Date: 2022-03-04T17:37:46+00:00

Actual source code: mpimatmatmult.c

      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/sfimpl.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:   /* backend general code */
     50:   PetscStrcmp(alg,"backend",&flg);
     51:   if (flg) {
     52:     MatProductSymbolic_MPIAIJBACKEND(C);
     53:     return(0);
     54:   }

     56: #if defined(PETSC_HAVE_HYPRE)
     57:   PetscStrcmp(alg,"hypre",&flg);
     58:   if (flg) {
     59:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     60:     return(0);
     61:   }
     62: #endif
     63:   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
     64: }

     66: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
     67: {
     69:   Mat_APMPI      *ptap = (Mat_APMPI*)data;

     72:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     73:   PetscFree(ptap->bufa);
     74:   MatDestroy(&ptap->P_loc);
     75:   MatDestroy(&ptap->P_oth);
     76:   MatDestroy(&ptap->Pt);
     77:   PetscFree(ptap->api);
     78:   PetscFree(ptap->apj);
     79:   PetscFree(ptap->apa);
     80:   PetscFree(ptap);
     81:   return(0);
     82: }

     84: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
     85: {
     86:   PetscErrorCode    ierr;
     87:   Mat_MPIAIJ        *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
     88:   Mat_SeqAIJ        *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
     89:   Mat_SeqAIJ        *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
     90:   PetscScalar       *cda=cd->a,*coa=co->a;
     91:   Mat_SeqAIJ        *p_loc,*p_oth;
     92:   PetscScalar       *apa,*ca;
     93:   PetscInt          cm =C->rmap->n;
     94:   Mat_APMPI         *ptap;
     95:   PetscInt          *api,*apj,*apJ,i,k;
     96:   PetscInt          cstart=C->cmap->rstart;
     97:   PetscInt          cdnz,conz,k0,k1;
     98:   const PetscScalar *dummy;
     99:   MPI_Comm          comm;
    100:   PetscMPIInt       size;

    103:   MatCheckProduct(C,3);
    104:   ptap = (Mat_APMPI*)C->product->data;
    105:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    106:   PetscObjectGetComm((PetscObject)A,&comm);
    107:   MPI_Comm_size(comm,&size);

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

    111:   /* flag CPU mask for C */
    112: #if defined(PETSC_HAVE_DEVICE)
    113:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    114:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
    115:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
    116: #endif

    118:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    119:   /*-----------------------------------------------------*/
    120:   /* update numerical values of P_oth and P_loc */
    121:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    122:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    124:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    125:   /*----------------------------------------------------------*/
    126:   /* get data from symbolic products */
    127:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    128:   p_oth = NULL;
    129:   if (size >1) {
    130:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    131:   }

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

    136:   api = ptap->api;
    137:   apj = ptap->apj;
    138:   /* trigger copy to CPU */
    139:   MatSeqAIJGetArrayRead(a->A,&dummy);
    140:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
    141:   MatSeqAIJGetArrayRead(a->B,&dummy);
    142:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
    143:   for (i=0; i<cm; i++) {
    144:     /* compute apa = A[i,:]*P */
    145:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

    147:     /* set values in C */
    148:     apJ  = apj + api[i];
    149:     cdnz = cd->i[i+1] - cd->i[i];
    150:     conz = co->i[i+1] - co->i[i];

    152:     /* 1st off-diagonal part of C */
    153:     ca = coa + co->i[i];
    154:     k  = 0;
    155:     for (k0=0; k0<conz; k0++) {
    156:       if (apJ[k] >= cstart) break;
    157:       ca[k0]      = apa[apJ[k]];
    158:       apa[apJ[k++]] = 0.0;
    159:     }

    161:     /* diagonal part of C */
    162:     ca = cda + cd->i[i];
    163:     for (k1=0; k1<cdnz; k1++) {
    164:       ca[k1]      = apa[apJ[k]];
    165:       apa[apJ[k++]] = 0.0;
    166:     }

    168:     /* 2nd off-diagonal part of C */
    169:     ca = coa + co->i[i];
    170:     for (; k0<conz; k0++) {
    171:       ca[k0]      = apa[apJ[k]];
    172:       apa[apJ[k++]] = 0.0;
    173:     }
    174:   }
    175:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    176:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    177:   return(0);
    178: }

    180: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
    181: {
    182:   PetscErrorCode     ierr;
    183:   MPI_Comm           comm;
    184:   PetscMPIInt        size;
    185:   Mat_APMPI          *ptap;
    186:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    187:   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
    188:   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    189:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    190:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    191:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
    192:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
    193:   PetscBT            lnkbt;
    194:   PetscReal          afill;
    195:   MatType            mtype;

    198:   MatCheckProduct(C,4);
    199:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    200:   PetscObjectGetComm((PetscObject)A,&comm);
    201:   MPI_Comm_size(comm,&size);

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

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

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

    212:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    213:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    214:   if (size > 1) {
    215:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    216:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    217:   } else {
    218:     p_oth = NULL;
    219:     pi_oth = NULL; pj_oth = NULL;
    220:   }

    222:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    223:   /*-------------------------------------------------------------------*/
    224:   PetscMalloc1(am+2,&api);
    225:   ptap->api = api;
    226:   api[0]    = 0;

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

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

    235:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    236:   for (i=0; i<am; i++) {
    237:     /* diagonal portion of A */
    238:     nzi = adi[i+1] - adi[i];
    239:     for (j=0; j<nzi; j++) {
    240:       row  = *adj++;
    241:       pnz  = pi_loc[row+1] - pi_loc[row];
    242:       Jptr = pj_loc + pi_loc[row];
    243:       /* add non-zero cols of P into the sorted linked list lnk */
    244:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    245:     }
    246:     /* off-diagonal portion of A */
    247:     nzi = aoi[i+1] - aoi[i];
    248:     for (j=0; j<nzi; j++) {
    249:       row  = *aoj++;
    250:       pnz  = pi_oth[row+1] - pi_oth[row];
    251:       Jptr = pj_oth + pi_oth[row];
    252:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    253:     }
    254:     /* add possible missing diagonal entry */
    255:     if (C->force_diagonals) {
    256:       j = i + rstart; /* column index */
    257:       PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);
    258:     }

    260:     apnz     = lnk[0];
    261:     api[i+1] = api[i] + apnz;

    263:     /* if free space is not available, double the total space in the list */
    264:     if (current_space->local_remaining<apnz) {
    265:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    266:       nspacedouble++;
    267:     }

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

    273:     current_space->array           += apnz;
    274:     current_space->local_used      += apnz;
    275:     current_space->local_remaining -= apnz;
    276:   }

    278:   /* Allocate space for apj, initialize apj, and */
    279:   /* destroy list of free space and other temporary array(s) */
    280:   PetscMalloc1(api[am]+1,&ptap->apj);
    281:   apj  = ptap->apj;
    282:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    283:   PetscLLDestroy(lnk,lnkbt);

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

    288:   /* set and assemble symbolic parallel matrix C */
    289:   /*---------------------------------------------*/
    290:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    291:   MatSetBlockSizesFromMats(C,A,P);

    293:   MatGetType(A,&mtype);
    294:   MatSetType(C,mtype);
    295:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    296:   MatPreallocateFinalize(dnz,onz);

    298:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    299:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    300:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    301:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    303:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    304:   C->ops->productnumeric = MatProductNumeric_AB;

    306:   /* attach the supporting struct to C for reuse */
    307:   C->product->data    = ptap;
    308:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    310:   /* set MatInfo */
    311:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    312:   if (afill < 1.0) afill = 1.0;
    313:   C->info.mallocs           = nspacedouble;
    314:   C->info.fill_ratio_given  = fill;
    315:   C->info.fill_ratio_needed = afill;

    317: #if defined(PETSC_USE_INFO)
    318:   if (api[am]) {
    319:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    320:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    321:   } else {
    322:     PetscInfo(C,"Empty matrix product\n");
    323:   }
    324: #endif
    325:   return(0);
    326: }

    328: /* ------------------------------------------------------- */
    329: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
    330: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);

    332: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
    333: {
    334:   Mat_Product *product = C->product;
    335:   Mat         A = product->A,B=product->B;

    338:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    339:     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);

    341:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
    342:   C->ops->productsymbolic = MatProductSymbolic_AB;
    343:   return(0);
    344: }
    345: /* -------------------------------------------------------------------- */
    346: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
    347: {
    348:   Mat_Product *product = C->product;
    349:   Mat         A = product->A,B=product->B;

    352:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    353:     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);

    355:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
    356:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
    357:   return(0);
    358: }

    360: /* --------------------------------------------------------------------- */
    361: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
    362: {
    364:   Mat_Product    *product = C->product;

    367:   switch (product->type) {
    368:   case MATPRODUCT_AB:
    369:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
    370:     break;
    371:   case MATPRODUCT_AtB:
    372:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
    373:     break;
    374:   default:
    375:     break;
    376:   }
    377:   return(0);
    378: }
    379: /* ------------------------------------------------------- */

