Date: 2015-10-02T22:07:08+00:00

Actual source code: mpimatmatmult.c
petsc-3.6.2 2015-10-02
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      2: /*
      3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
      4:           C = A * B
      5: */
      6: #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
      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>

     15: PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
     16: {
     18:   const char     *algTypes[2] = {"scalable","nonscalable"};
     19:   PetscInt       alg=0; /* set default algorithm */

     22:   if (scall == MAT_INITIAL_MATRIX) {
     23:     PetscObjectOptionsBegin((PetscObject)A);
     24:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,2,algTypes[0],&alg,NULL);
     25:     PetscOptionsEnd();

     27:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
     28:     switch (alg) {
     29:     case 1:
     30:       MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
     31:       break;
     32:     default:
     33:       MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
     34:       break;
     35:     }
     36:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
     37:   }
     38:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
     39:   (*(*C)->ops->matmultnumeric)(A,B,*C);
     40:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
     41:   return(0);
     42: }

     46: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
     47: {
     49:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
     50:   Mat_PtAPMPI    *ptap = a->ptap;

     53:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     54:   PetscFree(ptap->bufa);
     55:   MatDestroy(&ptap->P_loc);
     56:   MatDestroy(&ptap->P_oth);
     57:   MatDestroy(&ptap->Pt);
     58:   PetscFree(ptap->api);
     59:   PetscFree(ptap->apj);
     60:   PetscFree(ptap->apa);
     61:   ptap->destroy(A);
     62:   PetscFree(ptap);
     63:   return(0);
     64: }

     68: PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
     69: {
     71:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
     72:   Mat_PtAPMPI    *ptap = a->ptap;

     75:   (*ptap->duplicate)(A,op,M);

     77:   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
     78:   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
     79:   return(0);
     80: }

     84: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
     85: {
     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:   PetscInt       *adi=ad->i,*adj,*aoi=ao->i,*aoj;
     91:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
     92:   Mat_SeqAIJ     *p_loc,*p_oth;
     93:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
     94:   PetscScalar    *pa_loc,*pa_oth,*pa,*apa,valtmp,*ca;
     95:   PetscInt       cm   =C->rmap->n,anz,pnz;
     96:   Mat_PtAPMPI    *ptap=c->ptap;
     97:   PetscInt       *api,*apj,*apJ,i,j,k,row;
     98:   PetscInt       cstart=C->cmap->rstart;
     99:   PetscInt       cdnz,conz,k0,k1;
    100:   MPI_Comm       comm;
    101:   PetscMPIInt    size;

    104:   PetscObjectGetComm((PetscObject)A,&comm);
    105:   MPI_Comm_size(comm,&size);

    107:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    108:   /*-----------------------------------------------------*/
    109:   /* update numerical values of P_oth and P_loc */
    110:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    111:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    113:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    114:   /*----------------------------------------------------------*/
    115:   /* get data from symbolic products */
    116:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    117:   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
    118:   if (size >1) {
    119:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    120:     pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
    121:   } else {
    122:     pi_oth=NULL; pj_oth=NULL; pa_oth=NULL;
    123:   }

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

    128:   api = ptap->api;
    129:   apj = ptap->apj;
    130:   for (i=0; i<cm; i++) {
    131:     /* diagonal portion of A */
    132:     anz = adi[i+1] - adi[i];
    133:     adj = ad->j + adi[i];
    134:     ada = ad->a + adi[i];
    135:     for (j=0; j<anz; j++) {
    136:       row = adj[j];
    137:       pnz = pi_loc[row+1] - pi_loc[row];
    138:       pj  = pj_loc + pi_loc[row];
    139:       pa  = pa_loc + pi_loc[row];

    141:       /* perform dense axpy */
    142:       valtmp = ada[j];
    143:       for (k=0; k<pnz; k++) {
    144:         apa[pj[k]] += valtmp*pa[k];
    145:       }
    146:       PetscLogFlops(2.0*pnz);
    147:     }

    149:     /* off-diagonal portion of A */
    150:     anz = aoi[i+1] - aoi[i];
    151:     aoj = ao->j + aoi[i];
    152:     aoa = ao->a + aoi[i];
    153:     for (j=0; j<anz; j++) {
    154:       row = aoj[j];
    155:       pnz = pi_oth[row+1] - pi_oth[row];
    156:       pj  = pj_oth + pi_oth[row];
    157:       pa  = pa_oth + pi_oth[row];

    159:       /* perform dense axpy */
    160:       valtmp = aoa[j];
    161:       for (k=0; k<pnz; k++) {
    162:         apa[pj[k]] += valtmp*pa[k];
    163:       }
    164:       PetscLogFlops(2.0*pnz);
    165:     }

    167:     /* set values in C */
    168:     apJ  = apj + api[i];
    169:     cdnz = cd->i[i+1] - cd->i[i];
    170:     conz = co->i[i+1] - co->i[i];

    172:     /* 1st off-diagoanl part of C */
    173:     ca = coa + co->i[i];
    174:     k  = 0;
    175:     for (k0=0; k0<conz; k0++) {
    176:       if (apJ[k] >= cstart) break;
    177:       ca[k0]      = apa[apJ[k]];
    178:       apa[apJ[k]] = 0.0;
    179:       k++;
    180:     }

    182:     /* diagonal part of C */
    183:     ca = cda + cd->i[i];
    184:     for (k1=0; k1<cdnz; k1++) {
    185:       ca[k1]      = apa[apJ[k]];
    186:       apa[apJ[k]] = 0.0;
    187:       k++;
    188:     }

    190:     /* 2nd off-diagoanl part of C */
    191:     ca = coa + co->i[i];
    192:     for (; k0<conz; k0++) {
    193:       ca[k0]      = apa[apJ[k]];
    194:       apa[apJ[k]] = 0.0;
    195:       k++;
    196:     }
    197:   }
    198:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    199:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    200:   return(0);
    201: }

    205: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat *C)
    206: {
    207:   PetscErrorCode     ierr;
    208:   MPI_Comm           comm;
    209:   PetscMPIInt        size;
    210:   Mat                Cmpi;
    211:   Mat_PtAPMPI        *ptap;
    212:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    213:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data,*c;
    214:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    215:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    216:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    217:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
    218:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
    219:   PetscBT            lnkbt;
    220:   PetscScalar        *apa;
    221:   PetscReal          afill;
    222:   PetscInt           nlnk_max,armax,prmax;

    225:   PetscObjectGetComm((PetscObject)A,&comm);
    226:   MPI_Comm_size(comm,&size);

    228:   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
    229:     SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
    230:   }
    231:
    232:   /* create struct Mat_PtAPMPI and attached it to C later */
    233:   PetscNew(&ptap);

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

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

    241:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    242:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    243:   if (size > 1) {
    244:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    245:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    246:   } else {
    247:     p_oth = NULL;
    248:     pi_oth = NULL; pj_oth = NULL;
    249:   }

    251:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    252:   /*-------------------------------------------------------------------*/
    253:   PetscMalloc1(am+2,&api);
    254:   ptap->api = api;
    255:   api[0]    = 0;

