xref: /petsc/src/mat/impls/baij/mpi/mpibaij.c (revision 57b952d6c22e98ea0d8a99e8978d81f652deb08e)

#ifndef lint
static char vcid[] = "$Id: mpibaij.c,v 1.2 1996/06/04 21:40:25 balay Exp balay $";
#endif

#include "mpibaij.h"


#include "draw.h"
#include "pinclude/pviewer.h"

extern int MatSetUpMultiply_MPIBAIJ(Mat);
extern int DisAssemble_MPIBAIJ(Mat);

/* local utility routine that creates a mapping from the global column
number to the local number in the off-diagonal part of the local
storage of the matrix.  This is done in a non scable way since the
length of colmap equals the global matrix length.
*/
static int CreateColmap_MPIBAIJ_Private(Mat mat)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *) mat->data;
  Mat_SeqBAIJ *B = (Mat_SeqBAIJ*) baij->B->data;
  int        nbs = B->nbs,i;

  baij->colmap = (int *) PetscMalloc(baij->Nbs*sizeof(int));CHKPTRQ(baij->colmap);
  PLogObjectMemory(mat,baij->Nbs*sizeof(int));
  PetscMemzero(baij->colmap,baij->Nbs*sizeof(int));
  for ( i=0; i<nbs; i++ ) baij->colmap[baij->garray[i]] = i;
  return 0;
}


static int MatGetReordering_MPIBAIJ(Mat mat,MatOrdering type,IS *rperm,IS *cperm)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *) mat->data;
  int         ierr;
  if (baij->size == 1) {
    ierr = MatGetReordering(baij->A,type,rperm,cperm); CHKERRQ(ierr);
  } else SETERRQ(1,"MatGetReordering_MPIBAIJ:not supported in parallel");
  return 0;
}

static int MatSetValues_MPIBAIJ(Mat mat,int m,int *im,int n,int *in,Scalar *v,InsertMode addv)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *) mat->data;
  Scalar      value;
  int         ierr,i,j, rstart = baij->rstart, rend = baij->rend;
  int         cstart = baij->cstart, cend = baij->cend,row,col;
  int         roworiented = baij->roworiented,rstart_orig,rend_orig;
  int         cstart_orig,cend_orig,bs=baij->bs;

  if (baij->insertmode != NOT_SET_VALUES && baij->insertmode != addv) {
    SETERRQ(1,"MatSetValues_MPIBAIJ:Cannot mix inserts and adds");
  }
  baij->insertmode = addv;
  rstart_orig = rstart*bs;
  rend_orig   = rend*bs;
  cstart_orig = cstart*bs;
  cend_orig   = cend*bs;
  for ( i=0; i<m; i++ ) {
    if (im[i] < 0) SETERRQ(1,"MatSetValues_MPIBAIJ:Negative row");
    if (im[i] >= baij->M) SETERRQ(1,"MatSetValues_MPIBAIJ:Row too large");
    if (im[i] >= rstart_orig && im[i] < rend_orig) {
      row = im[i] - rstart_orig;
      for ( j=0; j<n; j++ ) {
        if (in[j] < 0) SETERRQ(1,"MatSetValues_MPIBAIJ:Negative column");
        if (in[j] >= baij->N) SETERRQ(1,"MatSetValues_MPIBAIJ:Col too large");
        if (in[j] >= cstart_orig && in[j] < cend_orig){
          col = in[j] - cstart_orig;
          if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
          ierr = MatSetValues(baij->A,1,&row,1,&col,&value,addv);CHKERRQ(ierr);
        }
        else {
          if (mat->was_assembled) {
            if (!baij->colmap) {ierr = CreateColmap_MPIBAIJ_Private(mat);CHKERRQ(ierr);}
            col = baij->colmap[in[j]];
            if (col < 0 && !((Mat_SeqBAIJ*)(baij->A->data))->nonew) {
              ierr = DisAssemble_MPIBAIJ(mat); CHKERRQ(ierr);
              col =  in[j];
            }
          }
          else col = in[j];
          if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
          ierr = MatSetValues(baij->B,1,&row,1,&col,&value,addv);CHKERRQ(ierr);
        }
      }
    }
    else {
      if (roworiented) {
        ierr = StashValues_Private(&baij->stash,im[i],n,in,v+i*n,addv);CHKERRQ(ierr);
      }
      else {
        row = im[i];
        for ( j=0; j<n; j++ ) {
          ierr = StashValues_Private(&baij->stash,row,1,in+j,v+i+j*m,addv);CHKERRQ(ierr);
        }
      }
    }
  }
  return 0;
}


