aij/mpi/mpiptap.c

/*
  Defines projective product routines where A is a MPIAIJ matrix
          C = P^T * A * P
*/

#include "src/mat/impls/aij/seq/aij.h"   /*I "petscmat.h" I*/
#include "src/mat/utils/freespace.h"
#include "src/mat/impls/aij/mpi/mpiaij.h"
#include "petscbt.h"

EXTERN PetscErrorCode MatDestroy_MPIAIJ(Mat);
#undef __FUNCT__
#define __FUNCT__ "MatDestroy_MPIAIJ_PtAP"
PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
{
  PetscErrorCode       ierr;
  Mat_MatMatMultMPI    *mult;
  PetscObjectContainer container;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)A,"MatPtAPMPI",(PetscObject *)&container);CHKERRQ(ierr);
  if (container) {
    ierr  = PetscObjectContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
    ierr = MatDestroy(mult->B_loc);CHKERRQ(ierr);
    ierr = MatDestroy(mult->B_oth);CHKERRQ(ierr);
    if (mult->abi) ierr = PetscFree(mult->abi);CHKERRQ(ierr);
    if (mult->abj) ierr = PetscFree(mult->abj);CHKERRQ(ierr);
    if (mult->startsj) ierr = PetscFree(mult->startsj);CHKERRQ(ierr);
    if (mult->bufa) ierr = PetscFree(mult->bufa);CHKERRQ(ierr);
    ierr = PetscObjectContainerDestroy(container);CHKERRQ(ierr);
    ierr = PetscObjectCompose((PetscObject)A,"MatPtAPMPI",0);CHKERRQ(ierr);
  }
  ierr = PetscFree(mult);CHKERRQ(ierr);

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

#undef __FUNCT__
#define __FUNCT__ "MatPtAP_MPIAIJ_MPIAIJ"
PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode       ierr;
  Mat_MatMatMultMPI    *mult;
  PetscObjectContainer container;

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
    ierr = PetscNew(Mat_MatMatMultMPI,&mult);CHKERRQ(ierr);
    mult->B_loc=PETSC_NULL; mult->B_oth=PETSC_NULL;
    mult->abi=PETSC_NULL; mult->abj=PETSC_NULL;
    mult->abnz_max = 0; /* symbolic A*P is not done yet */

    /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    ierr = MatGetBrowsOfAoCols(A,P,scall,&mult->startsj,&mult->bufa,&mult->B_oth);CHKERRQ(ierr);

    /* get P_loc by taking all local rows of P */
    ierr = MatGetLocalMat(P,scall,&mult->B_loc);CHKERRQ(ierr);

    /* attach the supporting struct to P for reuse */
    P->ops->destroy  = MatDestroy_MPIAIJ_PtAP;
    ierr = PetscObjectContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
    ierr = PetscObjectContainerSetPointer(container,mult);CHKERRQ(ierr);
    ierr = PetscObjectCompose((PetscObject)P,"MatPtAPMPI",(PetscObject)container);CHKERRQ(ierr);

    /* now, compute symbolic local P^T*A*P */
    ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);/* numeric product is computed as well */
    ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
  } else if (scall == MAT_REUSE_MATRIX){
    ierr = PetscObjectQuery((PetscObject)P,"MatPtAPMPI",(PetscObject *)&container);CHKERRQ(ierr);
    if (container) {
      ierr  = PetscObjectContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
    } else {
      SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
    }

    /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    ierr = MatGetBrowsOfAoCols(A,P,scall,&mult->startsj,&mult->bufa,&mult->B_oth);CHKERRQ(ierr);

    /* get P_loc by taking all local rows of P */
    ierr = MatGetLocalMat(P,scall,&mult->B_loc);CHKERRQ(ierr);