    381: typedef struct {
    382:   Mat          workB,workB1;
    383:   MPI_Request  *rwaits,*swaits;
    384:   PetscInt     nsends,nrecvs;
    385:   MPI_Datatype *stype,*rtype;
    386:   PetscInt     blda;
    387: } MPIAIJ_MPIDense;

    389: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    390: {
    391:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
    392:   PetscErrorCode  ierr;
    393:   PetscInt        i;

    396:   MatDestroy(&contents->workB);
    397:   MatDestroy(&contents->workB1);
    398:   for (i=0; i<contents->nsends; i++) {
    399:     MPI_Type_free(&contents->stype[i]);
    400:   }
    401:   for (i=0; i<contents->nrecvs; i++) {
    402:     MPI_Type_free(&contents->rtype[i]);
    403:   }
    404:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
    405:   PetscFree(contents);
    406:   return(0);
    407: }

    409: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
    410: {
    411:   PetscErrorCode  ierr;
    412:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
    413:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda,m,M,n,N;
    414:   MPIAIJ_MPIDense *contents;
    415:   VecScatter      ctx=aij->Mvctx;
    416:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
    417:   MPI_Comm        comm;
    418:   MPI_Datatype    type1,*stype,*rtype;
    419:   const PetscInt  *sindices,*sstarts,*rstarts;
    420:   PetscMPIInt     *disp;
    421:   PetscBool       cisdense;

    424:   MatCheckProduct(C,4);
    425:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
    426:   PetscObjectGetComm((PetscObject)A,&comm);
    427:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
    428:   if (!cisdense) {
    429:     MatSetType(C,((PetscObject)B)->type_name);
    430:   }
    431:   MatGetLocalSize(C,&m,&n);
    432:   MatGetSize(C,&M,&N);
    433:   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
    434:     MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
    435:   }
    436:   MatSetBlockSizesFromMats(C,A,B);
    437:   MatSetUp(C);
    438:   MatDenseGetLDA(B,&blda);
    439:   MatDenseGetLDA(C,&clda);
    440:   PetscNew(&contents);

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

    445:   /* Create column block of B and C for memory scalability when BN is too large */
    446:   /* Estimate Bbn, column size of Bb */
    447:   if (nz) {
    448:     Bbn1 = 2*Am*BN/nz;
    449:     if (!Bbn1) Bbn1 = 1;
    450:   } else Bbn1 = BN;

    452:   bs = PetscAbs(B->cmap->bs);
    453:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
    454:   if (Bbn1 > BN) Bbn1 = BN;
    455:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

    457:   /* Enable runtime option for Bbn */
    458:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
    459:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
    460:   PetscOptionsEnd();
    461:   Bbn  = PetscMin(Bbn,BN);

    463:   if (Bbn > 0 && Bbn < BN) {
    464:     numBb = BN/Bbn;
    465:     Bbn1 = BN - numBb*Bbn;
    466:   } else numBb = 0;

    468:   if (numBb) {
    469:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
    470:     if (Bbn1) { /* Create workB1 for the remaining columns */
    471:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
    472:       /* Create work matrix used to store off processor rows of B needed for local product */
    473:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
    474:     } else contents->workB1 = NULL;
    475:   }

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

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

    485:   contents->rtype  = rtype;
    486:   contents->nrecvs = nrecvs;
    487:   contents->blda   = blda;

    489:   PetscMalloc1(Bm+1,&disp);
    490:   for (i=0; i<nsends; i++) {
    491:     nrows_to = sstarts[i+1]-sstarts[i];
    492:     for (j=0; j<nrows_to; j++) {
    493:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
    494:     }
    495:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

    497:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
    498:     MPI_Type_commit(&stype[i]);
    499:     MPI_Type_free(&type1);
    500:   }

    502:   for (i=0; i<nrecvs; i++) {
    503:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    504:     nrows_from = rstarts[i+1]-rstarts[i];
    505:     disp[0] = 0;
    506:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
    507:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
    508:     MPI_Type_commit(&rtype[i]);
    509:     MPI_Type_free(&type1);
    510:   }

    512:   PetscFree(disp);
    513:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    514:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
    515:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    516:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    517:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    518:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    520:   C->product->data = contents;
    521:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
    522:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    523:   return(0);
    524: }

    526: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
    527: /*
    528:     Performs an efficient scatter on the rows of B needed by this process; this is
    529:     a modification of the VecScatterBegin_() routines.

    531:     Input: Bbidx = 0: B = Bb
    532:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
    533: */
    534: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
    535: {
    536:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
    537:   PetscErrorCode    ierr;
    538:   const PetscScalar *b;
    539:   PetscScalar       *rvalues;
    540:   VecScatter        ctx = aij->Mvctx;
    541:   const PetscInt    *sindices,*sstarts,*rstarts;
    542:   const PetscMPIInt *sprocs,*rprocs;
    543:   PetscInt          i,nsends,nrecvs;
    544:   MPI_Request       *swaits,*rwaits;
    545:   MPI_Comm          comm;
    546:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
    547:   MPIAIJ_MPIDense   *contents;
    548:   Mat               workB;
    549:   MPI_Datatype      *stype,*rtype;
    550:   PetscInt          blda;

    553:   MatCheckProduct(C,4);
    554:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    555:   contents = (MPIAIJ_MPIDense*)C->product->data;
    556:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
    557:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
    558:   PetscMPIIntCast(nsends,&nsends_mpi);
    559:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
    560:   if (Bbidx == 0) {
    561:     workB = *outworkB = contents->workB;
    562:   } else {
    563:     workB = *outworkB = contents->workB1;
    564:   }
    565:   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);
    566:   swaits = contents->swaits;
    567:   rwaits = contents->rwaits;

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

    574:   /* Post recv, use MPI derived data type to save memory */
    575:   PetscObjectGetComm((PetscObject)C,&comm);
    576:   rtype = contents->rtype;
    577:   for (i=0; i<nrecvs; i++) {
    578:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
    579:   }

    581:   stype = contents->stype;
    582:   for (i=0; i<nsends; i++) {
    583:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
    584:   }

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

    589:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
    590:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
    591:   MatDenseRestoreArrayRead(B,&b);
    592:   MatDenseRestoreArray(workB,&rvalues);
    593:   return(0);
    594: }

    596: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    597: {
    598:   PetscErrorCode  ierr;
    599:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
    600:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
    601:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
    602:   Mat             workB;
    603:   MPIAIJ_MPIDense *contents;

    606:   MatCheckProduct(C,3);
    607:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    608:   contents = (MPIAIJ_MPIDense*)C->product->data;
    609:   /* diagonal block of A times all local rows of B */
    610:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
    611:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
    612:   if (contents->workB->cmap->n == B->cmap->N) {
    613:     /* get off processor parts of B needed to complete C=A*B */
    614:     MatMPIDenseScatter(A,B,0,C,&workB);

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

    623:     for (i=0; i<BN; i+=n) {
    624:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
    625:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

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

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

    634:       MatDenseRestoreSubMatrix(B,&Bb);
    635:       MatDenseRestoreSubMatrix(C,&Cb);
    636:     }
    637:   }
    638:   return(0);
    639: }

    641: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    642: {
    643:   PetscErrorCode    ierr;
    644:   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    645:   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    646:   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    647:   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    648:   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
    649:   Mat_SeqAIJ        *p_loc,*p_oth;
    650:   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    651:   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
    652:   PetscInt          cm    = C->rmap->n,anz,pnz;
    653:   Mat_APMPI         *ptap;
    654:   PetscScalar       *apa_sparse;
    655:   const PetscScalar *dummy;
    656:   PetscInt          *api,*apj,*apJ,i,j,k,row;
    657:   PetscInt          cstart = C->cmap->rstart;
    658:   PetscInt          cdnz,conz,k0,k1,nextp;
    659:   MPI_Comm          comm;
    660:   PetscMPIInt       size;

    663:   MatCheckProduct(C,3);
    664:   ptap = (Mat_APMPI*)C->product->data;
    665:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    666:   PetscObjectGetComm((PetscObject)C,&comm);
    667:   MPI_Comm_size(comm,&size);
    668:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

    670:   /* flag CPU mask for C */
    671: #if defined(PETSC_HAVE_DEVICE)
    672:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    673:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
    674:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
    675: #endif
    676:   apa_sparse = ptap->apa;

    678:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    679:   /*-----------------------------------------------------*/
    680:   /* update numerical values of P_oth and P_loc */
    681:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    682:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    684:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    685:   /*----------------------------------------------------------*/
    686:   /* get data from symbolic products */
    687:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    688:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    689:   if (size >1) {
    690:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    691:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    692:   } else {
    693:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    694:   }

    696:   /* trigger copy to CPU */
    697:   MatSeqAIJGetArrayRead(a->A,&dummy);
    698:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
    699:   MatSeqAIJGetArrayRead(a->B,&dummy);
    700:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
    701:   api = ptap->api;
    702:   apj = ptap->apj;
    703:   for (i=0; i<cm; i++) {
    704:     apJ = apj + api[i];