static int MatAssemblyBegin_MPIBAIJ(Mat mat,MatAssemblyType mode)
{
  Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) mat->data;
  MPI_Comm    comm = mat->comm;
  int         size = baij->size, *owners = baij->rowners,bs=baij->bs;
  int         rank = baij->rank,tag = mat->tag, *owner,*starts,count,ierr;
  MPI_Request *send_waits,*recv_waits;
  int         *nprocs,i,j,idx,*procs,nsends,nreceives,nmax,*work;
  InsertMode  addv;
  Scalar      *rvalues,*svalues;

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

  /*  first count number of contributors to each processor */
  nprocs = (int *) PetscMalloc( 2*size*sizeof(int) ); CHKPTRQ(nprocs);
  PetscMemzero(nprocs,2*size*sizeof(int)); procs = nprocs + size;
  owner = (int *) PetscMalloc( (baij->stash.n+1)*sizeof(int) ); CHKPTRQ(owner);
  for ( i=0; i<baij->stash.n; i++ ) {
    idx = baij->stash.idx[i];
    for ( j=0; j<size; j++ ) {
      if (idx >= owners[j]*bs && idx < owners[j+1]*bs) {
        nprocs[j]++; procs[j] = 1; owner[i] = j; break;
      }
    }
  }
  nsends = 0;  for ( i=0; i<size; i++ ) { nsends += procs[i];}

  /* inform other processors of number of messages and max length*/
  work = (int *) PetscMalloc( size*sizeof(int) ); CHKPTRQ(work);
  MPI_Allreduce(procs, work,size,MPI_INT,MPI_SUM,comm);
  nreceives = work[rank];
  MPI_Allreduce( nprocs, work,size,MPI_INT,MPI_MAX,comm);
  nmax = work[rank];
  PetscFree(work);

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


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

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

  /* Free cache space */
  PLogInfo(0,"[%d]MatAssemblyBegin_MPIBAIJ:Number of off processor values %d\n",rank,baij->stash.n);
  ierr = StashDestroy_Private(&baij->stash); CHKERRQ(ierr);

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

  return 0;
}


static int MatAssemblyEnd_MPIBAIJ(Mat mat,MatAssemblyType mode)
{
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *) mat->data;
  MPI_Status  *send_status,recv_status;
  int         imdex,nrecvs = baij->nrecvs, count = nrecvs, i, n, ierr;
  int         bs=baij->bs,row,col,other_disassembled;
  Scalar      *values,val;
  InsertMode  addv = baij->insertmode;

  /*  wait on receives */
  while (count) {
    MPI_Waitany(nrecvs,baij->recv_waits,&imdex,&recv_status);
    /* unpack receives into our local space */
    values = baij->rvalues + 3*imdex*baij->rmax;
    MPI_Get_count(&recv_status,MPIU_SCALAR,&n);
    n = n/3;
    for ( i=0; i<n; i++ ) {
      row = (int) PetscReal(values[3*i]) - baij->rstart*bs;
      col = (int) PetscReal(values[3*i+1]);
      val = values[3*i+2];
      if (col >= baij->cstart*bs && col < baij->cend*bs) {
        col -= baij->cstart*bs;
        MatSetValues(baij->A,1,&row,1,&col,&val,addv);
      }
      else {
        if (mat->was_assembled) {
          if (!baij->colmap) {ierr = CreateColmap_MPIBAIJ_Private(mat); CHKERRQ(ierr);}
          col = baij->colmap[col/bs]*bs + col%bs;
          if (col < 0  && !((Mat_SeqBAIJ*)(baij->A->data))->nonew) {
            ierr = DisAssemble_MPIBAIJ(mat); CHKERRQ(ierr);
            col = (int) PetscReal(values[3*i+1]);
          }
        }
        MatSetValues(baij->B,1,&row,1,&col,&val,addv);
      }
    }
    count--;
  }
  PetscFree(baij->recv_waits); PetscFree(baij->rvalues);

