Date: 2021-03-03T22:26:14+00:00

Actual source code: mpimatmatmult.c
petsc-3.14.5 2021-03-03
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      2: /*
      3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
      4:           C = A * B
      5: */
      6: #include <../src/mat/impls/aij/seq/aij.h>
      7: #include <../src/mat/utils/freespace.h>
      8: #include <../src/mat/impls/aij/mpi/mpiaij.h>
      9: #include <petscbt.h>
     10: #include <../src/mat/impls/dense/mpi/mpidense.h>
     11: #include <petsc/private/vecimpl.h>
     12: #include <petsc/private/vecscatterimpl.h>

     14: #if defined(PETSC_HAVE_HYPRE)
     15: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
     16: #endif

     18: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
     19: {
     20:   PetscErrorCode      ierr;
     21:   Mat_Product         *product = C->product;
     22:   Mat                 A=product->A,B=product->B;
     23:   MatProductAlgorithm alg=product->alg;
     24:   PetscReal           fill=product->fill;
     25:   PetscBool           flg;

     28:   /* scalable */
     29:   PetscStrcmp(alg,"scalable",&flg);
     30:   if (flg) {
     31:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
     32:     return(0);
     33:   }

     35:   /* nonscalable */
     36:   PetscStrcmp(alg,"nonscalable",&flg);
     37:   if (flg) {
     38:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
     39:     return(0);
     40:   }

     42:   /* seqmpi */
     43:   PetscStrcmp(alg,"seqmpi",&flg);
     44:   if (flg) {
     45:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);
     46:     return(0);
     47:   }

     49: #if defined(PETSC_HAVE_HYPRE)
     50:   PetscStrcmp(alg,"hypre",&flg);
     51:   if (flg) {
     52:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     53:     return(0);
     54:   }
     55: #endif
     56:   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
     57: }

     59: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
     60: {
     62:   Mat_APMPI      *ptap = (Mat_APMPI*)data;

     65:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     66:   PetscFree(ptap->bufa);
     67:   MatDestroy(&ptap->P_loc);
     68:   MatDestroy(&ptap->P_oth);
     69:   MatDestroy(&ptap->Pt);
     70:   PetscFree(ptap->api);
     71:   PetscFree(ptap->apj);
     72:   PetscFree(ptap->apa);
     73:   PetscFree(ptap);
     74:   return(0);
     75: }

     77: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
     78: {
     80:   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
     81:   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
     82:   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
     83:   PetscScalar    *cda=cd->a,*coa=co->a;
     84:   Mat_SeqAIJ     *p_loc,*p_oth;
     85:   PetscScalar    *apa,*ca;
     86:   PetscInt       cm =C->rmap->n;
     87:   Mat_APMPI      *ptap;
     88:   PetscInt       *api,*apj,*apJ,i,k;
     89:   PetscInt       cstart=C->cmap->rstart;
     90:   PetscInt       cdnz,conz,k0,k1;
     91:   MPI_Comm       comm;
     92:   PetscMPIInt    size;

     95:   MatCheckProduct(C,3);
     96:   ptap = (Mat_APMPI*)C->product->data;
     97:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
     98:   PetscObjectGetComm((PetscObject)A,&comm);
     99:   MPI_Comm_size(comm,&size);

    101:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

    103:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    104:   /*-----------------------------------------------------*/
    105:   /* update numerical values of P_oth and P_loc */
    106:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    107:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    109:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    110:   /*----------------------------------------------------------*/
    111:   /* get data from symbolic products */
    112:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    113:   p_oth = NULL;
    114:   if (size >1) {
    115:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    116:   }

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

    121:   api = ptap->api;
    122:   apj = ptap->apj;
    123:   for (i=0; i<cm; i++) {
    124:     /* compute apa = A[i,:]*P */
    125:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

    127:     /* set values in C */
    128:     apJ  = apj + api[i];
    129:     cdnz = cd->i[i+1] - cd->i[i];
    130:     conz = co->i[i+1] - co->i[i];

    132:     /* 1st off-diagonal part of C */
    133:     ca = coa + co->i[i];
    134:     k  = 0;
    135:     for (k0=0; k0<conz; k0++) {
    136:       if (apJ[k] >= cstart) break;
    137:       ca[k0]      = apa[apJ[k]];
    138:       apa[apJ[k++]] = 0.0;
    139:     }

    141:     /* diagonal part of C */
    142:     ca = cda + cd->i[i];
    143:     for (k1=0; k1<cdnz; k1++) {
    144:       ca[k1]      = apa[apJ[k]];
    145:       apa[apJ[k++]] = 0.0;
    146:     }

    148:     /* 2nd off-diagonal part of C */
    149:     ca = coa + co->i[i];
    150:     for (; k0<conz; k0++) {
    151:       ca[k0]      = apa[apJ[k]];
    152:       apa[apJ[k++]] = 0.0;
    153:     }
    154:   }
    155:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    156:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    157:   return(0);
    158: }

    160: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
    161: {
    162:   PetscErrorCode     ierr;
    163:   MPI_Comm           comm;
    164:   PetscMPIInt        size;
    165:   Mat_APMPI          *ptap;
    166:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    167:   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
    168:   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    169:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    170:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    171:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
    172:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
    173:   PetscBT            lnkbt;
    174:   PetscReal          afill;
    175:   MatType            mtype;

    178:   MatCheckProduct(C,4);
    179:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    180:   PetscObjectGetComm((PetscObject)A,&comm);
    181:   MPI_Comm_size(comm,&size);

    183:   /* create struct Mat_APMPI and attached it to C later */
    184:   PetscNew(&ptap);

    186:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    187:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    189:   /* get P_loc by taking all local rows of P */
    190:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    192:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    193:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    194:   if (size > 1) {
    195:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    196:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    197:   } else {
    198:     p_oth = NULL;
    199:     pi_oth = NULL; pj_oth = NULL;
    200:   }

    202:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    203:   /*-------------------------------------------------------------------*/
    204:   PetscMalloc1(am+2,&api);
    205:   ptap->api = api;
    206:   api[0]    = 0;

    208:   /* create and initialize a linked list */
    209:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);

    211:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    212:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    213:   current_space = free_space;

    215:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    216:   for (i=0; i<am; i++) {
    217:     /* diagonal portion of A */
    218:     nzi = adi[i+1] - adi[i];
    219:     for (j=0; j<nzi; j++) {
    220:       row  = *adj++;
    221:       pnz  = pi_loc[row+1] - pi_loc[row];
    222:       Jptr = pj_loc + pi_loc[row];
    223:       /* add non-zero cols of P into the sorted linked list lnk */
    224:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    225:     }
    226:     /* off-diagonal portion of A */
    227:     nzi = aoi[i+1] - aoi[i];
    228:     for (j=0; j<nzi; j++) {
    229:       row  = *aoj++;
    230:       pnz  = pi_oth[row+1] - pi_oth[row];
    231:       Jptr = pj_oth + pi_oth[row];
    232:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    233:     }

    235:     apnz     = lnk[0];
    236:     api[i+1] = api[i] + apnz;

    238:     /* if free space is not available, double the total space in the list */
    239:     if (current_space->local_remaining<apnz) {
    240:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    241:       nspacedouble++;
    242:     }

    244:     /* Copy data into free space, then initialize lnk */
    245:     PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);
    246:     MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);

    248:     current_space->array           += apnz;
    249:     current_space->local_used      += apnz;
    250:     current_space->local_remaining -= apnz;
    251:   }

    253:   /* Allocate space for apj, initialize apj, and */
    254:   /* destroy list of free space and other temporary array(s) */
    255:   PetscMalloc1(api[am]+1,&ptap->apj);
    256:   apj  = ptap->apj;
    257:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    258:   PetscLLDestroy(lnk,lnkbt);

    260:   /* malloc apa to store dense row A[i,:]*P */
    261:   PetscCalloc1(pN,&ptap->apa);

    263:   /* set and assemble symbolic parallel matrix C */
    264:   /*---------------------------------------------*/
    265:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    266:   MatSetBlockSizesFromMats(C,A,P);

    268:   MatGetType(A,&mtype);
    269:   MatSetType(C,mtype);
    270:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    271:   MatPreallocateFinalize(dnz,onz);

    273:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    274:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    275:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    276:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    278:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    279:   C->ops->productnumeric = MatProductNumeric_AB;

    281:   /* attach the supporting struct to C for reuse */
    282:   C->product->data    = ptap;
    283:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    285:   /* set MatInfo */
    286:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    287:   if (afill < 1.0) afill = 1.0;
    288:   C->info.mallocs           = nspacedouble;
    289:   C->info.fill_ratio_given  = fill;
    290:   C->info.fill_ratio_needed = afill;

    292: #if defined(PETSC_USE_INFO)
    293:   if (api[am]) {
    294:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    295:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    296:   } else {
    297:     PetscInfo(C,"Empty matrix product\n");
    298:   }
    299: #endif
    300:   return(0);
    301: }

    303: /* ------------------------------------------------------- */
    304: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
    305: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);

    307: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
    308: {
    309:   Mat_Product *product = C->product;
    310:   Mat         A = product->A,B=product->B;