    706:     /* diagonal portion of A */
    707:     anz = adi[i+1] - adi[i];
    708:     adj = ad->j + adi[i];
    709:     ada = ad->a + adi[i];
    710:     for (j=0; j<anz; j++) {
    711:       row = adj[j];
    712:       pnz = pi_loc[row+1] - pi_loc[row];
    713:       pj  = pj_loc + pi_loc[row];
    714:       pa  = pa_loc + pi_loc[row];
    715:       /* perform sparse axpy */
    716:       valtmp = ada[j];
    717:       nextp  = 0;
    718:       for (k=0; nextp<pnz; k++) {
    719:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    720:           apa_sparse[k] += valtmp*pa[nextp++];
    721:         }
    722:       }
    723:       PetscLogFlops(2.0*pnz);
    724:     }

    726:     /* off-diagonal portion of A */
    727:     anz = aoi[i+1] - aoi[i];
    728:     aoj = ao->j + aoi[i];
    729:     aoa = ao->a + aoi[i];
    730:     for (j=0; j<anz; j++) {
    731:       row = aoj[j];
    732:       pnz = pi_oth[row+1] - pi_oth[row];
    733:       pj  = pj_oth + pi_oth[row];
    734:       pa  = pa_oth + pi_oth[row];
    735:       /* perform sparse axpy */
    736:       valtmp = aoa[j];
    737:       nextp  = 0;
    738:       for (k=0; nextp<pnz; k++) {
    739:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    740:           apa_sparse[k] += valtmp*pa[nextp++];
    741:         }
    742:       }
    743:       PetscLogFlops(2.0*pnz);
    744:     }

    746:     /* set values in C */
    747:     cdnz = cd->i[i+1] - cd->i[i];
    748:     conz = co->i[i+1] - co->i[i];

    750:     /* 1st off-diagonal part of C */
    751:     ca = coa + co->i[i];
    752:     k  = 0;
    753:     for (k0=0; k0<conz; k0++) {
    754:       if (apJ[k] >= cstart) break;
    755:       ca[k0]        = apa_sparse[k];
    756:       apa_sparse[k] = 0.0;
    757:       k++;
    758:     }

    760:     /* diagonal part of C */
    761:     ca = cda + cd->i[i];
    762:     for (k1=0; k1<cdnz; k1++) {
    763:       ca[k1]        = apa_sparse[k];
    764:       apa_sparse[k] = 0.0;
    765:       k++;
    766:     }

    768:     /* 2nd off-diagonal part of C */
    769:     ca = coa + co->i[i];
    770:     for (; k0<conz; k0++) {
    771:       ca[k0]        = apa_sparse[k];
    772:       apa_sparse[k] = 0.0;
    773:       k++;
    774:     }
    775:   }
    776:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    777:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    778:   return(0);
    779: }

    781: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    782: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
    783: {
    784:   PetscErrorCode     ierr;
    785:   MPI_Comm           comm;
    786:   PetscMPIInt        size;
    787:   Mat_APMPI          *ptap;
    788:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    789:   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
    790:   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    791:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    792:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    793:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
    794:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
    795:   PetscReal          afill;
    796:   MatType            mtype;

    799:   MatCheckProduct(C,4);
    800:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    801:   PetscObjectGetComm((PetscObject)A,&comm);
    802:   MPI_Comm_size(comm,&size);

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

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

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

    813:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    814:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    815:   if (size > 1) {
    816:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    817:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    818:   } else {
    819:     p_oth  = NULL;
    820:     pi_oth = NULL; pj_oth = NULL;
    821:   }

    823:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    824:   /*-------------------------------------------------------------------*/
    825:   PetscMalloc1(am+2,&api);
    826:   ptap->api = api;
    827:   api[0]    = 0;

    829:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

    831:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    832:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    833:   current_space = free_space;
    834:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    835:   for (i=0; i<am; i++) {
    836:     /* diagonal portion of A */
    837:     nzi = adi[i+1] - adi[i];
    838:     for (j=0; j<nzi; j++) {
    839:       row  = *adj++;
    840:       pnz  = pi_loc[row+1] - pi_loc[row];
    841:       Jptr = pj_loc + pi_loc[row];
    842:       /* Expand list if it is not long enough */
    843:       if (pnz+apnz_max > lsize) {
    844:         lsize = pnz+apnz_max;
    845:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    846:       }
    847:       /* add non-zero cols of P into the sorted linked list lnk */
    848:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    849:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
    850:       api[i+1] = api[i] + apnz;
    851:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    852:     }
    853:     /* off-diagonal portion of A */
    854:     nzi = aoi[i+1] - aoi[i];
    855:     for (j=0; j<nzi; j++) {
    856:       row  = *aoj++;
    857:       pnz  = pi_oth[row+1] - pi_oth[row];
    858:       Jptr = pj_oth + pi_oth[row];
    859:       /* Expand list if it is not long enough */
    860:       if (pnz+apnz_max > lsize) {
    861:         lsize = pnz + apnz_max;
    862:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    863:       }
    864:       /* add non-zero cols of P into the sorted linked list lnk */
    865:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    866:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
    867:       api[i+1] = api[i] + apnz;
    868:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    869:     }

    871:     /* add missing diagonal entry */
    872:     if (C->force_diagonals) {
    873:       j = i + rstart; /* column index */
    874:       PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
    875:     }

    877:     apnz     = *lnk;
    878:     api[i+1] = api[i] + apnz;
    879:     if (apnz > apnz_max) apnz_max = apnz;

    881:     /* if free space is not available, double the total space in the list */
    882:     if (current_space->local_remaining<apnz) {
    883:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    884:       nspacedouble++;
    885:     }

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

    891:     current_space->array           += apnz;
    892:     current_space->local_used      += apnz;
    893:     current_space->local_remaining -= apnz;
    894:   }

    896:   /* Allocate space for apj, initialize apj, and */
    897:   /* destroy list of free space and other temporary array(s) */
    898:   PetscMalloc1(api[am]+1,&ptap->apj);
    899:   apj  = ptap->apj;
    900:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    901:   PetscLLCondensedDestroy_Scalable(lnk);

    903:   /* create and assemble symbolic parallel matrix C */
    904:   /*----------------------------------------------------*/
    905:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    906:   MatSetBlockSizesFromMats(C,A,P);
    907:   MatGetType(A,&mtype);
    908:   MatSetType(C,mtype);
    909:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    910:   MatPreallocateFinalize(dnz,onz);

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

    915:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    916:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    917:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    918:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    920:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    921:   C->ops->productnumeric = MatProductNumeric_AB;

    923:   /* attach the supporting struct to C for reuse */
    924:   C->product->data    = ptap;
    925:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    927:   /* set MatInfo */
    928:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    929:   if (afill < 1.0) afill = 1.0;
    930:   C->info.mallocs           = nspacedouble;
    931:   C->info.fill_ratio_given  = fill;
    932:   C->info.fill_ratio_needed = afill;

    934: #if defined(PETSC_USE_INFO)
    935:   if (api[am]) {
    936:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    937:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    938:   } else {
    939:     PetscInfo(C,"Empty matrix product\n");
    940:   }
    941: #endif
    942:   return(0);
    943: }

    945: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    946: /* Three input arrays are merged to one output array. The size of the    */
    947: /* output array is also output. Duplicate entries only show up once.     */
    948: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
    949:                                PetscInt  size2, PetscInt *in2,
    950:                                PetscInt  size3, PetscInt *in3,
    951:                                PetscInt *size4, PetscInt *out)
    952: {
    953:   int i = 0, j = 0, k = 0, l = 0;

    955:   /* Traverse all three arrays */
    956:   while (i<size1 && j<size2 && k<size3) {
    957:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    958:       out[l++] = in1[i++];
    959:     }
    960:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
    961:       out[l++] = in2[j++];
    962:     }
    963:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
    964:       out[l++] = in3[k++];
    965:     }
    966:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
    967:       out[l++] = in1[i];
    968:       i++, j++;
    969:     }
    970:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
    971:       out[l++] = in1[i];
    972:       i++, k++;
    973:     }
    974:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
    975:       out[l++] = in2[j];
    976:       k++, j++;
    977:     }
    978:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
    979:       out[l++] = in1[i];
    980:       i++, j++, k++;
    981:     }
    982:   }

    984:   /* Traverse two remaining arrays */
    985:   while (i<size1 && j<size2) {
    986:     if (in1[i] < in2[j]) {
    987:       out[l++] = in1[i++];
    988:     }
    989:     else if (in1[i] > in2[j]) {
    990:       out[l++] = in2[j++];
    991:     }
    992:     else {
    993:       out[l++] = in1[i];
    994:       i++, j++;
    995:     }
    996:   }

    998:   while (i<size1 && k<size3) {
    999:     if (in1[i] < in3[k]) {
    1000:       out[l++] = in1[i++];
    1001:     }
    1002:     else if (in1[i] > in3[k]) {
    1003:       out[l++] = in3[k++];
    1004:     }
    1005:     else {
    1006:       out[l++] = in1[i];
    1007:       i++, k++;
    1008:     }
    1009:   }