  /* wait on sends */
  if (baij->nsends) {
    send_status = (MPI_Status *) PetscMalloc(baij->nsends*sizeof(MPI_Status));
    CHKPTRQ(send_status);
    MPI_Waitall(baij->nsends,baij->send_waits,send_status);
    PetscFree(send_status);
  }
  PetscFree(baij->send_waits); PetscFree(baij->svalues);

  baij->insertmode = NOT_SET_VALUES;
  ierr = MatAssemblyBegin(baij->A,mode); CHKERRQ(ierr);
  ierr = MatAssemblyEnd(baij->A,mode); CHKERRQ(ierr);

  /* determine if any processor has disassembled, if so we must
     also disassemble ourselfs, in order that we may reassemble. */
  MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,mat->comm);
  if (mat->was_assembled && !other_disassembled) {
    ierr = DisAssemble_MPIBAIJ(mat); CHKERRQ(ierr);
  }

  if (!mat->was_assembled && mode == FINAL_ASSEMBLY) {
    ierr = MatSetUpMultiply_MPIBAIJ(mat); CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(baij->B,mode); CHKERRQ(ierr);
  ierr = MatAssemblyEnd(baij->B,mode); CHKERRQ(ierr);

  if (baij->rowvalues) {PetscFree(baij->rowvalues); baij->rowvalues = 0;}
  return 0;
}

static int MatView_MPIBAIJ_Binary(Mat mat,Viewer viewer)
{
  Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) mat->data;
  int          ierr;

  if (baij->size == 1) {
    ierr = MatView(baij->A,viewer); CHKERRQ(ierr);
  }
  else SETERRQ(1,"MatView_MPIBAIJ_Binary:Only uniprocessor output supported");
  return 0;
}

static int MatView_MPIBAIJ_ASCIIorDraworMatlab(Mat mat,Viewer viewer)
{
  Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) mat->data;
  int          ierr, format,rank,bs=baij->bs,bs2=baij->bs2;
  FILE         *fd;
  ViewerType   vtype;

  ierr = ViewerGetType(viewer,&vtype); CHKERRQ(ierr);
  if (vtype  == ASCII_FILES_VIEWER || vtype == ASCII_FILE_VIEWER) {
    ierr = ViewerGetFormat(viewer,&format);
    if (format == ASCII_FORMAT_INFO_DETAILED) {
      int nz, nzalloc, mem;
      MPI_Comm_rank(mat->comm,&rank);
      ierr = ViewerASCIIGetPointer(viewer,&fd); CHKERRQ(ierr);
      ierr = MatGetInfo(mat,MAT_LOCAL,&nz,&nzalloc,&mem);
      PetscSequentialPhaseBegin(mat->comm,1);
      fprintf(fd,"[%d] Local rows %d nz %d nz alloced %d bs %d mem %d\n",
              rank,baij->m,nz*bs,nzalloc*bs,baij->bs,mem);
      ierr = MatGetInfo(baij->A,MAT_LOCAL,&nz,&nzalloc,&mem);
      fprintf(fd,"[%d] on-diagonal part: nz %d \n",rank,nz*bs);
      ierr = MatGetInfo(baij->B,MAT_LOCAL,&nz,&nzalloc,&mem);
      fprintf(fd,"[%d] off-diagonal part: nz %d \n",rank,nz*bs);
      fflush(fd);
      PetscSequentialPhaseEnd(mat->comm,1);
      ierr = VecScatterView(baij->Mvctx,viewer); CHKERRQ(ierr);
      return 0;
    }
    else if (format == ASCII_FORMAT_INFO) {
      return 0;
    }
  }

  if (vtype == DRAW_VIEWER) {
    Draw       draw;
    PetscTruth isnull;
    ierr = ViewerDrawGetDraw(viewer,&draw); CHKERRQ(ierr);
    ierr = DrawIsNull(draw,&isnull); CHKERRQ(ierr); if (isnull) return 0;
  }