    313:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    314:     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);

    316:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
    317:   C->ops->productsymbolic = MatProductSymbolic_AB;
    318:   return(0);
    319: }
    320: /* -------------------------------------------------------------------- */
    321: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
    322: {
    323:   Mat_Product *product = C->product;
    324:   Mat         A = product->A,B=product->B;

    327:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    328:     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);

    330:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
    331:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
    332:   return(0);
    333: }

    335: /* --------------------------------------------------------------------- */
    336: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
    337: {
    339:   Mat_Product    *product = C->product;

    342:   switch (product->type) {
    343:   case MATPRODUCT_AB:
    344:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
    345:     break;
    346:   case MATPRODUCT_AtB:
    347:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
    348:     break;
    349:   default:
    350:     break;
    351:   }
    352:   return(0);
    353: }
    354: /* ------------------------------------------------------- */

    356: typedef struct {
    357:   Mat          workB,workB1;
    358:   MPI_Request  *rwaits,*swaits;
    359:   PetscInt     nsends,nrecvs;
    360:   MPI_Datatype *stype,*rtype;
    361:   PetscInt     blda;
    362: } MPIAIJ_MPIDense;

    364: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    365: {
    366:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
    367:   PetscErrorCode  ierr;
    368:   PetscInt        i;

    371:   MatDestroy(&contents->workB);
    372:   MatDestroy(&contents->workB1);
    373:   for (i=0; i<contents->nsends; i++) {
    374:     MPI_Type_free(&contents->stype[i]);
    375:   }
    376:   for (i=0; i<contents->nrecvs; i++) {
    377:     MPI_Type_free(&contents->rtype[i]);
    378:   }
    379:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
    380:   PetscFree(contents);
    381:   return(0);
    382: }

    384: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
    385: {
    386:   PetscErrorCode  ierr;
    387:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
    388:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda;
    389:   MPIAIJ_MPIDense *contents;
    390:   VecScatter      ctx=aij->Mvctx;
    391:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
    392:   MPI_Comm        comm;
    393:   MPI_Datatype    type1,*stype,*rtype;
    394:   const PetscInt  *sindices,*sstarts,*rstarts;
    395:   PetscMPIInt     *disp;
    396:   PetscBool       cisdense;

    399:   MatCheckProduct(C,4);
    400:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
    401:   PetscObjectGetComm((PetscObject)A,&comm);
    402:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
    403:   if (!cisdense) {
    404:     MatSetType(C,((PetscObject)B)->type_name);
    405:   }
    406:   MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
    407:   MatSetBlockSizesFromMats(C,A,B);
    408:   MatSetUp(C);
    409:   MatDenseGetLDA(B,&blda);
    410:   MatDenseGetLDA(C,&clda);
    411:   PetscNew(&contents);

    413:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    414:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);

    416:   /* Create column block of B and C for memory scalability when BN is too large */
    417:   /* Estimate Bbn, column size of Bb */
    418:   if (nz) {
    419:     Bbn1 = 2*Am*BN/nz;
    420:     if (!Bbn1) Bbn1 = 1;
    421:   } else Bbn1 = BN;

    423:   bs = PetscAbs(B->cmap->bs);
    424:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
    425:   if (Bbn1 > BN) Bbn1 = BN;
    426:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

    428:   /* Enable runtime option for Bbn */
    429:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
    430:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
    431:   PetscOptionsEnd();
    432:   Bbn  = PetscMin(Bbn,BN);

    434:   if (Bbn > 0 && Bbn < BN) {
    435:     numBb = BN/Bbn;
    436:     Bbn1 = BN - numBb*Bbn;
    437:   } else numBb = 0;

    439:   if (numBb) {
    440:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
    441:     if (Bbn1) { /* Create workB1 for the remaining columns */
    442:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
    443:       /* Create work matrix used to store off processor rows of B needed for local product */
    444:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
    445:     } else contents->workB1 = NULL;
    446:   }

    448:   /* Create work matrix used to store off processor rows of B needed for local product */
    449:   MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);

    451:   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
    452:   PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);
    453:   contents->stype  = stype;
    454:   contents->nsends = nsends;

    456:   contents->rtype  = rtype;
    457:   contents->nrecvs = nrecvs;
    458:   contents->blda   = blda;

    460:   PetscMalloc1(Bm+1,&disp);
    461:   for (i=0; i<nsends; i++) {
    462:     nrows_to = sstarts[i+1]-sstarts[i];
    463:     for (j=0; j<nrows_to; j++){
    464:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
    465:     }
    466:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

    468:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
    469:     MPI_Type_commit(&stype[i]);
    470:     MPI_Type_free(&type1);
    471:   }

    473:   for (i=0; i<nrecvs; i++) {
    474:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    475:     nrows_from = rstarts[i+1]-rstarts[i];
    476:     disp[0] = 0;
    477:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
    478:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
    479:     MPI_Type_commit(&rtype[i]);
    480:     MPI_Type_free(&type1);
    481:   }

    483:   PetscFree(disp);
    484:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    485:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
    486:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    487:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    488:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    489:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    491:   C->product->data = contents;
    492:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
    493:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    494:   return(0);
    495: }

    497: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
    498: /*
    499:     Performs an efficient scatter on the rows of B needed by this process; this is
    500:     a modification of the VecScatterBegin_() routines.

    502:     Input: Bbidx = 0: B = Bb
    503:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
    504: */
    505: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
    506: {
    507:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
    508:   PetscErrorCode    ierr;
    509:   const PetscScalar *b;
    510:   PetscScalar       *rvalues;
    511:   VecScatter        ctx = aij->Mvctx;
    512:   const PetscInt    *sindices,*sstarts,*rstarts;
    513:   const PetscMPIInt *sprocs,*rprocs;
    514:   PetscInt          i,nsends,nrecvs;
    515:   MPI_Request       *swaits,*rwaits;
    516:   MPI_Comm          comm;
    517:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
    518:   MPIAIJ_MPIDense   *contents;
    519:   Mat               workB;
    520:   MPI_Datatype      *stype,*rtype;
    521:   PetscInt          blda;

    524:   MatCheckProduct(C,4);
    525:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    526:   contents = (MPIAIJ_MPIDense*)C->product->data;
    527:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
    528:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
    529:   PetscMPIIntCast(nsends,&nsends_mpi);
    530:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
    531:   if (Bbidx == 0) {
    532:     workB = *outworkB = contents->workB;
    533:   } else {
    534:     workB = *outworkB = contents->workB1;
    535:   }
    536:   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",workB->cmap->n,nrows);
    537:   swaits = contents->swaits;
    538:   rwaits = contents->rwaits;

    540:   MatDenseGetArrayRead(B,&b);
    541:   MatDenseGetLDA(B,&blda);
    542:   if (blda != contents->blda) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %D != %D",blda,contents->blda);
    543:   MatDenseGetArray(workB,&rvalues);

    545:   /* Post recv, use MPI derived data type to save memory */
    546:   PetscObjectGetComm((PetscObject)C,&comm);
    547:   rtype = contents->rtype;
    548:   for (i=0; i<nrecvs; i++) {
    549:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
    550:   }

    552:   stype = contents->stype;
    553:   for (i=0; i<nsends; i++) {
    554:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
    555:   }

    557:   if (nrecvs) {MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);}
    558:   if (nsends) {MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);}

    560:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
    561:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
    562:   MatDenseRestoreArrayRead(B,&b);
    563:   MatDenseRestoreArray(workB,&rvalues);
    564:   return(0);
    565: }

    567: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    568: {
    569:   PetscErrorCode  ierr;
    570:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
    571:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
    572:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
    573:   Mat             workB;
    574:   MPIAIJ_MPIDense *contents;

    577:   MatCheckProduct(C,3);
    578:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    579:   contents = (MPIAIJ_MPIDense*)C->product->data;
    580:   /* diagonal block of A times all local rows of B */
    581:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
    582:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
    583:   if (contents->workB->cmap->n == B->cmap->N) {
    584:     /* get off processor parts of B needed to complete C=A*B */
    585:     MatMPIDenseScatter(A,B,0,C,&workB);

    587:     /* off-diagonal block of A times nonlocal rows of B */
    588:     MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
    589:   } else {
    590:     Mat      Bb,Cb;
    591:     PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
    592:     if (n <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %D must be positive",n);

    594:     for (i=0; i<BN; i+=n) {
    595:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
    596:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

    598:       /* get off processor parts of B needed to complete C=A*B */
    599:       MatMPIDenseScatter(A,Bb,i+n>BN,C,&workB);

    601:       /* off-diagonal block of A times nonlocal rows of B */
    602:       cdense = (Mat_MPIDense*)Cb->data;
    603:       MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);

    605:       MatDenseRestoreSubMatrix(B,&Bb);
    606:       MatDenseRestoreSubMatrix(C,&Cb);
    607:     }
    608:   }
    609:   return(0);
    610: }

