = aij->colmap[in[j]] - 1;
#endif
            if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
              ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
              col =  in[j];
              /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
              B = aij->B;
              b = (Mat_SeqAIJ*)B->data;
              bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
              ba = b->a;
            }
          } else col = in[j];
          if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
          if (ignorezeroentries && value == 0.0) continue;
          MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
          /* ierr = MatSetValues_SeqAIJ(aij->B,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
        }
      }
    } else {
      if (!aij->donotstash) {
        if (roworiented) {
          if (ignorezeroentries && v[i*n] == 0.0) continue;
          ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n);CHKERRQ(ierr);
        } else {
          if (ignorezeroentries && v[i] == 0.0) continue;
          ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m);CHKERRQ(ierr);
        }
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetValues_MPIAIJ"
PetscErrorCode MatGetValues_MPIAIJ(Mat mat,int m,const int idxm[],int n,const int idxn[],PetscScalar v[])
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode ierr;
  int        i,j,rstart = aij->rstart,rend = aij->rend;
  int        cstart = aij->cstart,cend = aij->cend,row,col;

  PetscFunctionBegin;
  for (i=0; i<m; i++) {
    if (idxm[i] < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %d",idxm[i]);
    if (idxm[i] >= mat->M) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",idxm[i],mat->M-1);
    if (idxm[i] >= rstart && idxm[i] < rend) {
      row = idxm[i] - rstart;
      for (j=0; j<n; j++) {
        if (idxn[j] < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %d",idxn[j]);
        if (idxn[j] >= mat->N) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",idxn[j],mat->N-1);
        if (idxn[j] >= cstart && idxn[j] < cend){
          col = idxn[j] - cstart;
          ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
        } else {
          if (!aij->colmap) {
            ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
          }
#if defined (PETSC_USE_CTABLE)
          ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
          col --;
#else
          col = aij->colmap[idxn[j]] - 1;
#endif
          if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
          else {
            ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
          }
        }
      }
    } else {
      SETERRQ(PETSC_ERR_SUP,"Only local values currently supported");
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
{
  Mat_MPIAIJ  *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode ierr;
  int         nstash,reallocs;
  InsertMode  addv;

  PetscFunctionBegin;
  if (aij->donotstash) {
    PetscFunctionReturn(0);
  }

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

  ierr = MatStashScatterBegin_Private(&mat->stash,aij->rowners);CHKERRQ(ierr);
  ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
  PetscLogInfo(aij->A,"MatAssemblyBegin_MPIAIJ:Stash has %d entries, uses %d mallocs.\n",nstash,reallocs);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
{
  Mat_MPIAIJ  *aij = (Mat_MPIAIJ*)mat->data;
  Mat_SeqAIJ  *a=(Mat_SeqAIJ *)aij->A->data,*b= (Mat_SeqAIJ *)aij->B->data;
  PetscErrorCode ierr;
  int         i,j,rstart,ncols,n,flg;
  int         *row,*col,other_disassembled;
  PetscScalar *val;
  InsertMode  addv = mat->insertmode;

  PetscFunctionBegin;
  if (!aij->donotstash) {
    while (1) {
      ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
      if (!flg) break;

      for (i=0; i<n;) {
        /* Now identify the consecutive vals belonging to the same row */
        for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
        if (j < n) ncols = j-i;
        else       ncols = n-i;
        /* Now assemble all these values with a single function call */
        ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
        i = j;
      }
    }
    ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);

  /* determine if any processor has disassembled, if so we must
     also disassemble ourselfs, in order that we may reassemble. */
  /*
     if nonzero structure of submatrix B cannot change then we know that
     no processor disassembled thus we can skip this stuff
  */
  if (!((Mat_SeqAIJ*)aij->B->data)->nonew)  {
    ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,mat->comm);CHKERRQ(ierr);
    if (mat->was_assembled && !other_disassembled) {
      ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
    }
  }

  if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
    ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);

  if (aij->rowvalues) {
    ierr = PetscFree(aij->rowvalues);CHKERRQ(ierr);
    aij->rowvalues = 0;
  }

  /* used by MatAXPY() */
  a->xtoy = 0; b->xtoy = 0;
  a->XtoY = 0; b->XtoY = 0;

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroEntries_MPIAIJ"
PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
{
  Mat_MPIAIJ *l = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
  ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRows_MPIAIJ"
PetscErrorCode MatZeroRows_MPIAIJ(Mat A,IS is,const PetscScalar *diag)
{
  Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;
  int            i,N,*rows,*owners = l->rowners,size = l->size;
  int            *nprocs,j,idx,nsends,row;
  int            nmax,*svalues,*starts,*owner,nrecvs,rank = l->rank;
  int            *rvalues,tag = A->tag,count,base,slen,n,*source;
  int            *lens,imdex,*lrows,*values,rstart=l->rstart;
  MPI_Comm       comm = A->comm;
  MPI_Request    *send_waits,*recv_waits;
  MPI_Status     recv_status,*send_status;
  IS             istmp;
  PetscTruth     found;

  PetscFunctionBegin;
  ierr = ISGetLocalSize(is,&N);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);

  /*  first count number of contributors to each processor */
  ierr = PetscMalloc(2*size*sizeof(int),&nprocs);CHKERRQ(ierr);
  ierr   = PetscMemzero(nprocs,2*size*sizeof(int));CHKERRQ(ierr);
  ierr = PetscMalloc((N+1)*sizeof(int),&owner);CHKERRQ(ierr); /* see note*/
  for (i=0; i<N; i++) {
    idx = rows[i];
    found = PETSC_FALSE;
    for (j=0; j<size; j++) {
      if (idx >= owners[j] && idx < owners[j+1]) {
        nprocs[2*j]++; nprocs[2*j+1] = 1; owner[i] = j; found = PETSC_TRUE; break;
      }
    }
    if (!found) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
  }
  nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}

  /* inform other processors of number of messages and max length*/
  ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);

  /* post receives:   */
  ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(int),&rvalues);CHKERRQ(ierr);
  ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
  for (i=0; i<nrecvs; i++) {
    ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPI_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
  }

  /* do sends:
      1) starts[i] gives the starting index in svalues for stuff going to
         the ith processor
  */
  ierr = PetscMalloc((N+1)*sizeof(int),&svalues);CHKERRQ(ierr);
  ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
  ierr = PetscMalloc((size+1)*sizeof(int),&starts);CHKERRQ(ierr);
  starts[0] = 0;
  for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
  for (i=0; i<N; i++) {
    svalues[starts[owner[i]]++] = rows[i];
  }
  ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);

  starts[0] = 0;
  for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
  count = 0;
  for (i=0; i<size; i++) {
    if (nprocs[2*i+1]) {
      ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPI_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree(starts);CHKERRQ(ierr);

  base = owners[rank];

  /*  wait on receives */
  ierr   = PetscMalloc(2*(nrecvs+1)*sizeof(int),&lens);CHKERRQ(ierr);
  source = lens + nrecvs;
  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,MPI_INT,&n);CHKERRQ(ierr);
    source[imdex]  = recv_status.MPI_SOURCE;
    lens[imdex]    = n;
    slen          += n;
    count--;
  }
  ierr = PetscFree(recv_waits);CHKERRQ(ierr);

  /* move the data into the send scatter */
  ierr = PetscMalloc((slen+1)*sizeof(int),&lrows);CHKERRQ(ierr);
  count = 0;
  for (i=0; i<nrecvs; i++) {
    values = rvalues + i*nmax;
    for (j=0; j<lens[i]; j++) {
      lrows[count++] = values[j] - base;
    }
  }
  ierr = PetscFree(rvalues);CHKERRQ(ierr);
  ierr = PetscFree(lens);CHKERRQ(ierr);
  ierr = PetscFree(owner);CHKERRQ(ierr);
  ierr = PetscFree(nprocs);CHKERRQ(ierr);

  /* actually zap the local rows */
  ierr = ISCreateGeneral(PETSC_COMM_SELF,slen,lrows,&istmp);CHKERRQ(ierr);
  PetscLogObjectParent(A,istmp);

  /*
        Zero the required rows. If the "diagonal block" of the matrix
     is square and the user wishes to set the diagonal we use seperate
     code so that MatSetValues() is not called for each diagonal allocating
     new memory, thus calling lots of mallocs and slowing things down.

       Contributed by: Mathew Knepley
  */
  /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
  ierr = MatZeroRows(l->B,istmp,0);CHKERRQ(ierr);
  if (diag && (l->A->M == l->A->N)) {
    ierr      = MatZeroRows(l->A,istmp,diag);CHKERRQ(ierr);
  } else if (diag) {
    ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
    if (((Mat_SeqAIJ*)l->A->data)->nonew) {
      SETERRQ(PETSC_ERR_SUP,"MatZeroRows() on rectangular matrices cannot be used with the Mat options\n\
MAT_NO_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
    }
    for (i = 0; i < slen; i++) {
      row  = lrows[i] + rstart;
      ierr = MatSetValues(A,1,&row,1,&row,diag,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  } else {
    ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
  }
  ierr = ISDestroy(istmp);CHKERRQ(ierr);
  ierr = PetscFree(lrows);CHKERRQ(ierr);

  /* wait on sends */
  if (nsends) {
    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 = PetscFree(send_waits);CHKERRQ(ierr);
  ierr = PetscFree(svalues);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMult_MPIAIJ"
PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;
  int        nt;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
  if (nt != A->n) {
    SETERRQ2(PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%d) and xx (%d)",A->n,nt);
  }
  ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
  ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
  ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
  ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultAdd_MPIAIJ"
PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
  ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
  ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
  ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTranspose_MPIAIJ"
PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* do nondiagonal part */
  ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
  /* send it on its way */
  ierr = VecScatterBegin(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
  /* do local part */
  ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(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(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatIsTranspose_MPIAIJ"
PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscTruth tol,PetscTruth *f)
{
  MPI_Comm comm;
  Mat_MPIAIJ *Aij = (Mat_MPIAIJ *) Amat->data, *Bij;
  Mat        Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
  IS         Me,Notme;
  PetscErrorCode ierr;
  int        M,N,first,last,*notme,ntids,i;

  PetscFunctionBegin;

  /* Easy test: symmetric diagonal block */
  Bij = (Mat_MPIAIJ *) Bmat->data; Bdia = Bij->A;
  ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
  if (!*f) PetscFunctionReturn(0);
  ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&ntids);CHKERRQ(ierr);
  if (ntids==1) PetscFunctionReturn(0);

  /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
  ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
  ierr = PetscMalloc((N-last+first)*sizeof(int),&notme);CHKERRQ(ierr);
  for (i=0; i<first; i++) notme[i] = i;
  for (i=last; i<M; i++) notme[i-last+first] = i;
  ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,&Notme);CHKERRQ(ierr);
  ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
  ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
  Aoff = Aoffs[0];
  ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
  Boff = Boffs[0];
  ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
  ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
  ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
  ierr = ISDestroy(Me);CHKERRQ(ierr);
  ierr = ISDestroy(Notme);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* do nondiagonal part */
  ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
  /* send it on its way */
  ierr = VecScatterBegin(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
  /* do local part */
  ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(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(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
  This only works correctly for square matrices where the subblock A->A is the
   diagonal block
*/
#undef __FUNCT__
#define __FUNCT__ "MatGetDiagonal_MPIAIJ"
PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
{
  PetscErrorCode ierr;
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;