  } else {
    SETERRQ1(PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",scall);
  }
  /* now, compute numeric local P^T*A*P */
  ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
  ierr = MatPtAPNumeric_MPIAIJ_MPIAIJ(A,P,*C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
{
  PetscErrorCode       ierr;
  Mat                  P_loc,P_oth,B_mpi;
  Mat_MatMatMultMPI    *ap;
  PetscObjectContainer container;
  FreeSpaceList        free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
  Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
  Mat_SeqAIJ           *p_loc,*p_oth;
  PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ,*pjj;
  PetscInt             *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,nnz;
  PetscInt             nlnk,*lnk,*cdi,*cdj,*owners_co,*coi,*coj,*cji;
  PetscInt             am=A->m,pN=P->N,pn=P->n;
  PetscInt             i,j,k,pnz,row,cnz;
  PetscBT              lnkbt;
  MPI_Comm             comm=A->comm;
  PetscMPIInt          size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
  PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
  PetscInt             len,proc,*dnz,*onz,*owners;
  PetscInt             anzi,*bi,*bj,bnz;
  PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
  MPI_Request          *si_waits,*sj_waits,*ri_waits,*rj_waits;
  MPI_Status           *status;
  Mat_Merge_SeqsToMPI  *merge;
  PetscInt             *api,*apj,*apJ,apnz,*prmap=p->garray,pon;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)P,"MatPtAPMPI",(PetscObject *)&container);CHKERRQ(ierr);
  if (container) {
    ierr  = PetscObjectContainerGetPointer(container,(void **)&ap);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
  }
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);

  /* get data from P_loc and P_oth */
  P_loc=ap->B_loc; P_oth=ap->B_oth;
  p_loc=(Mat_SeqAIJ*)P_loc->data; p_oth=(Mat_SeqAIJ*)P_oth->data;
  pi_loc=p_loc->i; pj_loc=p_loc->j; pi_oth=p_oth->i; pj_oth=p_oth->j;

  /* first, compute symbolic AP = A_loc*P */
  /*--------------------------------------*/
  ierr  = PetscMalloc((am+2)*sizeof(PetscInt),&api);CHKERRQ(ierr);
  ap->abi = api;
  api[0] = 0;

  /* create and initialize a linked list */
  nlnk = pN+1;
  ierr = PetscLLCreate(pN,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);

  /* Initial FreeSpace size is fill*nnz(A) */
  ierr = GetMoreSpace((PetscInt)(fill*(adi[am]+aoi[am])),&free_space);CHKERRQ(ierr);
  current_space = free_space;

  for (i=0;i<am;i++) {
    apnz = 0;
    /* diagonal portion of A */
    anzi = adi[i+1] - adi[i];
    for (j=0; j<anzi; j++){
      row = *adj++;
      pnz = pi_loc[row+1] - pi_loc[row];
      pjj  = pj_loc + pi_loc[row];
      /* add non-zero cols of P into the sorted linked list lnk */
      ierr = PetscLLAdd(pnz,pjj,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
      apnz += nlnk;
    }
    /* off-diagonal portion of A */
    anzi = aoi[i+1] - aoi[i];
    for (j=0; j<anzi; j++){
      row = *aoj++;
      pnz = pi_oth[row+1] - pi_oth[row];
      pjj  = pj_oth + pi_oth[row];
      ierr = PetscLLAdd(pnz,pjj,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
      apnz += nlnk;
    }

    api[i+1] = api[i] + apnz;
    if (ap->abnz_max < apnz) ap->abnz_max = apnz;

    /* if free space is not available, double the total space in the list */
    if (current_space->local_remaining<apnz) {
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, then initialize lnk */
    ierr = PetscLLClean(pN,pN,apnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
    current_space->array           += apnz;
    current_space->local_used      += apnz;
    current_space->local_remaining -= apnz;
  }
  /* Allocate space for apj, initialize apj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&ap->abj);CHKERRQ(ierr);
  apj = ap->abj;
  ierr = MakeSpaceContiguous(&free_space,ap->abj);CHKERRQ(ierr);

  /* get ij structure of (p->A)^T and (p->B)^T */
  /*-------------------------------------------*/
  ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
  ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);

  /* then, compute symbolic Co_seq = (p->B)^T*AP */
  /* Allocate coi array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  pon = (p->B)->n; /* total num of rows to be sent to other processors
                         >= (num of nonzero rows of C_seq) - pn */
  ierr = PetscMalloc((pon+1)*sizeof(PetscInt),&coi);CHKERRQ(ierr);
  coi[0] = 0;

  /* set initial free space to be 3*pon*max( nnz(AP) per row) */
  nnz           = 3*pon*ap->abnz_max + 1;
  ierr          = GetMoreSpace(nnz,&free_space);
  current_space = free_space;

  /* determine symbolic Co=(p->B)^T*AP - send to others */
  /*----------------------------------------------------*/
  for (i=0; i<pon; i++) {
    cnz  = 0;
    pnz = poti[i+1] - poti[i];
    j     = pnz;
    ptJ   = potj + poti[i+1];
    while (j){/* assume cols are almost in increasing order, starting from its end saves computation */
      j--; ptJ--;
      row  = *ptJ; /* row of AP == col of Pot */
      apnz = api[row+1] - api[row];
      apJ   = apj + api[row];
      /* add non-zero cols of AP into the sorted linked list lnk */
      ierr = PetscLLAdd(apnz,apJ,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
      cnz += nlnk;
    }