  if (vtype == ASCII_FILE_VIEWER) {
    ierr = ViewerASCIIGetPointer(viewer,&fd); CHKERRQ(ierr);
    PetscSequentialPhaseBegin(mat->comm,1);
    fprintf(fd,"[%d] rows %d starts %d ends %d cols %d starts %d ends %d\n",
           baij->rank,baij->m,baij->rstart*bs,baij->rend*bs,baij->n,
            baij->cstart*bs,baij->cend*bs);
    ierr = MatView(baij->A,viewer); CHKERRQ(ierr);
    ierr = MatView(baij->B,viewer); CHKERRQ(ierr);
    fflush(fd);
    PetscSequentialPhaseEnd(mat->comm,1);
  }
  else {
    int size = baij->size;
    rank = baij->rank;
    if (size == 1) {
      ierr = MatView(baij->A,viewer); CHKERRQ(ierr);
    }
    else {
      /* assemble the entire matrix onto first processor. */
      Mat         A;
      Mat_SeqBAIJ *Aloc;
      int         M = baij->M, N = baij->N,*ai,*aj,row,col,i,j,k,*rvals;
      int         mbs=baij->mbs;
      Scalar      *a;

      if (!rank) {
        ierr = MatCreateMPIAIJ(mat->comm,M,N,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);
               CHKERRQ(ierr);
      }
      else {
        ierr = MatCreateMPIAIJ(mat->comm,0,0,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);
               CHKERRQ(ierr);
      }
      PLogObjectParent(mat,A);

      /* copy over the A part */
      Aloc = (Mat_SeqBAIJ*) baij->A->data;
      ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
      row = baij->rstart;
      rvals = (int *) PetscMalloc(bs*sizeof(int)); CHKPTRQ(rvals);

      for ( i=0; i<mbs; i++ ) {
        rvals[0] = bs*(baij->rstart + i);
        for ( j=1; j<bs; j++ ) { rvals[j] = rvals[j-1] + 1; }
        for ( j=ai[i]; j<ai[i+1]; j++ ) {
          col = (baij->cstart+aj[j])*bs;
          for (k=0; k<bs; k++ ) {
            ierr = MatSetValues(A,bs,rvals,1,&col,a+j*bs2,INSERT_VALUES);CHKERRQ(ierr);
            col++;
          }
        }
      }
      /* copy over the B part */
      Aloc = (Mat_SeqBAIJ*) baij->B->data;
      ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
      row = baij->rstart*bs;
      for ( i=0; i<mbs; i++ ) {
        rvals[0] = bs*(baij->rstart + i);
        for ( j=1; j<bs; j++ ) { rvals[j] = rvals[j-1] + 1; }
        for ( j=ai[i]; j<ai[i+1]; j++ ) {
          col = baij->garray[aj[j]]*bs;
          for (k=0; k<bs; k++ ) {
            ierr = MatSetValues(A,bs,rvals,1,&col,a+j*bs2,INSERT_VALUES);CHKERRQ(ierr);
            col++;
          }
        }
      }
      PetscFree(rvals);
      ierr = MatAssemblyBegin(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
      ierr = MatAssemblyEnd(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
      if (!rank) {
        ierr = MatView(((Mat_MPIBAIJ*)(A->data))->A,viewer); CHKERRQ(ierr);
      }
      ierr = MatDestroy(A); CHKERRQ(ierr);
    }
  }
  return 0;
}



static int MatView_MPIBAIJ(PetscObject obj,Viewer viewer)
{
  Mat         mat = (Mat) obj;
  int         ierr;
  ViewerType  vtype;

  if (!viewer) {
    viewer = STDOUT_VIEWER_SELF;
  }
  ierr = ViewerGetType(viewer,&vtype); CHKERRQ(ierr);
  if (vtype == ASCII_FILE_VIEWER || vtype == ASCII_FILES_VIEWER ||
      vtype == DRAW_VIEWER       || vtype == MATLAB_VIEWER) {
    ierr = MatView_MPIBAIJ_ASCIIorDraworMatlab(mat,viewer); CHKERRQ(ierr);
  }
  else if (vtype == BINARY_FILE_VIEWER) {
    return MatView_MPIBAIJ_Binary(mat,viewer);
  }
  return 0;
}

static int MatDestroy_MPIBAIJ(PetscObject obj)
{
  Mat         mat = (Mat) obj;
  Mat_MPIBAIJ *baij = (Mat_MPIBAIJ *) mat->data;
  int         ierr;

#if defined(PETSC_LOG)
  PLogObjectState(obj,"Rows=%d, Cols=%d",baij->M,baij->N);
#endif

  PetscFree(baij->rowners);
  ierr = MatDestroy(baij->A); CHKERRQ(ierr);
  ierr = MatDestroy(baij->B); CHKERRQ(ierr);
  if (baij->colmap) PetscFree(baij->colmap);
  if (baij->garray) PetscFree(baij->garray);
  if (baij->lvec)   VecDestroy(baij->lvec);
  if (baij->Mvctx)  VecScatterDestroy(baij->Mvctx);
  if (baij->rowvalues) PetscFree(baij->rowvalues);
  PetscFree(baij);
  PLogObjectDestroy(mat);
  PetscHeaderDestroy(mat);
  return 0;
}