  PetscFunctionBegin;
  if (A->M != A->N) SETERRQ(PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
  if (a->rstart != a->cstart || a->rend != a->cend) {
    SETERRQ(PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
  }
  ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatScale_MPIAIJ"
PetscErrorCode MatScale_MPIAIJ(const PetscScalar aa[],Mat A)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatScale(aa,a->A);CHKERRQ(ierr);
  ierr = MatScale(aa,a->B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_MPIAIJ"
PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
#if defined(PETSC_USE_LOG)
  PetscLogObjectState((PetscObject)mat,"Rows=%d, Cols=%d",mat->M,mat->N);
#endif
  ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
  ierr = PetscFree(aij->rowners);CHKERRQ(ierr);
  ierr = MatDestroy(aij->A);CHKERRQ(ierr);
  ierr = MatDestroy(aij->B);CHKERRQ(ierr);
#if defined (PETSC_USE_CTABLE)
  if (aij->colmap) {ierr = PetscTableDelete(aij->colmap);CHKERRQ(ierr);}
#else
  if (aij->colmap) {ierr = PetscFree(aij->colmap);CHKERRQ(ierr);}
#endif
  if (aij->garray) {ierr = PetscFree(aij->garray);CHKERRQ(ierr);}
  if (aij->lvec)   {ierr = VecDestroy(aij->lvec);CHKERRQ(ierr);}
  if (aij->Mvctx)  {ierr = VecScatterDestroy(aij->Mvctx);CHKERRQ(ierr);}
  if (aij->rowvalues) {ierr = PetscFree(aij->rowvalues);CHKERRQ(ierr);}
  ierr = PetscFree(aij);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatView_MPIAIJ_Binary"
PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
{
  Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
  Mat_SeqAIJ*       A = (Mat_SeqAIJ*)aij->A->data;
  Mat_SeqAIJ*       B = (Mat_SeqAIJ*)aij->B->data;
  PetscErrorCode    ierr;
  PetscMPIInt       rank,size,tag = ((PetscObject)viewer)->tag;
  int               nz,fd,header[4],*row_lengths,*range,rlen,i;
  int               nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = aij->cstart,rnz;
  PetscScalar       *column_values;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(mat->comm,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(mat->comm,&size);CHKERRQ(ierr);
  nz   = A->nz + B->nz;
  if (!rank) {
    header[0] = MAT_FILE_COOKIE;
    header[1] = mat->M;
    header[2] = mat->N;
    ierr = MPI_Reduce(&nz,&header[3],1,MPI_INT,MPI_SUM,0,mat->comm);CHKERRQ(ierr);
    ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
    ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,1);CHKERRQ(ierr);
    /* get largest number of rows any processor has */
    rlen = mat->m;
    ierr = PetscMapGetGlobalRange(mat->rmap,&range);CHKERRQ(ierr);
    for (i=1; i<size; i++) {
      rlen = PetscMax(rlen,range[i+1] - range[i]);
    }
  } else {
    ierr = MPI_Reduce(&nz,0,1,MPI_INT,MPI_SUM,0,mat->comm);CHKERRQ(ierr);
    rlen = mat->m;
  }

  /* load up the local row counts */
  ierr = PetscMalloc((rlen+1)*sizeof(int),&row_lengths);CHKERRQ(ierr);
  for (i=0; i<mat->m; i++) {
    row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
  }

  /* store the row lengths to the file */
  if (!rank) {
    MPI_Status status;
    ierr = PetscBinaryWrite(fd,row_lengths,mat->m,PETSC_INT,1);CHKERRQ(ierr);
    for (i=1; i<size; i++) {
      rlen = range[i+1] - range[i];
      ierr = MPI_Recv(row_lengths,rlen,MPI_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
      ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,1);CHKERRQ(ierr);
    }
  } else {
    ierr = MPI_Send(row_lengths,mat->m,MPI_INT,0,tag,mat->comm);CHKERRQ(ierr);
  }
  ierr = PetscFree(row_lengths);CHKERRQ(ierr);

  /* load up the local column indices */
  nzmax = nz; /* )th processor needs space a largest processor needs */
  ierr = MPI_Reduce(&nz,&nzmax,1,MPI_INT,MPI_MAX,0,mat->comm);CHKERRQ(ierr);
  ierr = PetscMalloc((nzmax+1)*sizeof(int),&column_indices);CHKERRQ(ierr);
  cnt  = 0;
  for (i=0; i<mat->m; i++) {
    for (j=B->i[i]; j<B->i[i+1]; j++) {
      if ( (col = garray[B->j[j]]) > cstart) break;
      column_indices[cnt++] = col;
    }
    for (k=A->i[i]; k<A->i[i+1]; k++) {
      column_indices[cnt++] = A->j[k] + cstart;
    }
    for (; j<B->i[i+1]; j++) {
      column_indices[cnt++] = garray[B->j[j]];
    }
  }
  if (cnt != A->nz + B->nz) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: cnt = %d nz = %d",cnt,A->nz+B->nz);

  /* store the column indices to the file */
  if (!rank) {
    MPI_Status status;
    ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,1);CHKERRQ(ierr);
    for (i=1; i<size; i++) {
      ierr = MPI_Recv(&rnz,1,MPI_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
      if (rnz > nzmax) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: nz = %d nzmax = %d",nz,nzmax);
      ierr = MPI_Recv(column_indices,rnz,MPI_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
      ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,1);CHKERRQ(ierr);
    }
  } else {
    ierr = MPI_Send(&nz,1,MPI_INT,0,tag,mat->comm);CHKERRQ(ierr);
    ierr = MPI_Send(column_indices,nz,MPI_INT,0,tag,mat->comm);CHKERRQ(ierr);
  }
  ierr = PetscFree(column_indices);CHKERRQ(ierr);

  /* load up the local column values */
  ierr = PetscMalloc((nzmax+1)*sizeof(PetscScalar),&column_values);CHKERRQ(ierr);
  cnt  = 0;
  for (i=0; i<mat->m; i++) {
    for (j=B->i[i]; j<B->i[i+1]; j++) {
      if ( garray[B->j[j]] > cstart) break;
      column_values[cnt++] = B->a[j];
    }
    for (k=A->i[i]; k<A->i[i+1]; k++) {
      column_values[cnt++] = A->a[k];
    }
    for (; j<B->i[i+1]; j++) {
      column_values[cnt++] = B->a[j];
    }
  }
  if (cnt != A->nz + B->nz) SETERRQ2(1,"Internal PETSc error: cnt = %d nz = %d",cnt,A->nz+B->nz);

  /* store the column values to the file */
  if (!rank) {
    MPI_Status status;
    ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,1);CHKERRQ(ierr);
    for (i=1; i<size; i++) {
      ierr = MPI_Recv(&rnz,1,MPI_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
      if (rnz > nzmax) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: nz = %d nzmax = %d",nz,nzmax);
      ierr = MPI_Recv(column_values,rnz,MPIU_SCALAR,i,tag,mat->comm,&status);CHKERRQ(ierr);
      ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,1);CHKERRQ(ierr);
    }
  } else {
    ierr = MPI_Send(&nz,1,MPI_INT,0,tag,mat->comm);CHKERRQ(ierr);
    ierr = MPI_Send(column_values,nz,MPIU_SCALAR,0,tag,mat->comm);CHKERRQ(ierr);
  }
  ierr = PetscFree(column_values);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
{
  Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode    ierr;
  PetscMPIInt       rank = aij->rank,size = aij->size;
  PetscTruth        isdraw,iascii,flg,isbinary;
  PetscViewer       sviewer;
  PetscViewerFormat format;

  PetscFunctionBegin;
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
  if (iascii) {
    ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
    if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
      MatInfo info;
      ierr = MPI_Comm_rank(mat->comm,&rank);CHKERRQ(ierr);
      ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
      ierr = PetscOptionsHasName(PETSC_NULL,"-mat_aij_no_inode",&flg);CHKERRQ(ierr);
      if (flg) {
        ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, not using I-node routines\n",
					      rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
      } else {
        ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, using I-node routines\n",
		    rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
      }
      ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
      ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
      ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
      ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
      PetscFunctionReturn(0);
    } else if (format == PETSC_VIEWER_ASCII_INFO) {
      PetscFunctionReturn(0);
    } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
      PetscFunctionReturn(0);
    }
  } else if (isbinary) {
    if (size == 1) {
      ierr = PetscObjectSetName((PetscObject)aij->A,mat->name);CHKERRQ(ierr);
      ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
    } else {
      ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  } else if (isdraw) {
    PetscDraw  draw;
    PetscTruth isnull;
    ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
    ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
  }

  if (size == 1) {
    ierr = PetscObjectSetName((PetscObject)aij->A,mat->name);CHKERRQ(ierr);
    ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
  } else {
    /* assemble the entire matrix onto first processor. */
    Mat         A;
    Mat_SeqAIJ *Aloc;
    int         M = mat->M,N = mat->N,m,*ai,*aj,row,*cols,i,*ct;
    PetscScalar *a;

    if (!rank) {
      ierr = MatCreate(mat->comm,M,N,M,N,&A);CHKERRQ(ierr);
    } else {
      ierr = MatCreate(mat->comm,0,0,M,N,&A);CHKERRQ(ierr);
    }
    /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
    ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
    ierr = MatMPIAIJSetPreallocation(A,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
    PetscLogObjectParent(mat,A);

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

    /* copy over the B part */
    Aloc = (Mat_SeqAIJ*)aij->B->data;
    m    = aij->B->m;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
    row  = aij->rstart;
    ierr = PetscMalloc((ai[m]+1)*sizeof(int),&cols);CHKERRQ(ierr);
    ct   = cols;
    for (i=0; i<ai[m]; i++) {cols[i] = aij->garray[aj[i]];}
    for (i=0; i<m; i++) {
      ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
      row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
    }
    ierr = PetscFree(ct);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    /*
       Everyone has to call to draw the matrix since the graphics waits are
       synchronized across all processors that share the PetscDraw object
    */
    ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
    if (!rank) {
      ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,mat->name);CHKERRQ(ierr);
      ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
    }
    ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
    ierr = MatDestroy(A);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatView_MPIAIJ"
PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscTruth iascii,isdraw,issocket,isbinary;

  PetscFunctionBegin;
  ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
  ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
  if (iascii || isdraw || isbinary || issocket) {
    ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
  } else {
    SETERRQ1(1,"Viewer type %s not supported by MPIAIJ matrices",((PetscObject)viewer)->type_name);
  }
  PetscFunctionReturn(0);
}



#undef __FUNCT__
#define __FUNCT__ "MatRelax_MPIAIJ"
PetscErrorCode MatRelax_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,int its,int lits,Vec xx)
{
  Mat_MPIAIJ   *mat = (Mat_MPIAIJ*)matin->data;
  PetscErrorCode ierr;
  Vec          bb1;
  PetscScalar  mone=-1.0;

  PetscFunctionBegin;
  if (its <= 0 || lits <= 0) SETERRQ2(PETSC_ERR_ARG_WRONG,"Relaxation requires global its %d and local its %d both positive",its,lits);

  ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);

  if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,lits,xx);CHKERRQ(ierr);
      its--;
    }

    while (its--) {
      ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
      ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);

      /* update rhs: bb1 = bb - B*x */
      ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
      ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);

      /* local sweep */
      ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,lits,xx);
      CHKERRQ(ierr);
    }
  } else if (flag & SOR_LOCAL_FORWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,PETSC_NULL,xx);CHKERRQ(ierr);
      its--;
    }
    while (its--) {
      ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
      ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);

      /* update rhs: bb1 = bb - B*x */
      ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
      ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);

      /* local sweep */
      ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,PETSC_NULL,xx);
      CHKERRQ(ierr);
    }
  } else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
    if (flag & SOR_ZERO_INITIAL_GUESS) {
      ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,PETSC_NULL,xx);CHKERRQ(ierr);
      its--;
    }
    while (its--) {
      ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
      ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);

