PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C) { PetscErrorCode ierr; Mat Cmpi; Mat_PtAPMPI *ptap; PetscFreeSpaceList free_space=NULL,current_space=NULL; Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->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,*pdti,*pdtj,*poti,*potj,*ptJ; PetscInt *adi=ad->i,*aj,*aoi=ao->i,nnz; PetscInt *lnk,*owners_co,*coi,*coj,i,k,pnz,row; PetscInt am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n; PetscBT lnkbt; MPI_Comm comm; PetscMPIInt size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0; PetscInt **buf_rj,**buf_ri,**buf_ri_k; PetscInt len,proc,*dnz,*onz,*owners; PetscInt nzi,*pti,*ptj; PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci; MPI_Request *swaits,*rwaits; MPI_Status *sstatus,rstatus; Mat_Merge_SeqsToMPI *merge; PetscInt *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0; PetscReal afill=1.0,afill_tmp; PetscInt rmax; #if defined(PTAP_PROFILE) PetscLogDouble t0,t1,t2,t3,t4; #endif PetscFunctionBegin; ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t0);CHKERRQ(ierr); #endif /* check if matrix local sizes are compatible */ if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) { SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend); } if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) { SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend); } 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(&ptap);CHKERRQ(ierr); ierr = PetscNew(&merge);CHKERRQ(ierr); ptap->merge = merge; ptap->reuse = MAT_INITIAL_MATRIX; /* 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_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); /* get P_loc by taking all local rows of P */ ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr); p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; pi_loc = p_loc->i; pj_loc = p_loc->j; pi_oth = p_oth->i; pj_oth = p_oth->j; #if defined(PTAP_PROFILE) ierr = PetscTime(&t1);CHKERRQ(ierr); #endif /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */ /*-------------------------------------------------------------------*/ ierr = PetscMalloc1((am+1),&api);CHKERRQ(ierr); api[0] = 0; /* create and initialize a linked list */ ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr); /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */ ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr); current_space = free_space; for (i=0; i<am; i++) { /* diagonal portion of A */ nzi = adi[i+1] - adi[i]; aj = ad->j + adi[i]; for (j=0; j<nzi; j++) { row = aj[j]; 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 = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); } /* off-diagonal portion of A */ nzi = aoi[i+1] - aoi[i]; aj = ao->j + aoi[i]; for (j=0; j<nzi; j++) { row = aj[j]; pnz = pi_oth[row+1] - pi_oth[row]; Jptr = pj_oth + pi_oth[row]; ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); } apnz = lnk[0]; api[i+1] = api[i] + apnz; if (ap_rmax < apnz) ap_rmax = 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,¤t_space);CHKERRQ(ierr); nspacedouble++; } /* Copy data into free space, then initialize lnk */ ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,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 = PetscMalloc1((api[am]+1),&apj);CHKERRQ(ierr); ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr); afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1); if (afill_tmp > afill) afill = afill_tmp; #if defined(PTAP_PROFILE) ierr = PetscTime(&t2);CHKERRQ(ierr); #endif /* determine symbolic Co=(p->B)^T*AP - send to others */ /*----------------------------------------------------*/ ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr); /* then, compute symbolic Co = (p->B)^T*AP */ pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors >= (num of nonzero rows of C_seq) - pn */ ierr = PetscMalloc1((pon+1),&coi);CHKERRQ(ierr); coi[0] = 0; /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */ nnz = fill*(poti[pon] + api[am]); ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr); current_space = free_space; for (i=0; i<pon; i++) { pnz = poti[i+1] - poti[i]; ptJ = potj + poti[i]; for (j=0; j<pnz; j++) { row = ptJ[j]; /* row of AP == col of Pot */ apnz = api[row+1] - api[row]; Jptr = apj + api[row]; /* add non-zero cols of AP into the sorted linked list lnk */ ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); } nnz = lnk[0]; /* If free space is not available, double the total space in the list */ if (current_space->local_remaining<nnz) { ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,¤t_space);CHKERRQ(ierr); nspacedouble++; } /* Copy data into free space, and zero out denserows */ ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr); current_space->array += nnz; current_space->local_used += nnz; current_space->local_remaining -= nnz; coi[i+1] = coi[i] + nnz; } ierr = PetscMalloc1((coi[pon]+1),&coj);CHKERRQ(ierr); ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr); afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1); if (afill_tmp > afill) afill = afill_tmp; ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr); /* send j-array (coj) of Co to other processors */ /*----------------------------------------------*/ /* determine row ownership */ ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr); merge->rowmap->n = pn; merge->rowmap->bs = 1; ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr); owners = merge->rowmap->range; /* determine the number of messages to send, their lengths */ ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr); ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr); ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr); len_s = merge->len_s; merge->nsend = 0; ierr = PetscMalloc1((size+2),&owners_co);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 coi and coj */ ierr = PetscGatherNumberOfMessages(comm,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 coj */ ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr); ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr); ierr = PetscMalloc1((merge->nsend+1),&swaits);CHKERRQ(ierr); 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,swaits+k);CHKERRQ(ierr); k++; } /* receives and sends of coj are complete */ for (i=0; i<merge->nrecv; i++) { ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); } ierr = PetscFree(rwaits);CHKERRQ(ierr); if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);} /* send and recv coi */ /*-------------------*/ ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr); ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr); ierr = PetscMalloc1((len+1),&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++) { nzi = coi[i+1] - coi[i]; buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* 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,swaits+k);CHKERRQ(ierr); k++; buf_si += len_si[proc]; } i = merge->nrecv; while (i--) { ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); } ierr = PetscFree(rwaits);CHKERRQ(ierr); if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);} ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr); ierr = PetscFree(len_ri);CHKERRQ(ierr); ierr = PetscFree(swaits);CHKERRQ(ierr); ierr = PetscFree(buf_s);CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t3);CHKERRQ(ierr); #endif /* compute the local portion of C (mpi mat) */ /*------------------------------------------*/ ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr); /* allocate pti array and free space for accumulating nonzero column info */ ierr = PetscMalloc1((pn+1),&pti);CHKERRQ(ierr); pti[0] = 0; /* set initial free space to be fill*(nnz(P) + nnz(AP)) */ nnz = fill*(pi_loc[pm] + api[am]); ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr); current_space = free_space; ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr); 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); rmax = 0; for (i=0; i<pn; i++) { /* add pdt[i,:]*AP into lnk */ pnz = pdti[i+1] - pdti[i]; ptJ = pdtj + pdti[i]; for (j=0; j<pnz; j++) { row = ptJ[j]; /* row of AP == col of Pt */ apnz = api[row+1] - api[row]; Jptr = apj + api[row]; /* add non-zero cols of AP into the sorted linked list lnk */ ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); } /* add received col data into lnk */ for (k=0; k<merge->nrecv; k++) { /* k-th received message */ if (i == *nextrow[k]) { /* i-th row */ nzi = *(nextci[k]+1) - *nextci[k]; Jptr = buf_rj[k] + *nextci[k]; ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr); nextrow[k]++; nextci[k]++; } } nnz = lnk[0]; /* if free space is not available, make more free space */ if (current_space->local_remaining<nnz) { ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,¤t_space);CHKERRQ(ierr); nspacedouble++; } /* copy data into free space, then initialize lnk */ ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr); ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr); current_space->array += nnz; current_space->local_used += nnz; current_space->local_remaining -= nnz; pti[i+1] = pti[i] + nnz; if (nnz > rmax) rmax = nnz; } ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr); ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr); ierr = PetscMalloc1((pti[pn]+1),&ptj);CHKERRQ(ierr); ierr = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr); afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1); if (afill_tmp > afill) afill = afill_tmp; ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); /* create symbolic parallel matrix Cmpi */ /*--------------------------------------*/ ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); ierr = MatSetBlockSizes(Cmpi,P->cmap->bs,P->cmap->bs);CHKERRQ(ierr); ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr); ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); merge->bi = pti; /* Cseq->i */ merge->bj = ptj; /* Cseq->j */ merge->coi = coi; /* Co->i */ merge->coj = coj; /* Co->j */ merge->buf_ri = buf_ri; merge->buf_rj = buf_rj; merge->owners_co = owners_co; merge->destroy = Cmpi->ops->destroy; merge->duplicate = Cmpi->ops->duplicate; /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */ Cmpi->assembled = PETSC_FALSE; Cmpi->ops->destroy = MatDestroy_MPIAIJ_PtAP; Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP; /* attach the supporting struct to Cmpi for reuse */ c = (Mat_MPIAIJ*)Cmpi->data; c->ptap = ptap; ptap->api = api; ptap->apj = apj; ptap->rmax = ap_rmax; *C = Cmpi; /* flag 'scalable' determines which implementations to be used: 0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa; 1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */ /* set default scalable */ ptap->scalable = PETSC_TRUE; ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr); if (!ptap->scalable) { /* Do dense axpy */ ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr); } else { ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr); } #if defined(PTAP_PROFILE) ierr = PetscTime(&t4);CHKERRQ(ierr); if (rank==1) PetscPrintf(MPI_COMM_SELF," [%d] PtAPSymbolic %g/P + %g/AP + %g/comm + %g/PtAP = %g\n",rank,t1-t0,t2-t1,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr); #endif #if defined(PETSC_USE_INFO) if (pti[pn] != 0) { ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr); ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr); } else { ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr); } #endif PetscFunctionReturn(0); }
/* PEPBuildDiagonalScaling - compute two diagonal matrices to be applied for balancing in polynomial eigenproblems. */ PetscErrorCode PEPBuildDiagonalScaling(PEP pep) { PetscErrorCode ierr; PetscInt it,i,j,k,nmat,nr,e,nz,lst,lend,nc=0,*cols,emax,emin,emaxl,eminl; const PetscInt *cidx,*ridx; Mat M,*T,A; PetscMPIInt n; PetscBool cont=PETSC_TRUE,flg=PETSC_FALSE; PetscScalar *array,*Dr,*Dl,t; PetscReal l2,d,*rsum,*aux,*csum,w=1.0; MatStructure str; MatInfo info; PetscFunctionBegin; l2 = 2*PetscLogReal(2.0); nmat = pep->nmat; ierr = PetscMPIIntCast(pep->n,&n); ierr = STGetMatStructure(pep->st,&str);CHKERRQ(ierr); ierr = PetscMalloc1(nmat,&T);CHKERRQ(ierr); for (k=0;k<nmat;k++) { ierr = STGetTOperators(pep->st,k,&T[k]);CHKERRQ(ierr); } /* Form local auxiliar matrix M */ ierr = PetscObjectTypeCompareAny((PetscObject)T[0],&cont,MATMPIAIJ,MATSEQAIJ);CHKERRQ(ierr); if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"Only for MPIAIJ or SEQAIJ matrix types"); ierr = PetscObjectTypeCompare((PetscObject)T[0],MATMPIAIJ,&cont);CHKERRQ(ierr); if (cont) { ierr = MatMPIAIJGetLocalMat(T[0],MAT_INITIAL_MATRIX,&M);CHKERRQ(ierr); flg = PETSC_TRUE; } else { ierr = MatDuplicate(T[0],MAT_COPY_VALUES,&M);CHKERRQ(ierr); } ierr = MatGetInfo(M,MAT_LOCAL,&info);CHKERRQ(ierr); nz = info.nz_used; ierr = MatSeqAIJGetArray(M,&array);CHKERRQ(ierr); for (i=0;i<nz;i++) { t = PetscAbsScalar(array[i]); array[i] = t*t; } ierr = MatSeqAIJRestoreArray(M,&array);CHKERRQ(ierr); for (k=1;k<nmat;k++) { if (flg) { ierr = MatMPIAIJGetLocalMat(T[k],MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr); } else { if (str==SAME_NONZERO_PATTERN) { ierr = MatCopy(T[k],A,SAME_NONZERO_PATTERN);CHKERRQ(ierr); } else { ierr = MatDuplicate(T[k],MAT_COPY_VALUES,&A);CHKERRQ(ierr); } } ierr = MatGetInfo(A,MAT_LOCAL,&info);CHKERRQ(ierr); nz = info.nz_used; ierr = MatSeqAIJGetArray(A,&array);CHKERRQ(ierr); for (i=0;i<nz;i++) { t = PetscAbsScalar(array[i]); array[i] = t*t; } ierr = MatSeqAIJRestoreArray(A,&array);CHKERRQ(ierr); w *= pep->slambda*pep->slambda*pep->sfactor; ierr = MatAXPY(M,w,A,str);CHKERRQ(ierr); if (flg || str!=SAME_NONZERO_PATTERN || k==nmat-2) { ierr = MatDestroy(&A);CHKERRQ(ierr); } } ierr = MatGetRowIJ(M,0,PETSC_FALSE,PETSC_FALSE,&nr,&ridx,&cidx,&cont);CHKERRQ(ierr); if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]), PETSC_ERR_SUP,"It is not possible to compute scaling diagonals for these PEP matrices"); ierr = MatGetInfo(M,MAT_LOCAL,&info);CHKERRQ(ierr); nz = info.nz_used; ierr = VecGetOwnershipRange(pep->Dl,&lst,&lend);CHKERRQ(ierr); ierr = PetscMalloc4(nr,&rsum,pep->n,&csum,pep->n,&aux,PetscMin(pep->n-lend+lst,nz),&cols);CHKERRQ(ierr); ierr = VecSet(pep->Dr,1.0);CHKERRQ(ierr); ierr = VecSet(pep->Dl,1.0);CHKERRQ(ierr); ierr = VecGetArray(pep->Dl,&Dl);CHKERRQ(ierr); ierr = VecGetArray(pep->Dr,&Dr);CHKERRQ(ierr); ierr = MatSeqAIJGetArray(M,&array);CHKERRQ(ierr); ierr = PetscMemzero(aux,pep->n*sizeof(PetscReal));CHKERRQ(ierr); for (j=0;j<nz;j++) { /* Search non-zero columns outsize lst-lend */ if (aux[cidx[j]]==0 && (cidx[j]<lst || lend<=cidx[j])) cols[nc++] = cidx[j]; /* Local column sums */ aux[cidx[j]] += PetscAbsScalar(array[j]); } for (it=0;it<pep->sits && cont;it++) { emaxl = 0; eminl = 0; /* Column sum */ if (it>0) { /* it=0 has been already done*/ ierr = MatSeqAIJGetArray(M,&array);CHKERRQ(ierr); ierr = PetscMemzero(aux,pep->n*sizeof(PetscReal));CHKERRQ(ierr); for (j=0;j<nz;j++) aux[cidx[j]] += PetscAbsScalar(array[j]); ierr = MatSeqAIJRestoreArray(M,&array);CHKERRQ(ierr); } ierr = MPI_Allreduce(aux,csum,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)pep->Dr)); /* Update Dr */ for (j=lst;j<lend;j++) { d = PetscLogReal(csum[j])/l2; e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5)); d = PetscPowReal(2.0,e); Dr[j-lst] *= d; aux[j] = d*d; emaxl = PetscMax(emaxl,e); eminl = PetscMin(eminl,e); } for (j=0;j<nc;j++) { d = PetscLogReal(csum[cols[j]])/l2; e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5)); d = PetscPowReal(2.0,e); aux[cols[j]] = d*d; emaxl = PetscMax(emaxl,e); eminl = PetscMin(eminl,e); } /* Scale M */ ierr = MatSeqAIJGetArray(M,&array);CHKERRQ(ierr); for (j=0;j<nz;j++) { array[j] *= aux[cidx[j]]; } ierr = MatSeqAIJRestoreArray(M,&array);CHKERRQ(ierr); /* Row sum */ ierr = PetscMemzero(rsum,nr*sizeof(PetscReal));CHKERRQ(ierr); ierr = MatSeqAIJGetArray(M,&array);CHKERRQ(ierr); for (i=0;i<nr;i++) { for (j=ridx[i];j<ridx[i+1];j++) rsum[i] += PetscAbsScalar(array[j]); /* Update Dl */ d = PetscLogReal(rsum[i])/l2; e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5)); d = PetscPowReal(2.0,e); Dl[i] *= d; /* Scale