    1011:   while (k<size3 && j<size2)  {
    1012:     if (in3[k] < in2[j]) {
    1013:       out[l++] = in3[k++];
    1014:     }
    1015:     else if (in3[k] > in2[j]) {
    1016:       out[l++] = in2[j++];
    1017:     }
    1018:     else {
    1019:       out[l++] = in3[k];
    1020:       k++, j++;
    1021:     }
    1022:   }

    1024:   /* Traverse one remaining array */
    1025:   while (i<size1) out[l++] = in1[i++];
    1026:   while (j<size2) out[l++] = in2[j++];
    1027:   while (k<size3) out[l++] = in3[k++];

    1029:   *size4 = l;
    1030: }

    1032: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    1033: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    1034: /* matrix-matrix multiplications.  */
    1035: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    1036: {
    1037:   PetscErrorCode     ierr;
    1038:   MPI_Comm           comm;
    1039:   PetscMPIInt        size;
    1040:   Mat_APMPI          *ptap;
    1041:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
    1042:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
    1043:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
    1044:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
    1045:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
    1046:   PetscInt           adponz, adpdnz;
    1047:   PetscInt           *pi_loc,*dnz,*onz;
    1048:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
    1049:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
    1050:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
    1051:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
    1052:   PetscBT            lnkbt;
    1053:   PetscReal          afill;
    1054:   PetscMPIInt        rank;
    1055:   Mat                adpd, aopoth;
    1056:   MatType            mtype;
    1057:   const char         *prefix;

    1060:   MatCheckProduct(C,4);
    1061:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    1062:   PetscObjectGetComm((PetscObject)A,&comm);
    1063:   MPI_Comm_size(comm,&size);
    1064:   MPI_Comm_rank(comm, &rank);
    1065:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

    1067:   /* create struct Mat_APMPI and attached it to C later */
    1068:   PetscNew(&ptap);

    1070:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1071:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    1073:   /* get P_loc by taking all local rows of P */
    1074:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    1076:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    1077:   pi_loc = p_loc->i;

    1079:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1080:   PetscMalloc1(am+2,&api);
    1081:   PetscMalloc1(am+2,&adpoi);

    1083:   adpoi[0]    = 0;
    1084:   ptap->api = api;
    1085:   api[0] = 0;

    1087:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1088:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
    1089:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

    1091:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1092:   MatGetOptionsPrefix(A,&prefix);
    1093:   MatProductCreate(a->A,p->A,NULL,&adpd);
    1094:   MatGetOptionsPrefix(A,&prefix);
    1095:   MatSetOptionsPrefix(adpd,prefix);
    1096:   MatAppendOptionsPrefix(adpd,"inner_diag_");

    1098:   MatProductSetType(adpd,MATPRODUCT_AB);
    1099:   MatProductSetAlgorithm(adpd,"sorted");
    1100:   MatProductSetFill(adpd,fill);
    1101:   MatProductSetFromOptions(adpd);

    1103:   adpd->force_diagonals = C->force_diagonals;
    1104:   MatProductSymbolic(adpd);

    1106:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
    1107:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
    1108:   p_off = (Mat_SeqAIJ*)((p->B)->data);
    1109:   poff_i = p_off->i; poff_j = p_off->j;

    1111:   /* j_temp stores indices of a result row before they are added to the linked list */
    1112:   PetscMalloc1(pN+2,&j_temp);

    1114:   /* Symbolic calc of the A_diag * p_loc_off */
    1115:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1116:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
    1117:   current_space = free_space_diag;

    1119:   for (i=0; i<am; i++) {
    1120:     /* A_diag * P_loc_off */
    1121:     nzi = adi[i+1] - adi[i];
    1122:     for (j=0; j<nzi; j++) {
    1123:       row  = *adj++;
    1124:       pnz  = poff_i[row+1] - poff_i[row];
    1125:       Jptr = poff_j + poff_i[row];
    1126:       for (i1 = 0; i1 < pnz; i1++) {
    1127:         j_temp[i1] = p->garray[Jptr[i1]];
    1128:       }
    1129:       /* add non-zero cols of P into the sorted linked list lnk */
    1130:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
    1131:     }

    1133:     adponz     = lnk[0];
    1134:     adpoi[i+1] = adpoi[i] + adponz;

    1136:     /* if free space is not available, double the total space in the list */
    1137:     if (current_space->local_remaining<adponz) {
    1138:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
    1139:       nspacedouble++;
    1140:     }

    1142:     /* Copy data into free space, then initialize lnk */
    1143:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

    1145:     current_space->array           += adponz;
    1146:     current_space->local_used      += adponz;
    1147:     current_space->local_remaining -= adponz;
    1148:   }

    1150:   /* Symbolic calc of A_off * P_oth */
    1151:   MatSetOptionsPrefix(a->B,prefix);
    1152:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
    1153:   MatCreate(PETSC_COMM_SELF,&aopoth);
    1154:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
    1155:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
    1156:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

    1158:   /* Allocate space for apj, adpj, aopj, ... */
    1159:   /* destroy lists of free space and other temporary array(s) */

    1161:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
    1162:   PetscMalloc1(adpoi[am]+2, &adpoj);

    1164:   /* Copy from linked list to j-array */
    1165:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
    1166:   PetscLLDestroy(lnk,lnkbt);

    1168:   adpoJ = adpoj;
    1169:   adpdJ = adpdj;
    1170:   aopJ = aopothj;
    1171:   apj  = ptap->apj;
    1172:   apJ = apj; /* still empty */

    1174:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1175:   /* A_diag * P_loc_diag to get A*P */
    1176:   for (i = 0; i < am; i++) {
    1177:     aopnz  =  aopothi[i+1] -  aopothi[i];
    1178:     adponz = adpoi[i+1] - adpoi[i];
    1179:     adpdnz = adpdi[i+1] - adpdi[i];

    1181:     /* Correct indices from A_diag*P_diag */
    1182:     for (i1 = 0; i1 < adpdnz; i1++) {
    1183:       adpdJ[i1] += p_colstart;
    1184:     }
    1185:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1186:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1187:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

    1189:     aopJ += aopnz;
    1190:     adpoJ += adponz;
    1191:     adpdJ += adpdnz;
    1192:     apJ += apnz;
    1193:     api[i+1] = api[i] + apnz;
    1194:   }

    1196:   /* malloc apa to store dense row A[i,:]*P */
    1197:   PetscCalloc1(pN+2,&ptap->apa);

    1199:   /* create and assemble symbolic parallel matrix C */
    1200:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    1201:   MatSetBlockSizesFromMats(C,A,P);
    1202:   MatGetType(A,&mtype);
    1203:   MatSetType(C,mtype);
    1204:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1205:   MatPreallocateFinalize(dnz,onz);

    1207:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    1208:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1209:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1210:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1212:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1213:   C->ops->productnumeric = MatProductNumeric_AB;

    1215:   /* attach the supporting struct to C for reuse */
    1216:   C->product->data    = ptap;
    1217:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    1219:   /* set MatInfo */
    1220:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1221:   if (afill < 1.0) afill = 1.0;
    1222:   C->info.mallocs           = nspacedouble;
    1223:   C->info.fill_ratio_given  = fill;
    1224:   C->info.fill_ratio_needed = afill;

    1226: #if defined(PETSC_USE_INFO)
    1227:   if (api[am]) {
    1228:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1229:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1230:   } else {
    1231:     PetscInfo(C,"Empty matrix product\n");
    1232:   }
    1233: #endif

    1235:   MatDestroy(&aopoth);
    1236:   MatDestroy(&adpd);
    1237:   PetscFree(j_temp);
    1238:   PetscFree(adpoj);
    1239:   PetscFree(adpoi);
    1240:   return(0);
    1241: }

    1243: /*-------------------------------------------------------------------------*/
    1244: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1245: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    1246: {
    1248:   Mat_APMPI      *ptap;
    1249:   Mat            Pt;

    1252:   MatCheckProduct(C,3);
    1253:   ptap = (Mat_APMPI*)C->product->data;
    1254:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1255:   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");

    1257:   Pt   = ptap->Pt;
    1258:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    1259:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
    1260:   return(0);
    1261: }

    1263: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1264: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
    1265: {
    1266:   PetscErrorCode      ierr;
    1267:   Mat_APMPI           *ptap;
    1268:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
    1269:   MPI_Comm            comm;
    1270:   PetscMPIInt         size,rank;
    1271:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1272:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
    1273:   PetscInt            *lnk,i,k,nsend,rstart;
    1274:   PetscBT             lnkbt;
    1275:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
    1276:   PETSC_UNUSED PetscMPIInt icompleted=0;
    1277:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
    1278:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
    1279:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1280:   MPI_Request         *swaits,*rwaits;
    1281:   MPI_Status          *sstatus,rstatus;
    1282:   PetscLayout         rowmap;
    1283:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
    1284:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
    1285:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
    1286:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
    1287:   PetscTable          ta;
    1288:   MatType             mtype;
    1289:   const char          *prefix;