      /* update rhs: bb1 = bb - B*x */
      ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
      ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);

      /* local sweep */
      ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,PETSC_NULL,xx);
      CHKERRQ(ierr);
    }
  } else {
    SETERRQ(PETSC_ERR_SUP,"Parallel SOR not supported");
  }

  ierr = VecDestroy(bb1);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetInfo_MPIAIJ"
PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
{
  Mat_MPIAIJ *mat = (Mat_MPIAIJ*)matin->data;
  Mat        A = mat->A,B = mat->B;
  PetscErrorCode ierr;
  PetscReal  isend[5],irecv[5];

  PetscFunctionBegin;
  info->block_size     = 1.0;
  ierr = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
  isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
  isend[3] = info->memory;  isend[4] = info->mallocs;
  ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
  isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
  isend[3] += info->memory;  isend[4] += info->mallocs;
  if (flag == MAT_LOCAL) {
    info->nz_used      = isend[0];
    info->nz_allocated = isend[1];
    info->nz_unneeded  = isend[2];
    info->memory       = isend[3];
    info->mallocs      = isend[4];
  } else if (flag == MAT_GLOBAL_MAX) {
    ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_MAX,matin->comm);CHKERRQ(ierr);
    info->nz_used      = irecv[0];
    info->nz_allocated = irecv[1];
    info->nz_unneeded  = irecv[2];
    info->memory       = irecv[3];
    info->mallocs      = irecv[4];
  } else if (flag == MAT_GLOBAL_SUM) {
    ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_SUM,matin->comm);CHKERRQ(ierr);
    info->nz_used      = irecv[0];
    info->nz_allocated = irecv[1];
    info->nz_unneeded  = irecv[2];
    info->memory       = irecv[3];
    info->mallocs      = irecv[4];
  }
  info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
  info->fill_ratio_needed = 0;
  info->factor_mallocs    = 0;
  info->rows_global       = (double)matin->M;
  info->columns_global    = (double)matin->N;
  info->rows_local        = (double)matin->m;
  info->columns_local     = (double)matin->N;

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetOption_MPIAIJ"
PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  switch (op) {
  case MAT_NO_NEW_NONZERO_LOCATIONS:
  case MAT_YES_NEW_NONZERO_LOCATIONS:
  case MAT_COLUMNS_UNSORTED:
  case MAT_COLUMNS_SORTED:
  case MAT_NEW_NONZERO_ALLOCATION_ERR:
  case MAT_KEEP_ZEROED_ROWS:
  case MAT_NEW_NONZERO_LOCATION_ERR:
  case MAT_USE_INODES:
  case MAT_DO_NOT_USE_INODES:
  case MAT_IGNORE_ZERO_ENTRIES:
    ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
    ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
    break;
  case MAT_ROW_ORIENTED:
    a->roworiented = PETSC_TRUE;
    ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
    ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
    break;
  case MAT_ROWS_SORTED:
  case MAT_ROWS_UNSORTED:
  case MAT_YES_NEW_DIAGONALS:
    PetscLogInfo(A,"MatSetOption_MPIAIJ:Option ignored\n");
    break;
  case MAT_COLUMN_ORIENTED:
    a->roworiented = PETSC_FALSE;
    ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
    ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
    break;
  case MAT_IGNORE_OFF_PROC_ENTRIES:
    a->donotstash = PETSC_TRUE;
    break;
  case MAT_NO_NEW_DIAGONALS:
    SETERRQ(PETSC_ERR_SUP,"MAT_NO_NEW_DIAGONALS");
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SYMMETRY_ETERNAL:
    ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
    break;
  case MAT_NOT_SYMMETRIC:
  case MAT_NOT_STRUCTURALLY_SYMMETRIC:
  case MAT_NOT_HERMITIAN:
  case MAT_NOT_SYMMETRY_ETERNAL:
    break;
  default:
    SETERRQ(PETSC_ERR_SUP,"unknown option");
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRow_MPIAIJ"
PetscErrorCode MatGetRow_MPIAIJ(Mat matin,int row,int *nz,int **idx,PetscScalar **v)
{
  Mat_MPIAIJ   *mat = (Mat_MPIAIJ*)matin->data;
  PetscScalar  *vworkA,*vworkB,**pvA,**pvB,*v_p;
  PetscErrorCode ierr;
  int          i,*cworkA,*cworkB,**pcA,**pcB,cstart = mat->cstart;
  int          nztot,nzA,nzB,lrow,rstart = mat->rstart,rend = mat->rend;
  int          *cmap,*idx_p;

  PetscFunctionBegin;
  if (mat->getrowactive == PETSC_TRUE) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Already active");
  mat->getrowactive = PETSC_TRUE;

  if (!mat->rowvalues && (idx || v)) {
    /*
        allocate enough space to hold information from the longest row.
    */
    Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
    int     max = 1,tmp;
    for (i=0; i<matin->m; i++) {
      tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
      if (max < tmp) { max = tmp; }
    }
    ierr = PetscMalloc(max*(sizeof(int)+sizeof(PetscScalar)),&mat->rowvalues);CHKERRQ(ierr);
    mat->rowindices = (int*)(mat->rowvalues + max);
  }

  if (row < rstart || row >= rend) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"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 = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
  ierr = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
  nztot = nzA + nzB;

  cmap  = mat->garray;
  if (v  || idx) {
    if (nztot) {
      /* Sort by increasing column numbers, assuming A and B already sorted */
      int imark = -1;
      if (v) {
        *v = v_p = mat->rowvalues;
        for (i=0; i<nzB; i++) {
          if (cmap[cworkB[i]] < cstart)   v_p[i] = vworkB[i];
          else break;
        }
        imark = i;
        for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
        for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
      }
      if (idx) {
        *idx = idx_p = mat->rowindices;
        if (imark > -1) {
          for (i=0; i<imark; i++) {
            idx_p[i] = cmap[cworkB[i]];
          }
        } else {
          for (i=0; i<nzB; i++) {
            if (cmap[cworkB[i]] < cstart)   idx_p[i] = cmap[cworkB[i]];
            else break;
          }
          imark = i;
        }
        for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
        for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
      }
    } else {
      if (idx) *idx = 0;
      if (v)   *v   = 0;
    }
  }
  *nz = nztot;
  ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
  ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreRow_MPIAIJ"
PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,int row,int *nz,int **idx,PetscScalar **v)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;

  PetscFunctionBegin;
  if (aij->getrowactive == PETSC_FALSE) {
    SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"MatGetRow not called");
  }
  aij->getrowactive = PETSC_FALSE;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNorm_MPIAIJ"
PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
{
  Mat_MPIAIJ   *aij = (Mat_MPIAIJ*)mat->data;
  Mat_SeqAIJ   *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
  PetscErrorCode ierr;
  int          i,j,cstart = aij->cstart;
  PetscReal    sum = 0.0;
  PetscScalar  *v;

  PetscFunctionBegin;
  if (aij->size == 1) {
    ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
  } else {
    if (type == NORM_FROBENIUS) {
      v = amat->a;
      for (i=0; i<amat->nz; i++) {
#if defined(PETSC_USE_COMPLEX)
        sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
#else
        sum += (*v)*(*v); v++;
#endif
      }
      v = bmat->a;
      for (i=0; i<bmat->nz; i++) {
#if defined(PETSC_USE_COMPLEX)
        sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
#else
        sum += (*v)*(*v); v++;
#endif
      }
      ierr = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPI_SUM,mat->comm);CHKERRQ(ierr);
      *norm = sqrt(*norm);
    } else if (type == NORM_1) { /* max column norm */
      PetscReal *tmp,*tmp2;
      int    *jj,*garray = aij->garray;
      ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
      ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp2);CHKERRQ(ierr);
      ierr = PetscMemzero(tmp,mat->N*sizeof(PetscReal));CHKERRQ(ierr);
      *norm = 0.0;
      v = amat->a; jj = amat->j;
      for (j=0; j<amat->nz; j++) {
        tmp[cstart + *jj++ ] += PetscAbsScalar(*v);  v++;
      }
      v = bmat->a; jj = bmat->j;
      for (j=0; j<bmat->nz; j++) {
        tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
      }
      ierr = MPI_Allreduce(tmp,tmp2,mat->N,MPIU_REAL,MPI_SUM,mat->comm);CHKERRQ(ierr);
      for (j=0; j<mat->N; j++) {
        if (tmp2[j] > *norm) *norm = tmp2[j];
      }
      ierr = PetscFree(tmp);CHKERRQ(ierr);
      ierr = PetscFree(tmp2);CHKERRQ(ierr);
    } else if (type == NORM_INFINITY) { /* max row norm */
      PetscReal ntemp = 0.0;
      for (j=0; j<aij->A->m; j++) {
        v = amat->a + amat->i[j];
        sum = 0.0;
        for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
          sum += PetscAbsScalar(*v); v++;
        }
        v = bmat->a + bmat->i[j];
        for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
          sum += PetscAbsScalar(*v); v++;
        }
        if (sum > ntemp) ntemp = sum;
      }
      ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPI_MAX,mat->comm);CHKERRQ(ierr);
    } else {
      SETERRQ(PETSC_ERR_SUP,"No support for two norm");
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTranspose_MPIAIJ"
PetscErrorCode MatTranspose_MPIAIJ(Mat A,Mat *matout)
{
  Mat_MPIAIJ   *a = (Mat_MPIAIJ*)A->data;
  Mat_SeqAIJ   *Aloc = (Mat_SeqAIJ*)a->A->data;
  PetscErrorCode ierr;
  int          M = A->M,N = A->N,m,*ai,*aj,row,*cols,i,*ct;
  Mat          B;
  PetscScalar  *array;

  PetscFunctionBegin;
  if (!matout && M != N) {
    SETERRQ(PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
  }

  ierr = MatCreate(A->comm,A->n,A->m,N,M,&B);CHKERRQ(ierr);
  ierr = MatSetType(B,A->type_name);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(B,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);

  /* copy over the A part */
  Aloc = (Mat_SeqAIJ*)a->A->data;
  m = a->A->m; ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
  row = a->rstart;
  for (i=0; i<ai[m]; i++) {aj[i] += a->cstart ;}
  for (i=0; i<m; i++) {
    ierr = MatSetValues(B,ai[i+1]-ai[i],aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
    row++; array += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
  }
  aj = Aloc->j;
  for (i=0; i<ai[m]; i++) {aj[i] -= a->cstart ;}

  /* copy over the B part */
  Aloc = (Mat_SeqAIJ*)a->B->data;
  m = a->B->m;  ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
  row  = a->rstart;
  ierr = PetscMalloc((1+ai[m])*sizeof(int),&cols);CHKERRQ(ierr);
  ct   = cols;
  for (i=0; i<ai[m]; i++) {cols[i] = a->garray[aj[i]];}
  for (i=0; i<m; i++) {
    ierr = MatSetValues(B,ai[i+1]-ai[i],cols,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
    row++; array += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
  }
  ierr = PetscFree(ct);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  if (matout) {
    *matout = B;
  } else {
    ierr = MatHeaderCopy(A,B);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDiagonalScale_MPIAIJ"
PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
  Mat        a = aij->A,b = aij->B;
  PetscErrorCode ierr;
  int        s1,s2,s3;