    /* If free space is not available, double the total space in the list */
    if (current_space->local_remaining<cnz) {
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, and zero out denserows */
    ierr = PetscLLClean(pN,pN,cnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
    current_space->array           += cnz;
    current_space->local_used      += cnz;
    current_space->local_remaining -= cnz;
    coi[i+1] = coi[i] + cnz;
  }
  ierr = PetscMalloc((coi[pon]+1)*sizeof(PetscInt),&coj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);

  /* send j structure of Co to other processors */
  /*--------------------------------------------*/
  /* determine row ownership */
  ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
  ierr = PetscMapCreate(comm,&merge->rowmap);CHKERRQ(ierr);
  ierr = PetscMapSetLocalSize(merge->rowmap,pn);CHKERRQ(ierr);
  ierr = PetscMapSetType(merge->rowmap,MAP_MPI);CHKERRQ(ierr);
  ierr = PetscMapGetGlobalRange(merge->rowmap,&owners);CHKERRQ(ierr);

  /* determine the number of messages to send, their lengths */
  /*---------------------------------------------------------*/
  ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
  ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
  ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
  len_s = merge->len_s;
  merge->nsend = 0;

  ierr = PetscMalloc((size+2)*sizeof(PetscInt),&owners_co);CHKERRQ(ierr);
  ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);

  proc = 0;
  for (i=0; i<pon; i++){
    while (prmap[i] >= owners[proc+1]) proc++;
    len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    len_s[proc] += coi[i+1] - coi[i];
  }

  len   = 0;  /* max length of buf_si[] */
  owners_co[0] = 0;
  for (proc=0; proc<size; proc++){
    owners_co[proc+1] = owners_co[proc] + len_si[proc];
    if (len_si[proc]){
      merge->nsend++;
      len_si[proc] = 2*(len_si[proc] + 1);
      len += len_si[proc];
    }
  }

  /* determine the number and length of messages to receive for ij-structure */
  /*-------------------------------------------------------------------------*/
  ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
  ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);

  /* post the Irecv and Isend of j-structure */
  /*-------------------------------*/
  ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&tagj);CHKERRQ(ierr);
  ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);

  ierr = PetscMalloc((2*merge->nsend+1)*sizeof(MPI_Request),&si_waits);CHKERRQ(ierr);
  sj_waits = si_waits + merge->nsend;

  for (proc=0, k=0; proc<size; proc++){
    if (!len_s[proc]) continue;
    i = owners_co[proc];
    ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
    k++;
  }

  /* determine symbolic Cd = (p->A)^T*AP - stay local */
  /*--------------------------------------------------*/
  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&cdi);CHKERRQ(ierr);
  cdi[0] = 0;

  /* Set initial free space to be 3*pn*max( nnz(AP) per row) */
  nnz           = 3*pn*ap->abnz_max + 1;
  ierr          = GetMoreSpace(nnz,&free_space);
  current_space = free_space;

  for (i=0; i<pn; i++) {
    cnz = 0;
    pnz  = pdti[i+1] - pdti[i];
    j    = pnz;
    ptJ  = pdtj + pdti[i+1];
    while (j){/* assume cols are almost in increasing order, starting from its end saves computation */
      j--; ptJ--;
      row  = *ptJ; /* row of AP == col of Pt */
      apnz = api[row+1] - api[row];
      apJ   = apj + api[row];
      /* add non-zero cols of AP into the sorted linked list lnk */
      ierr = PetscLLAdd(apnz,apJ,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
      cnz += nlnk;
    }

    /* If free space is not available, double the total space in the list */
    if (current_space->local_remaining<cnz) {
      /* printf("[%d] free space is not available, double\n",rank); */
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }

    /* Copy data into free space, and zero out denserows */
    ierr = PetscLLClean(pN,pN,cnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
    current_space->array           += cnz;
    current_space->local_used      += cnz;
    current_space->local_remaining -= cnz;
    cdi[i+1] = cdi[i] + cnz;
  }
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);

  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc((cdi[pn]+1)*sizeof(PetscInt),&cdj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,cdj);CHKERRQ(ierr);

  /* receives and sends of j-structure are complete */
  /*------------------------------------------------*/
  ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);