    612: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    613: {
    615:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    616:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    617:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    618:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    619:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
    620:   Mat_SeqAIJ     *p_loc,*p_oth;
    621:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    622:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
    623:   PetscInt       cm    = C->rmap->n,anz,pnz;
    624:   Mat_APMPI      *ptap;
    625:   PetscScalar    *apa_sparse;
    626:   PetscInt       *api,*apj,*apJ,i,j,k,row;
    627:   PetscInt       cstart = C->cmap->rstart;
    628:   PetscInt       cdnz,conz,k0,k1,nextp;
    629:   MPI_Comm       comm;
    630:   PetscMPIInt    size;

    633:   MatCheckProduct(C,3);
    634:   ptap = (Mat_APMPI*)C->product->data;
    635:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    636:   PetscObjectGetComm((PetscObject)C,&comm);
    637:   MPI_Comm_size(comm,&size);
    638:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

    640:   apa_sparse = ptap->apa;

    642:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    643:   /*-----------------------------------------------------*/
    644:   /* update numerical values of P_oth and P_loc */
    645:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    646:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    648:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    649:   /*----------------------------------------------------------*/
    650:   /* get data from symbolic products */
    651:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    652:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    653:   if (size >1) {
    654:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    655:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    656:   } else {
    657:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    658:   }

    660:   api = ptap->api;
    661:   apj = ptap->apj;
    662:   for (i=0; i<cm; i++) {
    663:     apJ = apj + api[i];

    665:     /* diagonal portion of A */
    666:     anz = adi[i+1] - adi[i];
    667:     adj = ad->j + adi[i];
    668:     ada = ad->a + adi[i];
    669:     for (j=0; j<anz; j++) {
    670:       row = adj[j];
    671:       pnz = pi_loc[row+1] - pi_loc[row];
    672:       pj  = pj_loc + pi_loc[row];
    673:       pa  = pa_loc + pi_loc[row];
    674:       /* perform sparse axpy */
    675:       valtmp = ada[j];
    676:       nextp  = 0;
    677:       for (k=0; nextp<pnz; k++) {
    678:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    679:           apa_sparse[k] += valtmp*pa[nextp++];
    680:         }
    681:       }
    682:       PetscLogFlops(2.0*pnz);
    683:     }

    685:     /* off-diagonal portion of A */
    686:     anz = aoi[i+1] - aoi[i];
    687:     aoj = ao->j + aoi[i];
    688:     aoa = ao->a + aoi[i];
    689:     for (j=0; j<anz; j++) {
    690:       row = aoj[j];
    691:       pnz = pi_oth[row+1] - pi_oth[row];
    692:       pj  = pj_oth + pi_oth[row];
    693:       pa  = pa_oth + pi_oth[row];
    694:       /* perform sparse axpy */
    695:       valtmp = aoa[j];
    696:       nextp  = 0;
    697:       for (k=0; nextp<pnz; k++) {
    698:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    699:           apa_sparse[k] += valtmp*pa[nextp++];
    700:         }
    701:       }
    702:       PetscLogFlops(2.0*pnz);
    703:     }

    705:     /* set values in C */
    706:     cdnz = cd->i[i+1] - cd->i[i];
    707:     conz = co->i[i+1] - co->i[i];

    709:     /* 1st off-diagonal part of C */
    710:     ca = coa + co->i[i];
    711:     k  = 0;
    712:     for (k0=0; k0<conz; k0++) {
    713:       if (apJ[k] >= cstart) break;
    714:       ca[k0]        = apa_sparse[k];
    715:       apa_sparse[k] = 0.0;
    716:       k++;
    717:     }

    719:     /* diagonal part of C */
    720:     ca = cda + cd->i[i];
    721:     for (k1=0; k1<cdnz; k1++) {
    722:       ca[k1]        = apa_sparse[k];
    723:       apa_sparse[k] = 0.0;
    724:       k++;
    725:     }

    727:     /* 2nd off-diagonal part of C */
    728:     ca = coa + co->i[i];
    729:     for (; k0<conz; k0++) {
    730:       ca[k0]        = apa_sparse[k];
    731:       apa_sparse[k] = 0.0;
    732:       k++;
    733:     }
    734:   }
    735:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    736:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    737:   return(0);
    738: }

    740: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    741: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
    742: {
    743:   PetscErrorCode     ierr;
    744:   MPI_Comm           comm;
    745:   PetscMPIInt        size;
    746:   Mat_APMPI          *ptap;
    747:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    748:   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
    749:   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    750:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    751:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    752:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
    753:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
    754:   PetscReal          afill;
    755:   MatType            mtype;

    758:   MatCheckProduct(C,4);
    759:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    760:   PetscObjectGetComm((PetscObject)A,&comm);
    761:   MPI_Comm_size(comm,&size);

    763:   /* create struct Mat_APMPI and attached it to C later */
    764:   PetscNew(&ptap);

    766:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    767:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    769:   /* get P_loc by taking all local rows of P */
    770:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    772:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    773:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    774:   if (size > 1) {
    775:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    776:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    777:   } else {
    778:     p_oth  = NULL;
    779:     pi_oth = NULL; pj_oth = NULL;
    780:   }

    782:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    783:   /*-------------------------------------------------------------------*/
    784:   PetscMalloc1(am+2,&api);
    785:   ptap->api = api;
    786:   api[0]    = 0;

    788:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

    790:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    791:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    792:   current_space = free_space;
    793:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    794:   for (i=0; i<am; i++) {
    795:     /* diagonal portion of A */
    796:     nzi = adi[i+1] - adi[i];
    797:     for (j=0; j<nzi; j++) {
    798:       row  = *adj++;
    799:       pnz  = pi_loc[row+1] - pi_loc[row];
    800:       Jptr = pj_loc + pi_loc[row];
    801:       /* Expand list if it is not long enough */
    802:       if (pnz+apnz_max > lsize) {
    803:         lsize = pnz+apnz_max;
    804:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    805:       }
    806:       /* add non-zero cols of P into the sorted linked list lnk */
    807:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    808:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
    809:       api[i+1] = api[i] + apnz;
    810:       if (apnz > apnz_max) apnz_max = apnz;
    811:     }
    812:     /* off-diagonal portion of A */
    813:     nzi = aoi[i+1] - aoi[i];
    814:     for (j=0; j<nzi; j++) {
    815:       row  = *aoj++;
    816:       pnz  = pi_oth[row+1] - pi_oth[row];
    817:       Jptr = pj_oth + pi_oth[row];
    818:       /* Expand list if it is not long enough */
    819:       if (pnz+apnz_max > lsize) {
    820:         lsize = pnz + apnz_max;
    821:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    822:       }
    823:       /* add non-zero cols of P into the sorted linked list lnk */
    824:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    825:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
    826:       api[i+1] = api[i] + apnz;
    827:       if (apnz > apnz_max) apnz_max = apnz;
    828:     }
    829:     apnz     = *lnk;
    830:     api[i+1] = api[i] + apnz;
    831:     if (apnz > apnz_max) apnz_max = apnz;

    833:     /* if free space is not available, double the total space in the list */
    834:     if (current_space->local_remaining<apnz) {
    835:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    836:       nspacedouble++;
    837:     }

    839:     /* Copy data into free space, then initialize lnk */
    840:     PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);
    841:     MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);

    843:     current_space->array           += apnz;
    844:     current_space->local_used      += apnz;
    845:     current_space->local_remaining -= apnz;
    846:   }

    848:   /* Allocate space for apj, initialize apj, and */
    849:   /* destroy list of free space and other temporary array(s) */
    850:   PetscMalloc1(api[am]+1,&ptap->apj);
    851:   apj  = ptap->apj;
    852:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    853:   PetscLLCondensedDestroy_Scalable(lnk);

    855:   /* create and assemble symbolic parallel matrix C */
    856:   /*----------------------------------------------------*/
    857:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    858:   MatSetBlockSizesFromMats(C,A,P);
    859:   MatGetType(A,&mtype);
    860:   MatSetType(C,mtype);
    861:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    862:   MatPreallocateFinalize(dnz,onz);

    864:   /* malloc apa for assembly C */
    865:   PetscCalloc1(apnz_max,&ptap->apa);

    867:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    868:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    869:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    870:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    872:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    873:   C->ops->productnumeric = MatProductNumeric_AB;

    875:   /* attach the supporting struct to C for reuse */
    876:   C->product->data    = ptap;
    877:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    879:   /* set MatInfo */
    880:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    881:   if (afill < 1.0) afill = 1.0;
    882:   C->info.mallocs           = nspacedouble;
    883:   C->info.fill_ratio_given  = fill;
    884:   C->info.fill_ratio_needed = afill;

    886: #if defined(PETSC_USE_INFO)
    887:   if (api[am]) {
    888:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    889:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    890:   } else {
    891:     PetscInfo(C,"Empty matrix product\n");
    892:   }
    893: #endif
    894:   return(0);
    895: }

    897: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    898: /* Three input arrays are merged to one output array. The size of the    */
    899: /* output array is also output. Duplicate entries only show up once.     */
    900: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
    901:                                PetscInt  size2, PetscInt *in2,
    902:                                PetscInt  size3, PetscInt *in3,
    903:                                PetscInt *size4, PetscInt *out)
    904: {
    905:   int i = 0, j = 0, k = 0, l = 0;