  PetscFunctionBegin;
  ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
  if (rr) {
    ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
    if (s1!=s3) SETERRQ(PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
    /* Overlap communication with computation. */
    ierr = VecScatterBegin(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
  }
  if (ll) {
    ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
    if (s1!=s2) SETERRQ(PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
    ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
  }
  /* scale  the diagonal block */
  ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);

  if (rr) {
    /* Do a scatter end and then right scale the off-diagonal block */
    ierr = VecScatterEnd(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
    ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatPrintHelp_MPIAIJ"
PetscErrorCode MatPrintHelp_MPIAIJ(Mat A)
{
  Mat_MPIAIJ *a   = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!a->rank) {
    ierr = MatPrintHelp_SeqAIJ(a->A);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetBlockSize_MPIAIJ"
PetscErrorCode MatGetBlockSize_MPIAIJ(Mat A,int *bs)
{
  PetscFunctionBegin;
  *bs = 1;
  PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "MatSetUnfactored_MPIAIJ"
PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
{
  Mat_MPIAIJ *a   = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatEqual_MPIAIJ"
PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscTruth *flag)
{
  Mat_MPIAIJ *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
  Mat        a,b,c,d;
  PetscTruth flg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  a = matA->A; b = matA->B;
  c = matB->A; d = matB->B;

  ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
  if (flg == PETSC_TRUE) {
    ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
  }
  ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,A->comm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCopy_MPIAIJ"
PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
{
  PetscErrorCode ierr;
  Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
  Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;

  PetscFunctionBegin;
  /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
  if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    /* because of the column compression in the off-processor part of the matrix a->B,
       the number of columns in a->B and b->B may be different, hence we cannot call
       the MatCopy() directly on the two parts. If need be, we can provide a more
       efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
       then copying the submatrices */
    ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
  } else {
    ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
    ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetUpPreallocation_MPIAIJ"
PetscErrorCode MatSetUpPreallocation_MPIAIJ(Mat A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include "petscblaslapack.h"
#undef __FUNCT__
#define __FUNCT__ "MatAXPY_MPIAIJ"
PetscErrorCode MatAXPY_MPIAIJ(const PetscScalar a[],Mat X,Mat Y,MatStructure str)
{
  PetscErrorCode ierr;
  int            i;
  Mat_MPIAIJ     *xx = (Mat_MPIAIJ *)X->data,*yy = (Mat_MPIAIJ *)Y->data;
  PetscBLASInt   bnz,one=1;
  Mat_SeqAIJ     *x,*y;

  PetscFunctionBegin;
  if (str == SAME_NONZERO_PATTERN) {
    x = (Mat_SeqAIJ *)xx->A->data;
    y = (Mat_SeqAIJ *)yy->A->data;
    bnz = (PetscBLASInt)x->nz;
    BLaxpy_(&bnz,(PetscScalar*)a,x->a,&one,y->a,&one);
    x = (Mat_SeqAIJ *)xx->B->data;
    y = (Mat_SeqAIJ *)yy->B->data;
    bnz = (PetscBLASInt)x->nz;
    BLaxpy_(&bnz,(PetscScalar*)a,x->a,&one,y->a,&one);
  } else if (str == SUBSET_NONZERO_PATTERN) {
    ierr = MatAXPY_SeqAIJ(a,xx->A,yy->A,str);CHKERRQ(ierr);

    x = (Mat_SeqAIJ *)xx->B->data;
    y = (Mat_SeqAIJ *)yy->B->data;
    if (y->xtoy && y->XtoY != xx->B) {
      ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
      ierr = MatDestroy(y->XtoY);CHKERRQ(ierr);
    }
    if (!y->xtoy) { /* get xtoy */
      ierr = MatAXPYGetxtoy_Private(xx->B->m,x->i,x->j,xx->garray,y->i,y->j,yy->garray,&y->xtoy);CHKERRQ(ierr);
      y->XtoY = xx->B;
    }
    for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += (*a)*(x->a[i]);
  } else {
    ierr = MatAXPY_Basic(a,X,Y,str);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
       MatGetRow_MPIAIJ,
       MatRestoreRow_MPIAIJ,
       MatMult_MPIAIJ,
/* 4*/ MatMultAdd_MPIAIJ,
       MatMultTranspose_MPIAIJ,
       MatMultTransposeAdd_MPIAIJ,
       0,
       0,
       0,
/*10*/ 0,
       0,
       0,
       MatRelax_MPIAIJ,
       MatTranspose_MPIAIJ,
/*15*/ MatGetInfo_MPIAIJ,
       MatEqual_MPIAIJ,
       MatGetDiagonal_MPIAIJ,
       MatDiagonalScale_MPIAIJ,
       MatNorm_MPIAIJ,
/*20*/ MatAssemblyBegin_MPIAIJ,
       MatAssemblyEnd_MPIAIJ,
       0,
       MatSetOption_MPIAIJ,
       MatZeroEntries_MPIAIJ,
/*25*/ MatZeroRows_MPIAIJ,
#if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_SINGLE)
       MatLUFactorSymbolic_MPIAIJ_TFS,
#else
       0,
#endif
       0,
       0,
       0,
/*30*/ MatSetUpPreallocation_MPIAIJ,
       0,
       0,
       0,
       0,
/*35*/ MatDuplicate_MPIAIJ,
       0,
       0,
       0,
       0,
/*40*/ MatAXPY_MPIAIJ,
       MatGetSubMatrices_MPIAIJ,
       MatIncreaseOverlap_MPIAIJ,
       MatGetValues_MPIAIJ,
       MatCopy_MPIAIJ,
/*45*/ MatPrintHelp_MPIAIJ,
       MatScale_MPIAIJ,
       0,
       0,
       0,
/*50*/ MatGetBlockSize_MPIAIJ,
       0,
       0,
       0,
       0,
/*55*/ MatFDColoringCreate_MPIAIJ,
       0,
       MatSetUnfactored_MPIAIJ,
       0,
       0,
/*60*/ MatGetSubMatrix_MPIAIJ,
       MatDestroy_MPIAIJ,
       MatView_MPIAIJ,
       MatGetPetscMaps_Petsc,
       0,
/*65*/ 0,
       0,
       0,
       0,
       0,
/*70*/ 0,
       0,
       MatSetColoring_MPIAIJ,
       MatSetValuesAdic_MPIAIJ,
       MatSetValuesAdifor_MPIAIJ,
/*75*/ 0,
       0,
       0,
       0,
       0,
/*80*/ 0,
       0,
       0,
       0,
/*84*/ MatLoad_MPIAIJ,
       0,
       0,
       0,
       0,
/*89*/ 0,
       MatMatMult_MPIAIJ_MPIAIJ,
       MatMatMultSymbolic_MPIAIJ_MPIAIJ,
       MatMatMultNumeric_MPIAIJ_MPIAIJ,
       MatPtAP_MPIAIJ_MPIAIJ,
/*94*/ MatPtAPSymbolic_MPIAIJ_MPIAIJ,
       MatPtAPNumeric_MPIAIJ_MPIAIJ,
};

/* ----------------------------------------------------------------------------------------*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatStoreValues_MPIAIJ"
PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
  ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatRetrieveValues_MPIAIJ"
PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
{
  Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
  ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

#include "petscpc.h"
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B,int d_nz,const int d_nnz[],int o_nz,const int o_nnz[])
{
  Mat_MPIAIJ   *b;
  PetscErrorCode ierr;
  int          i;

  PetscFunctionBegin;
  B->preallocated = PETSC_TRUE;
  if (d_nz == PETSC_DEFAULT || d_nz == PETSC_DECIDE) d_nz = 5;
  if (o_nz == PETSC_DEFAULT || o_nz == PETSC_DECIDE) o_nz = 2;
  if (d_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"d_nz cannot be less than 0: value %d",d_nz);
  if (o_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"o_nz cannot be less than 0: value %d",o_nz);
  if (d_nnz) {
    for (i=0; i<B->m; i++) {
      if (d_nnz[i] < 0) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"d_nnz cannot be less than 0: local row %d value %d",i,d_nnz[i]);
    }
  }
  if (o_nnz) {
    for (i=0; i<B->m; i++) {
      if (o_nnz[i] < 0) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"o_nnz cannot be less than 0: local row %d value %d",i,o_nnz[i]);
    }
  }
  b = (Mat_MPIAIJ*)B->data;
  ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}
EXTERN_C_END

/*MC
   MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.

   Options Database Keys:
. -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()

  Level: beginner

.seealso: MatCreateMPIAIJ
M*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatCreate_MPIAIJ"
PetscErrorCode MatCreate_MPIAIJ(Mat B)
{
  Mat_MPIAIJ *b;
  PetscErrorCode ierr;
  int        i,size;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(B->comm,&size);CHKERRQ(ierr);

  ierr            = PetscNew(Mat_MPIAIJ,&b);CHKERRQ(ierr);
  B->data         = (void*)b;
  ierr            = PetscMemzero(b,sizeof(Mat_MPIAIJ));CHKERRQ(ierr);
  ierr            = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
  B->factor       = 0;
  B->assembled    = PETSC_FALSE;
  B->mapping      = 0;

  B->insertmode      = NOT_SET_VALUES;
  b->size            = size;
  ierr = MPI_Comm_rank(B->comm,&b->rank);CHKERRQ(ierr);

  ierr = PetscSplitOwnership(B->comm,&B->m,&B->M);CHKERRQ(ierr);
  ierr = PetscSplitOwnership(B->comm,&B->n,&B->N);CHKERRQ(ierr);

  /* the information in the maps duplicates the information computed below, eventually
     we should remove the duplicate information that is not contained in the maps */
  ierr = PetscMapCreateMPI(B->comm,B->m,B->M,&B->rmap);CHKERRQ(ierr);
  ierr = PetscMapCreateMPI(B->comm,B->n,B->N,&B->cmap);CHKERRQ(ierr);

  /* build local table of row and column ownerships */
  ierr = PetscMalloc(2*(b->size+2)*sizeof(int),&b->rowners);CHKERRQ(ierr);
  PetscLogObjectMemory(B,2*(b->size+2)*sizeof(int)+sizeof(struct _p_Mat)+sizeof(Mat_MPIAIJ));
  b->cowners = b->rowners + b->size + 2;
  ierr = MPI_Allgather(&B->m,1,MPI_INT,b->rowners+1,1,MPI_INT,B->comm);CHKERRQ(ierr);
  b->rowners[0] = 0;
  for (i=2; i<=b->size; i++) {
    b->rowners[i] += b->rowners[i-1];
  }
  b->rstart = b->rowners[b->rank];
  b->rend   = b->rowners[b->rank+1];
  ierr = MPI_Allgather(&B->n,1,MPI_INT,b->cowners+1,1,MPI_INT,B->comm);CHKERRQ(ierr);
  b->cowners[0] = 0;
  for (i=2; i<=b->size; i++) {
    b->cowners[i] += b->cowners[i-1];
  }
  b->cstart = b->cowners[b->rank];
  b->cend   = b->cowners[b->rank+1];

  /* build cache for off array entries formed */
  ierr = MatStashCreate_Private(B->comm,1,&B->stash);CHKERRQ(ierr);
  b->donotstash  = PETSC_FALSE;
  b->colmap      = 0;
  b->garray      = 0;
  b->roworiented = PETSC_TRUE;

  /* stuff used for matrix vector multiply */
  b->lvec      = PETSC_NULL;
  b->Mvctx     = PETSC_NULL;

  /* stuff for MatGetRow() */
  b->rowindices   = 0;
  b->rowvalues    = 0;
  b->getrowactive = PETSC_FALSE;

  /* Explicitly create 2 MATSEQAIJ matrices. */
  ierr = MatCreate(PETSC_COMM_SELF,B->m,B->n,B->m,B->n,&b->A);CHKERRQ(ierr);
  ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
  PetscLogObjectParent(B,b->A);
  ierr = MatCreate(PETSC_COMM_SELF,B->m,B->N,B->m,B->N,&b->B);CHKERRQ(ierr);
  ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
  PetscLogObjectParent(B,b->B);

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
                                     "MatStoreValues_MPIAIJ",
                                     MatStoreValues_MPIAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
                                     "MatRetrieveValues_MPIAIJ",
                                     MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetDiagonalBlock_C",
				     "MatGetDiagonalBlock_MPIAIJ",
                                     MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatIsTranspose_C",
				     "MatIsTranspose_MPIAIJ",
				     MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocation_C",
				     "MatMPIAIJSetPreallocation_MPIAIJ",
				     MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatDiagonalScaleLocal_C",
				     "MatDiagonalScaleLocal_MPIAIJ",
				     MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

/*MC
   MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.