    257:   /* create and initialize a linked list */
    258:   armax    = ad->rmax+ao->rmax;
    259:   if (size >1) {
    260:     prmax    = PetscMax(p_loc->rmax,p_oth->rmax);
    261:   } else {
    262:     prmax = p_loc->rmax;
    263:   }
    264:   nlnk_max = armax*prmax;
    265:   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
    266:   PetscLLCondensedCreate(nlnk_max,pN,&lnk,&lnkbt);

    268:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    269:   PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);

    271:   current_space = free_space;

    273:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    274:   for (i=0; i<am; i++) {
    275:     /* diagonal portion of A */
    276:     nzi = adi[i+1] - adi[i];
    277:     for (j=0; j<nzi; j++) {
    278:       row  = *adj++;
    279:       pnz  = pi_loc[row+1] - pi_loc[row];
    280:       Jptr = pj_loc + pi_loc[row];
    281:       /* add non-zero cols of P into the sorted linked list lnk */
    282:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    283:     }
    284:     /* off-diagonal portion of A */
    285:     nzi = aoi[i+1] - aoi[i];
    286:     for (j=0; j<nzi; j++) {
    287:       row  = *aoj++;
    288:       pnz  = pi_oth[row+1] - pi_oth[row];
    289:       Jptr = pj_oth + pi_oth[row];
    290:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    291:     }

    293:     apnz     = lnk[0];
    294:     api[i+1] = api[i] + apnz;

    296:     /* if free space is not available, double the total space in the list */
    297:     if (current_space->local_remaining<apnz) {
    298:       PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);
    299:       nspacedouble++;
    300:     }

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

    306:     current_space->array           += apnz;
    307:     current_space->local_used      += apnz;
    308:     current_space->local_remaining -= apnz;
    309:   }

    311:   /* Allocate space for apj, initialize apj, and */
    312:   /* destroy list of free space and other temporary array(s) */
    313:   PetscMalloc1(api[am]+1,&ptap->apj);
    314:   apj  = ptap->apj;
    315:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    316:   PetscLLDestroy(lnk,lnkbt);

    318:   /* malloc apa to store dense row A[i,:]*P */
    319:   PetscCalloc1(pN,&apa);

    321:   ptap->apa = apa;

    323:   /* create and assemble symbolic parallel matrix Cmpi */
    324:   /*----------------------------------------------------*/
    325:   MatCreate(comm,&Cmpi);
    326:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    327:   MatSetBlockSizesFromMats(Cmpi,A,P);

    329:   MatSetType(Cmpi,MATMPIAIJ);
    330:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    331:   MatPreallocateFinalize(dnz,onz);
    332:   for (i=0; i<am; i++) {
    333:     row  = i + rstart;
    334:     apnz = api[i+1] - api[i];
    335:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
    336:     apj += apnz;
    337:   }
    338:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    339:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

    341:   ptap->destroy        = Cmpi->ops->destroy;
    342:   ptap->duplicate      = Cmpi->ops->duplicate;
    343:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    344:   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
    345:   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatMatMult;

    347:   /* attach the supporting struct to Cmpi for reuse */
    348:   c       = (Mat_MPIAIJ*)Cmpi->data;
    349:   c->ptap = ptap;

    351:   *C = Cmpi;

    353:   /* set MatInfo */
    354:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    355:   if (afill < 1.0) afill = 1.0;
    356:   Cmpi->info.mallocs           = nspacedouble;
    357:   Cmpi->info.fill_ratio_given  = fill;
    358:   Cmpi->info.fill_ratio_needed = afill;

    360: #if defined(PETSC_USE_INFO)
    361:   if (api[am]) {
    362:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    363:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    364:   } else {
    365:     PetscInfo(Cmpi,"Empty matrix product\n");
    366:   }
    367: #endif
    368:   return(0);
    369: }

    373: PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    374: {

    378:   if (scall == MAT_INITIAL_MATRIX) {
    379:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
    380:     MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);
    381:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
    382:   }
    383:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
    384:   MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);
    385:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
    386:   return(0);
    387: }

    389: typedef struct {
    390:   Mat         workB;
    391:   PetscScalar *rvalues,*svalues;
    392:   MPI_Request *rwaits,*swaits;
    393: } MPIAIJ_MPIDense;

    397: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    398: {
    399:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
    400:   PetscErrorCode  ierr;

    403:   MatDestroy(&contents->workB);
    404:   PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);
    405:   PetscFree(contents);
    406:   return(0);
    407: }

    411: /*
    412:     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
    413:   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option

    415:   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C
    416: */
    417: PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
    418: {
    419:   PetscErrorCode         ierr;
    420:   PetscBool              flg;
    421:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
    422:   PetscInt               nz   = aij->B->cmap->n;
    423:   PetscContainer         container;
    424:   MPIAIJ_MPIDense        *contents;
    425:   VecScatter             ctx   = aij->Mvctx;
    426:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    427:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;

    430:   PetscObjectTypeCompare((PetscObject)B,MATMPIDENSE,&flg);
    431:   if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Second matrix must be mpidense");

    433:   /* Handle case where where user provided the final C matrix rather than calling MatMatMult() with MAT_INITIAL_MATRIX*/
    434:   PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);
    435:   if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"First matrix must be MPIAIJ");

    437:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;

    439:   PetscNew(&contents);
    440:   /* Create work matrix used to store off processor rows of B needed for local product */
    441:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
    442:   /* Create work arrays needed */
    443:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
    444:                       B->cmap->N*to->starts[to->n],&contents->svalues,
    445:                       from->n,&contents->rwaits,
    446:                       to->n,&contents->swaits);

    448:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
    449:   PetscContainerSetPointer(container,contents);
    450:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
    451:   PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);
    452:   PetscContainerDestroy(&container);

    454:   (*C->ops->matmultnumeric)(A,B,C);
    455:   return(0);
    456: }

    460: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
    461: {
    462:   PetscErrorCode         ierr;
    463:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
    464:   PetscInt               nz   = aij->B->cmap->n;
    465:   PetscContainer         container;
    466:   MPIAIJ_MPIDense        *contents;
    467:   VecScatter             ctx   = aij->Mvctx;
    468:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    469:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
    470:   PetscInt               m     = A->rmap->n,n=B->cmap->n;

    473:   MatCreate(PetscObjectComm((PetscObject)B),C);
    474:   MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);
    475:   MatSetBlockSizesFromMats(*C,A,B);
    476:   MatSetType(*C,MATMPIDENSE);
    477:   MatMPIDenseSetPreallocation(*C,NULL);
    478:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
    479:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);

    481:   (*C)->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;

    483:   PetscNew(&contents);
    484:   /* Create work matrix used to store off processor rows of B needed for local product */
    485:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
    486:   /* Create work arrays needed */
    487:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
    488:                       B->cmap->N*to->starts[to->n],&contents->svalues,
    489:                       from->n,&contents->rwaits,
    490:                       to->n,&contents->swaits);

    492:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
    493:   PetscContainerSetPointer(container,contents);
    494:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
    495:   PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);
    496:   PetscContainerDestroy(&container);
    497:   return(0);
    498: }