    907:   /* Traverse all three arrays */
    908:   while (i<size1 && j<size2 && k<size3) {
    909:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    910:       out[l++] = in1[i++];
    911:     }
    912:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
    913:       out[l++] = in2[j++];
    914:     }
    915:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
    916:       out[l++] = in3[k++];
    917:     }
    918:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
    919:       out[l++] = in1[i];
    920:       i++, j++;
    921:     }
    922:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
    923:       out[l++] = in1[i];
    924:       i++, k++;
    925:     }
    926:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
    927:       out[l++] = in2[j];
    928:       k++, j++;
    929:     }
    930:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
    931:       out[l++] = in1[i];
    932:       i++, j++, k++;
    933:     }
    934:   }

    936:   /* Traverse two remaining arrays */
    937:   while (i<size1 && j<size2) {
    938:     if (in1[i] < in2[j]) {
    939:       out[l++] = in1[i++];
    940:     }
    941:     else if (in1[i] > in2[j]) {
    942:       out[l++] = in2[j++];
    943:     }
    944:     else {
    945:       out[l++] = in1[i];
    946:       i++, j++;
    947:     }
    948:   }

    950:   while (i<size1 && k<size3) {
    951:     if (in1[i] < in3[k]) {
    952:       out[l++] = in1[i++];
    953:     }
    954:     else if (in1[i] > in3[k]) {
    955:       out[l++] = in3[k++];
    956:     }
    957:     else {
    958:       out[l++] = in1[i];
    959:       i++, k++;
    960:     }
    961:   }

    963:   while (k<size3 && j<size2)  {
    964:     if (in3[k] < in2[j]) {
    965:       out[l++] = in3[k++];
    966:     }
    967:     else if (in3[k] > in2[j]) {
    968:       out[l++] = in2[j++];
    969:     }
    970:     else {
    971:       out[l++] = in3[k];
    972:       k++, j++;
    973:     }
    974:   }

    976:   /* Traverse one remaining array */
    977:   while (i<size1) out[l++] = in1[i++];
    978:   while (j<size2) out[l++] = in2[j++];
    979:   while (k<size3) out[l++] = in3[k++];

    981:   *size4 = l;
    982: }

    984: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    985: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    986: /* matrix-matrix multiplications.  */
    987: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    988: {
    989:   PetscErrorCode     ierr;
    990:   MPI_Comm           comm;
    991:   PetscMPIInt        size;
    992:   Mat_APMPI          *ptap;
    993:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
    994:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
    995:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
    996:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
    997:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
    998:   PetscInt           adponz, adpdnz;
    999:   PetscInt           *pi_loc,*dnz,*onz;
    1000:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
    1001:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
    1002:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
    1003:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
    1004:   PetscBT            lnkbt;
    1005:   PetscReal          afill;
    1006:   PetscMPIInt        rank;
    1007:   Mat                adpd, aopoth;
    1008:   MatType            mtype;
    1009:   const char         *prefix;

    1012:   MatCheckProduct(C,4);
    1013:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    1014:   PetscObjectGetComm((PetscObject)A,&comm);
    1015:   MPI_Comm_size(comm,&size);
    1016:   MPI_Comm_rank(comm, &rank);
    1017:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

    1019:   /* create struct Mat_APMPI and attached it to C later */
    1020:   PetscNew(&ptap);

    1022:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1023:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    1025:   /* get P_loc by taking all local rows of P */
    1026:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    1029:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    1030:   pi_loc = p_loc->i;

    1032:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1033:   PetscMalloc1(am+2,&api);
    1034:   PetscMalloc1(am+2,&adpoi);

    1036:   adpoi[0]    = 0;
    1037:   ptap->api = api;
    1038:   api[0] = 0;

    1040:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1041:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
    1042:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

    1044:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1045:   MatGetOptionsPrefix(A,&prefix);
    1046:   MatProductCreate(a->A,p->A,NULL,&adpd);
    1047:   MatGetOptionsPrefix(A,&prefix);
    1048:   MatSetOptionsPrefix(adpd,prefix);
    1049:   MatAppendOptionsPrefix(adpd,"inner_diag_");

    1051:   MatProductSetType(adpd,MATPRODUCT_AB);
    1052:   MatProductSetAlgorithm(adpd,"sorted");
    1053:   MatProductSetFill(adpd,fill);
    1054:   MatProductSetFromOptions(adpd);
    1055:   MatProductSymbolic(adpd);

    1057:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
    1058:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
    1059:   p_off = (Mat_SeqAIJ*)((p->B)->data);
    1060:   poff_i = p_off->i; poff_j = p_off->j;

    1062:   /* j_temp stores indices of a result row before they are added to the linked list */
    1063:   PetscMalloc1(pN+2,&j_temp);

    1066:   /* Symbolic calc of the A_diag * p_loc_off */
    1067:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1068:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
    1069:   current_space = free_space_diag;

    1071:   for (i=0; i<am; i++) {
    1072:     /* A_diag * P_loc_off */
    1073:     nzi = adi[i+1] - adi[i];
    1074:     for (j=0; j<nzi; j++) {
    1075:       row  = *adj++;
    1076:       pnz  = poff_i[row+1] - poff_i[row];
    1077:       Jptr = poff_j + poff_i[row];
    1078:       for (i1 = 0; i1 < pnz; i1++) {
    1079:         j_temp[i1] = p->garray[Jptr[i1]];
    1080:       }
    1081:       /* add non-zero cols of P into the sorted linked list lnk */
    1082:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
    1083:     }

    1085:     adponz     = lnk[0];
    1086:     adpoi[i+1] = adpoi[i] + adponz;

    1088:     /* if free space is not available, double the total space in the list */
    1089:     if (current_space->local_remaining<adponz) {
    1090:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
    1091:       nspacedouble++;
    1092:     }

    1094:     /* Copy data into free space, then initialize lnk */
    1095:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

    1097:     current_space->array           += adponz;
    1098:     current_space->local_used      += adponz;
    1099:     current_space->local_remaining -= adponz;
    1100:   }

    1102:   /* Symbolic calc of A_off * P_oth */
    1103:   MatSetOptionsPrefix(a->B,prefix);
    1104:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
    1105:   MatCreate(PETSC_COMM_SELF,&aopoth);
    1106:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
    1107:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
    1108:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

    1110:   /* Allocate space for apj, adpj, aopj, ... */
    1111:   /* destroy lists of free space and other temporary array(s) */

    1113:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
    1114:   PetscMalloc1(adpoi[am]+2, &adpoj);

    1116:   /* Copy from linked list to j-array */
    1117:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
    1118:   PetscLLDestroy(lnk,lnkbt);

    1120:   adpoJ = adpoj;
    1121:   adpdJ = adpdj;
    1122:   aopJ = aopothj;
    1123:   apj  = ptap->apj;
    1124:   apJ = apj; /* still empty */

    1126:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1127:   /* A_diag * P_loc_diag to get A*P */
    1128:   for (i = 0; i < am; i++) {
    1129:     aopnz  =  aopothi[i+1] -  aopothi[i];
    1130:     adponz = adpoi[i+1] - adpoi[i];
    1131:     adpdnz = adpdi[i+1] - adpdi[i];

    1133:     /* Correct indices from A_diag*P_diag */
    1134:     for (i1 = 0; i1 < adpdnz; i1++) {
    1135:       adpdJ[i1] += p_colstart;
    1136:     }
    1137:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1138:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1139:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

    1141:     aopJ += aopnz;
    1142:     adpoJ += adponz;
    1143:     adpdJ += adpdnz;
    1144:     apJ += apnz;
    1145:     api[i+1] = api[i] + apnz;
    1146:   }

    1148:   /* malloc apa to store dense row A[i,:]*P */
    1149:   PetscCalloc1(pN+2,&ptap->apa);

    1151:   /* create and assemble symbolic parallel matrix C */
    1152:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    1153:   MatSetBlockSizesFromMats(C,A,P);
    1154:   MatGetType(A,&mtype);
    1155:   MatSetType(C,mtype);
    1156:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1157:   MatPreallocateFinalize(dnz,onz);

    1159:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    1160:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1161:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1162:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1164:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1165:   C->ops->productnumeric = MatProductNumeric_AB;

    1167:   /* attach the supporting struct to C for reuse */
    1168:   C->product->data    = ptap;
    1169:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    1171:   /* set MatInfo */
    1172:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1173:   if (afill < 1.0) afill = 1.0;
    1174:   C->info.mallocs           = nspacedouble;
    1175:   C->info.fill_ratio_given  = fill;
    1176:   C->info.fill_ratio_needed = afill;

    1178: #if defined(PETSC_USE_INFO)
    1179:   if (api[am]) {
    1180:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1181:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1182:   } else {
    1183:     PetscInfo(C,"Empty matrix product\n");
    1184:   }
    1185: #endif

    1187:   MatDestroy(&aopoth);
    1188:   MatDestroy(&adpd);
    1189:   PetscFree(j_temp);
    1190:   PetscFree(adpoj);
    1191:   PetscFree(adpoi);
    1192:   return(0);
    1193: }

    1195: /*-------------------------------------------------------------------------*/
    1196: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1197: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    1198: {
    1200:   Mat_APMPI      *ptap;
    1201:   Mat            Pt;