   This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
   and MATMPIAIJ otherwise.  As a result, for single process communicators,
  MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
  for communicators controlling multiple processes.  It is recommended that you call both of
  the above preallocation routines for simplicity.

   Options Database Keys:
. -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()

  Level: beginner

.seealso: MatCreateMPIAIJ,MATSEQAIJ,MATMPIAIJ
M*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatCreate_AIJ"
PetscErrorCode MatCreate_AIJ(Mat A)
{
  PetscErrorCode ierr;
  int size;

  PetscFunctionBegin;
  ierr = PetscObjectChangeTypeName((PetscObject)A,MATAIJ);CHKERRQ(ierr);
  ierr = MPI_Comm_size(A->comm,&size);CHKERRQ(ierr);
  if (size == 1) {
    ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
  } else {
    ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate_MPIAIJ"
PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
{
  Mat        mat;
  Mat_MPIAIJ *a,*oldmat = (Mat_MPIAIJ*)matin->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  *newmat       = 0;
  ierr = MatCreate(matin->comm,matin->m,matin->n,matin->M,matin->N,&mat);CHKERRQ(ierr);
  ierr = MatSetType(mat,matin->type_name);CHKERRQ(ierr);
  ierr = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
  a    = (Mat_MPIAIJ*)mat->data;

  mat->factor       = matin->factor;
  mat->assembled    = PETSC_TRUE;
  mat->insertmode   = NOT_SET_VALUES;
  mat->preallocated = PETSC_TRUE;

  a->rstart       = oldmat->rstart;
  a->rend         = oldmat->rend;
  a->cstart       = oldmat->cstart;
  a->cend         = oldmat->cend;
  a->size         = oldmat->size;
  a->rank         = oldmat->rank;
  a->donotstash   = oldmat->donotstash;
  a->roworiented  = oldmat->roworiented;
  a->rowindices   = 0;
  a->rowvalues    = 0;
  a->getrowactive = PETSC_FALSE;

  ierr       = PetscMemcpy(a->rowners,oldmat->rowners,2*(a->size+2)*sizeof(int));CHKERRQ(ierr);
  ierr       = MatStashCreate_Private(matin->comm,1,&mat->stash);CHKERRQ(ierr);
  if (oldmat->colmap) {
#if defined (PETSC_USE_CTABLE)
    ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
#else
    ierr = PetscMalloc((mat->N)*sizeof(int),&a->colmap);CHKERRQ(ierr);
    PetscLogObjectMemory(mat,(mat->N)*sizeof(int));
    ierr      = PetscMemcpy(a->colmap,oldmat->colmap,(mat->N)*sizeof(int));CHKERRQ(ierr);
#endif
  } else a->colmap = 0;
  if (oldmat->garray) {
    int len;
    len  = oldmat->B->n;
    ierr = PetscMalloc((len+1)*sizeof(int),&a->garray);CHKERRQ(ierr);
    PetscLogObjectMemory(mat,len*sizeof(int));
    if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(int));CHKERRQ(ierr); }
  } else a->garray = 0;

  ierr =  VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
  PetscLogObjectParent(mat,a->lvec);
  ierr =  VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
  PetscLogObjectParent(mat,a->Mvctx);
  ierr =  MatDestroy(a->A);CHKERRQ(ierr);
  ierr =  MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
  PetscLogObjectParent(mat,a->A);
  ierr =  MatDestroy(a->B);CHKERRQ(ierr);
  ierr =  MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
  PetscLogObjectParent(mat,a->B);
  ierr = PetscFListDuplicate(matin->qlist,&mat->qlist);CHKERRQ(ierr);
  *newmat = mat;
  PetscFunctionReturn(0);
}

#include "petscsys.h"

#undef __FUNCT__
#define __FUNCT__ "MatLoad_MPIAIJ"
PetscErrorCode MatLoad_MPIAIJ(PetscViewer viewer,const MatType type,Mat *newmat)
{
  Mat            A;
  PetscScalar    *vals,*svals;
  MPI_Comm       comm = ((PetscObject)viewer)->comm;
  MPI_Status     status;
  PetscErrorCode ierr;
  PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
  int            i,nz,j,rstart,rend,fd;
  int            header[4],*rowlengths = 0,M,N,m,*rowners,maxnz,*cols;
  int            *ourlens,*sndcounts = 0,*procsnz = 0,*offlens,jj,*mycols,*smycols;
  int            cend,cstart,n;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
  if (!rank) {
    ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
    ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
    if (header[0] != MAT_FILE_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
    if (header[3] < 0) {
      SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"Matrix in special format on disk, cannot load as MPIAIJ");
    }
  }

  ierr = MPI_Bcast(header+1,3,MPI_INT,0,comm);CHKERRQ(ierr);
  M = header[1]; N = header[2];
  /* determine ownership of all rows */
  m = M/size + ((M % size) > rank);
  ierr = PetscMalloc((size+2)*sizeof(int),&rowners);CHKERRQ(ierr);
  ierr = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
  rowners[0] = 0;
  for (i=2; i<=size; i++) {
    rowners[i] += rowners[i-1];
  }
  rstart = rowners[rank];
  rend   = rowners[rank+1];

  /* distribute row lengths to all processors */
  ierr    = PetscMalloc(2*(rend-rstart+1)*sizeof(int),&ourlens);CHKERRQ(ierr);
  offlens = ourlens + (rend-rstart);
  if (!rank) {
    ierr = PetscMalloc(M*sizeof(int),&rowlengths);CHKERRQ(ierr);
    ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
    ierr = PetscMalloc(size*sizeof(int),&sndcounts);CHKERRQ(ierr);
    for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
    ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPI_INT,ourlens,rend-rstart,MPI_INT,0,comm);CHKERRQ(ierr);
    ierr = PetscFree(sndcounts);CHKERRQ(ierr);
  } else {
    ierr = MPI_Scatterv(0,0,0,MPI_INT,ourlens,rend-rstart,MPI_INT,0,comm);CHKERRQ(ierr);
  }

  if (!rank) {
    /* calculate the number of nonzeros on each processor */
    ierr = PetscMalloc(size*sizeof(int),&procsnz);CHKERRQ(ierr);
    ierr = PetscMemzero(procsnz,size*sizeof(int));CHKERRQ(ierr);
    for (i=0; i<size; i++) {
      for (j=rowners[i]; j< rowners[i+1]; j++) {
        procsnz[i] += rowlengths[j];
      }
    }
    ierr = PetscFree(rowlengths);CHKERRQ(ierr);

    /* determine max buffer needed and allocate it */
    maxnz = 0;
    for (i=0; i<size; i++) {
      maxnz = PetscMax(maxnz,procsnz[i]);
    }
    ierr = PetscMalloc(maxnz*sizeof(int),&cols);CHKERRQ(ierr);

    /* read in my part of the matrix column indices  */
    nz   = procsnz[0];
    ierr = PetscMalloc(nz*sizeof(int),&mycols);CHKERRQ(ierr);
    ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);

    /* read in every one elses and ship off */
    for (i=1; i<size; i++) {
      nz   = procsnz[i];
      ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
      ierr = MPI_Send(cols,nz,MPI_INT,i,tag,comm);CHKERRQ(ierr);
    }
    ierr = PetscFree(cols);CHKERRQ(ierr);
  } else {
    /* determine buffer space needed for message */
    nz = 0;
    for (i=0; i<m; i++) {
      nz += ourlens[i];
    }
    ierr = PetscMalloc((nz+1)*sizeof(int),&mycols);CHKERRQ(ierr);

    /* receive message of column indices*/
    ierr = MPI_Recv(mycols,nz,MPI_INT,0,tag,comm,&status);CHKERRQ(ierr);
    ierr = MPI_Get_count(&status,MPI_INT,&maxnz);CHKERRQ(ierr);
    if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
  }

  /* determine column ownership if matrix is not square */
  if (N != M) {
    n      = N/size + ((N % size) > rank);
    ierr   = MPI_Scan(&n,&cend,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
    cstart = cend - n;
  } else {
    cstart = rstart;
    cend   = rend;
    n      = cend - cstart;
  }

  /* loop over local rows, determining number of off diagonal entries */
  ierr = PetscMemzero(offlens,m*sizeof(int));CHKERRQ(ierr);
  jj = 0;
  for (i=0; i<m; i++) {
    for (j=0; j<ourlens[i]; j++) {
      if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
      jj++;
    }
  }

  /* create our matrix */
  for (i=0; i<m; i++) {
    ourlens[i] -= offlens[i];
  }
  ierr = MatCreate(comm,m,n,M,N,&A);CHKERRQ(ierr);
  ierr = MatSetType(A,type);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(A,0,ourlens,0,offlens);CHKERRQ(ierr);

  ierr = MatSetOption(A,MAT_COLUMNS_SORTED);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    ourlens[i] += offlens[i];
  }

  if (!rank) {
    ierr = PetscMalloc(maxnz*sizeof(PetscScalar),&vals);CHKERRQ(ierr);

    /* read in my part of the matrix numerical values  */
    nz   = procsnz[0];
    ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);

    /* insert into matrix */
    jj      = rstart;
    smycols = mycols;
    svals   = vals;
    for (i=0; i<m; i++) {
      ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
      smycols += ourlens[i];
      svals   += ourlens[i];
      jj++;
    }

    /* read in other processors and ship out */
    for (i=1; i<size; i++) {
      nz   = procsnz[i];
      ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
      ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,A->tag,comm);CHKERRQ(ierr);
    }
    ierr = PetscFree(procsnz);CHKERRQ(ierr);
  } else {
    /* receive numeric values */
    ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);

    /* receive message of values*/
    ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,A->tag,comm,&status);CHKERRQ(ierr);
    ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
    if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");

    /* insert into matrix */
    jj      = rstart;
    smycols = mycols;
    svals   = vals;
    for (i=0; i<m; i++) {
      ierr     = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
      smycols += ourlens[i];
      svals   += ourlens[i];
      jj++;
    }
  }
  ierr = PetscFree(ourlens);CHKERRQ(ierr);
  ierr = PetscFree(vals);CHKERRQ(ierr);
  ierr = PetscFree(mycols);CHKERRQ(ierr);
  ierr = PetscFree(rowners);CHKERRQ(ierr);

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  *newmat = A;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
/*
    Not great since it makes two copies of the submatrix, first an SeqAIJ
  in local and then by concatenating the local matrices the end result.
  Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
*/
PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,int csize,MatReuse call,Mat *newmat)
{
  PetscErrorCode ierr;
  PetscMPIInt    rank,size;
  int            i,m,n,rstart,row,rend,nz,*cwork,j;
  int            *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
  Mat            *local,M,Mreuse;
  PetscScalar    *vwork,*aa;
  MPI_Comm       comm = mat->comm;
  Mat_SeqAIJ     *aij;


