xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 4ae0847b5407bb1f61dd4d8dd55bc243d48f67c9)

/*
  Defines matrix-matrix product routines for pairs of MPIAIJ matrices
          C = A * B
*/
#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>
#include <../src/mat/impls/dense/mpi/mpidense.h>

#undef __FUNCT__
#define __FUNCT__ "MatMatMult_MPIAIJ_MPIAIJ"
PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
    ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);/* numeric product is computed as well in old version! */
    ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
  }
  ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
  ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscContainerDestroy_Mat_MatMatMultMPI"
PetscErrorCode PetscContainerDestroy_Mat_MatMatMultMPI(void *ptr)
{
  PetscErrorCode       ierr;
  Mat_MatMatMultMPI    *mult=(Mat_MatMatMultMPI*)ptr;

  PetscFunctionBegin;
  ierr = ISDestroy(&mult->isrowa);CHKERRQ(ierr);
  ierr = ISDestroy(&mult->isrowb);CHKERRQ(ierr);
  ierr = ISDestroy(&mult->iscolb);CHKERRQ(ierr);
  ierr = MatDestroy(&mult->C_seq);CHKERRQ(ierr);
  ierr = MatDestroy(&mult->A_loc);CHKERRQ(ierr);
  ierr = MatDestroy(&mult->B_seq);CHKERRQ(ierr);
  ierr = PetscFree(mult);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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

  PetscFunctionBegin;
  ierr = PetscFree2(ptap->startsj,ptap->startsj_r);CHKERRQ(ierr);
  ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
  ierr = MatDestroy(&ptap->B_loc);CHKERRQ(ierr);
  ierr = MatDestroy(&ptap->B_oth);CHKERRQ(ierr);
  ierr = PetscFree(ptap->abi);CHKERRQ(ierr);
  ierr = PetscFree(ptap->abj);CHKERRQ(ierr);
  ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
  ierr = ptap->destroy(A);CHKERRQ(ierr);
  ierr = PetscFree(ptap);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_MPIAIJ_MatMatMult"
PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
{
  PetscErrorCode     ierr;
  PetscContainer     container;
  Mat_MatMatMultMPI  *mult=PETSC_NULL;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
  if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
  ierr = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
  A->ops->destroy   = mult->destroy;
  A->ops->duplicate = mult->duplicate;
  if (A->ops->destroy) {
    ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
  }
  ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatMultMPI",0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult"
PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
{
  PetscErrorCode     ierr;
  Mat_MatMatMultMPI  *mult;
  PetscContainer     container;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
  if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
  ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
  /* Note: the container is not duplicated, because it requires deep copying of
     several large data sets (see PetscContainerDestroy_Mat_MatMatMultMPI()).
     These data sets are only used for repeated calling of MatMatMultNumeric().
     *M is unlikely being used in this way. Thus we create *M with pure mpiaij format */
  ierr = (*mult->duplicate)(A,op,M);CHKERRQ(ierr);
  (*M)->ops->destroy   = mult->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's container! */
  (*M)->ops->duplicate = mult->duplicate; /* = MatDuplicate_MPIAIJ */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult_new"
PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult_new(Mat A, MatDuplicateOption op, Mat *M)
{
  PetscErrorCode     ierr;
  Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
  Mat_PtAPMPI        *ptap=a->ptap;

  PetscFunctionBegin;
  ierr = (*ptap->duplicate)(A,op,M);CHKERRQ(ierr);
  (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
  (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ_new"
PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_new(Mat A,Mat P,Mat C)
{
  PetscErrorCode     ierr;
  Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
  Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
  Mat_SeqAIJ         *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
  PetscInt           *adi=ad->i,*adj,*aoi=ao->i,*aoj;
  PetscScalar        *ada,*aoa,*cda=cd->a,*coa=co->a;
  Mat_SeqAIJ         *p_loc,*p_oth;
  PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
  PetscScalar        *pa_loc,*pa_oth,*pa,*apa,valtmp,*ca;
  PetscInt           cm=C->rmap->n,anz,pnz;
  Mat_PtAPMPI        *ptap=c->ptap;
  PetscInt           *api,*apj,*apJ,cnz,i,j,k,row;
  PetscInt           rstart=C->rmap->rstart,cstart=C->cmap->rstart;
  PetscInt           cdnz,conz,k0,k1;

  PetscFunctionBegin;
  /* 1) get P_oth = ptap->B_oth  and P_loc = ptap->B_loc */
  /*-----------------------------------------------------*/
  if (ptap->reuse == MAT_INITIAL_MATRIX){
    ptap->reuse = MAT_REUSE_MATRIX;
  } else { /* update numerical values of P_oth and P_loc */
    ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->B_oth);CHKERRQ(ierr);
    ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->B_loc);CHKERRQ(ierr);
  }