    1204:   MatCheckProduct(C,3);
    1205:   ptap = (Mat_APMPI*)C->product->data;
    1206:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1207:   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");

    1209:   Pt   = ptap->Pt;
    1210:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    1211:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
    1212:   return(0);
    1213: }

    1215: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1216: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
    1217: {
    1218:   PetscErrorCode      ierr;
    1219:   Mat_APMPI           *ptap;
    1220:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
    1221:   MPI_Comm            comm;
    1222:   PetscMPIInt         size,rank;
    1223:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1224:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
    1225:   PetscInt            *lnk,i,k,nsend,rstart;
    1226:   PetscBT             lnkbt;
    1227:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
    1228:   PETSC_UNUSED PetscMPIInt icompleted=0;
    1229:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1230:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
    1231:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1232:   MPI_Request         *swaits,*rwaits;
    1233:   MPI_Status          *sstatus,rstatus;
    1234:   PetscLayout         rowmap;
    1235:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
    1236:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
    1237:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
    1238:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
    1239:   PetscTable          ta;
    1240:   MatType             mtype;
    1241:   const char          *prefix;

    1244:   PetscObjectGetComm((PetscObject)A,&comm);
    1245:   MPI_Comm_size(comm,&size);
    1246:   MPI_Comm_rank(comm,&rank);

    1248:   /* create symbolic parallel matrix C */
    1249:   MatGetType(A,&mtype);
    1250:   MatSetType(C,mtype);

    1252:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1254:   /* create struct Mat_APMPI and attached it to C later */
    1255:   PetscNew(&ptap);
    1256:   ptap->reuse = MAT_INITIAL_MATRIX;

    1258:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1259:   /* --------------------------------- */
    1260:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
    1261:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

    1263:   /* (1) compute symbolic A_loc */
    1264:   /* ---------------------------*/
    1265:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

    1267:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1268:   /* ------------------------------------ */
    1269:   MatGetOptionsPrefix(A,&prefix);
    1270:   MatSetOptionsPrefix(ptap->Ro,prefix);
    1271:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
    1272:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
    1273:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

    1275:   /* (3) send coj of C_oth to other processors  */
    1276:   /* ------------------------------------------ */
    1277:   /* determine row ownership */
    1278:   PetscLayoutCreate(comm,&rowmap);
    1279:   rowmap->n  = pn;
    1280:   rowmap->bs = 1;
    1281:   PetscLayoutSetUp(rowmap);
    1282:   owners = rowmap->range;

    1284:   /* determine the number of messages to send, their lengths */
    1285:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
    1286:   PetscArrayzero(len_s,size);
    1287:   PetscArrayzero(len_si,size);

    1289:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
    1290:   coi   = c_oth->i; coj = c_oth->j;
    1291:   con   = ptap->C_oth->rmap->n;
    1292:   proc  = 0;
    1293:   for (i=0; i<con; i++) {
    1294:     while (prmap[i] >= owners[proc+1]) proc++;
    1295:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1296:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1297:   }

    1299:   len          = 0; /* max length of buf_si[], see (4) */
    1300:   owners_co[0] = 0;
    1301:   nsend        = 0;
    1302:   for (proc=0; proc<size; proc++) {
    1303:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1304:     if (len_s[proc]) {
    1305:       nsend++;
    1306:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1307:       len         += len_si[proc];
    1308:     }
    1309:   }

    1311:   /* determine the number and length of messages to receive for coi and coj  */
    1312:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
    1313:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

    1315:   /* post the Irecv and Isend of coj */
    1316:   PetscCommGetNewTag(comm,&tagj);
    1317:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
    1318:   PetscMalloc1(nsend+1,&swaits);
    1319:   for (proc=0, k=0; proc<size; proc++) {
    1320:     if (!len_s[proc]) continue;
    1321:     i    = owners_co[proc];
    1322:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1323:     k++;
    1324:   }

    1326:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1327:   /* ---------------------------------------- */
    1328:   MatSetOptionsPrefix(ptap->Rd,prefix);
    1329:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
    1330:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
    1331:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
    1332:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

    1334:   /* receives coj are complete */
    1335:   for (i=0; i<nrecv; i++) {
    1336:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1337:   }
    1338:   PetscFree(rwaits);
    1339:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1341:   /* add received column indices into ta to update Crmax */
    1342:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

    1344:   /* create and initialize a linked list */
    1345:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
    1346:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

    1348:   for (k=0; k<nrecv; k++) {/* k-th received message */
    1349:     Jptr = buf_rj[k];
    1350:     for (j=0; j<len_r[k]; j++) {
    1351:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1352:     }
    1353:   }
    1354:   PetscTableGetCount(ta,&Crmax);
    1355:   PetscTableDestroy(&ta);

    1357:   /* (4) send and recv coi */
    1358:   /*-----------------------*/
    1359:   PetscCommGetNewTag(comm,&tagi);
    1360:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
    1361:   PetscMalloc1(len+1,&buf_s);
    1362:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1363:   for (proc=0,k=0; proc<size; proc++) {
    1364:     if (!len_s[proc]) continue;
    1365:     /* form outgoing message for i-structure:
    1366:          buf_si[0]:                 nrows to be sent
    1367:                [1:nrows]:           row index (global)
    1368:                [nrows+1:2*nrows+1]: i-structure index
    1369:     */
    1370:     /*-------------------------------------------*/
    1371:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
    1372:     buf_si_i    = buf_si + nrows+1;
    1373:     buf_si[0]   = nrows;
    1374:     buf_si_i[0] = 0;
    1375:     nrows       = 0;
    1376:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1377:       nzi = coi[i+1] - coi[i];
    1378:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1379:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1380:       nrows++;
    1381:     }
    1382:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1383:     k++;
    1384:     buf_si += len_si[proc];
    1385:   }
    1386:   for (i=0; i<nrecv; i++) {
    1387:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1388:   }
    1389:   PetscFree(rwaits);
    1390:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1392:   PetscFree4(len_s,len_si,sstatus,owners_co);
    1393:   PetscFree(len_ri);
    1394:   PetscFree(swaits);
    1395:   PetscFree(buf_s);

    1397:   /* (5) compute the local portion of C      */
    1398:   /* ------------------------------------------ */
    1399:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
    1400:   PetscFreeSpaceGet(Crmax,&free_space);
    1401:   current_space = free_space;

    1403:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
    1404:   for (k=0; k<nrecv; k++) {
    1405:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1406:     nrows       = *buf_ri_k[k];
    1407:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1408:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1409:   }

    1411:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
    1412:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
    1413:   for (i=0; i<pn; i++) {
    1414:     /* add C_loc into C */
    1415:     nzi  = c_loc->i[i+1] - c_loc->i[i];
    1416:     Jptr = c_loc->j + c_loc->i[i];
    1417:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

    1419:     /* add received col data into lnk */
    1420:     for (k=0; k<nrecv; k++) { /* k-th received message */
    1421:       if (i == *nextrow[k]) { /* i-th row */
    1422:         nzi  = *(nextci[k]+1) - *nextci[k];
    1423:         Jptr = buf_rj[k] + *nextci[k];
    1424:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1425:         nextrow[k]++; nextci[k]++;
    1426:       }
    1427:     }
    1428:     nzi = lnk[0];

    1430:     /* copy data into free space, then initialize lnk */
    1431:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
    1432:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
    1433:   }
    1434:   PetscFree3(buf_ri_k,nextrow,nextci);
    1435:   PetscLLDestroy(lnk,lnkbt);
    1436:   PetscFreeSpaceDestroy(free_space);

    1438:   /* local sizes and preallocation */
    1439:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
    1440:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
    1441:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
    1442:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1443:   MatPreallocateFinalize(dnz,onz);

    1445:   /* add C_loc and C_oth to C */
    1446:   MatGetOwnershipRange(C,&rstart,NULL);
    1447:   for (i=0; i<pn; i++) {
    1448:     const PetscInt ncols = c_loc->i[i+1] - c_loc->i[i];
    1449:     const PetscInt *cols = c_loc->j + c_loc->i[i];
    1450:     const PetscInt row = rstart + i;
    1451:     MatSetValues(C,1,&row,ncols,cols,NULL,INSERT_VALUES);
    1452:   }
    1453:   for (i=0; i<con; i++) {
    1454:     const PetscInt ncols = c_oth->i[i+1] - c_oth->i[i];
    1455:     const PetscInt *cols = c_oth->j + c_oth->i[i];
    1456:     const PetscInt row = prmap[i];
    1457:     MatSetValues(C,1,&row,ncols,cols,NULL,INSERT_VALUES);
    1458:   }
    1459:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1460:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1461:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1463:   /* members in merge */
    1464:   PetscFree(id_r);
    1465:   PetscFree(len_r);
    1466:   PetscFree(buf_ri[0]);
    1467:   PetscFree(buf_ri);
    1468:   PetscFree(buf_rj[0]);
    1469:   PetscFree(buf_rj);
    1470:   PetscLayoutDestroy(&rowmap);

    1472:   /* attach the supporting struct to C for reuse */
    1473:   C->product->data    = ptap;
    1474:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    1475:   return(0);
    1476: }