    1292:   PetscObjectGetComm((PetscObject)A,&comm);
    1293:   MPI_Comm_size(comm,&size);
    1294:   MPI_Comm_rank(comm,&rank);

    1296:   /* create symbolic parallel matrix C */
    1297:   MatGetType(A,&mtype);
    1298:   MatSetType(C,mtype);

    1300:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1302:   /* create struct Mat_APMPI and attached it to C later */
    1303:   PetscNew(&ptap);
    1304:   ptap->reuse = MAT_INITIAL_MATRIX;

    1306:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1307:   /* --------------------------------- */
    1308:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
    1309:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

    1311:   /* (1) compute symbolic A_loc */
    1312:   /* ---------------------------*/
    1313:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

    1315:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1316:   /* ------------------------------------ */
    1317:   MatGetOptionsPrefix(A,&prefix);
    1318:   MatSetOptionsPrefix(ptap->Ro,prefix);
    1319:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
    1320:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
    1321:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

    1323:   /* (3) send coj of C_oth to other processors  */
    1324:   /* ------------------------------------------ */
    1325:   /* determine row ownership */
    1326:   PetscLayoutCreate(comm,&rowmap);
    1327:   rowmap->n  = pn;
    1328:   rowmap->bs = 1;
    1329:   PetscLayoutSetUp(rowmap);
    1330:   owners = rowmap->range;

    1332:   /* determine the number of messages to send, their lengths */
    1333:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
    1334:   PetscArrayzero(len_s,size);
    1335:   PetscArrayzero(len_si,size);

    1337:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
    1338:   coi   = c_oth->i; coj = c_oth->j;
    1339:   con   = ptap->C_oth->rmap->n;
    1340:   proc  = 0;
    1341:   for (i=0; i<con; i++) {
    1342:     while (prmap[i] >= owners[proc+1]) proc++;
    1343:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1344:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1345:   }

    1347:   len          = 0; /* max length of buf_si[], see (4) */
    1348:   owners_co[0] = 0;
    1349:   nsend        = 0;
    1350:   for (proc=0; proc<size; proc++) {
    1351:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1352:     if (len_s[proc]) {
    1353:       nsend++;
    1354:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1355:       len         += len_si[proc];
    1356:     }
    1357:   }

    1359:   /* determine the number and length of messages to receive for coi and coj  */
    1360:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
    1361:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

    1363:   /* post the Irecv and Isend of coj */
    1364:   PetscCommGetNewTag(comm,&tagj);
    1365:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
    1366:   PetscMalloc1(nsend+1,&swaits);
    1367:   for (proc=0, k=0; proc<size; proc++) {
    1368:     if (!len_s[proc]) continue;
    1369:     i    = owners_co[proc];
    1370:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1371:     k++;
    1372:   }

    1374:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1375:   /* ---------------------------------------- */
    1376:   MatSetOptionsPrefix(ptap->Rd,prefix);
    1377:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
    1378:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
    1379:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
    1380:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

    1382:   /* receives coj are complete */
    1383:   for (i=0; i<nrecv; i++) {
    1384:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1385:   }
    1386:   PetscFree(rwaits);
    1387:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1389:   /* add received column indices into ta to update Crmax */
    1390:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

    1392:   /* create and initialize a linked list */
    1393:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
    1394:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

    1396:   for (k=0; k<nrecv; k++) {/* k-th received message */
    1397:     Jptr = buf_rj[k];
    1398:     for (j=0; j<len_r[k]; j++) {
    1399:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1400:     }
    1401:   }
    1402:   PetscTableGetCount(ta,&Crmax);
    1403:   PetscTableDestroy(&ta);

    1405:   /* (4) send and recv coi */
    1406:   /*-----------------------*/
    1407:   PetscCommGetNewTag(comm,&tagi);
    1408:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
    1409:   PetscMalloc1(len+1,&buf_s);
    1410:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1411:   for (proc=0,k=0; proc<size; proc++) {
    1412:     if (!len_s[proc]) continue;
    1413:     /* form outgoing message for i-structure:
    1414:          buf_si[0]:                 nrows to be sent
    1415:                [1:nrows]:           row index (global)
    1416:                [nrows+1:2*nrows+1]: i-structure index
    1417:     */
    1418:     /*-------------------------------------------*/
    1419:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
    1420:     buf_si_i    = buf_si + nrows+1;
    1421:     buf_si[0]   = nrows;
    1422:     buf_si_i[0] = 0;
    1423:     nrows       = 0;
    1424:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1425:       nzi = coi[i+1] - coi[i];
    1426:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1427:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1428:       nrows++;
    1429:     }
    1430:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1431:     k++;
    1432:     buf_si += len_si[proc];
    1433:   }
    1434:   for (i=0; i<nrecv; i++) {
    1435:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1436:   }
    1437:   PetscFree(rwaits);
    1438:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1440:   PetscFree4(len_s,len_si,sstatus,owners_co);
    1441:   PetscFree(len_ri);
    1442:   PetscFree(swaits);
    1443:   PetscFree(buf_s);

    1445:   /* (5) compute the local portion of C      */
    1446:   /* ------------------------------------------ */
    1447:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
    1448:   PetscFreeSpaceGet(Crmax,&free_space);
    1449:   current_space = free_space;

    1451:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
    1452:   for (k=0; k<nrecv; k++) {
    1453:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1454:     nrows       = *buf_ri_k[k];
    1455:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1456:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1457:   }

    1459:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
    1460:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
    1461:   for (i=0; i<pn; i++) { /* for each local row of C */
    1462:     /* add C_loc into C */
    1463:     nzi  = c_loc->i[i+1] - c_loc->i[i];
    1464:     Jptr = c_loc->j + c_loc->i[i];
    1465:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

    1467:     /* add received col data into lnk */
    1468:     for (k=0; k<nrecv; k++) { /* k-th received message */
    1469:       if (i == *nextrow[k]) { /* i-th row */
    1470:         nzi  = *(nextci[k]+1) - *nextci[k];
    1471:         Jptr = buf_rj[k] + *nextci[k];
    1472:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1473:         nextrow[k]++; nextci[k]++;
    1474:       }
    1475:     }

    1477:     /* add missing diagonal entry */
    1478:     if (C->force_diagonals) {
    1479:       k = i + owners[rank]; /* column index */
    1480:       PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
    1481:     }

    1483:     nzi = lnk[0];

    1485:     /* copy data into free space, then initialize lnk */
    1486:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
    1487:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
    1488:   }
    1489:   PetscFree3(buf_ri_k,nextrow,nextci);
    1490:   PetscLLDestroy(lnk,lnkbt);
    1491:   PetscFreeSpaceDestroy(free_space);

    1493:   /* local sizes and preallocation */
    1494:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
    1495:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
    1496:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
    1497:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1498:   MatPreallocateFinalize(dnz,onz);

    1500:   /* add C_loc and C_oth to C */
    1501:   MatGetOwnershipRange(C,&rstart,NULL);
    1502:   for (i=0; i<pn; i++) {
    1503:     ncols = c_loc->i[i+1] - c_loc->i[i];
    1504:     cols  = c_loc->j + c_loc->i[i];
    1505:     row   = rstart + i;
    1506:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);

    1508:     if (C->force_diagonals) {
    1509:       MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
    1510:     }
    1511:   }
    1512:   for (i=0; i<con; i++) {
    1513:     ncols = c_oth->i[i+1] - c_oth->i[i];
    1514:     cols  = c_oth->j + c_oth->i[i];
    1515:     row   = prmap[i];
    1516:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
    1517:   }
    1518:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1519:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1520:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1522:   /* members in merge */
    1523:   PetscFree(id_r);
    1524:   PetscFree(len_r);
    1525:   PetscFree(buf_ri[0]);
    1526:   PetscFree(buf_ri);
    1527:   PetscFree(buf_rj[0]);
    1528:   PetscFree(buf_rj);
    1529:   PetscLayoutDestroy(&rowmap);

    1531:   /* attach the supporting struct to C for reuse */
    1532:   C->product->data    = ptap;
    1533:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    1534:   return(0);
    1535: }

    1537: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    1538: {
    1539:   PetscErrorCode    ierr;
    1540:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
    1541:   Mat_SeqAIJ        *c_seq;
    1542:   Mat_APMPI         *ptap;
    1543:   Mat               A_loc,C_loc,C_oth;
    1544:   PetscInt          i,rstart,rend,cm,ncols,row;
    1545:   const PetscInt    *cols;
    1546:   const PetscScalar *vals;

    1549:   MatCheckProduct(C,3);
    1550:   ptap = (Mat_APMPI*)C->product->data;
    1551:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1552:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1553:   MatZeroEntries(C);

    1555:   if (ptap->reuse == MAT_REUSE_MATRIX) {
    1556:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1557:     /* 1) get R = Pd^T, Ro = Po^T */
    1558:     /*----------------------------*/
    1559:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
    1560:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