  PetscFunctionBegin;
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);

  if (call ==  MAT_REUSE_MATRIX) {
    ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject *)&Mreuse);CHKERRQ(ierr);
    if (!Mreuse) SETERRQ(1,"Submatrix passed in was not used before, cannot reuse");
    local = &Mreuse;
    ierr  = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&local);CHKERRQ(ierr);
  } else {
    ierr   = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
    Mreuse = *local;
    ierr   = PetscFree(local);CHKERRQ(ierr);
  }

  /*
      m - number of local rows
      n - number of columns (same on all processors)
      rstart - first row in new global matrix generated
  */
  ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
  if (call == MAT_INITIAL_MATRIX) {
    aij = (Mat_SeqAIJ*)(Mreuse)->data;
    ii  = aij->i;
    jj  = aij->j;

    /*
        Determine the number of non-zeros in the diagonal and off-diagonal
        portions of the matrix in order to do correct preallocation
    */

    /* first get start and end of "diagonal" columns */
    if (csize == PETSC_DECIDE) {
      ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
      if (mglobal == n) { /* square matrix */
	nlocal = m;
      } else {
        nlocal = n/size + ((n % size) > rank);
      }
    } else {
      nlocal = csize;
    }
    ierr   = MPI_Scan(&nlocal,&rend,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
    rstart = rend - nlocal;
    if (rank == size - 1 && rend != n) {
      SETERRQ2(1,"Local column sizes %d do not add up to total number of columns %d",rend,n);
    }

    /* next, compute all the lengths */
    ierr  = PetscMalloc((2*m+1)*sizeof(int),&dlens);CHKERRQ(ierr);
    olens = dlens + m;
    for (i=0; i<m; i++) {
      jend = ii[i+1] - ii[i];
      olen = 0;
      dlen = 0;
      for (j=0; j<jend; j++) {
        if (*jj < rstart || *jj >= rend) olen++;
        else dlen++;
        jj++;
      }
      olens[i] = olen;
      dlens[i] = dlen;
    }
    ierr = MatCreate(comm,m,nlocal,PETSC_DECIDE,n,&M);CHKERRQ(ierr);
    ierr = MatSetType(M,mat->type_name);CHKERRQ(ierr);
    ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
    ierr = PetscFree(dlens);CHKERRQ(ierr);
  } else {
    int ml,nl;

    M = *newmat;
    ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
    if (ml != m) SETERRQ(PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
    ierr = MatZeroEntries(M);CHKERRQ(ierr);
    /*
         The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
       rather than the slower MatSetValues().
    */
    M->was_assembled = PETSC_TRUE;
    M->assembled     = PETSC_FALSE;
  }
  ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
  aij = (Mat_SeqAIJ*)(Mreuse)->data;
  ii  = aij->i;
  jj  = aij->j;
  aa  = aij->a;
  for (i=0; i<m; i++) {
    row   = rstart + i;
    nz    = ii[i+1] - ii[i];
    cwork = jj;     jj += nz;
    vwork = aa;     aa += nz;
    ierr = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  *newmat = M;

  /* save submatrix used in processor for next request */
  if (call ==  MAT_INITIAL_MATRIX) {
    ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
    ierr = PetscObjectDereference((PetscObject)Mreuse);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMPIAIJSetPreallocation"
/*@C
   MatMPIAIJSetPreallocation - Creates a sparse parallel matrix in AIJ format
   (the default parallel PETSc format).  For good matrix assembly performance
   the user should preallocate the matrix storage by setting the parameters
   d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
   performance can be increased by more than a factor of 50.

   Collective on MPI_Comm

   Input Parameters:
+  A - the matrix
.  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
           (same value is used for all local rows)
.  d_nnz - array containing the number of nonzeros in the various rows of the
           DIAGONAL portion of the local submatrix (possibly different for each row)
           or PETSC_NULL, if d_nz is used to specify the nonzero structure.
           The size of this array is equal to the number of local rows, i.e 'm'.
           You must leave room for the diagonal entry even if it is zero.
.  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
           submatrix (same value is used for all local rows).
-  o_nnz - array containing the number of nonzeros in the various rows of the
           OFF-DIAGONAL portion of the local submatrix (possibly different for
           each row) or PETSC_NULL, if o_nz is used to specify the nonzero
           structure. The size of this array is equal to the number
           of local rows, i.e 'm'.

   The AIJ format (also called the Yale sparse matrix format or
   compressed row storage), is fully compatible with standard Fortran 77
   storage.  That is, the stored row and column indices can begin at
   either one (as in Fortran) or zero.  See the users manual for details.

   The user MUST specify either the local or global matrix dimensions
   (possibly both).

   The parallel matrix is partitioned such that the first m0 rows belong to
   process 0, the next m1 rows belong to process 1, the next m2 rows belong
   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

   The DIAGONAL portion of the local submatrix of a processor can be defined
   as the submatrix which is obtained by extraction the part corresponding
   to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
   first row that belongs to the processor, and r2 is the last row belonging
   to the this processor. This is a square mxm matrix. The remaining portion
   of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.

   If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.

   By default, this format uses inodes (identical nodes) when possible.
   We search for consecutive rows with the same nonzero structure, thereby
   reusing matrix information to achieve increased efficiency.

   Options Database Keys:
+  -mat_aij_no_inode  - Do not use inodes
.  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
-  -mat_aij_oneindex - Internally use indexing starting at 1
        rather than 0.  Note that when calling MatSetValues(),
        the user still MUST index entries starting at 0!

   Example usage:

   Consider the following 8x8 matrix with 34 non-zero values, that is
   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
   as follows:

.vb
            1  2  0  |  0  3  0  |  0  4
    Proc0   0  5  6  |  7  0  0  |  8  0
            9  0 10  | 11  0  0  | 12  0
    -------------------------------------
           13  0 14  | 15 16 17  |  0  0
    Proc1   0 18  0  | 19 20 21  |  0  0
            0  0  0  | 22 23  0  | 24  0
    -------------------------------------
    Proc2  25 26 27  |  0  0 28  | 29  0
           30  0  0  | 31 32 33  |  0 34
.ve

   This can be represented as a collection of submatrices as:

.vb
      A B C
      D E F
      G H I
.ve

   Where the submatrices A,B,C are owned by proc0, D,E,F are
   owned by proc1, G,H,I are owned by proc2.

   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
   The 'M','N' parameters are 8,8, and have the same values on all procs.

   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
   part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
   matrix, ans [DF] as another SeqAIJ matrix.

   When d_nz, o_nz parameters are specified, d_nz storage elements are
   allocated for every row of the local diagonal submatrix, and o_nz
   storage locations are allocated for every row of the OFF-DIAGONAL submat.
   One way to choose d_nz and o_nz is to use the max nonzerors per local
   rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
   In this case, the values of d_nz,o_nz are:
.vb
     proc0 : dnz = 2, o_nz = 2
     proc1 : dnz = 3, o_nz = 2
     proc2 : dnz = 1, o_nz = 4
.ve
   We are allocating m*(d_nz+o_nz) storage locations for every proc. This
   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
   for proc3. i.e we are using 12+15+10=37 storage locations to store
   34 values.

   When d_nnz, o_nnz parameters are specified, the storage is specified
   for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
   In the above case the values for d_nnz,o_nnz are:
.vb
     proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
     proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
     proc2: d_nnz = [1,1]   and o_nnz = [4,4]
.ve
   Here the space allocated is sum of all the above values i.e 34, and
   hence pre-allocation is perfect.

   Level: intermediate

.keywords: matrix, aij, compressed row, sparse, parallel

.seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
@*/
PetscErrorCode MatMPIAIJSetPreallocation(Mat B,int d_nz,const int d_nnz[],int o_nz,const int o_nnz[])
{
  PetscErrorCode ierr,(*f)(Mat,int,const int[],int,const int[]);

  PetscFunctionBegin;
  ierr = PetscObjectQueryFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",(void (**)(void))&f);CHKERRQ(ierr);
  if (f) {
    ierr = (*f)(B,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateMPIAIJ"
/*@C
   MatCreateMPIAIJ - Creates a sparse parallel matrix in AIJ format
   (the default parallel PETSc format).  For good matrix assembly performance
   the user should preallocate the matrix storage by setting the parameters
   d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
   performance can be increased by more than a factor of 50.

   Collective on MPI_Comm

   Input Parameters:
+  comm - MPI communicator
.  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
           This value should be the same as the local size used in creating the
           y vector for the matrix-vector product y = Ax.
.  n - This value should be the same as the local size used in creating the
       x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
       calculated if N is given) For square matrices n is almost always m.
.  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
.  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
.  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
           (same value is used for all local rows)
.  d_nnz - array containing the number of nonzeros in the various rows of the
           DIAGONAL portion of the local submatrix (possibly different for each row)
           or PETSC_NULL, if d_nz is used to specify the nonzero structure.
           The size of this array is equal to the number of local rows, i.e 'm'.
           You must leave room for the diagonal entry even if it is zero.
.  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
           submatrix (same value is used for all local rows).
-  o_nnz - array containing the number of nonzeros in the various rows of the
           OFF-DIAGONAL portion of the local submatrix (possibly different for
           each row) or PETSC_NULL, if o_nz is used to specify the nonzero
           structure. The size of this array is equal to the number
           of local rows, i.e 'm'.

   Output Parameter:
.  A - the matrix

   Notes:
   m,n,M,N parameters specify the size of the matrix, and its partitioning across
   processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
   storage requirements for this matrix.

   If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
   processor than it must be used on all processors that share the object for
   that argument.

   The AIJ format (also called the Yale sparse matrix format or
   compressed row storage), is fully compatible with standard Fortran 77
   storage.  That is, the stored row and column indices can begin at
   either one (as in Fortran) or zero.  See the users manual for details.

   The user MUST specify either the local or global matrix dimensions
   (possibly both).

   The parallel matrix is partitioned such that the first m0 rows belong to
   process 0, the next m1 rows belong to process 1, the next m2 rows belong
   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

   The DIAGONAL portion of the local submatrix of a processor can be defined
   as the submatrix which is obtained by extraction the part corresponding
   to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
   first row that belongs to the processor, and r2 is the last row belonging
   to the this processor. This is a square mxm matrix. The remaining portion
   of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.

   If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.

   When calling this routine with a single process communicator, a matrix of
   type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
   type of communicator, use the construction mechanism:
     MatCreate(...,&A); MatSetType(A,MPIAIJ); MatMPIAIJSetPreallocation(A,...);

   By default, this format uses inodes (identical nodes) when possible.
   We search for consecutive rows with the same nonzero structure, thereby
   reusing matrix information to achieve increased efficiency.

   Options Database Keys:
+  -mat_aij_no_inode  - Do not use inodes
.  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
-  -mat_aij_oneindex - Internally use indexing starting at 1
        rather than 0.  Note that when calling MatSetValues(),
        the user still MUST index entries starting at 0!


   Example usage:

   Consider the following 8x8 matrix with 34 non-zero values, that is
   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
   as follows:

.vb
            1  2  0  |  0  3  0  |  0  4
    Proc0   0  5  6  |  7  0  0  |  8  0
            9  0 10  | 11  0  0  | 12  0
    -------------------------------------
           13  0 14  | 15 16 17  |  0  0
    Proc1   0 18  0  | 19 20 21  |  0  0
            0  0  0  | 22 23  0  | 24  0
    -------------------------------------
    Proc2  25 26 27  |  0  0 28  | 29  0
           30  0  0  | 31 32 33  |  0 34
.ve

   This can be represented as a collection of submatrices as:

.vb
      A B C
      D E F
      G H I
.ve

   Where the submatrices A,B,C are owned by proc0, D,E,F are
   owned by proc1, G,H,I are owned by proc2.