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

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

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

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps = {
  MatSetValues_MPIBAIJ,0,0,0,
  0,0,0,0,
  0,0,0,0,
  0,0,0,0,
  0,0,0,0,
  MatAssemblyBegin_MPIBAIJ,MatAssemblyEnd_MPIBAIJ,0,0,
  0,0,MatGetReordering_MPIBAIJ,0,
  0,0,0,MatGetSize_MPIBAIJ,
  MatGetLocalSize_MPIBAIJ,MatGetOwnershipRange_MPIBAIJ,0,0,
  0,0,0,0,
  0,0,0,0,
  0,0,0,0,
  0,0,0,0,
  0};


/*@C
   MatCreateMPIBAIJ - Creates a sparse parallel matrix in block AIJ format
   (block compressed row).  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.

   Input Parameters:
.  comm - MPI communicator
.  bs   - size of blockk
.  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
.  n - number of local columns (or PETSC_DECIDE to have calculated
           if N is given)
.  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
.  N - number of global columns (or PETSC_DECIDE to have calculated
           if n is given)
.  d_nz  - number of block nonzeros per block row in diagonal portion of local
           submatrix  (same for all local rows)
.  d_nzz - number of block nonzeros per block row in diagonal portion of local
           submatrix or null (possibly different for each row).  You must leave
           room for the diagonal entry even if it is zero.
.  o_nz  - number of block nonzeros per block row in off-diagonal portion of local
           submatrix (same for all local rows).
.  o_nzz - number of block nonzeros per block row in off-diagonal portion of local
           submatrix or null (possibly different for each row).

   Output Parameter:
.  A - the matrix

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

   Storage Information:
   For a square global matrix we define each processor's diagonal portion
   to be its local rows and the corresponding columns (a square submatrix);
   each processor's off-diagonal portion encompasses the remainder of the
   local matrix (a rectangular submatrix).

   The user can specify preallocated storage for the diagonal part of
   the local submatrix with either d_nz or d_nnz (not both).  Set
   d_nz=PETSC_DEFAULT and d_nnz=PETSC_NULL for PETSc to control dynamic
   memory allocation.  Likewise, specify preallocated storage for the
   off-diagonal part of the local submatrix with o_nz or o_nnz (not both).

   Consider a processor that owns rows 3, 4 and 5 of a parallel matrix. In
   the figure below we depict these three local rows and all columns (0-11).

$          0 1 2 3 4 5 6 7 8 9 10 11
$         -------------------
$  row 3  |  o o o d d d o o o o o o
$  row 4  |  o o o d d d o o o o o o
$  row 5  |  o o o d d d o o o o o o
$         -------------------
$

   Thus, any entries in the d locations are stored in the d (diagonal)
   submatrix, and any entries in the o locations are stored in the
   o (off-diagonal) submatrix.  Note that the d and the o submatrices are
   stored simply in the MATSEQBAIJ format for compressed row storage.

   Now d_nz should indicate the number of nonzeros per row in the d matrix,
   and o_nz should indicate the number of nonzeros per row in the o matrix.
   In general, for PDE problems in which most nonzeros are near the diagonal,
   one expects d_nz >> o_nz.   For additional details, see the users manual
   chapter on matrices and the file $(PETSC_DIR)/Performance.

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

.seealso: MatCreate(), MatCreateSeqBAIJ(), MatSetValues()
@*/
int MatCreateMPIBAIJ(MPI_Comm comm,int bs,int m,int n,int M,int N,
                    int d_nz,int *d_nnz,int o_nz,int *o_nnz,Mat *A)
{
  Mat          B;
  Mat_MPIBAIJ  *b;
  int          ierr, i,sum[2],work[2],mbs,nbs,Mbs,Nbs;

  if (bs < 1) SETERRQ(1,"MatCreateMPIBAIJ: invalid block size specified");
  *A = 0;
  PetscHeaderCreate(B,_Mat,MAT_COOKIE,MATMPIBAIJ,comm);
  PLogObjectCreate(B);
  B->data       = (void *) (b = PetscNew(Mat_MPIBAIJ)); CHKPTRQ(b);
  PetscMemzero(b,sizeof(Mat_MPIBAIJ));
  PetscMemcpy(&B->ops,&MatOps,sizeof(struct _MatOps));
  B->destroy    = MatDestroy_MPIBAIJ;
  B->view       = MatView_MPIBAIJ;