    1478: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    1479: {
    1480:   PetscErrorCode    ierr;
    1481:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
    1482:   Mat_SeqAIJ        *c_seq;
    1483:   Mat_APMPI         *ptap;
    1484:   Mat               A_loc,C_loc,C_oth;
    1485:   PetscInt          i,rstart,rend,cm,ncols,row;
    1486:   const PetscInt    *cols;
    1487:   const PetscScalar *vals;

    1490:   MatCheckProduct(C,3);
    1491:   ptap = (Mat_APMPI*)C->product->data;
    1492:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1493:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1494:   MatZeroEntries(C);

    1496:   if (ptap->reuse == MAT_REUSE_MATRIX) {
    1497:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1498:     /* 1) get R = Pd^T, Ro = Po^T */
    1499:     /*----------------------------*/
    1500:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
    1501:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

    1503:     /* 2) compute numeric A_loc */
    1504:     /*--------------------------*/
    1505:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
    1506:   }

    1508:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1509:   A_loc = ptap->A_loc;
    1510:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
    1511:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
    1512:   C_loc = ptap->C_loc;
    1513:   C_oth = ptap->C_oth;

    1515:   /* add C_loc and C_oth to C */
    1516:   MatGetOwnershipRange(C,&rstart,&rend);

    1518:   /* C_loc -> C */
    1519:   cm    = C_loc->rmap->N;
    1520:   c_seq = (Mat_SeqAIJ*)C_loc->data;
    1521:   cols = c_seq->j;
    1522:   vals = c_seq->a;
    1523:   for (i=0; i<cm; i++) {
    1524:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1525:     row = rstart + i;
    1526:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1527:     cols += ncols; vals += ncols;
    1528:   }

    1530:   /* Co -> C, off-processor part */
    1531:   cm    = C_oth->rmap->N;
    1532:   c_seq = (Mat_SeqAIJ*)C_oth->data;
    1533:   cols  = c_seq->j;
    1534:   vals  = c_seq->a;
    1535:   for (i=0; i<cm; i++) {
    1536:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1537:     row = p->garray[i];
    1538:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1539:     cols += ncols; vals += ncols;
    1540:   }
    1541:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1542:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1543:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1545:   ptap->reuse = MAT_REUSE_MATRIX;
    1546:   return(0);
    1547: }

    1549: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1550: {
    1551:   PetscErrorCode      ierr;
    1552:   Mat_Merge_SeqsToMPI *merge;
    1553:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
    1554:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1555:   Mat_APMPI           *ptap;
    1556:   PetscInt            *adj;
    1557:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1558:   MatScalar           *ada,*ca,valtmp;
    1559:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1560:   MPI_Comm            comm;
    1561:   PetscMPIInt         size,rank,taga,*len_s;
    1562:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1563:   PetscInt            **buf_ri,**buf_rj;
    1564:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1565:   MPI_Request         *s_waits,*r_waits;
    1566:   MPI_Status          *status;
    1567:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1568:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
    1569:   Mat                 A_loc;
    1570:   Mat_SeqAIJ          *a_loc;

    1573:   MatCheckProduct(C,3);
    1574:   ptap = (Mat_APMPI*)C->product->data;
    1575:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1576:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1577:   PetscObjectGetComm((PetscObject)C,&comm);
    1578:   MPI_Comm_size(comm,&size);
    1579:   MPI_Comm_rank(comm,&rank);

    1581:   merge = ptap->merge;

    1583:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1584:   /*------------------------------------------*/
    1585:   /* get data from symbolic products */
    1586:   coi    = merge->coi; coj = merge->coj;
    1587:   PetscCalloc1(coi[pon]+1,&coa);
    1588:   bi     = merge->bi; bj = merge->bj;
    1589:   owners = merge->rowmap->range;
    1590:   PetscCalloc1(bi[cm]+1,&ba);

    1592:   /* get A_loc by taking all local rows of A */
    1593:   A_loc = ptap->A_loc;
    1594:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1595:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1596:   ai    = a_loc->i;
    1597:   aj    = a_loc->j;

    1599:   for (i=0; i<am; i++) {
    1600:     anz = ai[i+1] - ai[i];
    1601:     adj = aj + ai[i];
    1602:     ada = a_loc->a + ai[i];

    1604:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1605:     /*-------------------------------------------------------------*/
    1606:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1607:     pnz = po->i[i+1] - po->i[i];
    1608:     poJ = po->j + po->i[i];
    1609:     pA  = po->a + po->i[i];
    1610:     for (j=0; j<pnz; j++) {
    1611:       row = poJ[j];
    1612:       cj  = coj + coi[row];
    1613:       ca  = coa + coi[row];
    1614:       /* perform sparse axpy */
    1615:       nexta  = 0;
    1616:       valtmp = pA[j];
    1617:       for (k=0; nexta<anz; k++) {
    1618:         if (cj[k] == adj[nexta]) {
    1619:           ca[k] += valtmp*ada[nexta];
    1620:           nexta++;
    1621:         }
    1622:       }
    1623:       PetscLogFlops(2.0*anz);
    1624:     }

    1626:     /* put the value into Cd (diagonal part) */
    1627:     pnz = pd->i[i+1] - pd->i[i];
    1628:     pdJ = pd->j + pd->i[i];
    1629:     pA  = pd->a + pd->i[i];
    1630:     for (j=0; j<pnz; j++) {
    1631:       row = pdJ[j];
    1632:       cj  = bj + bi[row];
    1633:       ca  = ba + bi[row];
    1634:       /* perform sparse axpy */
    1635:       nexta  = 0;
    1636:       valtmp = pA[j];
    1637:       for (k=0; nexta<anz; k++) {
    1638:         if (cj[k] == adj[nexta]) {
    1639:           ca[k] += valtmp*ada[nexta];
    1640:           nexta++;
    1641:         }
    1642:       }
    1643:       PetscLogFlops(2.0*anz);
    1644:     }
    1645:   }

    1647:   /* 3) send and recv matrix values coa */
    1648:   /*------------------------------------*/
    1649:   buf_ri = merge->buf_ri;
    1650:   buf_rj = merge->buf_rj;
    1651:   len_s  = merge->len_s;
    1652:   PetscCommGetNewTag(comm,&taga);
    1653:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1655:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1656:   for (proc=0,k=0; proc<size; proc++) {
    1657:     if (!len_s[proc]) continue;
    1658:     i    = merge->owners_co[proc];
    1659:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1660:     k++;
    1661:   }
    1662:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1663:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1665:   PetscFree2(s_waits,status);
    1666:   PetscFree(r_waits);
    1667:   PetscFree(coa);

    1669:   /* 4) insert local Cseq and received values into Cmpi */
    1670:   /*----------------------------------------------------*/
    1671:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1672:   for (k=0; k<merge->nrecv; k++) {
    1673:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1674:     nrows       = *(buf_ri_k[k]);
    1675:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1676:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1677:   }

    1679:   for (i=0; i<cm; i++) {
    1680:     row  = owners[rank] + i; /* global row index of C_seq */
    1681:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1682:     ba_i = ba + bi[i];
    1683:     bnz  = bi[i+1] - bi[i];
    1684:     /* add received vals into ba */
    1685:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1686:       /* i-th row */
    1687:       if (i == *nextrow[k]) {
    1688:         cnz    = *(nextci[k]+1) - *nextci[k];
    1689:         cj     = buf_rj[k] + *(nextci[k]);
    1690:         ca     = abuf_r[k] + *(nextci[k]);
    1691:         nextcj = 0;
    1692:         for (j=0; nextcj<cnz; j++) {
    1693:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1694:             ba_i[j] += ca[nextcj++];
    1695:           }
    1696:         }
    1697:         nextrow[k]++; nextci[k]++;
    1698:         PetscLogFlops(2.0*cnz);
    1699:       }
    1700:     }
    1701:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1702:   }
    1703:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1704:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1706:   PetscFree(ba);
    1707:   PetscFree(abuf_r[0]);
    1708:   PetscFree(abuf_r);
    1709:   PetscFree3(buf_ri_k,nextrow,nextci);
    1710:   return(0);
    1711: }

    1713: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
    1714: {
    1715:   PetscErrorCode      ierr;
    1716:   Mat                 A_loc,POt,PDt;
    1717:   Mat_APMPI           *ptap;
    1718:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1719:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
    1720:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1721:   PetscInt            nnz;
    1722:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1723:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1724:   MPI_Comm            comm;
    1725:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1726:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1727:   PetscInt            len,proc,*dnz,*onz,*owners;
    1728:   PetscInt            nzi,*bi,*bj;
    1729:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1730:   MPI_Request         *swaits,*rwaits;
    1731:   MPI_Status          *sstatus,rstatus;
    1732:   Mat_Merge_SeqsToMPI *merge;
    1733:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1734:   PetscReal           afill  =1.0,afill_tmp;
    1735:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1736:   Mat_SeqAIJ          *a_loc,*pdt,*pot;
    1737:   PetscTable          ta;
    1738:   MatType             mtype;

    1741:   PetscObjectGetComm((PetscObject)A,&comm);
    1742:   /* check if matrix local sizes are compatible */
    1743:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);