    1562:     /* 2) compute numeric A_loc */
    1563:     /*--------------------------*/
    1564:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
    1565:   }

    1567:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1568:   A_loc = ptap->A_loc;
    1569:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
    1570:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
    1571:   C_loc = ptap->C_loc;
    1572:   C_oth = ptap->C_oth;

    1574:   /* add C_loc and C_oth to C */
    1575:   MatGetOwnershipRange(C,&rstart,&rend);

    1577:   /* C_loc -> C */
    1578:   cm    = C_loc->rmap->N;
    1579:   c_seq = (Mat_SeqAIJ*)C_loc->data;
    1580:   cols = c_seq->j;
    1581:   vals = c_seq->a;
    1582:   for (i=0; i<cm; i++) {
    1583:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1584:     row = rstart + i;
    1585:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1586:     cols += ncols; vals += ncols;
    1587:   }

    1589:   /* Co -> C, off-processor part */
    1590:   cm    = C_oth->rmap->N;
    1591:   c_seq = (Mat_SeqAIJ*)C_oth->data;
    1592:   cols  = c_seq->j;
    1593:   vals  = c_seq->a;
    1594:   for (i=0; i<cm; i++) {
    1595:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1596:     row = p->garray[i];
    1597:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1598:     cols += ncols; vals += ncols;
    1599:   }
    1600:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1601:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1602:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1604:   ptap->reuse = MAT_REUSE_MATRIX;
    1605:   return(0);
    1606: }

    1608: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1609: {
    1610:   PetscErrorCode      ierr;
    1611:   Mat_Merge_SeqsToMPI *merge;
    1612:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
    1613:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1614:   Mat_APMPI           *ptap;
    1615:   PetscInt            *adj;
    1616:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1617:   MatScalar           *ada,*ca,valtmp;
    1618:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1619:   MPI_Comm            comm;
    1620:   PetscMPIInt         size,rank,taga,*len_s;
    1621:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1622:   PetscInt            **buf_ri,**buf_rj;
    1623:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1624:   MPI_Request         *s_waits,*r_waits;
    1625:   MPI_Status          *status;
    1626:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1627:   const PetscScalar   *dummy;
    1628:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
    1629:   Mat                 A_loc;
    1630:   Mat_SeqAIJ          *a_loc;

    1633:   MatCheckProduct(C,3);
    1634:   ptap = (Mat_APMPI*)C->product->data;
    1635:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1636:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1637:   PetscObjectGetComm((PetscObject)C,&comm);
    1638:   MPI_Comm_size(comm,&size);
    1639:   MPI_Comm_rank(comm,&rank);

    1641:   merge = ptap->merge;

    1643:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1644:   /*------------------------------------------*/
    1645:   /* get data from symbolic products */
    1646:   coi    = merge->coi; coj = merge->coj;
    1647:   PetscCalloc1(coi[pon]+1,&coa);
    1648:   bi     = merge->bi; bj = merge->bj;
    1649:   owners = merge->rowmap->range;
    1650:   PetscCalloc1(bi[cm]+1,&ba);

    1652:   /* get A_loc by taking all local rows of A */
    1653:   A_loc = ptap->A_loc;
    1654:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1655:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1656:   ai    = a_loc->i;
    1657:   aj    = a_loc->j;

    1659:   /* trigger copy to CPU */
    1660:   MatSeqAIJGetArrayRead(p->A,&dummy);
    1661:   MatSeqAIJRestoreArrayRead(p->A,&dummy);
    1662:   MatSeqAIJGetArrayRead(p->B,&dummy);
    1663:   MatSeqAIJRestoreArrayRead(p->B,&dummy);
    1664:   for (i=0; i<am; i++) {
    1665:     anz = ai[i+1] - ai[i];
    1666:     adj = aj + ai[i];
    1667:     ada = a_loc->a + ai[i];

    1669:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1670:     /*-------------------------------------------------------------*/
    1671:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1672:     pnz = po->i[i+1] - po->i[i];
    1673:     poJ = po->j + po->i[i];
    1674:     pA  = po->a + po->i[i];
    1675:     for (j=0; j<pnz; j++) {
    1676:       row = poJ[j];
    1677:       cj  = coj + coi[row];
    1678:       ca  = coa + coi[row];
    1679:       /* perform sparse axpy */
    1680:       nexta  = 0;
    1681:       valtmp = pA[j];
    1682:       for (k=0; nexta<anz; k++) {
    1683:         if (cj[k] == adj[nexta]) {
    1684:           ca[k] += valtmp*ada[nexta];
    1685:           nexta++;
    1686:         }
    1687:       }
    1688:       PetscLogFlops(2.0*anz);
    1689:     }

    1691:     /* put the value into Cd (diagonal part) */
    1692:     pnz = pd->i[i+1] - pd->i[i];
    1693:     pdJ = pd->j + pd->i[i];
    1694:     pA  = pd->a + pd->i[i];
    1695:     for (j=0; j<pnz; j++) {
    1696:       row = pdJ[j];
    1697:       cj  = bj + bi[row];
    1698:       ca  = ba + bi[row];
    1699:       /* perform sparse axpy */
    1700:       nexta  = 0;
    1701:       valtmp = pA[j];
    1702:       for (k=0; nexta<anz; k++) {
    1703:         if (cj[k] == adj[nexta]) {
    1704:           ca[k] += valtmp*ada[nexta];
    1705:           nexta++;
    1706:         }
    1707:       }
    1708:       PetscLogFlops(2.0*anz);
    1709:     }
    1710:   }

    1712:   /* 3) send and recv matrix values coa */
    1713:   /*------------------------------------*/
    1714:   buf_ri = merge->buf_ri;
    1715:   buf_rj = merge->buf_rj;
    1716:   len_s  = merge->len_s;
    1717:   PetscCommGetNewTag(comm,&taga);
    1718:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1720:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1721:   for (proc=0,k=0; proc<size; proc++) {
    1722:     if (!len_s[proc]) continue;
    1723:     i    = merge->owners_co[proc];
    1724:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1725:     k++;
    1726:   }
    1727:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1728:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1730:   PetscFree2(s_waits,status);
    1731:   PetscFree(r_waits);
    1732:   PetscFree(coa);

    1734:   /* 4) insert local Cseq and received values into Cmpi */
    1735:   /*----------------------------------------------------*/
    1736:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1737:   for (k=0; k<merge->nrecv; k++) {
    1738:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1739:     nrows       = *(buf_ri_k[k]);
    1740:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1741:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1742:   }

    1744:   for (i=0; i<cm; i++) {
    1745:     row  = owners[rank] + i; /* global row index of C_seq */
    1746:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1747:     ba_i = ba + bi[i];
    1748:     bnz  = bi[i+1] - bi[i];
    1749:     /* add received vals into ba */
    1750:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1751:       /* i-th row */
    1752:       if (i == *nextrow[k]) {
    1753:         cnz    = *(nextci[k]+1) - *nextci[k];
    1754:         cj     = buf_rj[k] + *(nextci[k]);
    1755:         ca     = abuf_r[k] + *(nextci[k]);
    1756:         nextcj = 0;
    1757:         for (j=0; nextcj<cnz; j++) {
    1758:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1759:             ba_i[j] += ca[nextcj++];
    1760:           }
    1761:         }
    1762:         nextrow[k]++; nextci[k]++;
    1763:         PetscLogFlops(2.0*cnz);
    1764:       }
    1765:     }
    1766:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1767:   }
    1768:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1769:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1771:   PetscFree(ba);
    1772:   PetscFree(abuf_r[0]);
    1773:   PetscFree(abuf_r);
    1774:   PetscFree3(buf_ri_k,nextrow,nextci);
    1775:   return(0);
    1776: }

    1778: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
    1779: {
    1780:   PetscErrorCode      ierr;
    1781:   Mat                 A_loc;
    1782:   Mat_APMPI           *ptap;
    1783:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1784:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
    1785:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1786:   PetscInt            nnz;
    1787:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1788:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1789:   MPI_Comm            comm;
    1790:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1791:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1792:   PetscInt            len,proc,*dnz,*onz,*owners;
    1793:   PetscInt            nzi,*bi,*bj;
    1794:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1795:   MPI_Request         *swaits,*rwaits;
    1796:   MPI_Status          *sstatus,rstatus;
    1797:   Mat_Merge_SeqsToMPI *merge;
    1798:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1799:   PetscReal           afill  =1.0,afill_tmp;
    1800:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1801:   Mat_SeqAIJ          *a_loc;
    1802:   PetscTable          ta;
    1803:   MatType             mtype;

    1806:   PetscObjectGetComm((PetscObject)A,&comm);
    1807:   /* check if matrix local sizes are compatible */
    1808:   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);

    1810:   MPI_Comm_size(comm,&size);
    1811:   MPI_Comm_rank(comm,&rank);

    1813:   /* create struct Mat_APMPI and attached it to C later */
    1814:   PetscNew(&ptap);