  /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
  /*----------------------------------------------------------*/
  /* get data from symbolic products */
  p_loc = (Mat_SeqAIJ*)(ptap->B_loc)->data;
  p_oth = (Mat_SeqAIJ*)(ptap->B_oth)->data;
  pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
  pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;

  /* get apa for storing dense row A[i,:]*P */
  apa = ptap->apa;

  for (i=0; i<cm; i++) {
    /* diagonal portion of A */
    anz = adi[i+1] - adi[i];
    adj = ad->j + adi[i];
    ada = ad->a + adi[i];
    for (j=0; j<anz; j++) {
      row = adj[j];
      pnz = pi_loc[row+1] - pi_loc[row];
      pj  = pj_loc + pi_loc[row];
      pa  = pa_loc + pi_loc[row];

      /* perform dense axpy */
      valtmp = ada[j];
      for (k=0; k<pnz; k++){
        apa[pj[k]] += valtmp*pa[k];
      }
      ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
    }

    /* off-diagonal portion of A */
    anz = aoi[i+1] - aoi[i];
    aoj = ao->j + aoi[i];
    aoa = ao->a + aoi[i];
    for (j=0; j<anz; j++) {
      row = aoj[j];
      pnz = pi_oth[row+1] - pi_oth[row];
      pj  = pj_oth + pi_oth[row];
      pa  = pa_oth + pi_oth[row];

      /* perform dense axpy */
      valtmp = aoa[j];
      for (k=0; k<pnz; k++){
        apa[pj[k]] += valtmp*pa[k];
      }
      ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
    }

    /* set values in C */
    row = rstart + i;
    api = ptap->abi;
    apj = ptap->abj;
    apJ = apj + api[i];
    cnz = api[i+1] - api[i];
    cdnz = cd->i[i+1] - cd->i[i];
    conz = co->i[i+1] - co->i[i];

    /* 1st off-diagoanl part of C */
    ca = coa + co->i[i];
    k  = 0;
    for (k0=0; k0<conz; k0++){
      if (apJ[k] >= cstart) break;
      ca[k0]      = apa[apJ[k]];
      apa[apJ[k]] = 0.0;
      k++;
    }

    /* diagonal part of C */
    ca = cda + cd->i[i];
    for (k1=0; k1<cdnz; k1++){
      ca[k1]      = apa[apJ[k]];
      apa[apJ[k]] = 0.0;
      k++;
    }

    /* 2nd off-diagoanl part of C */
    ca = coa + co->i[i];
    for (; k0<conz; k0++){
      ca[k0]      = apa[apJ[k]];
      apa[apJ[k]] = 0.0;
      k++;
    }
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ_new"
PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_new(Mat A,Mat P,PetscReal fill,Mat *C)
{
  PetscErrorCode       ierr;
  MPI_Comm             comm=((PetscObject)A)->comm;
  PetscMPIInt          size,rank;
  Mat                  B_mpi;
  Mat_PtAPMPI          *ptap;
  PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
  Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*c;
  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,*dnz,*onz;
  PetscInt             *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
  PetscInt             nlnk,*lnk,i,pnz,row;
  PetscInt             am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
  PetscBT              lnkbt;
  PetscInt             nzi;
  PetscInt             *api,*apj,*Jptr,apnz,nspacedouble=0,j;
  PetscScalar          *apa;

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

  /* create struct Mat_PtAPMPI and attached it to C later */
  ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
  ptap->abnz_max = 0;
  ptap->reuse    = MAT_INITIAL_MATRIX;

  /* malloc apa to store dense row A[i,:]*P */
  ierr = PetscMalloc((P->cmap->N)*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
  ierr = PetscMemzero(apa,P->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
  ptap->apa = apa;


  /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
  ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->B_oth);CHKERRQ(ierr);
  /* get P_loc by taking all local rows of P */
  ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->B_loc);CHKERRQ(ierr);

  p_loc = (Mat_SeqAIJ*)(ptap->B_loc)->data;
  p_oth = (Mat_SeqAIJ*)(ptap->B_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 = A_diag*P_loc + A_off*P_oth */
  /*-------------------------------------------------------------------*/
  ierr  = PetscMalloc((am+2)*sizeof(PetscInt),&api);CHKERRQ(ierr);
  ptap->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 = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am])),&free_space);CHKERRQ(ierr);
  current_space = free_space;

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

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

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

    /* Copy data into free space, then initialize lnk */
    ierr = PetscLLClean(pN,pN,apnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
    ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);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),&ptap->abj);CHKERRQ(ierr);
  apj = ptap->abj;
  ierr = PetscFreeSpaceContiguous(&free_space,ptap->abj);CHKERRQ(ierr);
  ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);