    1745:   MPI_Comm_size(comm,&size);
    1746:   MPI_Comm_rank(comm,&rank);

    1748:   /* create struct Mat_APMPI and attached it to C later */
    1749:   PetscNew(&ptap);

    1751:   /* get A_loc by taking all local rows of A */
    1752:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1754:   ptap->A_loc = A_loc;
    1755:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1756:   ai          = a_loc->i;
    1757:   aj          = a_loc->j;

    1759:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1760:   /*----------------------------------------------------*/
    1761:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1762:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1763:   pdti = pdt->i; pdtj = pdt->j;

    1765:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1766:   pot  = (Mat_SeqAIJ*)POt->data;
    1767:   poti = pot->i; potj = pot->j;

    1769:   /* then, compute symbolic Co = (p->B)^T*A */
    1770:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1771:                          >= (num of nonzero rows of C_seq) - pn */
    1772:   PetscMalloc1(pon+1,&coi);
    1773:   coi[0] = 0;

    1775:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1776:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1777:   PetscFreeSpaceGet(nnz,&free_space);
    1778:   current_space = free_space;

    1780:   /* create and initialize a linked list */
    1781:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
    1782:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1783:   PetscTableGetCount(ta,&Armax);

    1785:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1787:   for (i=0; i<pon; i++) {
    1788:     pnz = poti[i+1] - poti[i];
    1789:     ptJ = potj + poti[i];
    1790:     for (j=0; j<pnz; j++) {
    1791:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1792:       anz  = ai[row+1] - ai[row];
    1793:       Jptr = aj + ai[row];
    1794:       /* add non-zero cols of AP into the sorted linked list lnk */
    1795:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1796:     }
    1797:     nnz = lnk[0];

    1799:     /* If free space is not available, double the total space in the list */
    1800:     if (current_space->local_remaining<nnz) {
    1801:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1802:       nspacedouble++;
    1803:     }

    1805:     /* Copy data into free space, and zero out denserows */
    1806:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1808:     current_space->array           += nnz;
    1809:     current_space->local_used      += nnz;
    1810:     current_space->local_remaining -= nnz;

    1812:     coi[i+1] = coi[i] + nnz;
    1813:   }

    1815:   PetscMalloc1(coi[pon]+1,&coj);
    1816:   PetscFreeSpaceContiguous(&free_space,coj);
    1817:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1819:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1820:   if (afill_tmp > afill) afill = afill_tmp;

    1822:   /* send j-array (coj) of Co to other processors */
    1823:   /*----------------------------------------------*/
    1824:   /* determine row ownership */
    1825:   PetscNew(&merge);
    1826:   PetscLayoutCreate(comm,&merge->rowmap);

    1828:   merge->rowmap->n  = pn;
    1829:   merge->rowmap->bs = 1;

    1831:   PetscLayoutSetUp(merge->rowmap);
    1832:   owners = merge->rowmap->range;

    1834:   /* determine the number of messages to send, their lengths */
    1835:   PetscCalloc1(size,&len_si);
    1836:   PetscCalloc1(size,&merge->len_s);

    1838:   len_s        = merge->len_s;
    1839:   merge->nsend = 0;

    1841:   PetscMalloc1(size+2,&owners_co);

    1843:   proc = 0;
    1844:   for (i=0; i<pon; i++) {
    1845:     while (prmap[i] >= owners[proc+1]) proc++;
    1846:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1847:     len_s[proc] += coi[i+1] - coi[i];
    1848:   }

    1850:   len          = 0; /* max length of buf_si[] */
    1851:   owners_co[0] = 0;
    1852:   for (proc=0; proc<size; proc++) {
    1853:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1854:     if (len_si[proc]) {
    1855:       merge->nsend++;
    1856:       len_si[proc] = 2*(len_si[proc] + 1);
    1857:       len         += len_si[proc];
    1858:     }
    1859:   }

    1861:   /* determine the number and length of messages to receive for coi and coj  */
    1862:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1863:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1865:   /* post the Irecv and Isend of coj */
    1866:   PetscCommGetNewTag(comm,&tagj);
    1867:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1868:   PetscMalloc1(merge->nsend+1,&swaits);
    1869:   for (proc=0, k=0; proc<size; proc++) {
    1870:     if (!len_s[proc]) continue;
    1871:     i    = owners_co[proc];
    1872:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1873:     k++;
    1874:   }

    1876:   /* receives and sends of coj are complete */
    1877:   PetscMalloc1(size,&sstatus);
    1878:   for (i=0; i<merge->nrecv; i++) {
    1879:     PETSC_UNUSED PetscMPIInt icompleted;
    1880:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1881:   }
    1882:   PetscFree(rwaits);
    1883:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1885:   /* add received column indices into table to update Armax */
    1886:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    1887:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    1888:     Jptr = buf_rj[k];
    1889:     for (j=0; j<merge->len_r[k]; j++) {
    1890:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1891:     }
    1892:   }
    1893:   PetscTableGetCount(ta,&Armax);
    1894:   /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */

    1896:   /* send and recv coi */
    1897:   /*-------------------*/
    1898:   PetscCommGetNewTag(comm,&tagi);
    1899:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1900:   PetscMalloc1(len+1,&buf_s);
    1901:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1902:   for (proc=0,k=0; proc<size; proc++) {
    1903:     if (!len_s[proc]) continue;
    1904:     /* form outgoing message for i-structure:
    1905:          buf_si[0]:                 nrows to be sent
    1906:                [1:nrows]:           row index (global)
    1907:                [nrows+1:2*nrows+1]: i-structure index
    1908:     */
    1909:     /*-------------------------------------------*/
    1910:     nrows       = len_si[proc]/2 - 1;
    1911:     buf_si_i    = buf_si + nrows+1;
    1912:     buf_si[0]   = nrows;
    1913:     buf_si_i[0] = 0;
    1914:     nrows       = 0;
    1915:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1916:       nzi               = coi[i+1] - coi[i];
    1917:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1918:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1919:       nrows++;
    1920:     }
    1921:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1922:     k++;
    1923:     buf_si += len_si[proc];
    1924:   }
    1925:   i = merge->nrecv;
    1926:   while (i--) {
    1927:     PETSC_UNUSED PetscMPIInt icompleted;
    1928:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1929:   }
    1930:   PetscFree(rwaits);
    1931:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1932:   PetscFree(len_si);
    1933:   PetscFree(len_ri);
    1934:   PetscFree(swaits);
    1935:   PetscFree(sstatus);
    1936:   PetscFree(buf_s);

    1938:   /* compute the local portion of C (mpi mat) */
    1939:   /*------------------------------------------*/
    1940:   /* allocate bi array and free space for accumulating nonzero column info */
    1941:   PetscMalloc1(pn+1,&bi);
    1942:   bi[0] = 0;

    1944:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1945:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    1946:   PetscFreeSpaceGet(nnz,&free_space);
    1947:   current_space = free_space;

    1949:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1950:   for (k=0; k<merge->nrecv; k++) {
    1951:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1952:     nrows       = *buf_ri_k[k];
    1953:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1954:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    1955:   }

    1957:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    1958:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1959:   rmax = 0;
    1960:   for (i=0; i<pn; i++) {
    1961:     /* add pdt[i,:]*AP into lnk */
    1962:     pnz = pdti[i+1] - pdti[i];
    1963:     ptJ = pdtj + pdti[i];
    1964:     for (j=0; j<pnz; j++) {
    1965:       row  = ptJ[j];  /* row of AP == col of Pt */
    1966:       anz  = ai[row+1] - ai[row];
    1967:       Jptr = aj + ai[row];
    1968:       /* add non-zero cols of AP into the sorted linked list lnk */
    1969:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1970:     }

    1972:     /* add received col data into lnk */
    1973:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1974:       if (i == *nextrow[k]) { /* i-th row */
    1975:         nzi  = *(nextci[k]+1) - *nextci[k];
    1976:         Jptr = buf_rj[k] + *nextci[k];
    1977:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    1978:         nextrow[k]++; nextci[k]++;
    1979:       }
    1980:     }
    1981:     nnz = lnk[0];

    1983:     /* if free space is not available, make more free space */
    1984:     if (current_space->local_remaining<nnz) {
    1985:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1986:       nspacedouble++;
    1987:     }
    1988:     /* copy data into free space, then initialize lnk */
    1989:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    1990:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    1992:     current_space->array           += nnz;
    1993:     current_space->local_used      += nnz;
    1994:     current_space->local_remaining -= nnz;

    1996:     bi[i+1] = bi[i] + nnz;
    1997:     if (nnz > rmax) rmax = nnz;
    1998:   }
    1999:   PetscFree3(buf_ri_k,nextrow,nextci);

    2001:   PetscMalloc1(bi[pn]+1,&bj);
    2002:   PetscFreeSpaceContiguous(&free_space,bj);
    2003:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    2004:   if (afill_tmp > afill) afill = afill_tmp;
    2005:   PetscLLCondensedDestroy_Scalable(lnk);
    2006:   PetscTableDestroy(&ta);

    2008:   MatDestroy(&POt);
    2009:   MatDestroy(&PDt);