    502: /*
    503:     Performs an efficient scatter on the rows of B needed by this process; this is
    504:     a modification of the VecScatterBegin_() routines.
    505: */
    506: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
    507: {
    508:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
    509:   PetscErrorCode         ierr;
    510:   PetscScalar            *b,*w,*svalues,*rvalues;
    511:   VecScatter             ctx   = aij->Mvctx;
    512:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    513:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
    514:   PetscInt               i,j,k;
    515:   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
    516:   PetscMPIInt            *sprocs,*rprocs,nrecvs;
    517:   MPI_Request            *swaits,*rwaits;
    518:   MPI_Comm               comm;
    519:   PetscMPIInt            tag  = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
    520:   MPI_Status             status;
    521:   MPIAIJ_MPIDense        *contents;
    522:   PetscContainer         container;
    523:   Mat                    workB;

    526:   PetscObjectGetComm((PetscObject)A,&comm);
    527:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
    528:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
    529:   PetscContainerGetPointer(container,(void**)&contents);

    531:   workB = *outworkB = contents->workB;
    532:   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
    533:   sindices = to->indices;
    534:   sstarts  = to->starts;
    535:   sprocs   = to->procs;
    536:   swaits   = contents->swaits;
    537:   svalues  = contents->svalues;

    539:   rindices = from->indices;
    540:   rstarts  = from->starts;
    541:   rprocs   = from->procs;
    542:   rwaits   = contents->rwaits;
    543:   rvalues  = contents->rvalues;

    545:   MatDenseGetArray(B,&b);
    546:   MatDenseGetArray(workB,&w);

    548:   for (i=0; i<from->n; i++) {
    549:     MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);
    550:   }

    552:   for (i=0; i<to->n; i++) {
    553:     /* pack a message at a time */
    554:     for (j=0; j<sstarts[i+1]-sstarts[i]; j++) {
    555:       for (k=0; k<ncols; k++) {
    556:         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
    557:       }
    558:     }
    559:     MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);
    560:   }

    562:   nrecvs = from->n;
    563:   while (nrecvs) {
    564:     MPI_Waitany(from->n,rwaits,&imdex,&status);
    565:     nrecvs--;
    566:     /* unpack a message at a time */
    567:     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++) {
    568:       for (k=0; k<ncols; k++) {
    569:         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
    570:       }
    571:     }
    572:   }
    573:   if (to->n) {MPI_Waitall(to->n,swaits,to->sstatus);}

    575:   MatDenseRestoreArray(B,&b);
    576:   MatDenseRestoreArray(workB,&w);
    577:   MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);
    578:   MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);
    579:   return(0);
    580: }
    581: extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);

    585: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    586: {
    588:   Mat_MPIAIJ     *aij    = (Mat_MPIAIJ*)A->data;
    589:   Mat_MPIDense   *bdense = (Mat_MPIDense*)B->data;
    590:   Mat_MPIDense   *cdense = (Mat_MPIDense*)C->data;
    591:   Mat            workB;

    594:   /* diagonal block of A times all local rows of B*/
    595:   MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);

    597:   /* get off processor parts of B needed to complete the product */
    598:   MatMPIDenseScatter(A,B,C,&workB);

    600:   /* off-diagonal block of A times nonlocal rows of B */
    601:   MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);
    602:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    603:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    604:   return(0);
    605: }

    609: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    610: {
    612:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    613:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    614:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    615:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    616:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
    617:   Mat_SeqAIJ     *p_loc,*p_oth;
    618:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    619:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
    620:   PetscInt       cm          = C->rmap->n,anz,pnz;
    621:   Mat_PtAPMPI    *ptap       = c->ptap;
    622:   PetscScalar    *apa_sparse = ptap->apa;
    623:   PetscInt       *api,*apj,*apJ,i,j,k,row;
    624:   PetscInt       cstart = C->cmap->rstart;
    625:   PetscInt       cdnz,conz,k0,k1,nextp;
    626:   MPI_Comm       comm;
    627:   PetscMPIInt    size;

    630:   PetscObjectGetComm((PetscObject)A,&comm);
    631:   MPI_Comm_size(comm,&size);

    633:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    634:   /*-----------------------------------------------------*/
    635:   /* update numerical values of P_oth and P_loc */
    636:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    637:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    639:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    640:   /*----------------------------------------------------------*/
    641:   /* get data from symbolic products */
    642:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    643:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    644:   if (size >1) {
    645:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    646:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    647:   } else {
    648:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    649:   }

    651:   api = ptap->api;
    652:   apj = ptap->apj;
    653:   for (i=0; i<cm; i++) {
    654:     apJ = apj + api[i];

    656:     /* diagonal portion of A */
    657:     anz = adi[i+1] - adi[i];
    658:     adj = ad->j + adi[i];
    659:     ada = ad->a + adi[i];
    660:     for (j=0; j<anz; j++) {
    661:       row = adj[j];
    662:       pnz = pi_loc[row+1] - pi_loc[row];
    663:       pj  = pj_loc + pi_loc[row];
    664:       pa  = pa_loc + pi_loc[row];
    665:       /* perform sparse axpy */
    666:       valtmp = ada[j];
    667:       nextp  = 0;
    668:       for (k=0; nextp<pnz; k++) {
    669:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    670:           apa_sparse[k] += valtmp*pa[nextp++];
    671:         }
    672:       }
    673:       PetscLogFlops(2.0*pnz);
    674:     }

    676:     /* off-diagonal portion of A */
    677:     anz = aoi[i+1] - aoi[i];
    678:     aoj = ao->j + aoi[i];
    679:     aoa = ao->a + aoi[i];
    680:     for (j=0; j<anz; j++) {
    681:       row = aoj[j];
    682:       pnz = pi_oth[row+1] - pi_oth[row];
    683:       pj  = pj_oth + pi_oth[row];
    684:       pa  = pa_oth + pi_oth[row];
    685:       /* perform sparse axpy */
    686:       valtmp = aoa[j];
    687:       nextp  = 0;
    688:       for (k=0; nextp<pnz; k++) {
    689:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    690:           apa_sparse[k] += valtmp*pa[nextp++];
    691:         }
    692:       }
    693:       PetscLogFlops(2.0*pnz);
    694:     }

    696:     /* set values in C */
    697:     cdnz = cd->i[i+1] - cd->i[i];
    698:     conz = co->i[i+1] - co->i[i];

    700:     /* 1st off-diagoanl part of C */
    701:     ca = coa + co->i[i];
    702:     k  = 0;
    703:     for (k0=0; k0<conz; k0++) {
    704:       if (apJ[k] >= cstart) break;
    705:       ca[k0]        = apa_sparse[k];
    706:       apa_sparse[k] = 0.0;
    707:       k++;
    708:     }

    710:     /* diagonal part of C */
    711:     ca = cda + cd->i[i];
    712:     for (k1=0; k1<cdnz; k1++) {
    713:       ca[k1]        = apa_sparse[k];
    714:       apa_sparse[k] = 0.0;
    715:       k++;
    716:     }