  B->factor     = 0;
  B->assembled  = PETSC_FALSE;

  b->insertmode = NOT_SET_VALUES;
  MPI_Comm_rank(comm,&b->rank);
  MPI_Comm_size(comm,&b->size);

  if (m == PETSC_DECIDE && (d_nnz != PETSC_NULL || o_nnz != PETSC_NULL))
    SETERRQ(1,"MatCreateMPIBAIJ:Cannot have PETSC_DECIDE rows but set d_nnz or o_nnz");

  if (M == PETSC_DECIDE || N == PETSC_DECIDE) {
    work[0] = m; work[1] = n;
    mbs = m/bs; nbs = n/bs;
    if (mbs*bs != m || nbs*n != nbs) SETERRQ(1,"MatCreateMPIBAIJ: No of local rows, cols must be divisible by blocksize");
    MPI_Allreduce( work, sum,2,MPI_INT,MPI_SUM,comm );
    if (M == PETSC_DECIDE) {M = sum[0]; Mbs = M/bs;}
    if (N == PETSC_DECIDE) {N = sum[1]; Nbs = N/bs;}
  }
  if (m == PETSC_DECIDE) {
    Mbs = M/bs;
    if (Mbs*bs != M) SETERRQ(1,"MatCreateMPIBAIJ: No of global rows must be divisible by blocksize");
    mbs = Mbs/b->size + ((Mbs % b->size) > b->rank);
    m   = mbs*bs;
  }
  if (n == PETSC_DECIDE) {
    Nbs = N/bs;
    if (Nbs*bs != N) SETERRQ(1,"MatCreateMPIBAIJ: No of global cols must be divisible by blocksize");
    nbs = Nbs/b->size + ((Nbs % b->size) > b->rank);
    n   = nbs*bs;
  }

  b->m = m; B->m = m;
  b->n = n; B->n = n;
  b->N = N; B->N = N;
  b->M = M; B->M = M;
  b->bs  = bs;
  b->bs2 = bs*bs;
  b->mbs = mbs;
  b->nbs = nbs;
  b->Mbs = Mbs;
  b->Nbs = Nbs;

  /* build local table of row and column ownerships */
  b->rowners = (int *) PetscMalloc(2*(b->size+2)*sizeof(int)); CHKPTRQ(b->rowners);
  PLogObjectMemory(B,2*(b->size+2)*sizeof(int)+sizeof(struct _Mat)+sizeof(Mat_MPIBAIJ));
  b->cowners = b->rowners + b->size + 1;
  MPI_Allgather(&mbs,1,MPI_INT,b->rowners+1,1,MPI_INT,comm);
  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];
  MPI_Allgather(&nbs,1,MPI_INT,b->cowners+1,1,MPI_INT,comm);
  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];

  if (d_nz == PETSC_DEFAULT) d_nz = 5;
  ierr = MatCreateSeqBAIJ(MPI_COMM_SELF,bs,m,n,d_nz,d_nnz,&b->A); CHKERRQ(ierr);
  PLogObjectParent(B,b->A);
  if (o_nz == PETSC_DEFAULT) o_nz = 0;
  ierr = MatCreateSeqBAIJ(MPI_COMM_SELF,bs,m,N,o_nz,o_nnz,&b->B); CHKERRQ(ierr);
  PLogObjectParent(B,b->B);

  /* build cache for off array entries formed */
  ierr = StashBuild_Private(&b->stash); CHKERRQ(ierr);
  b->colmap      = 0;
  b->garray      = 0;
  b->roworiented = 1;