   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
   The 'M','N' parameters are 8,8, and have the same values on all procs.

   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
   part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
   matrix, ans [DF] as another SeqAIJ matrix.

   When d_nz, o_nz parameters are specified, d_nz storage elements are
   allocated for every row of the local diagonal submatrix, and o_nz
   storage locations are allocated for every row of the OFF-DIAGONAL submat.
   One way to choose d_nz and o_nz is to use the max nonzerors per local
   rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
   In this case, the values of d_nz,o_nz are:
.vb
     proc0 : dnz = 2, o_nz = 2
     proc1 : dnz = 3, o_nz = 2
     proc2 : dnz = 1, o_nz = 4
.ve
   We are allocating m*(d_nz+o_nz) storage locations for every proc. This
   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
   for proc3. i.e we are using 12+15+10=37 storage locations to store
   34 values.

   When d_nnz, o_nnz parameters are specified, the storage is specified
   for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
   In the above case the values for d_nnz,o_nnz are:
.vb
     proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
     proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
     proc2: d_nnz = [1,1]   and o_nnz = [4,4]
.ve
   Here the space allocated is sum of all the above values i.e 34, and
   hence pre-allocation is perfect.

   Level: intermediate

.keywords: matrix, aij, compressed row, sparse, parallel

.seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
@*/
PetscErrorCode MatCreateMPIAIJ(MPI_Comm comm,int m,int n,int M,int N,int d_nz,const int d_nnz[],int o_nz,const int o_nnz[],Mat *A)
{
  PetscErrorCode ierr;
  int size;

  PetscFunctionBegin;
  ierr = MatCreate(comm,m,n,M,N,A);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  if (size > 1) {
    ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
    ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
  } else {
    ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
    ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMPIAIJGetSeqAIJ"
PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,int *colmap[])
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
  PetscFunctionBegin;
  *Ad     = a->A;
  *Ao     = a->B;
  *colmap = a->garray;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetColoring_MPIAIJ"
PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
{
  PetscErrorCode ierr;
  int        i;
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;

  PetscFunctionBegin;
  if (coloring->ctype == IS_COLORING_LOCAL) {
    ISColoringValue *allcolors,*colors;
    ISColoring      ocoloring;

    /* set coloring for diagonal portion */
    ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);

    /* set coloring for off-diagonal portion */
    ierr = ISAllGatherColors(A->comm,coloring->n,coloring->colors,PETSC_NULL,&allcolors);CHKERRQ(ierr);
    ierr = PetscMalloc((a->B->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
    for (i=0; i<a->B->n; i++) {
      colors[i] = allcolors[a->garray[i]];
    }
    ierr = PetscFree(allcolors);CHKERRQ(ierr);
    ierr = ISColoringCreate(MPI_COMM_SELF,a->B->n,colors,&ocoloring);CHKERRQ(ierr);
    ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);
  } else if (coloring->ctype == IS_COLORING_GHOSTED) {
    ISColoringValue *colors;
    int             *larray;
    ISColoring      ocoloring;

    /* set coloring for diagonal portion */
    ierr = PetscMalloc((a->A->n+1)*sizeof(int),&larray);CHKERRQ(ierr);
    for (i=0; i<a->A->n; i++) {
      larray[i] = i + a->cstart;
    }
    ierr = ISGlobalToLocalMappingApply(A->mapping,IS_GTOLM_MASK,a->A->n,larray,PETSC_NULL,larray);CHKERRQ(ierr);
    ierr = PetscMalloc((a->A->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
    for (i=0; i<a->A->n; i++) {
      colors[i] = coloring->colors[larray[i]];
    }
    ierr = PetscFree(larray);CHKERRQ(ierr);
    ierr = ISColoringCreate(PETSC_COMM_SELF,a->A->n,colors,&ocoloring);CHKERRQ(ierr);
    ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);

    /* set coloring for off-diagonal portion */
    ierr = PetscMalloc((a->B->n+1)*sizeof(int),&larray);CHKERRQ(ierr);
    ierr = ISGlobalToLocalMappingApply(A->mapping,IS_GTOLM_MASK,a->B->n,a->garray,PETSC_NULL,larray);CHKERRQ(ierr);
    ierr = PetscMalloc((a->B->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
    for (i=0; i<a->B->n; i++) {
      colors[i] = coloring->colors[larray[i]];
    }
    ierr = PetscFree(larray);CHKERRQ(ierr);
    ierr = ISColoringCreate(MPI_COMM_SELF,a->B->n,colors,&ocoloring);CHKERRQ(ierr);
    ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);
  } else {
    SETERRQ1(1,"No support ISColoringType %d",coloring->ctype);
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesAdic_MPIAIJ"
PetscErrorCode MatSetValuesAdic_MPIAIJ(Mat A,void *advalues)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSetValuesAdic_SeqAIJ(a->A,advalues);CHKERRQ(ierr);
  ierr = MatSetValuesAdic_SeqAIJ(a->B,advalues);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,int nl,void *advalues)
{
  Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
  ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMerge"
/*@C
      MatMerge - Creates a single large PETSc matrix by concatinating sequential
                 matrices from each processor

    Collective on MPI_Comm

   Input Parameters:
+    comm - the communicators the parallel matrix will live on
.    inmat - the input sequential matrices
-    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.    outmat - the parallel matrix generated

    Level: advanced

   Notes: The number of columns of the matrix in EACH processor MUST be the same.

@*/
PetscErrorCode MatMerge(MPI_Comm comm,Mat inmat,MatReuse scall,Mat *outmat)
{
  PetscErrorCode ierr;
  int               m,n,i,rstart,nnz,I,*dnz,*onz;
  const int         *indx;
  const PetscScalar *values;
  PetscMap          columnmap,rowmap;

  PetscFunctionBegin;

  ierr = MatGetSize(inmat,&m,&n);CHKERRQ(ierr);
  if (scall == MAT_INITIAL_MATRIX){
    /* count nonzeros in each row, for diagonal and off diagonal portion of matrix */
    ierr = PetscMapCreate(comm,&columnmap);CHKERRQ(ierr);
    ierr = PetscMapSetSize(columnmap,n);CHKERRQ(ierr);
    ierr = PetscMapSetType(columnmap,MAP_MPI);CHKERRQ(ierr);
    ierr = PetscMapGetLocalSize(columnmap,&n);CHKERRQ(ierr);
    ierr = PetscMapDestroy(columnmap);CHKERRQ(ierr);

    ierr = PetscMapCreate(comm,&rowmap);CHKERRQ(ierr);
    ierr = PetscMapSetLocalSize(rowmap,m);CHKERRQ(ierr);
    ierr = PetscMapSetType(rowmap,MAP_MPI);CHKERRQ(ierr);
    ierr = PetscMapGetLocalRange(rowmap,&rstart,0);CHKERRQ(ierr);
    ierr = PetscMapDestroy(rowmap);CHKERRQ(ierr);

    ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
    for (i=0;i<m;i++) {
      ierr = MatGetRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
      ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
      ierr = MatRestoreRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
    }
    /* This routine will ONLY return MPIAIJ type matrix */
    ierr = MatCreate(comm,m,n,PETSC_DETERMINE,PETSC_DETERMINE,outmat);CHKERRQ(ierr);
    ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
    ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
    ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);

  } else if (scall == MAT_REUSE_MATRIX){
    ierr = MatGetOwnershipRange(*outmat,&rstart,PETSC_NULL);CHKERRQ(ierr);
  } else {
    SETERRQ1(PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",scall);
  }

  for (i=0;i<m;i++) {
    ierr = MatGetRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
    I    = i + rstart;
    ierr = MatSetValues(*outmat,1,&I,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
  }
  ierr = MatDestroy(inmat);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFileSplit"
PetscErrorCode MatFileSplit(Mat A,char *outfile)
{
  PetscErrorCode    ierr;
  PetscMPIInt       rank;
  int               m,N,i,rstart,nnz;
  size_t            len;
  const int         *indx;
  PetscViewer       out;
  char              *name;
  Mat               B;
  const PetscScalar *values;

  PetscFunctionBegin;

  ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
  ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
  /* Should this be the type of the diagonal block of A? */
  ierr = MatCreate(PETSC_COMM_SELF,m,N,m,N,&B);CHKERRQ(ierr);
  ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
  for (i=0;i<m;i++) {
    ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
    ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MPI_Comm_rank(A->comm,&rank);CHKERRQ(ierr);
  ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
  ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
  sprintf(name,"%s.%d",outfile,rank);
  ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,PETSC_FILE_CREATE,&out);CHKERRQ(ierr);
  ierr = PetscFree(name);
  ierr = MatView(B,out);CHKERRQ(ierr);
  ierr = PetscViewerDestroy(out);CHKERRQ(ierr);
  ierr = MatDestroy(B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

typedef struct { /* used by MatMerge_SeqsToMPI for reusing the merged matrix */
  PetscMap  rowmap;
  int       nrecv,nsend,*id_r,*bi,*bj,**ijbuf_r;
  int       *len_sra; /* array of length 2*size, len_sra[i]/len_sra[size+i]
                         store length of i-th send/recv matrix values */
  MatScalar *abuf_s;
} Mat_Merge_SeqsToMPI;

EXTERN PetscErrorCode MatDestroy_MPIAIJ(Mat);
#undef __FUNCT__
#define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
{
  PetscErrorCode ierr;
  Mat_Merge_SeqsToMPI *merge=(Mat_Merge_SeqsToMPI*)A->spptr;

  PetscFunctionBegin;
  ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
  ierr = PetscFree(merge->abuf_s);CHKERRQ(ierr);
  ierr = PetscFree(merge->len_sra);CHKERRQ(ierr);
  ierr = PetscFree(merge->bi);CHKERRQ(ierr);
  ierr = PetscFree(merge->bj);CHKERRQ(ierr);
  ierr = PetscFree(merge->ijbuf_r);CHKERRQ(ierr);
  ierr = PetscMapDestroy(merge->rowmap);CHKERRQ(ierr);
  ierr = PetscFree(merge);CHKERRQ(ierr);

  ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include "src/mat/utils/freespace.h"
#undef __FUNCT__
#define __FUNCT__ "MatMerge_SeqsToMPI"
/*@C
      MatMerge_SeqsToMPI - Creates a MPIAIJ matrix by adding sequential
                 matrices from each processor

    Collective on MPI_Comm

   Input Parameters:
+    comm - the communicators the parallel matrix will live on
.    seqmat - the input sequential matrices
-    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.    mpimat - the parallel matrix generated

    Level: advanced

   Notes: The dimensions of the sequential matrix in each processor
      MUST be the same.