    718:     /* 2nd off-diagoanl part of C */
    719:     ca = coa + co->i[i];
    720:     for (; k0<conz; k0++) {
    721:       ca[k0]        = apa_sparse[k];
    722:       apa_sparse[k] = 0.0;
    723:       k++;
    724:     }
    725:   }
    726:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    727:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    728:   return(0);
    729: }

    731: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    734: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
    735: {
    736:   PetscErrorCode     ierr;
    737:   MPI_Comm           comm;
    738:   PetscMPIInt        size;
    739:   Mat                Cmpi;
    740:   Mat_PtAPMPI        *ptap;
    741:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    742:   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
    743:   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    744:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    745:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    746:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
    747:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
    748:   PetscInt           nlnk_max,armax,prmax;
    749:   PetscReal          afill;
    750:   PetscScalar        *apa;

    753:   PetscObjectGetComm((PetscObject)A,&comm);
    754:   MPI_Comm_size(comm,&size);

    756:   /* create struct Mat_PtAPMPI and attached it to C later */
    757:   PetscNew(&ptap);

    759:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    760:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    761:
    762:   /* get P_loc by taking all local rows of P */
    763:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    765:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    766:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    767:   if (size > 1) {
    768:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    769:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    770:   } else {
    771:     p_oth  = NULL;
    772:     pi_oth = NULL; pj_oth = NULL;
    773:   }

    775:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    776:   /*-------------------------------------------------------------------*/
    777:   PetscMalloc1(am+2,&api);
    778:   ptap->api = api;
    779:   api[0]    = 0;

    781:   /* create and initialize a linked list */
    782:   armax = ad->rmax+ao->rmax;
    783:   if (size >1) {
    784:     prmax = PetscMax(p_loc->rmax,p_oth->rmax);
    785:   } else {
    786:     prmax = p_loc->rmax;
    787:   }
    788:   nlnk_max = armax*prmax;
    789:   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
    790:   PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);

    792:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    793:   PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);

    795:   current_space = free_space;

    797:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    798:   for (i=0; i<am; i++) {
    799:     /* diagonal portion of A */
    800:     nzi = adi[i+1] - adi[i];
    801:     for (j=0; j<nzi; j++) {
    802:       row  = *adj++;
    803:       pnz  = pi_loc[row+1] - pi_loc[row];
    804:       Jptr = pj_loc + pi_loc[row];
    805:       /* add non-zero cols of P into the sorted linked list lnk */
    806:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    807:     }
    808:     /* off-diagonal portion of A */
    809:     nzi = aoi[i+1] - aoi[i];
    810:     for (j=0; j<nzi; j++) {
    811:       row  = *aoj++;
    812:       pnz  = pi_oth[row+1] - pi_oth[row];
    813:       Jptr = pj_oth + pi_oth[row];
    814:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    815:     }

    817:     apnz     = *lnk;
    818:     api[i+1] = api[i] + apnz;
    819:     if (apnz > apnz_max) apnz_max = apnz;

    821:     /* if free space is not available, double the total space in the list */
    822:     if (current_space->local_remaining<apnz) {
    823:       PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);
    824:       nspacedouble++;
    825:     }

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

    831:     current_space->array           += apnz;
    832:     current_space->local_used      += apnz;
    833:     current_space->local_remaining -= apnz;
    834:   }

    836:   /* Allocate space for apj, initialize apj, and */
    837:   /* destroy list of free space and other temporary array(s) */
    838:   PetscMalloc1(api[am]+1,&ptap->apj);
    839:   apj  = ptap->apj;
    840:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    841:   PetscLLCondensedDestroy_Scalable(lnk);

    843:   /* create and assemble symbolic parallel matrix Cmpi */
    844:   /*----------------------------------------------------*/
    845:   MatCreate(comm,&Cmpi);
    846:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    847:   MatSetBlockSizesFromMats(Cmpi,A,P);
    848:   MatSetType(Cmpi,MATMPIAIJ);
    849:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    850:   MatPreallocateFinalize(dnz,onz);

    852:   /* malloc apa for assembly Cmpi */
    853:   PetscCalloc1(apnz_max,&apa);

    855:   ptap->apa = apa;
    856:   for (i=0; i<am; i++) {
    857:     row  = i + rstart;
    858:     apnz = api[i+1] - api[i];
    859:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
    860:     apj += apnz;
    861:   }
    862:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    863:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

    865:   ptap->destroy             = Cmpi->ops->destroy;
    866:   ptap->duplicate           = Cmpi->ops->duplicate;
    867:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    868:   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
    869:   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;

    871:   /* attach the supporting struct to Cmpi for reuse */
    872:   c       = (Mat_MPIAIJ*)Cmpi->data;
    873:   c->ptap = ptap;

    875:   *C = Cmpi;

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

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

    895: /*-------------------------------------------------------------------------*/
    898: PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C)
    899: {
    901:   const char     *algTypes[3] = {"scalable","nonscalable","matmatmult"};
    902:   PetscInt       alg=0; /* set default algorithm */

    905:   if (scall == MAT_INITIAL_MATRIX) {
    906:     PetscObjectOptionsBegin((PetscObject)A);
    907:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,3,algTypes[0],&alg,NULL);
    908:     PetscOptionsEnd();

    910:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,P,A,0,0);
    911:     switch (alg) {
    912:     case 1:
    913:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(P,A,fill,C);
    914:       break;
    915:     case 2:
    916:     {
    917:       Mat         Pt;
    918:       Mat_PtAPMPI *ptap;
    919:       Mat_MPIAIJ  *c;
    920:       MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);
    921:       MatMatMult(Pt,A,MAT_INITIAL_MATRIX,fill,C);
    922:       c        = (Mat_MPIAIJ*)(*C)->data;
    923:       ptap     = c->ptap;
    924:       ptap->Pt = Pt;
    925:       (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    926:       return(0);
    927:     }
    928:       break;
    929:     default:
    930:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);
    931:       break;
    932:     }
    933:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,P,A,0,0);
    934:   }
    935:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,P,A,0,0);
    936:   (*(*C)->ops->mattransposemultnumeric)(P,A,*C);
    937:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,P,A,0,0);
    938:   return(0);
    939: }

    941: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    944: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    945: {
    947:   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
    948:   Mat_PtAPMPI    *ptap= c->ptap;
    949:   Mat            Pt=ptap->Pt;

    952:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    953:   MatMatMultNumeric(Pt,A,C);
    954:   return(0);
    955: }

    957: /* Non-scalable version, use dense axpy */
    960: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    961: {
    962:   PetscErrorCode      ierr;
    963:   Mat_Merge_SeqsToMPI *merge;
    964:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    965:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    966:   Mat_PtAPMPI         *ptap;
    967:   PetscInt            *adj,*aJ;
    968:   PetscInt            i,j,k,anz,pnz,row,*cj;
    969:   MatScalar           *ada,*aval,*ca,valtmp;
    970:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    971:   MPI_Comm            comm;
    972:   PetscMPIInt         size,rank,taga,*len_s;
    973:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    974:   PetscInt            **buf_ri,**buf_rj;
    975:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    976:   MPI_Request         *s_waits,*r_waits;
    977:   MPI_Status          *status;
    978:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    979:   PetscInt            *ai,*aj,*coi,*coj;
    980:   PetscInt            *poJ,*pdJ;
    981:   Mat                 A_loc;
    982:   Mat_SeqAIJ          *a_loc;