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

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

  *A = B;
  return 0;
}

#include "sys.h"

int MatLoad_MPIBAIJ(Viewer viewer,MatType type,Mat *newmat)
{
  Mat          A;
  int          i, nz, ierr, j,rstart, rend, fd;
  Scalar       *vals,*buf;
  MPI_Comm     comm = ((PetscObject)viewer)->comm;
  MPI_Status   status;
  int          header[4],rank,size,*rowlengths = 0,M,N,m,*rowners,maxnz,*cols;
  int          *locrowlens,*sndcounts = 0,*procsnz = 0, jj,*mycols,*ibuf;
  int          flg,tag = ((PetscObject)viewer)->tag,bs=1,bs2,Mbs,mbs,extra_rows;
  int          *dlens,*odlens,*mask,*masked1,*masked2,rowcount,odcount;
  int          dcount,kmax,k,nzcount,tmp;


  ierr = OptionsGetInt(PETSC_NULL,"-matload_block_size",&bs,&flg);CHKERRQ(ierr);
  bs2  = bs*bs;

  MPI_Comm_size(comm,&size); MPI_Comm_rank(comm,&rank);
  if (!rank) {
    ierr = ViewerBinaryGetDescriptor(viewer,&fd); CHKERRQ(ierr);
    ierr = PetscBinaryRead(fd,(char *)header,4,BINARY_INT); CHKERRQ(ierr);
    if (header[0] != MAT_COOKIE) SETERRQ(1,"MatLoad_MPIAIJ:not matrix object");
  }

  MPI_Bcast(header+1,3,MPI_INT,0,comm);
  M = header[1]; N = header[2];


  if (M != N) SETERRQ(1,"MatLoad_SeqBAIJ:Can only do square matrices");

  /*
     This code adds extra rows to make sure the number of rows is
     divisible by the blocksize
  */
  Mbs        = M/bs;
  extra_rows = bs - M + bs*(Mbs);
  if (extra_rows == bs) extra_rows = 0;
  else                  Mbs++;
  if (extra_rows &&!rank) {
    PLogInfo(0,"MatLoad_SeqBAIJ:Padding loaded matrix to match blocksize");
  }
  /* determine ownership of all rows */
  mbs = Mbs/size + ((Mbs % size) > rank);
  m   = mbs * bs;
  rowners = (int *) PetscMalloc((size+2)*sizeof(int)); CHKPTRQ(rowners);
  MPI_Allgather(&mbs,1,MPI_INT,rowners+1,1,MPI_INT,comm);
  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 */
  locrowlens = (int*) PetscMalloc( (rend-rstart)*bs*sizeof(int) ); CHKPTRQ(locrowlens);
  if (!rank) {
    rowlengths = (int*) PetscMalloc( (M+extra_rows)*sizeof(int) ); CHKPTRQ(rowlengths);
    ierr = PetscBinaryRead(fd,rowlengths,M,BINARY_INT); CHKERRQ(ierr);
    for ( i=0; i<extra_rows; i++ ) rowlengths[M+i] = 1;
    sndcounts = (int*) PetscMalloc( size*sizeof(int) ); CHKPTRQ(sndcounts);
    for ( i=0; i<size; i++ ) sndcounts[i] = (rowners[i+1] - rowners[i])*bs;
    MPI_Scatterv(rowlengths,sndcounts,rowners,MPI_INT,locrowlens,(rend-rstart)*bs,MPI_INT,0,comm);
    PetscFree(sndcounts);
  }
  else {
    MPI_Scatterv(0,0,0,MPI_INT,locrowlens,(rend-rstart)*bs,MPI_INT, 0,comm);
  }

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

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

    /* read in my part of the matrix column indices  */
    nz = procsnz[0];
    ibuf = (int *) PetscMalloc( nz*sizeof(int) ); CHKPTRQ(ibuf);
    mycols = ibuf;
    ierr = PetscBinaryRead(fd,mycols,nz,BINARY_INT); CHKERRQ(ierr);
    /* read in every ones (except the last) and ship off */
    for ( i=1; i<size-1; i++ ) {
      nz = procsnz[i];
      ierr = PetscBinaryRead(fd,cols,nz,BINARY_INT); CHKERRQ(ierr);
      MPI_Send(cols,nz,MPI_INT,i,tag,comm);
    }
    /* read in the stuff for the last proc */
    if ( size != 1 ) {
      nz = procsnz[size-1] - extra_rows;  /* the extra rows are not on the disk */
      ierr = PetscBinaryRead(fd,cols,nz,BINARY_INT); CHKERRQ(ierr);
      for ( i=0; i<extra_rows; i++ ) cols[nz+i] = M+i;
      MPI_Send(cols,nz+extra_rows,MPI_INT,i,tag,comm);
    }
    PetscFree(cols);
  }
  else {
    /* determine buffer space needed for message */
    nz = 0;
    for ( i=0; i<m; i++ ) {
      nz += locrowlens[i];
    }
    ibuf = (int*) PetscMalloc( nz*sizeof(int) ); CHKPTRQ(ibuf);
    mycols = ibuf;
    /* receive message of column indices*/
    MPI_Recv(mycols,nz,MPI_INT,0,tag,comm,&status);
    MPI_Get_count(&status,MPI_INT,&maxnz);
    if (maxnz != nz) SETERRQ(1,"MatLoad_MPIAIJ:something is wrong with file");
  }