@*/
PetscErrorCode MatMerge_SeqsToMPI(MPI_Comm comm,Mat seqmat,MatReuse scall,Mat *mpimat)
{
  PetscErrorCode    ierr;
  Mat               B_seq,B_mpi;
  Mat_SeqAIJ        *a=(Mat_SeqAIJ*)seqmat->data;
  PetscMPIInt       size,rank;
  int               M=seqmat->m,N=seqmat->n,m,i,j,*owners,*ai=a->i,*aj=a->j,tag,taga,len,len_a = 0,*len_s,*len_sa,proc,*len_r,*len_ra;
  int               **ijbuf_r,*ijbuf_s,*nnz_ptr,k,anzi,*bj_i,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0,nextaj;
  MPI_Request       *s_waits,*r_waits,*s_waitsa,*r_waitsa;
  MPI_Status        *status;
  MatScalar         *ba,*aa=a->a,**abuf_r,*abuf_i,*ba_i;
  FreeSpaceList     free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_Merge_SeqsToMPI *merge;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
  } else if (scall == MAT_REUSE_MATRIX){
    B_mpi = *mpimat;
    merge = (Mat_Merge_SeqsToMPI*)B_mpi->spptr;
    bi      = merge->bi;
    bj      = merge->bj;
    ijbuf_r = merge->ijbuf_r;
  } else {
    SETERRQ1(PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",scall);
  }
  ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);

  /* determine the number of messages to send, their lengths */
  /*---------------------------------------------------------*/
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscMapCreate(comm,&merge->rowmap);CHKERRQ(ierr);
    ierr = PetscMapSetSize(merge->rowmap,M);CHKERRQ(ierr);
    ierr = PetscMapSetType(merge->rowmap,MAP_MPI);CHKERRQ(ierr);
    ierr = PetscMalloc(size*sizeof(int),&len_s);CHKERRQ(ierr);
    ierr = PetscMalloc(2*size*sizeof(int),&merge->len_sra);CHKERRQ(ierr);
  }
  ierr = PetscMapGetLocalSize(merge->rowmap,&m);CHKERRQ(ierr);
  ierr = PetscMapGetGlobalRange(merge->rowmap,&owners);CHKERRQ(ierr);

  len_sa  = merge->len_sra;
  len_ra = merge->len_sra + size;

  if (scall == MAT_INITIAL_MATRIX){
    merge->nsend = 0;
    len = len_a = 0;
    for (proc=0; proc<size; proc++){
      if (proc == rank) continue;
      len_s[proc] = len_sa[proc] = 0;
      for (i=owners[proc]; i<owners[proc+1]; i++){ /* rows sent to [proc] */
        len_sa[proc] += ai[i+1] - ai[i]; /* num of cols sent to [proc] */
      }
      if (len_sa[proc]) {
        merge->nsend++;
        len_s[proc] = len_sa[proc] + owners[proc+1] - owners[proc];
        if (len < len_s[proc]) len = len_s[proc];
        if (len_a < len_sa[proc]) len_a = len_sa[proc];
      }
    }

    /* determine the number and length of messages to receive */
    /*--------------------------------------------------------*/
    ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
    ierr = PetscGatherMessageLengths(comm,merge->nsend,merge->nrecv,len_s,&merge->id_r,&len_r);CHKERRQ(ierr);

    /* post the Irecvs corresponding to these messages */
    /*-------------------------------------------------*/
    /* get new tag to keep the communication clean */
    ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&tag);CHKERRQ(ierr);
    ierr = PetscPostIrecvInt(comm,tag,merge->nrecv,merge->id_r,len_r,&ijbuf_r,&r_waits);CHKERRQ(ierr);

    /* post the sends */
    /*----------------*/
    ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
    ierr = PetscMalloc((len+1)*sizeof(int),&ijbuf_s);CHKERRQ(ierr);
    k = 0;
    for (proc=0; proc<size; proc++){
      if (!len_s[proc]) continue;
      /* form outgoing ij data to be sent to [proc] */
      nnz_ptr = ijbuf_s + owners[proc+1] - owners[proc];
      for (i=owners[proc]; i<owners[proc+1]; i++){ /* rows sent to [proc] */
        anzi = ai[i+1] - ai[i];
        if (i==owners[proc]){
          ijbuf_s[i-owners[proc]] = anzi;
        } else {
          ijbuf_s[i-owners[proc]] = ijbuf_s[i-owners[proc]-1]+ anzi;
        }
        for (j=0; j <anzi; j++){
          *nnz_ptr = *(aj+ai[i]+j); nnz_ptr++;
      }
      }
      ierr = MPI_Isend(ijbuf_s,len_s[proc],MPI_INT,proc,tag,comm,s_waits+k);CHKERRQ(ierr);
      k++;
    }

    /* receives and sends of ij-structure are complete, deallocate memories */
    /*----------------------------------------------------------------------*/
    ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);
    ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);

    ierr = PetscFree(ijbuf_s);CHKERRQ(ierr);
    ierr = PetscFree(s_waits);CHKERRQ(ierr);
    ierr = PetscFree(r_waits);CHKERRQ(ierr);
  }

  /* send and recv matrix values */
  /*-----------------------------*/
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscMalloc((len_a+1)*sizeof(MatScalar),&merge->abuf_s);CHKERRQ(ierr);
    for (i=0; i<merge->nrecv; i++) len_ra[i] = len_r[i]-m; /* length of seqmat->a to be received from a proc */
  }
  ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&taga);CHKERRQ(ierr);
  ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,len_ra,&abuf_r,&r_waitsa);CHKERRQ(ierr);

  ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waitsa);CHKERRQ(ierr);
  k = 0;
  for (proc=0; proc<size; proc++){
    if (!len_sa[proc]) continue;
    /* form outgoing mat value data to be sent to [proc] */
    abuf_i = merge->abuf_s;
    for (i=owners[proc]; i<owners[proc+1]; i++){ /* rows sent to [proc] */
      anzi = ai[i+1] - ai[i];
      for (j=0; j <anzi; j++){
        *abuf_i = *(aa+ai[i]+j); abuf_i++;
      }
    }
    ierr = MPI_Isend(merge->abuf_s,len_sa[proc],MPIU_MATSCALAR,proc,taga,comm,s_waitsa+k);CHKERRQ(ierr);
    k++;
  }

  ierr = MPI_Waitall(merge->nrecv,r_waitsa,status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nsend,s_waitsa,status);CHKERRQ(ierr);
  ierr = PetscFree(status);CHKERRQ(ierr);

  ierr = PetscFree(s_waitsa);CHKERRQ(ierr);
  ierr = PetscFree(r_waitsa);CHKERRQ(ierr);

  /* create seq matrix B_seq in each processor */
  /*-------------------------------------------*/
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscFree(len_s);CHKERRQ(ierr);
    /* allocate bi array and free space for accumulating nonzero column info */
    ierr = PetscMalloc((m+1)*sizeof(int),&bi);CHKERRQ(ierr);
    bi[0] = 0;

    ierr = PetscMalloc((N+1)*sizeof(int),&lnk);CHKERRQ(ierr);
    ierr = PetscLLInitialize(N,N);CHKERRQ(ierr);

    /* initial FreeSpace size is (nproc)*(num of local nnz(seqmat)) */
    len = 0;
    for (i=owners[rank]; i<owners[rank+1]; i++) len += ai[i+1] - ai[i];
    ierr = GetMoreSpace((int)(size*len+1),&free_space);CHKERRQ(ierr);
    current_space = free_space;

    /* determine symbolic info for each row of B_seq */
    for (i=0;i<m;i++) {
      bnzi   = 0;
      /* add local non-zero cols of this proc's seqmat into lnk */
      arow   = owners[rank] + i;
      anzi   = ai[arow+1] - ai[arow];
      aj     = a->j + ai[arow];
      ierr = PetscLLAdd(anzi,aj,N,nlnk,lnk);CHKERRQ(ierr);
      bnzi += nlnk;
      /* add received col data into lnk */
      for (k=0; k<merge->nrecv; k++){ /* k-th received message */
        /* i-th row */
        if (i == 0){
          anzi = *(ijbuf_r[k]+i);
          aj   = ijbuf_r[k] + m;
        } else {
          anzi = *(ijbuf_r[k]+i) - *(ijbuf_r[k]+i-1);
          aj   = ijbuf_r[k]+m + *(ijbuf_r[k]+i-1);
        }
        ierr = PetscLLAdd(anzi,aj,N,nlnk,lnk);CHKERRQ(ierr);
        bnzi += nlnk;
      }

      /* if free space is not available, make more free space */
      if (current_space->local_remaining<bnzi) {
        ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
        nspacedouble++;
      }
      /* copy data into free space, then initialize lnk */
      ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array);CHKERRQ(ierr);
      current_space->array           += bnzi;
      current_space->local_used      += bnzi;
      current_space->local_remaining -= bnzi;

      bi[i+1] = bi[i] + bnzi;
    }
    ierr = PetscMalloc((bi[m]+1)*sizeof(int),&bj);CHKERRQ(ierr);
    ierr = MakeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);

    ierr = PetscFree(lnk);CHKERRQ(ierr);
    ierr = PetscFree(len_r);CHKERRQ(ierr);

    /* allocate space for ba */
    ierr = PetscMalloc((bi[m]+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
    ierr = PetscMemzero(ba,(bi[m]+1)*sizeof(MatScalar));CHKERRQ(ierr);

    /* put together B_seq */
    ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,bi,bj,ba,&B_seq);CHKERRQ(ierr);
    ierr = PetscFree(ba);CHKERRQ(ierr); /* bi and bj are saved for reuse */

    /* create symbolic parallel matrix B_mpi by concatinating B_seq */
    /*--------------------------------------------------------------*/
    ierr = MatMerge(comm,B_seq,scall,&B_mpi);CHKERRQ(ierr);
  } /* endof if (scall == MAT_INITIAL_MATRIX) */

  /* insert mat values of B_mpi */
  /*----------------------------*/
  ierr = PetscMalloc(N*sizeof(MatScalar),&ba_i);CHKERRQ(ierr);

  /* set values of ba */
  for (i=0; i<m; i++) {
    arow = owners[rank] + i;
    bj_i = bj+bi[i];  /* col indices of the i-th row of B_seq */
    bnzi = bi[i+1] - bi[i];
    ierr = PetscMemzero(ba_i,bnzi*sizeof(MatScalar));CHKERRQ(ierr);

    /* add local non-zero vals of this proc's seqmat into ba */
    anzi = ai[arow+1] - ai[arow];
    aj   = a->j + ai[arow];
    aa   = a->a + ai[arow];
    nextaj = 0;
    for (j=0; nextaj<anzi; j++){
      if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
        ba_i[j] += aa[nextaj++];
      }
    }

    /* add received vals into ba */
    for (k=0; k<merge->nrecv; k++){ /* k-th received message */
      /* i-th row */
      if (i == 0){
        anzi = *(ijbuf_r[k]+i);
        aj   = ijbuf_r[k] + m;
        aa   = abuf_r[k];
      } else {
        anzi = *(ijbuf_r[k]+i) - *(ijbuf_r[k]+i-1);
        aj   = ijbuf_r[k]+m + *(ijbuf_r[k]+i-1);
        aa   = abuf_r[k] + *(ijbuf_r[k]+i-1);
      }
      nextaj = 0;
      for (j=0; nextaj<anzi; j++){
        if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
          ba_i[j] += aa[nextaj++];
        }
      }
    }

    ierr = MatSetValues(B_mpi,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = PetscFree(abuf_r);CHKERRQ(ierr);
  ierr = PetscFree(ba_i);CHKERRQ(ierr);

  /* attach the supporting struct to B_mpi for reuse */
  /*-------------------------------------------------*/
  if (scall == MAT_INITIAL_MATRIX){
    B_mpi->spptr         = (void*)merge;
    B_mpi->ops->destroy  = MatDestroy_MPIAIJ_SeqsToMPI;
    merge->bi            = bi;
    merge->bj            = bj;
    merge->ijbuf_r       = ijbuf_r;

    *mpimat = B_mpi;
  }
  PetscFunctionReturn(0);
}