    1816:   /* get A_loc by taking all local rows of A */
    1817:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1819:   ptap->A_loc = A_loc;
    1820:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1821:   ai          = a_loc->i;
    1822:   aj          = a_loc->j;

    1824:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1825:   /*----------------------------------------------------*/
    1826:   MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    1827:   MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
    1828:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1829:                          >= (num of nonzero rows of C_seq) - pn */
    1830:   PetscMalloc1(pon+1,&coi);
    1831:   coi[0] = 0;

    1833:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1834:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1835:   PetscFreeSpaceGet(nnz,&free_space);
    1836:   current_space = free_space;

    1838:   /* create and initialize a linked list */
    1839:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
    1840:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1841:   PetscTableGetCount(ta,&Armax);

    1843:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1845:   for (i=0; i<pon; i++) {
    1846:     pnz = poti[i+1] - poti[i];
    1847:     ptJ = potj + poti[i];
    1848:     for (j=0; j<pnz; j++) {
    1849:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1850:       anz  = ai[row+1] - ai[row];
    1851:       Jptr = aj + ai[row];
    1852:       /* add non-zero cols of AP into the sorted linked list lnk */
    1853:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1854:     }
    1855:     nnz = lnk[0];

    1857:     /* If free space is not available, double the total space in the list */
    1858:     if (current_space->local_remaining<nnz) {
    1859:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1860:       nspacedouble++;
    1861:     }

    1863:     /* Copy data into free space, and zero out denserows */
    1864:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1866:     current_space->array           += nnz;
    1867:     current_space->local_used      += nnz;
    1868:     current_space->local_remaining -= nnz;

    1870:     coi[i+1] = coi[i] + nnz;
    1871:   }

    1873:   PetscMalloc1(coi[pon]+1,&coj);
    1874:   PetscFreeSpaceContiguous(&free_space,coj);
    1875:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1877:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1878:   if (afill_tmp > afill) afill = afill_tmp;

    1880:   /* send j-array (coj) of Co to other processors */
    1881:   /*----------------------------------------------*/
    1882:   /* determine row ownership */
    1883:   PetscNew(&merge);
    1884:   PetscLayoutCreate(comm,&merge->rowmap);

    1886:   merge->rowmap->n  = pn;
    1887:   merge->rowmap->bs = 1;

    1889:   PetscLayoutSetUp(merge->rowmap);
    1890:   owners = merge->rowmap->range;

    1892:   /* determine the number of messages to send, their lengths */
    1893:   PetscCalloc1(size,&len_si);
    1894:   PetscCalloc1(size,&merge->len_s);

    1896:   len_s        = merge->len_s;
    1897:   merge->nsend = 0;

    1899:   PetscMalloc1(size+2,&owners_co);

    1901:   proc = 0;
    1902:   for (i=0; i<pon; i++) {
    1903:     while (prmap[i] >= owners[proc+1]) proc++;
    1904:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1905:     len_s[proc] += coi[i+1] - coi[i];
    1906:   }

    1908:   len          = 0; /* max length of buf_si[] */
    1909:   owners_co[0] = 0;
    1910:   for (proc=0; proc<size; proc++) {
    1911:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1912:     if (len_si[proc]) {
    1913:       merge->nsend++;
    1914:       len_si[proc] = 2*(len_si[proc] + 1);
    1915:       len         += len_si[proc];
    1916:     }
    1917:   }

    1919:   /* determine the number and length of messages to receive for coi and coj  */
    1920:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1921:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1923:   /* post the Irecv and Isend of coj */
    1924:   PetscCommGetNewTag(comm,&tagj);
    1925:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1926:   PetscMalloc1(merge->nsend+1,&swaits);
    1927:   for (proc=0, k=0; proc<size; proc++) {
    1928:     if (!len_s[proc]) continue;
    1929:     i    = owners_co[proc];
    1930:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1931:     k++;
    1932:   }

    1934:   /* receives and sends of coj are complete */
    1935:   PetscMalloc1(size,&sstatus);
    1936:   for (i=0; i<merge->nrecv; i++) {
    1937:     PETSC_UNUSED PetscMPIInt icompleted;
    1938:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1939:   }
    1940:   PetscFree(rwaits);
    1941:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1943:   /* add received column indices into table to update Armax */
    1944:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    1945:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    1946:     Jptr = buf_rj[k];
    1947:     for (j=0; j<merge->len_r[k]; j++) {
    1948:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1949:     }
    1950:   }
    1951:   PetscTableGetCount(ta,&Armax);
    1952:   /* 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); */

    1954:   /* send and recv coi */
    1955:   /*-------------------*/
    1956:   PetscCommGetNewTag(comm,&tagi);
    1957:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1958:   PetscMalloc1(len+1,&buf_s);
    1959:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1960:   for (proc=0,k=0; proc<size; proc++) {
    1961:     if (!len_s[proc]) continue;
    1962:     /* form outgoing message for i-structure:
    1963:          buf_si[0]:                 nrows to be sent
    1964:                [1:nrows]:           row index (global)
    1965:                [nrows+1:2*nrows+1]: i-structure index
    1966:     */
    1967:     /*-------------------------------------------*/
    1968:     nrows       = len_si[proc]/2 - 1;
    1969:     buf_si_i    = buf_si + nrows+1;
    1970:     buf_si[0]   = nrows;
    1971:     buf_si_i[0] = 0;
    1972:     nrows       = 0;
    1973:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1974:       nzi               = coi[i+1] - coi[i];
    1975:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1976:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1977:       nrows++;
    1978:     }
    1979:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1980:     k++;
    1981:     buf_si += len_si[proc];
    1982:   }
    1983:   i = merge->nrecv;
    1984:   while (i--) {
    1985:     PETSC_UNUSED PetscMPIInt icompleted;
    1986:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1987:   }
    1988:   PetscFree(rwaits);
    1989:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1990:   PetscFree(len_si);
    1991:   PetscFree(len_ri);
    1992:   PetscFree(swaits);
    1993:   PetscFree(sstatus);
    1994:   PetscFree(buf_s);

    1996:   /* compute the local portion of C (mpi mat) */
    1997:   /*------------------------------------------*/
    1998:   /* allocate bi array and free space for accumulating nonzero column info */
    1999:   PetscMalloc1(pn+1,&bi);
    2000:   bi[0] = 0;

    2002:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    2003:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    2004:   PetscFreeSpaceGet(nnz,&free_space);
    2005:   current_space = free_space;

    2007:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    2008:   for (k=0; k<merge->nrecv; k++) {
    2009:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    2010:     nrows       = *buf_ri_k[k];
    2011:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    2012:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    2013:   }

    2015:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    2016:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    2017:   rmax = 0;
    2018:   for (i=0; i<pn; i++) {
    2019:     /* add pdt[i,:]*AP into lnk */
    2020:     pnz = pdti[i+1] - pdti[i];
    2021:     ptJ = pdtj + pdti[i];
    2022:     for (j=0; j<pnz; j++) {
    2023:       row  = ptJ[j];  /* row of AP == col of Pt */
    2024:       anz  = ai[row+1] - ai[row];
    2025:       Jptr = aj + ai[row];
    2026:       /* add non-zero cols of AP into the sorted linked list lnk */
    2027:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    2028:     }

    2030:     /* add received col data into lnk */
    2031:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    2032:       if (i == *nextrow[k]) { /* i-th row */
    2033:         nzi  = *(nextci[k]+1) - *nextci[k];
    2034:         Jptr = buf_rj[k] + *nextci[k];
    2035:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    2036:         nextrow[k]++; nextci[k]++;
    2037:       }
    2038:     }

    2040:     /* add missing diagonal entry */
    2041:     if (C->force_diagonals) {
    2042:       k = i + owners[rank]; /* column index */
    2043:       PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
    2044:     }

    2046:     nnz = lnk[0];

    2048:     /* if free space is not available, make more free space */
    2049:     if (current_space->local_remaining<nnz) {
    2050:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    2051:       nspacedouble++;
    2052:     }
    2053:     /* copy data into free space, then initialize lnk */
    2054:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    2055:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    2057:     current_space->array           += nnz;
    2058:     current_space->local_used      += nnz;
    2059:     current_space->local_remaining -= nnz;

    2061:     bi[i+1] = bi[i] + nnz;
    2062:     if (nnz > rmax) rmax = nnz;
    2063:   }
    2064:   PetscFree3(buf_ri_k,nextrow,nextci);

    2066:   PetscMalloc1(bi[pn]+1,&bj);
    2067:   PetscFreeSpaceContiguous(&free_space,bj);
    2068:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    2069:   if (afill_tmp > afill) afill = afill_tmp;
    2070:   PetscLLCondensedDestroy_Scalable(lnk);
    2071:   PetscTableDestroy(&ta);
    2072:   MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    2073:   MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);