    2011:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2012:   /*-------------------------------------------------------------------------------*/
    2013:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    2014:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    2015:   MatGetType(A,&mtype);
    2016:   MatSetType(C,mtype);
    2017:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    2018:   MatPreallocateFinalize(dnz,onz);
    2019:   MatSetBlockSize(C,1);
    2020:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    2021:   for (i=0; i<pn; i++) {
    2022:     row  = i + rstart;
    2023:     nnz  = bi[i+1] - bi[i];
    2024:     Jptr = bj + bi[i];
    2025:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
    2026:   }
    2027:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    2028:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    2029:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    2030:   merge->bi        = bi;
    2031:   merge->bj        = bj;
    2032:   merge->coi       = coi;
    2033:   merge->coj       = coj;
    2034:   merge->buf_ri    = buf_ri;
    2035:   merge->buf_rj    = buf_rj;
    2036:   merge->owners_co = owners_co;

    2038:   /* attach the supporting struct to C for reuse */
    2039:   C->product->data    = ptap;
    2040:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2041:   ptap->merge         = merge;

    2043:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

    2045: #if defined(PETSC_USE_INFO)
    2046:   if (bi[pn] != 0) {
    2047:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    2048:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    2049:   } else {
    2050:     PetscInfo(C,"Empty matrix product\n");
    2051:   }
    2052: #endif
    2053:   return(0);
    2054: }

    2056: /* ---------------------------------------------------------------- */
    2057: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2058: {
    2060:   Mat_Product    *product = C->product;
    2061:   Mat            A=product->A,B=product->B;
    2062:   PetscReal      fill=product->fill;
    2063:   PetscBool      flg;

    2066:   /* scalable */
    2067:   PetscStrcmp(product->alg,"scalable",&flg);
    2068:   if (flg) {
    2069:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
    2070:     goto next;
    2071:   }

    2073:   /* nonscalable */
    2074:   PetscStrcmp(product->alg,"nonscalable",&flg);
    2075:   if (flg) {
    2076:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
    2077:     goto next;
    2078:   }

    2080:   /* matmatmult */
    2081:   PetscStrcmp(product->alg,"at*b",&flg);
    2082:   if (flg) {
    2083:     Mat       At;
    2084:     Mat_APMPI *ptap;

    2086:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
    2087:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
    2088:     ptap = (Mat_APMPI*)C->product->data;
    2089:     if (ptap) {
    2090:       ptap->Pt = At;
    2091:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2092:     }
    2093:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2094:     goto next;
    2095:   }

    2097:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

    2099: next:
    2100:   C->ops->productnumeric = MatProductNumeric_AtB;
    2101:   return(0);
    2102: }

    2104: /* ---------------------------------------------------------------- */
    2105: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2106: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2107: {
    2109:   Mat_Product    *product = C->product;
    2110:   Mat            A=product->A,B=product->B;
    2111: #if defined(PETSC_HAVE_HYPRE)
    2112:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
    2113:   PetscInt       nalg = 4;
    2114: #else
    2115:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2116:   PetscInt       nalg = 3;
    2117: #endif
    2118:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
    2119:   PetscBool      flg;
    2120:   MPI_Comm       comm;

    2123:   /* Check matrix local sizes */
    2124:   PetscObjectGetComm((PetscObject)C,&comm);
    2125:   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);

    2127:   /* Set "nonscalable" as default algorithm */
    2128:   PetscStrcmp(C->product->alg,"default",&flg);
    2129:   if (flg) {
    2130:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2132:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2133:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2134:       MatInfo     Ainfo,Binfo;
    2135:       PetscInt    nz_local;
    2136:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2138:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2139:       MatGetInfo(B,MAT_LOCAL,&Binfo);
    2140:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2142:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2143:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2145:       if (alg_scalable) {
    2146:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2147:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2148:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2149:       }
    2150:     }
    2151:   }

    2153:   /* Get runtime option */
    2154:   if (product->api_user) {
    2155:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
    2156:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2157:     PetscOptionsEnd();
    2158:   } else {
    2159:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
    2160:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2161:     PetscOptionsEnd();
    2162:   }
    2163:   if (flg) {
    2164:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2165:   }

    2167:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2168:   return(0);
    2169: }

    2171: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2172: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2173: {
    2175:   Mat_Product    *product = C->product;
    2176:   Mat            A=product->A,B=product->B;
    2177:   const char     *algTypes[3] = {"scalable","nonscalable","at*b"};
    2178:   PetscInt       nalg = 3;
    2179:   PetscInt       alg = 1; /* set default algorithm  */
    2180:   PetscBool      flg;
    2181:   MPI_Comm       comm;

    2184:   /* Check matrix local sizes */
    2185:   PetscObjectGetComm((PetscObject)C,&comm);
    2186:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != B (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);

    2188:   /* Set default algorithm */
    2189:   PetscStrcmp(C->product->alg,"default",&flg);
    2190:   if (flg) {
    2191:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2192:   }

    2194:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2195:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2196:     MatInfo     Ainfo,Binfo;
    2197:     PetscInt    nz_local;
    2198:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2200:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2201:     MatGetInfo(B,MAT_LOCAL,&Binfo);
    2202:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2204:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2205:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2207:     if (alg_scalable) {
    2208:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2209:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2210:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2211:     }
    2212:   }

    2214:   /* Get runtime option */
    2215:   if (product->api_user) {
    2216:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
    2217:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2218:     PetscOptionsEnd();
    2219:   } else {
    2220:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
    2221:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2222:     PetscOptionsEnd();
    2223:   }
    2224:   if (flg) {
    2225:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2226:   }

    2228:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2229:   return(0);
    2230: }

    2232: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2233: {
    2235:   Mat_Product    *product = C->product;
    2236:   Mat            A=product->A,P=product->B;
    2237:   MPI_Comm       comm;
    2238:   PetscBool      flg;
    2239:   PetscInt       alg=1; /* set default algorithm */
    2240: #if !defined(PETSC_HAVE_HYPRE)
    2241:   const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
    2242:   PetscInt       nalg=4;
    2243: #else
    2244:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
    2245:   PetscInt       nalg=5;
    2246: #endif
    2247:   PetscInt       pN=P->cmap->N;

    2250:   /* Check matrix local sizes */
    2251:   PetscObjectGetComm((PetscObject)C,&comm);
    2252:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,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);
    2253:   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,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);

    2255:   /* Set "nonscalable" as default algorithm */
    2256:   PetscStrcmp(C->product->alg,"default",&flg);
    2257:   if (flg) {
    2258:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2260:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2261:     if (pN > 100000) {
    2262:       MatInfo     Ainfo,Pinfo;
    2263:       PetscInt    nz_local;
    2264:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2266:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2267:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
    2268:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2270:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2271:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2273:       if (alg_scalable) {
    2274:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2275:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2276:       }
    2277:     }
    2278:   }

    2280:   /* Get runtime option */
    2281:   if (product->api_user) {
    2282:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
    2283:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2284:     PetscOptionsEnd();
    2285:   } else {
    2286:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
    2287:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2288:     PetscOptionsEnd();
    2289:   }
    2290:   if (flg) {
    2291:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2292:   }

    2294:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2295:   return(0);
    2296: }

    2298: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2299: {
    2300:   Mat_Product *product = C->product;
    2301:   Mat         A = product->A,R=product->B;

    2304:   /* Check matrix local sizes */
    2305:   if (A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%D, %D), R local (%D,%D)",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);

    2307:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2308:   return(0);
    2309: }

    2311: /*
    2312:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2313: */
    2314: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2315: {
    2317:   Mat_Product    *product = C->product;
    2318:   PetscBool      flg = PETSC_FALSE;
    2319:   PetscInt       alg = 1; /* default algorithm */
    2320:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2321:   PetscInt       nalg = 3;

    2324:   /* Set default algorithm */
    2325:   PetscStrcmp(C->product->alg,"default",&flg);
    2326:   if (flg) {
    2327:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2328:   }

    2330:   /* Get runtime option */
    2331:   if (product->api_user) {
    2332:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
    2333:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2334:     PetscOptionsEnd();
    2335:   } else {
    2336:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
    2337:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
    2338:     PetscOptionsEnd();
    2339:   }
    2340:   if (flg) {
    2341:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2342:   }

    2344:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2345:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2346:   return(0);
    2347: }

    2349: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2350: {
    2352:   Mat_Product    *product = C->product;

    2355:   switch (product->type) {
    2356:   case MATPRODUCT_AB:
    2357:     MatProductSetFromOptions_MPIAIJ_AB(C);
    2358:     break;
    2359:   case MATPRODUCT_AtB:
    2360:     MatProductSetFromOptions_MPIAIJ_AtB(C);
    2361:     break;
    2362:   case MATPRODUCT_PtAP:
    2363:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
    2364:     break;
    2365:   case MATPRODUCT_RARt:
    2366:     MatProductSetFromOptions_MPIAIJ_RARt(C);
    2367:     break;
    2368:   case MATPRODUCT_ABC:
    2369:     MatProductSetFromOptions_MPIAIJ_ABC(C);
    2370:     break;
    2371:   default:
    2372:     break;
    2373:   }
    2374:   return(0);
    2375: }