  /* send and recv i-structure */
  /*---------------------------*/
  ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&tagi);CHKERRQ(ierr);
  ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);

  ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
  buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
  for (proc=0,k=0; proc<size; proc++){
    if (!len_s[proc]) continue;
    /* form outgoing message for i-structure:
         buf_si[0]:                 nrows to be sent
               [1:nrows]:           row index (global)
               [nrows+1:2*nrows+1]: i-structure index
    */
    /*-------------------------------------------*/
    nrows = len_si[proc]/2 - 1;
    buf_si_i    = buf_si + nrows+1;
    buf_si[0]   = nrows;
    buf_si_i[0] = 0;
    nrows = 0;
    for (i=owners_co[proc]; i<owners_co[proc+1]; i++){
      anzi = coi[i+1] - coi[i];
      if (!anzi) SETERRQ1(1,"i=%d, ani = 0",i);
      buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
      buf_si[nrows+1] =prmap[i] -owners[proc]; /* local row index */
      nrows++;
    }
    ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
    k++;
    buf_si += len_si[proc];
  }

  ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);

  ierr = PetscLogInfo((PetscObject)A,"MatMerge_SeqsToMPI: nsend: %d, nrecv: %d\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
  for (i=0; i<merge->nrecv; i++){
    ierr = PetscLogInfo((PetscObject)A,"MatMerge_SeqsToMPI:   recv len_ri=%d, len_rj=%d from [%d]\n",len_ri[i],merge->len_r[i],merge->id_r[i]);CHKERRQ(ierr);
  }

  ierr = PetscFree(len_si);CHKERRQ(ierr);
  ierr = PetscFree(len_ri);CHKERRQ(ierr);
  ierr = PetscFree(rj_waits);CHKERRQ(ierr);
  ierr = PetscFree(si_waits);CHKERRQ(ierr);
  ierr = PetscFree(ri_waits);CHKERRQ(ierr);
  ierr = PetscFree(buf_s);CHKERRQ(ierr);
  ierr = PetscFree(status);CHKERRQ(ierr);

  /* compute the local portion of C (mpi mat) */
  /*------------------------------------------*/
  /* allocate bi array and free space for accumulating nonzero column info */
  ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
  bi[0] = 0;

  /* initial FreeSpace size is 2*(num of local nnz(C_seq)) */
  ierr = GetMoreSpace((PetscInt)(2*cdi[pn]+1),&free_space);CHKERRQ(ierr);
  current_space = free_space;

  /* determine symbolic info for each local row */
  ierr = PetscMalloc((3*merge->nrecv+1)*sizeof(PetscInt**),&buf_ri_k);CHKERRQ(ierr);
  nextrow = buf_ri_k + merge->nrecv;
  nextci  = nextrow + merge->nrecv;
  for (k=0; k<merge->nrecv; k++){
    buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    nrows       = *buf_ri_k[k];
    nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
  }

  ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
  len = 0;
  for (i=0; i<pn; i++) {
    bnz = 0;
    /* add local non-zero cols of this proc's C_seq into lnk */
    anzi = cdi[i+1] - cdi[i];
    cji  = cdj + cdi[i];
    ierr = PetscLLAdd(anzi,cji,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
    bnz += nlnk;
    /* add received col data into lnk */
    for (k=0; k<merge->nrecv; k++){ /* k-th received message */
      if (i == *nextrow[k]) { /* i-th row */
        anzi = *(nextci[k]+1) - *nextci[k];
        cji  = buf_rj[k] + *nextci[k];
        ierr = PetscLLAdd(anzi,cji,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
        bnz += nlnk;
        nextrow[k]++; nextci[k]++;
      }
    }
    if (len < bnz) len = bnz;  /* =max(bnz) */

    /* if free space is not available, make more free space */
    if (current_space->local_remaining<bnz) {
      ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
    }
    /* copy data into free space, then initialize lnk */
    ierr = PetscLLClean(pN,pN,bnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
    ierr = MatPreallocateSet(i+owners[rank],bnz,current_space->array,dnz,onz);CHKERRQ(ierr);

    current_space->array           += bnz;
    current_space->local_used      += bnz;
    current_space->local_remaining -= bnz;

    bi[i+1] = bi[i] + bnz;
  }
  ierr = PetscFree(cdi);CHKERRQ(ierr);
  ierr = PetscFree(cdj);CHKERRQ(ierr);
  ierr = PetscFree(buf_ri_k);CHKERRQ(ierr);

  ierr = PetscMalloc((bi[pn]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
  ierr = MakeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
  ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);