    2075:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2076:   /*-------------------------------------------------------------------------------*/
    2077:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    2078:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    2079:   MatGetType(A,&mtype);
    2080:   MatSetType(C,mtype);
    2081:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    2082:   MatPreallocateFinalize(dnz,onz);
    2083:   MatSetBlockSize(C,1);
    2084:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    2085:   for (i=0; i<pn; i++) {
    2086:     row  = i + rstart;
    2087:     nnz  = bi[i+1] - bi[i];
    2088:     Jptr = bj + bi[i];
    2089:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
    2090:   }
    2091:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    2092:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    2093:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    2094:   merge->bi        = bi;
    2095:   merge->bj        = bj;
    2096:   merge->coi       = coi;
    2097:   merge->coj       = coj;
    2098:   merge->buf_ri    = buf_ri;
    2099:   merge->buf_rj    = buf_rj;
    2100:   merge->owners_co = owners_co;

    2102:   /* attach the supporting struct to C for reuse */
    2103:   C->product->data    = ptap;
    2104:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2105:   ptap->merge         = merge;

    2107:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

    2109: #if defined(PETSC_USE_INFO)
    2110:   if (bi[pn] != 0) {
    2111:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    2112:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    2113:   } else {
    2114:     PetscInfo(C,"Empty matrix product\n");
    2115:   }
    2116: #endif
    2117:   return(0);
    2118: }

    2120: /* ---------------------------------------------------------------- */
    2121: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2122: {
    2124:   Mat_Product    *product = C->product;
    2125:   Mat            A=product->A,B=product->B;
    2126:   PetscReal      fill=product->fill;
    2127:   PetscBool      flg;

    2130:   /* scalable */
    2131:   PetscStrcmp(product->alg,"scalable",&flg);
    2132:   if (flg) {
    2133:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
    2134:     goto next;
    2135:   }

    2137:   /* nonscalable */
    2138:   PetscStrcmp(product->alg,"nonscalable",&flg);
    2139:   if (flg) {
    2140:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
    2141:     goto next;
    2142:   }

    2144:   /* matmatmult */
    2145:   PetscStrcmp(product->alg,"at*b",&flg);
    2146:   if (flg) {
    2147:     Mat       At;
    2148:     Mat_APMPI *ptap;

    2150:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
    2151:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
    2152:     ptap = (Mat_APMPI*)C->product->data;
    2153:     if (ptap) {
    2154:       ptap->Pt = At;
    2155:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2156:     }
    2157:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2158:     goto next;
    2159:   }

    2161:   /* backend general code */
    2162:   PetscStrcmp(product->alg,"backend",&flg);
    2163:   if (flg) {
    2164:     MatProductSymbolic_MPIAIJBACKEND(C);
    2165:     return(0);
    2166:   }

    2168:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

    2170: next:
    2171:   C->ops->productnumeric = MatProductNumeric_AtB;
    2172:   return(0);
    2173: }

    2175: /* ---------------------------------------------------------------- */
    2176: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2177: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2178: {
    2180:   Mat_Product    *product = C->product;
    2181:   Mat            A=product->A,B=product->B;
    2182: #if defined(PETSC_HAVE_HYPRE)
    2183:   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
    2184:   PetscInt       nalg = 5;
    2185: #else
    2186:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
    2187:   PetscInt       nalg = 4;
    2188: #endif
    2189:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
    2190:   PetscBool      flg;
    2191:   MPI_Comm       comm;

    2194:   /* Check matrix local sizes */
    2195:   PetscObjectGetComm((PetscObject)C,&comm);
    2196:   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);

    2198:   /* Set "nonscalable" as default algorithm */
    2199:   PetscStrcmp(C->product->alg,"default",&flg);
    2200:   if (flg) {
    2201:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2203:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2204:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2205:       MatInfo     Ainfo,Binfo;
    2206:       PetscInt    nz_local;
    2207:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2209:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2210:       MatGetInfo(B,MAT_LOCAL,&Binfo);
    2211:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2213:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2214:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2216:       if (alg_scalable) {
    2217:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2218:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2219:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2220:       }
    2221:     }
    2222:   }

    2224:   /* Get runtime option */
    2225:   if (product->api_user) {
    2226:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
    2227:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2228:     PetscOptionsEnd();
    2229:   } else {
    2230:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
    2231:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2232:     PetscOptionsEnd();
    2233:   }
    2234:   if (flg) {
    2235:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2236:   }

    2238:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2239:   return(0);
    2240: }

    2242: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2243: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2244: {
    2246:   Mat_Product    *product = C->product;
    2247:   Mat            A=product->A,B=product->B;
    2248:   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
    2249:   PetscInt       nalg = 4;
    2250:   PetscInt       alg = 1; /* set default algorithm  */
    2251:   PetscBool      flg;
    2252:   MPI_Comm       comm;

    2255:   /* Check matrix local sizes */
    2256:   PetscObjectGetComm((PetscObject)C,&comm);
    2257:   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);

    2259:   /* Set default algorithm */
    2260:   PetscStrcmp(C->product->alg,"default",&flg);
    2261:   if (flg) {
    2262:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2263:   }

    2265:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2266:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2267:     MatInfo     Ainfo,Binfo;
    2268:     PetscInt    nz_local;
    2269:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2271:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2272:     MatGetInfo(B,MAT_LOCAL,&Binfo);
    2273:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2275:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2276:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2278:     if (alg_scalable) {
    2279:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2280:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2281:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2282:     }
    2283:   }

    2285:   /* Get runtime option */
    2286:   if (product->api_user) {
    2287:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
    2288:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2289:     PetscOptionsEnd();
    2290:   } else {
    2291:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
    2292:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2293:     PetscOptionsEnd();
    2294:   }
    2295:   if (flg) {
    2296:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2297:   }

    2299:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2300:   return(0);
    2301: }

    2303: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2304: {
    2306:   Mat_Product    *product = C->product;
    2307:   Mat            A=product->A,P=product->B;
    2308:   MPI_Comm       comm;
    2309:   PetscBool      flg;
    2310:   PetscInt       alg=1; /* set default algorithm */
    2311: #if !defined(PETSC_HAVE_HYPRE)
    2312:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
    2313:   PetscInt       nalg=5;
    2314: #else
    2315:   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
    2316:   PetscInt       nalg=6;
    2317: #endif
    2318:   PetscInt       pN=P->cmap->N;

    2321:   /* Check matrix local sizes */
    2322:   PetscObjectGetComm((PetscObject)C,&comm);
    2323:   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);
    2324:   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);

    2326:   /* Set "nonscalable" as default algorithm */
    2327:   PetscStrcmp(C->product->alg,"default",&flg);
    2328:   if (flg) {
    2329:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2331:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2332:     if (pN > 100000) {
    2333:       MatInfo     Ainfo,Pinfo;
    2334:       PetscInt    nz_local;
    2335:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2337:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2338:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
    2339:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2341:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2342:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2344:       if (alg_scalable) {
    2345:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2346:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2347:       }
    2348:     }
    2349:   }

    2351:   /* Get runtime option */
    2352:   if (product->api_user) {
    2353:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
    2354:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2355:     PetscOptionsEnd();
    2356:   } else {
    2357:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
    2358:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2359:     PetscOptionsEnd();
    2360:   }
    2361:   if (flg) {
    2362:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2363:   }

    2365:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2366:   return(0);
    2367: }

    2369: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2370: {
    2371:   Mat_Product *product = C->product;
    2372:   Mat         A = product->A,R=product->B;

    2375:   /* Check matrix local sizes */
    2376:   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);

    2378:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2379:   return(0);
    2380: }

    2382: /*
    2383:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2384: */
    2385: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2386: {
    2388:   Mat_Product    *product = C->product;
    2389:   PetscBool      flg = PETSC_FALSE;
    2390:   PetscInt       alg = 1; /* default algorithm */
    2391:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2392:   PetscInt       nalg = 3;

    2395:   /* Set default algorithm */
    2396:   PetscStrcmp(C->product->alg,"default",&flg);
    2397:   if (flg) {
    2398:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2399:   }

    2401:   /* Get runtime option */
    2402:   if (product->api_user) {
    2403:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
    2404:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2405:     PetscOptionsEnd();
    2406:   } else {
    2407:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
    2408:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
    2409:     PetscOptionsEnd();
    2410:   }
    2411:   if (flg) {
    2412:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2413:   }

    2415:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2416:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2417:   return(0);
    2418: }

    2420: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2421: {
    2423:   Mat_Product    *product = C->product;

    2426:   switch (product->type) {
    2427:   case MATPRODUCT_AB:
    2428:     MatProductSetFromOptions_MPIAIJ_AB(C);
    2429:     break;
    2430:   case MATPRODUCT_AtB:
    2431:     MatProductSetFromOptions_MPIAIJ_AtB(C);
    2432:     break;
    2433:   case MATPRODUCT_PtAP:
    2434:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
    2435:     break;
    2436:   case MATPRODUCT_RARt:
    2437:     MatProductSetFromOptions_MPIAIJ_RARt(C);
    2438:     break;
    2439:   case MATPRODUCT_ABC:
    2440:     MatProductSetFromOptions_MPIAIJ_ABC(C);
    2441:     break;
    2442:   default:
    2443:     break;
    2444:   }
    2445:   return(0);
    2446: }