    985:   PetscObjectGetComm((PetscObject)C,&comm);
    986:   MPI_Comm_size(comm,&size);
    987:   MPI_Comm_rank(comm,&rank);

    989:   ptap  = c->ptap;
    990:   merge = ptap->merge;

    992:   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
    993:   /*--------------------------------------------------------------*/
    994:   /* get data from symbolic products */
    995:   coi  = merge->coi; coj = merge->coj;
    996:   PetscCalloc1(coi[pon]+1,&coa);

    998:   bi     = merge->bi; bj = merge->bj;
    999:   owners = merge->rowmap->range;
    1000:   PetscCalloc1(bi[cm]+1,&ba);

    1002:   /* get A_loc by taking all local rows of A */
    1003:   A_loc = ptap->A_loc;
    1004:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1005:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1006:   ai    = a_loc->i;
    1007:   aj    = a_loc->j;

    1009:   PetscCalloc1(A->cmap->N,&aval); /* non-scalable!!! */

    1011:   for (i=0; i<am; i++) {
    1012:     /* 2-a) put A[i,:] to dense array aval */
    1013:     anz = ai[i+1] - ai[i];
    1014:     adj = aj + ai[i];
    1015:     ada = a_loc->a + ai[i];
    1016:     for (j=0; j<anz; j++) {
    1017:       aval[adj[j]] = ada[j];
    1018:     }

    1020:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1021:     /*--------------------------------------------------------------*/
    1022:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1023:     pnz = po->i[i+1] - po->i[i];
    1024:     poJ = po->j + po->i[i];
    1025:     pA  = po->a + po->i[i];
    1026:     for (j=0; j<pnz; j++) {
    1027:       row = poJ[j];
    1028:       cnz = coi[row+1] - coi[row];
    1029:       cj  = coj + coi[row];
    1030:       ca  = coa + coi[row];
    1031:       /* perform dense axpy */
    1032:       valtmp = pA[j];
    1033:       for (k=0; k<cnz; k++) {
    1034:         ca[k] += valtmp*aval[cj[k]];
    1035:       }
    1036:       PetscLogFlops(2.0*cnz);
    1037:     }

    1039:     /* put the value into Cd (diagonal part) */
    1040:     pnz = pd->i[i+1] - pd->i[i];
    1041:     pdJ = pd->j + pd->i[i];
    1042:     pA  = pd->a + pd->i[i];
    1043:     for (j=0; j<pnz; j++) {
    1044:       row = pdJ[j];
    1045:       cnz = bi[row+1] - bi[row];
    1046:       cj  = bj + bi[row];
    1047:       ca  = ba + bi[row];
    1048:       /* perform dense axpy */
    1049:       valtmp = pA[j];
    1050:       for (k=0; k<cnz; k++) {
    1051:         ca[k] += valtmp*aval[cj[k]];
    1052:       }
    1053:       PetscLogFlops(2.0*cnz);
    1054:     }

    1056:     /* zero the current row of Pt*A */
    1057:     aJ = aj + ai[i];
    1058:     for (k=0; k<anz; k++) aval[aJ[k]] = 0.0;
    1059:   }

    1061:   /* 3) send and recv matrix values coa */
    1062:   /*------------------------------------*/
    1063:   buf_ri = merge->buf_ri;
    1064:   buf_rj = merge->buf_rj;
    1065:   len_s  = merge->len_s;
    1066:   PetscCommGetNewTag(comm,&taga);
    1067:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1069:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1070:   for (proc=0,k=0; proc<size; proc++) {
    1071:     if (!len_s[proc]) continue;
    1072:     i    = merge->owners_co[proc];
    1073:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1074:     k++;
    1075:   }
    1076:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1077:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1079:   PetscFree2(s_waits,status);
    1080:   PetscFree(r_waits);
    1081:   PetscFree(coa);

    1083:   /* 4) insert local Cseq and received values into Cmpi */
    1084:   /*----------------------------------------------------*/
    1085:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1086:   for (k=0; k<merge->nrecv; k++) {
    1087:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1088:     nrows       = *(buf_ri_k[k]);
    1089:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1090:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1091:   }

    1093:   for (i=0; i<cm; i++) {
    1094:     row  = owners[rank] + i; /* global row index of C_seq */
    1095:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1096:     ba_i = ba + bi[i];
    1097:     bnz  = bi[i+1] - bi[i];
    1098:     /* add received vals into ba */
    1099:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1100:       /* i-th row */
    1101:       if (i == *nextrow[k]) {
    1102:         cnz    = *(nextci[k]+1) - *nextci[k];
    1103:         cj     = buf_rj[k] + *(nextci[k]);
    1104:         ca     = abuf_r[k] + *(nextci[k]);
    1105:         nextcj = 0;
    1106:         for (j=0; nextcj<cnz; j++) {
    1107:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1108:             ba_i[j] += ca[nextcj++];
    1109:           }
    1110:         }
    1111:         nextrow[k]++; nextci[k]++;
    1112:         PetscLogFlops(2.0*cnz);
    1113:       }
    1114:     }
    1115:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1116:   }
    1117:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1118:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1120:   PetscFree(ba);
    1121:   PetscFree(abuf_r[0]);
    1122:   PetscFree(abuf_r);
    1123:   PetscFree3(buf_ri_k,nextrow,nextci);
    1124:   PetscFree(aval);
    1125:   return(0);
    1126: }

    1128: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
    1129: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1132: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat *C)
    1133: {
    1134:   PetscErrorCode      ierr;
    1135:   Mat                 Cmpi,A_loc,POt,PDt;
    1136:   Mat_PtAPMPI         *ptap;
    1137:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1138:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
    1139:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1140:   PetscInt            nnz;
    1141:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1142:   PetscInt            am=A->rmap->n,pn=P->cmap->n;
    1143:   PetscBT             lnkbt;
    1144:   MPI_Comm            comm;
    1145:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1146:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1147:   PetscInt            len,proc,*dnz,*onz,*owners;
    1148:   PetscInt            nzi,*bi,*bj;
    1149:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1150:   MPI_Request         *swaits,*rwaits;
    1151:   MPI_Status          *sstatus,rstatus;
    1152:   Mat_Merge_SeqsToMPI *merge;
    1153:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1154:   PetscReal           afill  =1.0,afill_tmp;
    1155:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
    1156:   PetscScalar         *vals;
    1157:   Mat_SeqAIJ          *a_loc, *pdt,*pot;

    1160:   PetscObjectGetComm((PetscObject)A,&comm);
    1161:   /* check if matrix local sizes are compatible */
    1162:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
    1163:     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);
    1164:   }

    1166:   MPI_Comm_size(comm,&size);
    1167:   MPI_Comm_rank(comm,&rank);

    1169:   /* create struct Mat_PtAPMPI and attached it to C later */
    1170:   PetscNew(&ptap);

    1172:   /* get A_loc by taking all local rows of A */
    1173:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1175:   ptap->A_loc = A_loc;

    1177:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1178:   ai    = a_loc->i;
    1179:   aj    = a_loc->j;