  /* create symbolic parallel matrix B_mpi */
  /*---------------------------------------*/
  ierr = MatCreate(comm,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE,&B_mpi);CHKERRQ(ierr);
  ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);

  /* B_mpi is not ready for use - assembly will be done by MatPtAPNumeric() */
  B_mpi->assembled     = PETSC_FALSE;
  B_mpi->ops->destroy  = MatDestroy_MPIAIJ_SeqsToMPI;
  merge->bi            = bi;
  merge->bj            = bj;
  merge->coi           = coi;
  merge->coj           = coj;
  merge->buf_ri        = buf_ri;
  merge->buf_rj        = buf_rj;
  merge->owners_co     = owners_co;

  /* attach the supporting struct to B_mpi for reuse */
  ierr = PetscObjectContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
  ierr = PetscObjectContainerSetPointer(container,merge);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
  *C = B_mpi;

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ"
PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
{
  PetscErrorCode       ierr;
  Mat_Merge_SeqsToMPI  *merge;
  Mat_MatMatMultMPI    *ap;
  PetscObjectContainer cont_merge,cont_ptap;
  Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
  Mat_SeqAIJ     *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
  Mat_SeqAIJ     *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
  Mat_SeqAIJ     *p_loc,*p_oth;
  PetscInt       *adi=ad->i,*aoi=ao->i,*adj=ad->j,*aoj=ao->j,*apJ,nextp,flops=0;
  PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
  PetscInt       i,j,k,anz,pnz,apnz,nextap,row,*cj;
  MatScalar      *ada=ad->a,*aoa=ao->a,*apa,*pa,*ca,*pa_loc,*pa_oth;
  PetscInt       am=A->m,cm=C->m,pon=(p->B)->n;
  MPI_Comm       comm=C->comm;
  PetscMPIInt    size,rank,taga,*len_s;
  PetscInt       *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
  PetscInt       **buf_ri,**buf_rj;
  PetscInt       cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
  MPI_Request    *s_waits,*r_waits;
  MPI_Status     *status;
  MatScalar      **abuf_r,*ba_i,*pA,*coa,*ba;
  PetscInt       *api,*apj,*coi,*coj;
  PetscInt       *poJ=po->j,*pdJ=pd->j,pcstart=p->cstart,pcend=p->cend;

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

  ierr = PetscObjectQuery((PetscObject)C,"MatMergeSeqsToMPI",(PetscObject *)&cont_merge);CHKERRQ(ierr);
  if (cont_merge) {
    ierr  = PetscObjectContainerGetPointer(cont_merge,(void **)&merge);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "Matrix C does not posses an object container");
  }
  ierr = PetscObjectQuery((PetscObject)P,"MatPtAPMPI",(PetscObject *)&cont_ptap);CHKERRQ(ierr);
  if (cont_ptap) {
    ierr  = PetscObjectContainerGetPointer(cont_ptap,(void **)&ap);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
  }

  /* get data from symbolic products */
  p_loc = (Mat_SeqAIJ*)(ap->B_loc)->data;
  p_oth = (Mat_SeqAIJ*)(ap->B_oth)->data;
  pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a,pA=pa_loc;
  pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;

  coi = merge->coi; coj = merge->coj;
  ierr = PetscMalloc((coi[pon]+1)*sizeof(MatScalar),&coa);CHKERRQ(ierr);
  ierr = PetscMemzero(coa,coi[pon]*sizeof(MatScalar));CHKERRQ(ierr);

  bi = merge->bi; bj = merge->bj;
  ierr  = PetscMapGetGlobalRange(merge->rowmap,&owners);CHKERRQ(ierr);
  ierr  = PetscMalloc((bi[cm]+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
  ierr  = PetscMemzero(ba,bi[cm]*sizeof(MatScalar));CHKERRQ(ierr);

  /* get data from symbolic A*P */
  ierr = PetscMalloc((ap->abnz_max+1)*sizeof(MatScalar),&apa);CHKERRQ(ierr);
  ierr = PetscMemzero(apa,ap->abnz_max*sizeof(MatScalar));CHKERRQ(ierr);