  /* loop over local rows, determining number of off diagonal entries */
  dlens  = (int *) PetscMalloc( 2*(rend-rstart)*sizeof(int) ); CHKPTRQ(dlens);
  odlens = dlens + (rstart-rend);
  mask   = (int *) PetscMalloc( 3*Mbs*sizeof(int) ); CHKPTRQ(mask);
  PetscMemzero(mask,Mbs*sizeof(int));
  masked1 = mask    + Mbs;
  masked2 = masked1 + Mbs;
  rowcount = 0; nzcount = 0;
  for ( i=0; i<mbs; i++ ) {
    dcount  = 0;
    odcount = 0;
    for ( j=0; j<bs; j++ ) {
      kmax = locrowlens[rowcount];
      for ( k=0; k<kmax; k++ ) {
        tmp = mycols[nzcount++]/bs;
        if (!mask[tmp]) {
          mask[tmp] = 1;
          if (tmp < rstart || tmp >= rend ) masked2[odcount++] = tmp;
          else masked1[dcount++] = tmp;
        }
      }
      rowcount++;
    }
    dlens[i]  = dcount;
    odlens[i] = odcount;
    /* zero out the mask elements we set */
    for ( j=0; j<dcount; j++ ) mask[masked1[j]] = 0;
    for ( j=0; j<odcount; j++ ) mask[masked2[j]] = 0;
  }
  /* create our matrix */
  ierr = MatCreateMPIBAIJ(comm,bs,m,PETSC_DECIDE,M+extra_rows,N+extra_rows,0,dlens,0,odlens,newmat);CHKERRQ(ierr);
  A = *newmat;
  MatSetOption(A,COLUMNS_SORTED);

  if (!rank) {
    buf = (Scalar *) PetscMalloc( maxnz*sizeof(Scalar) ); CHKPTRQ(buf);

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

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

    /* read in other processors( except the last one) and ship out */
    for ( i=1; i<size-1; i++ ) {
      nz = procsnz[i];
      vals = buf;
      ierr = PetscBinaryRead(fd,vals,nz,BINARY_SCALAR); CHKERRQ(ierr);
      MPI_Send(vals,nz,MPIU_SCALAR,i,A->tag,comm);
    }
    /* the last proc */
    if ( size != 1 ){
      nz = procsnz[i] - extra_rows;
      ierr = PetscBinaryRead(fd,vals,nz,BINARY_SCALAR); CHKERRQ(ierr);
      for ( i=0; i<extra_rows; i++ ) vals[nz+i] = 1.0;
      MPI_Send(vals,nz+extra_rows,MPIU_SCALAR,i,A->tag,comm);
    }
    PetscFree(procsnz);
  }
  else {
    /* receive numeric values */
    buf = (Scalar*) PetscMalloc( nz*sizeof(Scalar) ); CHKPTRQ(buf);

    /* receive message of values*/
    vals = buf;
    MPI_Recv(vals,nz,MPIU_SCALAR,0,A->tag,comm,&status);
    MPI_Get_count(&status,MPIU_SCALAR,&maxnz);
    if (maxnz != nz) SETERRQ(1,"MatLoad_MPIAIJ:something is wrong with file");

    /* insert into matrix */
    jj      = rstart*bs;
    for ( i=0; i<mbs; i++ ) {
      ierr = MatSetValues(A,1,&jj,locrowlens[i],mycols,vals,INSERT_VALUES);CHKERRQ(ierr);
      mycols += locrowlens[i];
      vals   += locrowlens[i];
      jj++;
    }
  }
  PetscFree(locrowlens);
  PetscFree(buf);
  PetscFree(ibuf);
  PetscFree(rowners);
  PetscFree(dlens);
  ierr = MatAssemblyBegin(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
  return 0;
}