    1181:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1182:   /*----------------------------------------------------*/
    1183:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1184:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1185:   pdti = pdt->i; pdtj = pdt->j;

    1187:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1188:   pot  = (Mat_SeqAIJ*)POt->data;
    1189:   poti = pot->i; potj = pot->j;

    1191:   /* then, compute symbolic Co = (p->B)^T*A */
    1192:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors >= (num of nonzero rows of C_seq) - pn */
    1193:   PetscMalloc1(pon+1,&coi);
    1194:   coi[0] = 0;

    1196:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1197:   nnz           = fill*(poti[pon] + ai[am]);
    1198:   PetscFreeSpaceGet(nnz,&free_space);
    1199:   current_space = free_space;

    1201:   /* create and initialize a linked list */
    1202:   i     = PetscMax(pdt->rmax,pot->rmax);
    1203:   Crmax = i*a_loc->rmax*size;
    1204:   if (!Crmax || Crmax > aN) Crmax = aN;
    1205:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);

    1207:   for (i=0; i<pon; i++) {
    1208:     pnz = poti[i+1] - poti[i];
    1209:     ptJ = potj + poti[i];
    1210:     for (j=0; j<pnz; j++) {
    1211:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1212:       anz  = ai[row+1] - ai[row];
    1213:       Jptr = aj + ai[row];
    1214:       /* add non-zero cols of AP into the sorted linked list lnk */
    1215:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
    1216:     }
    1217:     nnz = lnk[0];

    1219:     /* If free space is not available, double the total space in the list */
    1220:     if (current_space->local_remaining<nnz) {
    1221:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
    1222:       nspacedouble++;
    1223:     }

    1225:     /* Copy data into free space, and zero out denserows */
    1226:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);

    1228:     current_space->array           += nnz;
    1229:     current_space->local_used      += nnz;
    1230:     current_space->local_remaining -= nnz;

    1232:     coi[i+1] = coi[i] + nnz;
    1233:   }

    1235:   PetscMalloc1(coi[pon]+1,&coj);
    1236:   PetscFreeSpaceContiguous(&free_space,coj);

    1238:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1239:   if (afill_tmp > afill) afill = afill_tmp;

    1241:   /* send j-array (coj) of Co to other processors */
    1242:   /*----------------------------------------------*/
    1243:   /* determine row ownership */
    1244:   PetscNew(&merge);
    1245:   PetscLayoutCreate(comm,&merge->rowmap);

    1247:   merge->rowmap->n  = pn;
    1248:   merge->rowmap->bs = 1;

    1250:   PetscLayoutSetUp(merge->rowmap);
    1251:   owners = merge->rowmap->range;

    1253:   /* determine the number of messages to send, their lengths */
    1254:   PetscCalloc1(size,&len_si);
    1255:   PetscMalloc1(size,&merge->len_s);

    1257:   len_s        = merge->len_s;
    1258:   merge->nsend = 0;

    1260:   PetscMalloc1(size+2,&owners_co);
    1261:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

    1263:   proc = 0;
    1264:   for (i=0; i<pon; i++) {
    1265:     while (prmap[i] >= owners[proc+1]) proc++;
    1266:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1267:     len_s[proc] += coi[i+1] - coi[i];
    1268:   }

    1270:   len          = 0; /* max length of buf_si[] */
    1271:   owners_co[0] = 0;
    1272:   for (proc=0; proc<size; proc++) {
    1273:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1274:     if (len_si[proc]) {
    1275:       merge->nsend++;
    1276:       len_si[proc] = 2*(len_si[proc] + 1);
    1277:       len         += len_si[proc];
    1278:     }
    1279:   }

    1281:   /* determine the number and length of messages to receive for coi and coj  */
    1282:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1283:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1285:   /* post the Irecv and Isend of coj */
    1286:   PetscCommGetNewTag(comm,&tagj);
    1287:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1288:   PetscMalloc1(merge->nsend+1,&swaits);
    1289:   for (proc=0, k=0; proc<size; proc++) {
    1290:     if (!len_s[proc]) continue;
    1291:     i    = owners_co[proc];
    1292:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1293:     k++;
    1294:   }

    1296:   /* receives and sends of coj are complete */
    1297:   PetscMalloc1(size,&sstatus);
    1298:   for (i=0; i<merge->nrecv; i++) {
    1299:     PetscMPIInt icompleted;
    1300:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1301:   }
    1302:   PetscFree(rwaits);
    1303:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1305:   /* send and recv coi */
    1306:   /*-------------------*/
    1307:   PetscCommGetNewTag(comm,&tagi);
    1308:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1309:   PetscMalloc1(len+1,&buf_s);
    1310:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1311:   for (proc=0,k=0; proc<size; proc++) {
    1312:     if (!len_s[proc]) continue;
    1313:     /* form outgoing message for i-structure:
    1314:          buf_si[0]:                 nrows to be sent
    1315:                [1:nrows]:           row index (global)
    1316:                [nrows+1:2*nrows+1]: i-structure index
    1317:     */
    1318:     /*-------------------------------------------*/
    1319:     nrows       = len_si[proc]/2 - 1;
    1320:     buf_si_i    = buf_si + nrows+1;
    1321:     buf_si[0]   = nrows;
    1322:     buf_si_i[0] = 0;
    1323:     nrows       = 0;
    1324:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1325:       nzi               = coi[i+1] - coi[i];
    1326:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
    1327:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1328:       nrows++;
    1329:     }
    1330:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1331:     k++;
    1332:     buf_si += len_si[proc];
    1333:   }
    1334:   i = merge->nrecv;
    1335:   while (i--) {
    1336:     PetscMPIInt icompleted;
    1337:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1338:   }
    1339:   PetscFree(rwaits);
    1340:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1341:   PetscFree(len_si);
    1342:   PetscFree(len_ri);
    1343:   PetscFree(swaits);
    1344:   PetscFree(sstatus);
    1345:   PetscFree(buf_s);

    1347:   /* compute the local portion of C (mpi mat) */
    1348:   /*------------------------------------------*/
    1349:   /* allocate bi array and free space for accumulating nonzero column info */
    1350:   PetscMalloc1(pn+1,&bi);
    1351:   bi[0] = 0;

    1353:   /* set initial free space to be fill*(nnz(P) + nnz(A)) */
    1354:   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
    1355:   PetscFreeSpaceGet(nnz,&free_space);
    1356:   current_space = free_space;

    1358:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1359:   for (k=0; k<merge->nrecv; k++) {
    1360:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1361:     nrows       = *buf_ri_k[k];
    1362:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1363:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1364:   }

    1366:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1367:   rmax = 0;
    1368:   for (i=0; i<pn; i++) {
    1369:     /* add pdt[i,:]*AP into lnk */
    1370:     pnz = pdti[i+1] - pdti[i];
    1371:     ptJ = pdtj + pdti[i];
    1372:     for (j=0; j<pnz; j++) {
    1373:       row  = ptJ[j];  /* row of AP == col of Pt */
    1374:       anz  = ai[row+1] - ai[row];
    1375:       Jptr = aj + ai[row];
    1376:       /* add non-zero cols of AP into the sorted linked list lnk */
    1377:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
    1378:     }