M */ for (j=ridx[i];j<ridx[i+1];j++) array[j] *= d*d; emaxl = PetscMax(emaxl,e); eminl = PetscMin(eminl,e); } ierr = MatSeqAIJRestoreArray(M,&array);CHKERRQ(ierr); /* Compute global max and min */ ierr = MPI_Allreduce(&emaxl,&emax,1,MPIU_INT,MPIU_MAX,PetscObjectComm((PetscObject)pep->Dl)); ierr = MPI_Allreduce(&eminl,&emin,1,MPIU_INT,MPIU_MIN,PetscObjectComm((PetscObject)pep->Dl)); if (emax<=emin+2) cont = PETSC_FALSE; } ierr = VecRestoreArray(pep->Dr,&Dr);CHKERRQ(ierr); ierr = VecRestoreArray(pep->Dl,&Dl);CHKERRQ(ierr); /* Free memory*/ ierr = MatDestroy(&M);CHKERRQ(ierr); ierr = PetscFree4(rsum,csum,aux,cols);CHKERRQ(ierr); ierr = PetscFree(T);CHKERRQ(ierr); PetscFunctionReturn(0); }
PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C) { PetscErrorCode ierr; Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->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; Mat_PtAPMPI *ptap; Mat_Merge_SeqsToMPI *merge; PetscInt *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp; PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj; PetscInt i,j,k,anz,pnz,apnz,nextap,row,*cj; MatScalar *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp; PetscInt am =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n; MPI_Comm 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->cmap->rstart,pcend=P->cmap->rend; PetscBool scalable; #if defined(PTAP_PROFILE) PetscLogDouble t0,t1,t2,t3,t4,et2_AP=0.0,et2_PtAP=0.0,t2_0,t2_1,t2_2; #endif PetscFunctionBegin; ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t0);CHKERRQ(ierr); #endif ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr); ptap = c->ptap; if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_INCOMP,"MatPtAP() has not been called to create matrix C yet, cannot use MAT_REUSE_MATRIX"); merge = ptap->merge; apa = ptap->apa; scalable = ptap->scalable; /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */ /*--------------------------------------------------*/ if (ptap->reuse == MAT_INITIAL_MATRIX) { /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */ 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_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr); } #if defined(PTAP_PROFILE) ierr = PetscTime(&t1);CHKERRQ(ierr); #endif /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */ /*--------------------------------------------------------------*/ /* get data from symbolic products */ p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a; pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a; coi = merge->coi; coj = merge->coj; ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr); bi = merge->bi; bj = merge->bj; owners = merge->rowmap->range; ierr = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr); /* ba: Cseq->a */ api = ptap->api; apj = ptap->apj; if (!scalable) { /* Do dense axpy on apa (length of pN, stores A[i,:]*P) - nonscalable, but fast */ ierr = PetscInfo(C,"Using non-scalable dense axpy\n");CHKERRQ(ierr); /*-----------------------------------------------------------------------------------------------------*/ for (i=0; i<am; i++) { #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_0);CHKERRQ(ierr); #endif /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */ /*------------------------------------------------------------*/ apJ = apj + api[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); } #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_1);CHKERRQ(ierr); et2_AP += t2_1 - t2_0; #endif /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */ /*--------------------------------------------------------------*/ apnz = api[i+1] - api[i]; /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */ pnz = po->i[i+1] - po->i[i]; poJ = po->j + po->i[i]; pA = po->a + po->i[i]; for (j=0; j<pnz; j++) { row = poJ[j]; cnz = coi[row+1] - coi[row]; cj = coj + coi[row]; ca = coa + coi[row]; /* perform dense axpy */ valtmp = pA[j]; for (k=0; k<cnz; k++) { ca[k] += valtmp*apa[cj[k]]; } ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); } /* put the value into Cd (diagonal part) */ pnz = pd->i[i+1] - pd->i[i]; pdJ = pd->j + pd->i[i]; pA = pd->a + pd->i[i]; for (j=0; j<pnz; j++) { row = pdJ[j]; cnz = bi[row+1] - bi[row]; cj = bj + bi[row]; ca = ba + bi[row]; /* perform dense axpy */ valtmp = pA[j]; for (k=0; k<cnz; k++) { ca[k] += valtmp*apa[cj[k]]; } ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); } /* zero the current row of A*P */ for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0; #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_2);CHKERRQ(ierr); et2_PtAP += t2_2 - t2_1; #endif } } else { /* Do sparse axpy on apa (length of ap_rmax, stores A[i,:]*P) - scalable, but slower */ ierr = PetscInfo(C,"Using scalable sparse axpy\n");CHKERRQ(ierr); /*-----------------------------------------------------------------------------------------*/ pA=pa_loc; for (i=0; i<am; i++) { #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_0);CHKERRQ(ierr); #endif /* 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]; 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]; valtmp = ada[j]; nextp = 0; for (k=0; nextp<pnz; k++) { if (apJ[k] == pj[nextp]) { /* col of AP == col of P */ apa[k] += valtmp*pa[nextp++]; } } 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]; valtmp = aoa[j]; nextp = 0; for (k=0; nextp<pnz; k++) { if (apJ[k] == pj[nextp]) { /* col of AP == col of P */ apa[k] += valtmp*pa[nextp++]; } } ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); } #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_1);CHKERRQ(ierr); et2_AP += t2_1 - t2_0; #endif /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */ /*--------------------------------------------------------------*/ pnz = pi_loc[i+1] - pi_loc[i]; pJ = pj_loc + pi_loc[i]; for (j=0; j<pnz; j++) { nextap = 0; row = pJ[j]; /* global index */ if (row < pcstart || row >=pcend) { /* put the value into Co */ row = *poJ; cj = coj + coi[row]; ca = coa + coi[row]; poJ++; } else { /* put the value into Cd */ row = *pdJ; cj = bj + bi[row]; ca = ba + bi[row]; pdJ++; } valtmp = pA[j]; for (k=0; nextap<apnz; k++) { if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++]; } ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr); } pA += pnz; /* zero the current row info for A*P */ ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t2_2);CHKERRQ(ierr); et2_PtAP += t2_2 - t2_1; #endif } } #if defined(PTAP_PROFILE) ierr = PetscTime(&t2);CHKERRQ(ierr); #endif /* 3) send and recv matrix values coa */ /*------------------------------------*/ buf_ri = merge->buf_ri; buf_rj = merge->buf_rj; len_s = merge->len_s; ierr = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr); ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr); ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);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++; } if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);} if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);} ierr = PetscFree2(s_waits,status);CHKERRQ(ierr); ierr = PetscFree(r_waits);CHKERRQ(ierr); ierr = PetscFree(coa);CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t3);CHKERRQ(ierr); #endif /* 4) insert local Cseq and received values into Cmpi */ /*------------------------------------------------------*/ ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr); 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 = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); } } ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr); } 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[0]);CHKERRQ(ierr); ierr = PetscFree(abuf_r);CHKERRQ(ierr); ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr); #if defined(PTAP_PROFILE) ierr = PetscTime(&t4);CHKERRQ(ierr); if (rank==1) PetscPrintf(MPI_COMM_SELF," [%d] PtAPNum %g/P + %g/PtAP( %g + %g ) + %g/comm + %g/Cloc = %g\n\n",rank,t1-t0,t2-t1,et2_AP,et2_PtAP,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr); #endif PetscFunctionReturn(0); }