  /* compute numeric C_seq=P_loc^T*A_loc*P */
  api = ap->abi; apj = ap->abj;
  for (i=0;i<am;i++) {
    /* form i-th sparse row of A*P */
    apnz = api[i+1] - api[i];
    apJ  = apj + api[i];
    /* diagonal portion of A */
    anz  = adi[i+1] - adi[i];
    for (j=0;j<anz;j++) {
      row = *adj++;
      pnz = pi_loc[row+1] - pi_loc[row];
      pj  = pj_loc + pi_loc[row];
      pa  = pa_loc + pi_loc[row];
      nextp = 0;
      for (k=0; nextp<pnz; k++) {
        if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
          apa[k] += (*ada)*pa[nextp++];
        }
      }
      flops += 2*pnz;
      ada++;
    }
    /* off-diagonal portion of A */
    anz  = aoi[i+1] - aoi[i];
    for (j=0; j<anz; j++) {
      row = *aoj++;
      pnz = pi_oth[row+1] - pi_oth[row];
      pj  = pj_oth + pi_oth[row];
      pa  = pa_oth + pi_oth[row];
      nextp = 0;
      for (k=0; nextp<pnz; k++) {
        if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
          apa[k] += (*aoa)*pa[nextp++];
        }
      }
      flops += 2*pnz;
      aoa++;
    }

    /* Compute P_loc[i,:]^T*AP[i,:] using outer product */
    pnz = pi_loc[i+1] - pi_loc[i];
    for (j=0; j<pnz; j++) {
      nextap = 0;
      row    = *pJ++; /* global index */
      if (row < pcstart || row >=pcend) { /* put the value into Co */
        cj  = coj + coi[*poJ];
        ca  = coa + coi[*poJ++];
      } else {                            /* put the value into Cd */
        cj   = bj + bi[*pdJ];
        ca   = ba + bi[*pdJ++];
      }
      for (k=0; nextap<apnz; k++) {
        if (cj[k]==apJ[nextap]) ca[k] += (*pA)*apa[nextap++];
      }
      flops += 2*apnz;
      pA++;
    }

    /* zero the current row info for A*P */
    ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
  }
  ierr = PetscFree(apa);CHKERRQ(ierr);

  /* send and recv matrix values */
  /*-----------------------------*/
  buf_ri = merge->buf_ri;
  buf_rj = merge->buf_rj;
  len_s  = merge->len_s;
  ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&taga);CHKERRQ(ierr);
  ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);

  ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
  for (proc=0,k=0; proc<size; proc++){
    if (!len_s[proc]) continue;
    i = merge->owners_co[proc];
    ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
    k++;
  }
  ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);
  ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);
  ierr = PetscFree(status);CHKERRQ(ierr);

  ierr = PetscFree(s_waits);CHKERRQ(ierr);
  ierr = PetscFree(r_waits);CHKERRQ(ierr);
  ierr = PetscFree(coa);CHKERRQ(ierr);

  /* insert local and received values into C */
  /*-----------------------------------------*/
  ierr = PetscMalloc((3*merge->nrecv+1)*sizeof(PetscInt**),&buf_ri_k);CHKERRQ(ierr);
  nextrow   = buf_ri_k + merge->nrecv;
  nextci = nextrow + merge->nrecv;

  for (k=0; k<merge->nrecv; k++){
    buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    nrows       = *(buf_ri_k[k]);
    nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
  }

  for (i=0; i<cm; i++) {
    row = owners[rank] + i; /* global row index of C_seq */
    bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    ba_i = ba + bi[i];
    bnz  = bi[i+1] - bi[i];
    /* add received vals into ba */
    for (k=0; k<merge->nrecv; k++){ /* k-th received message */
      /* i-th row */
      if (i == *nextrow[k]) {
        cnz = *(nextci[k]+1) - *nextci[k];
        cj  = buf_rj[k] + *(nextci[k]);
        ca  = abuf_r[k] + *(nextci[k]);
        nextcj = 0;
        for (j=0; nextcj<cnz; j++){
          if (bj_i[j] == cj[nextcj]){ /* bcol == ccol */
            ba_i[j] += ca[nextcj++];
          }
        }
        nextrow[k]++; nextci[k]++;
      }
    }
    ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
    flops += 2*cnz;
  }
  ierr = MatSetOption(C,MAT_COLUMNS_SORTED);CHKERRQ(ierr); /* -cause delay? */
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = PetscFree(ba);CHKERRQ(ierr);
  ierr = PetscFree(abuf_r);CHKERRQ(ierr);
  ierr = PetscFree(buf_ri_k);CHKERRQ(ierr);
  ierr = PetscLogFlops(flops);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}