    1380:     /* add received col data into lnk */
    1381:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1382:       if (i == *nextrow[k]) { /* i-th row */
    1383:         nzi  = *(nextci[k]+1) - *nextci[k];
    1384:         Jptr = buf_rj[k] + *nextci[k];
    1385:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1386:         nextrow[k]++; nextci[k]++;
    1387:       }
    1388:     }
    1389:     nnz = lnk[0];

    1391:     /* if free space is not available, make more free space */
    1392:     if (current_space->local_remaining<nnz) {
    1393:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
    1394:       nspacedouble++;
    1395:     }
    1396:     /* copy data into free space, then initialize lnk */
    1397:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);
    1398:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    1400:     current_space->array           += nnz;
    1401:     current_space->local_used      += nnz;
    1402:     current_space->local_remaining -= nnz;

    1404:     bi[i+1] = bi[i] + nnz;
    1405:     if (nnz > rmax) rmax = nnz;
    1406:   }
    1407:   PetscFree3(buf_ri_k,nextrow,nextci);

    1409:   PetscMalloc1(bi[pn]+1,&bj);
    1410:   PetscFreeSpaceContiguous(&free_space,bj);

    1412:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    1413:   if (afill_tmp > afill) afill = afill_tmp;
    1414:   PetscLLCondensedDestroy(lnk,lnkbt);
    1415:   MatDestroy(&POt);
    1416:   MatDestroy(&PDt);

    1418:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
    1419:   /*----------------------------------------------------------------------------------*/
    1420:   PetscCalloc1(rmax+1,&vals);

    1422:   MatCreate(comm,&Cmpi);
    1423:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    1424:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    1425:   MatSetType(Cmpi,MATMPIAIJ);
    1426:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    1427:   MatPreallocateFinalize(dnz,onz);
    1428:   MatSetBlockSize(Cmpi,1);
    1429:   for (i=0; i<pn; i++) {
    1430:     row  = i + rstart;
    1431:     nnz  = bi[i+1] - bi[i];
    1432:     Jptr = bj + bi[i];
    1433:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
    1434:   }
    1435:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    1436:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
    1437:   PetscFree(vals);

    1439:   merge->bi        = bi;
    1440:   merge->bj        = bj;
    1441:   merge->coi       = coi;
    1442:   merge->coj       = coj;
    1443:   merge->buf_ri    = buf_ri;
    1444:   merge->buf_rj    = buf_rj;
    1445:   merge->owners_co = owners_co;
    1446:   merge->destroy   = Cmpi->ops->destroy;
    1447:   merge->duplicate = Cmpi->ops->duplicate;

    1449:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1450:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
    1451:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

    1453:   /* attach the supporting struct to Cmpi for reuse */
    1454:   c           = (Mat_MPIAIJ*)Cmpi->data;
    1455:   c->ptap     = ptap;
    1456:   ptap->api   = NULL;
    1457:   ptap->apj   = NULL;
    1458:   ptap->merge = merge;
    1459:   ptap->rmax  = rmax;

    1461:   *C = Cmpi;
    1462: #if defined(PETSC_USE_INFO)
    1463:   if (bi[pn] != 0) {
    1464:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1465:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    1466:   } else {
    1467:     PetscInfo(Cmpi,"Empty matrix product\n");
    1468:   }
    1469: #endif
    1470:   return(0);
    1471: }

    1475: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1476: {
    1477:   PetscErrorCode      ierr;
    1478:   Mat_Merge_SeqsToMPI *merge;
    1479:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    1480:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1481:   Mat_PtAPMPI         *ptap;
    1482:   PetscInt            *adj;
    1483:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1484:   MatScalar           *ada,*ca,valtmp;
    1485:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1486:   MPI_Comm            comm;
    1487:   PetscMPIInt         size,rank,taga,*len_s;
    1488:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1489:   PetscInt            **buf_ri,**buf_rj;
    1490:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1491:   MPI_Request         *s_waits,*r_waits;
    1492:   MPI_Status          *status;
    1493:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1494:   PetscInt            *ai,*aj,*coi,*coj;
    1495:   PetscInt            *poJ,*pdJ;
    1496:   Mat                 A_loc;
    1497:   Mat_SeqAIJ          *a_loc;

    1500:   PetscObjectGetComm((PetscObject)C,&comm);
    1501:   MPI_Comm_size(comm,&size);
    1502:   MPI_Comm_rank(comm,&rank);

    1504:   ptap  = c->ptap;
    1505:   merge = ptap->merge;

    1507:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1508:   /*------------------------------------------*/
    1509:   /* get data from symbolic products */
    1510:   coi    = merge->coi; coj = merge->coj;
    1511:   PetscCalloc1(coi[pon]+1,&coa);
    1512:   bi     = merge->bi; bj = merge->bj;
    1513:   owners = merge->rowmap->range;
    1514:   PetscCalloc1(bi[cm]+1,&ba);

    1516:   /* get A_loc by taking all local rows of A */
    1517:   A_loc = ptap->A_loc;
    1518:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1519:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1520:   ai    = a_loc->i;
    1521:   aj    = a_loc->j;

    1523:   for (i=0; i<am; i++) {
    1524:     anz = ai[i+1] - ai[i];
    1525:     adj = aj + ai[i];
    1526:     ada = a_loc->a + ai[i];

    1528:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1529:     /*-------------------------------------------------------------*/
    1530:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1531:     pnz = po->i[i+1] - po->i[i];
    1532:     poJ = po->j + po->i[i];
    1533:     pA  = po->a + po->i[i];
    1534:     for (j=0; j<pnz; j++) {
    1535:       row = poJ[j];
    1536:       cj  = coj + coi[row];
    1537:       ca  = coa + coi[row];
    1538:       /* perform sparse axpy */
    1539:       nexta  = 0;
    1540:       valtmp = pA[j];
    1541:       for (k=0; nexta<anz; k++) {
    1542:         if (cj[k] == adj[nexta]) {
    1543:           ca[k] += valtmp*ada[nexta];
    1544:           nexta++;
    1545:         }
    1546:       }
    1547:       PetscLogFlops(2.0*anz);
    1548:     }

    1550:     /* put the value into Cd (diagonal part) */
    1551:     pnz = pd->i[i+1] - pd->i[i];
    1552:     pdJ = pd->j + pd->i[i];
    1553:     pA  = pd->a + pd->i[i];
    1554:     for (j=0; j<pnz; j++) {
    1555:       row = pdJ[j];
    1556:       cj  = bj + bi[row];
    1557:       ca  = ba + bi[row];
    1558:       /* perform sparse axpy */
    1559:       nexta  = 0;
    1560:       valtmp = pA[j];
    1561:       for (k=0; nexta<anz; k++) {
    1562:         if (cj[k] == adj[nexta]) {
    1563:           ca[k] += valtmp*ada[nexta];
    1564:           nexta++;
    1565:         }
    1566:       }
    1567:       PetscLogFlops(2.0*anz);
    1568:     }
    1569:   }