  /* create and assemble symbolic parallel matrix B_mpi */
  /*----------------------------------------------------*/
  ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
  ierr = MatSetSizes(B_mpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);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);
  ierr = MatSetBlockSize(B_mpi,1);CHKERRQ(ierr);
  for (i=0; i<am; i++){
    row = i + rstart;
    apnz = api[i+1] - api[i];
    ierr = MatSetValues(B_mpi,1,&row,apnz,apj,apa,INSERT_VALUES);CHKERRQ(ierr);
    apj += apnz;
  }
  ierr = MatAssemblyBegin(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ptap->destroy              = B_mpi->ops->destroy;
  ptap->duplicate            = B_mpi->ops->duplicate;
  B_mpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_new;
  B_mpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult_new;
  B_mpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult_new;

  /* attach the supporting struct to B_mpi for reuse */
  c = (Mat_MPIAIJ*)B_mpi->data;
  c->ptap  = ptap;

  *C = B_mpi;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ"
PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
{
  PetscErrorCode     ierr;
  Mat_MatMatMultMPI  *mult;
  PetscContainer     container;
  Mat                AB,*seq;
  Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
  PetscInt           *idx,i,start,ncols,nzA,nzB,*cmap,imark;
  PetscBool          matmatmult_new=PETSC_FALSE;

  PetscFunctionBegin;
  if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
    SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
  }
  ierr = PetscOptionsGetBool(PETSC_NULL,"-matmatmult_new",&matmatmult_new,PETSC_NULL);CHKERRQ(ierr);
  if (matmatmult_new){
    ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_new(A,B,fill,C);;CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = PetscNew(Mat_MatMatMultMPI,&mult);CHKERRQ(ierr);

  /* get isrowb: nonzero col of A */
  start = A->cmap->rstart;
  cmap  = a->garray;
  nzA   = a->A->cmap->n;
  nzB   = a->B->cmap->n;
  ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
  ncols = 0;
  for (i=0; i<nzB; i++) {  /* row < local row index */
    if (cmap[i] < start) idx[ncols++] = cmap[i];
    else break;
  }
  imark = i;
  for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
  for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
  ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&mult->isrowb);CHKERRQ(ierr);
  ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&mult->iscolb);CHKERRQ(ierr);

  /*  get isrowa: all local rows of A */
  ierr = ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,&mult->isrowa);CHKERRQ(ierr);

  /* Below should go to MatMatMultNumeric_MPIAIJ_MPIAIJ() - How to generate C there? */
  /* create a seq matrix B_seq = submatrix of B by taking rows of B that equal to nonzero col of A */
  ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
  mult->B_seq = *seq;
  ierr = PetscFree(seq);CHKERRQ(ierr);

  /*  create a seq matrix A_seq = submatrix of A by taking all local rows of A */
  ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
  mult->A_loc = *seq;
  ierr = PetscFree(seq);CHKERRQ(ierr);

  /* compute C_seq = A_seq * B_seq */
  ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(mult->A_loc,mult->B_seq,fill,&mult->C_seq);CHKERRQ(ierr);
  ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);

  /* create mpi matrix C by concatinating C_seq */
  ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr); /* prevent C_seq being destroyed by MatMerge() */
  ierr = MatMergeSymbolic(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,&AB);CHKERRQ(ierr);
  ierr = MatMergeNumeric(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,AB);CHKERRQ(ierr);

  /* attach the supporting struct to C for reuse of symbolic C */
  ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
  ierr = PetscContainerSetPointer(container,mult);CHKERRQ(ierr);
  ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatMultMPI);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)AB,"Mat_MatMatMultMPI",(PetscObject)container);CHKERRQ(ierr);
  ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
  mult->destroy      = AB->ops->destroy;
  mult->duplicate    = AB->ops->duplicate;
  AB->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
  AB->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
  AB->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;
  AB->ops->matmult        = MatMatMult_MPIAIJ_MPIAIJ;
  *C                      = AB;
  PetscFunctionReturn(0);
}

/* This routine is called ONLY in the case of reusing previously computed symbolic C */
#undef __FUNCT__
#define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ"
PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat B,Mat C)
{
  PetscErrorCode     ierr;
  Mat                *seq;
  Mat_MatMatMultMPI  *mult;
  PetscContainer     container;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
  if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
  ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
  seq = &mult->B_seq;
  ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
  mult->B_seq = *seq;

  seq = &mult->A_loc;
  ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
  mult->A_loc = *seq;

  ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_SparseAxpy(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);

  ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr);
  ierr = MatMerge(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMult_MPIAIJ_MPIDense"
PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX){
    ierr = MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);CHKERRQ(ierr);
  }
  ierr = MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

typedef struct {
  Mat         workB;
  PetscScalar *rvalues,*svalues;
  MPI_Request *rwaits,*swaits;
} MPIAIJ_MPIDense;

#undef __FUNCT__
#define __FUNCT__ "MPIAIJ_MPIDenseDestroy"
PetscErrorCode MPIAIJ_MPIDenseDestroy(void *ctx)
{
  MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
  ierr = PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);CHKERRQ(ierr);
  ierr = PetscFree(contents);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIDense"
PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
{
  PetscErrorCode         ierr;
  Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
  PetscInt               nz = aij->B->cmap->n;
  PetscContainer         container;
  MPIAIJ_MPIDense        *contents;
  VecScatter             ctx = aij->Mvctx;
  VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
  VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
  PetscInt               m=A->rmap->n,n=B->cmap->n;

  PetscFunctionBegin;
  ierr = MatCreate(((PetscObject)B)->comm,C);CHKERRQ(ierr);
  ierr = MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);CHKERRQ(ierr);
  ierr = MatSetType(*C,MATMPIDENSE);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  (*C)->ops->matmult = MatMatMult_MPIAIJ_MPIDense;

  ierr = PetscNew(MPIAIJ_MPIDense,&contents);CHKERRQ(ierr);
  /* Create work matrix used to store off processor rows of B needed for local product */
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,PETSC_NULL,&contents->workB);CHKERRQ(ierr);
  /* Create work arrays needed */
  ierr = PetscMalloc4(B->cmap->N*from->starts[from->n],PetscScalar,&contents->rvalues,
                      B->cmap->N*to->starts[to->n],PetscScalar,&contents->svalues,
                      from->n,MPI_Request,&contents->rwaits,
                      to->n,MPI_Request,&contents->swaits);CHKERRQ(ierr);

  ierr = PetscContainerCreate(((PetscObject)A)->comm,&container);CHKERRQ(ierr);
  ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr);
  ierr = PetscContainerSetUserDestroy(container,MPIAIJ_MPIDenseDestroy);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);CHKERRQ(ierr);
  ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMPIDenseScatter"
/*
    Performs an efficient scatter on the rows of B needed by this process; this is
    a modification of the VecScatterBegin_() routines.
*/
PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
{
  Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
  PetscErrorCode         ierr;
  PetscScalar            *b,*w,*svalues,*rvalues;
  VecScatter             ctx = aij->Mvctx;
  VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
  VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
  PetscInt               i,j,k;
  PetscInt               *sindices,*sstarts,*rindices,*rstarts;
  PetscMPIInt            *sprocs,*rprocs,nrecvs;
  MPI_Request            *swaits,*rwaits;
  MPI_Comm               comm = ((PetscObject)A)->comm;
  PetscMPIInt            tag = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
  MPI_Status             status;
  MPIAIJ_MPIDense        *contents;
  PetscContainer         container;
  Mat                    workB;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
  if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
  ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);

  workB = *outworkB = contents->workB;
  if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
  sindices  = to->indices;
  sstarts   = to->starts;
  sprocs    = to->procs;
  swaits    = contents->swaits;
  svalues   = contents->svalues;

  rindices  = from->indices;
  rstarts   = from->starts;
  rprocs    = from->procs;
  rwaits    = contents->rwaits;
  rvalues   = contents->rvalues;

  ierr = MatGetArray(B,&b);CHKERRQ(ierr);
  ierr = MatGetArray(workB,&w);CHKERRQ(ierr);

  for (i=0; i<from->n; i++) {
    ierr = MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
  }

  for (i=0; i<to->n; i++) {
    /* pack a message at a time */
    CHKMEMQ;
    for (j=0; j<sstarts[i+1]-sstarts[i]; j++){
      for (k=0; k<ncols; k++) {
        svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
      }
    }
    CHKMEMQ;
    ierr = MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
  }

  nrecvs = from->n;
  while (nrecvs) {
    ierr = MPI_Waitany(from->n,rwaits,&imdex,&status);CHKERRQ(ierr);
    nrecvs--;
    /* unpack a message at a time */
    CHKMEMQ;
    for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++){
      for (k=0; k<ncols; k++) {
        w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
      }
    }
    CHKMEMQ;
  }
  if (to->n) {ierr = MPI_Waitall(to->n,swaits,to->sstatus);CHKERRQ(ierr);}

  ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
  ierr = MatRestoreArray(workB,&w);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);

#undef __FUNCT__
#define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIDense"
PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
{
  PetscErrorCode       ierr;
  Mat_MPIAIJ           *aij = (Mat_MPIAIJ*)A->data;
  Mat_MPIDense         *bdense = (Mat_MPIDense*)B->data;
  Mat_MPIDense         *cdense = (Mat_MPIDense*)C->data;
  Mat                  workB;

  PetscFunctionBegin;

  /* diagonal block of A times all local rows of B*/
  ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr);

  /* get off processor parts of B needed to complete the product */
  ierr = MatMPIDenseScatter(A,B,C,&workB);CHKERRQ(ierr);

  /* off-diagonal block of A times nonlocal rows of B */
  ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}