    1571:   /* 3) send and recv matrix values coa */
    1572:   /*------------------------------------*/
    1573:   buf_ri = merge->buf_ri;
    1574:   buf_rj = merge->buf_rj;
    1575:   len_s  = merge->len_s;
    1576:   PetscCommGetNewTag(comm,&taga);
    1577:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1579:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1580:   for (proc=0,k=0; proc<size; proc++) {
    1581:     if (!len_s[proc]) continue;
    1582:     i    = merge->owners_co[proc];
    1583:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1584:     k++;
    1585:   }
    1586:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1587:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1589:   PetscFree2(s_waits,status);
    1590:   PetscFree(r_waits);
    1591:   PetscFree(coa);

    1593:   /* 4) insert local Cseq and received values into Cmpi */
    1594:   /*----------------------------------------------------*/
    1595:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1596:   for (k=0; k<merge->nrecv; k++) {
    1597:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1598:     nrows       = *(buf_ri_k[k]);
    1599:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1600:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1601:   }

    1603:   for (i=0; i<cm; i++) {
    1604:     row  = owners[rank] + i; /* global row index of C_seq */
    1605:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1606:     ba_i = ba + bi[i];
    1607:     bnz  = bi[i+1] - bi[i];
    1608:     /* add received vals into ba */
    1609:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1610:       /* i-th row */
    1611:       if (i == *nextrow[k]) {
    1612:         cnz    = *(nextci[k]+1) - *nextci[k];
    1613:         cj     = buf_rj[k] + *(nextci[k]);
    1614:         ca     = abuf_r[k] + *(nextci[k]);
    1615:         nextcj = 0;
    1616:         for (j=0; nextcj<cnz; j++) {
    1617:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1618:             ba_i[j] += ca[nextcj++];
    1619:           }
    1620:         }
    1621:         nextrow[k]++; nextci[k]++;
    1622:         PetscLogFlops(2.0*cnz);
    1623:       }
    1624:     }
    1625:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1626:   }
    1627:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1628:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1630:   PetscFree(ba);
    1631:   PetscFree(abuf_r[0]);
    1632:   PetscFree(abuf_r);
    1633:   PetscFree3(buf_ri_k,nextrow,nextci);
    1634:   return(0);
    1635: }

    1637: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
    1638: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ();
    1639:    differ from MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable in using LLCondensedCreate_Scalable() */
    1642: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C)
    1643: {
    1644:   PetscErrorCode      ierr;
    1645:   Mat                 Cmpi,A_loc,POt,PDt;
    1646:   Mat_PtAPMPI         *ptap;
    1647:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1648:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
    1649:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1650:   PetscInt            nnz;
    1651:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1652:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1653:   MPI_Comm            comm;
    1654:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1655:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1656:   PetscInt            len,proc,*dnz,*onz,*owners;
    1657:   PetscInt            nzi,*bi,*bj;
    1658:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1659:   MPI_Request         *swaits,*rwaits;
    1660:   MPI_Status          *sstatus,rstatus;
    1661:   Mat_Merge_SeqsToMPI *merge;
    1662:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1663:   PetscReal           afill  =1.0,afill_tmp;
    1664:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
    1665:   PetscScalar         *vals;
    1666:   Mat_SeqAIJ          *a_loc, *pdt,*pot;

    1669:   PetscObjectGetComm((PetscObject)A,&comm);
    1670:   /* check if matrix local sizes are compatible */
    1671:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
    1672:     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);
    1673:   }

    1675:   MPI_Comm_size(comm,&size);
    1676:   MPI_Comm_rank(comm,&rank);

    1678:   /* create struct Mat_PtAPMPI and attached it to C later */
    1679:   PetscNew(&ptap);

    1681:   /* get A_loc by taking all local rows of A */
    1682:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1684:   ptap->A_loc = A_loc;
    1685:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1686:   ai          = a_loc->i;
    1687:   aj          = a_loc->j;

    1689:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1690:   /*----------------------------------------------------*/
    1691:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1692:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1693:   pdti = pdt->i; pdtj = pdt->j;

    1695:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1696:   pot  = (Mat_SeqAIJ*)POt->data;
    1697:   poti = pot->i; potj = pot->j;

    1699:   /* then, compute symbolic Co = (p->B)^T*A */
    1700:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1701:                          >= (num of nonzero rows of C_seq) - pn */
    1702:   PetscMalloc1(pon+1,&coi);
    1703:   coi[0] = 0;

    1705:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1706:   nnz           = fill*(poti[pon] + ai[am]);
    1707:   PetscFreeSpaceGet(nnz,&free_space);
    1708:   current_space = free_space;

    1710:   /* create and initialize a linked list */
    1711:   i     = PetscMax(pdt->rmax,pot->rmax);
    1712:   Crmax = i*a_loc->rmax*size; /* non-scalable! */
    1713:   if (!Crmax || Crmax > aN) Crmax = aN;
    1714:   PetscLLCondensedCreate_Scalable(Crmax,&lnk);

    1716:   for (i=0; i<pon; i++) {
    1717:     pnz = poti[i+1] - poti[i];
    1718:     ptJ = potj + poti[i];
    1719:     for (j=0; j<pnz; j++) {
    1720:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1721:       anz  = ai[row+1] - ai[row];
    1722:       Jptr = aj + ai[row];
    1723:       /* add non-zero cols of AP into the sorted linked list lnk */
    1724:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1725:     }
    1726:     nnz = lnk[0];

    1728:     /* If free space is not available, double the total space in the list */
    1729:     if (current_space->local_remaining<nnz) {
    1730:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
    1731:       nspacedouble++;
    1732:     }

    1734:     /* Copy data into free space, and zero out denserows */
    1735:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1737:     current_space->array           += nnz;
    1738:     current_space->local_used      += nnz;
    1739:     current_space->local_remaining -= nnz;

    1741:     coi[i+1] = coi[i] + nnz;
    1742:   }

    1744:   PetscMalloc1(coi[pon]+1,&coj);
    1745:   PetscFreeSpaceContiguous(&free_space,coj);

    1747:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1748:   if (afill_tmp > afill) afill = afill_tmp;

    1750:   /* send j-array (coj) of Co to other processors */
    1751:   /*----------------------------------------------*/
    1752:   /* determine row ownership */
    1753:   PetscNew(&merge);
    1754:   PetscLayoutCreate(comm,&merge->rowmap);

    1756:   merge->rowmap->n  = pn;
    1757:   merge->rowmap->bs = 1;

    1759:   PetscLayoutSetUp(merge->rowmap);
    1760:   owners = merge->rowmap->range;

    1762:   /* determine the number of messages to send, their lengths */
    1763:   PetscCalloc1(size,&len_si);
    1764:   PetscMalloc1(size,&merge->len_s);

    1766:   len_s        = merge->len_s;
    1767:   merge->nsend = 0;

    1769:   PetscMalloc1(size+2,&owners_co);
    1770:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

    1772:   proc = 0;
    1773:   for (i=0; i<pon; i++) {
    1774:     while (prmap[i] >= owners[proc+1]) proc++;
    1775:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1776:     len_s[proc] += coi[i+1] - coi[i];
    1777:   }

    1779:   len          = 0; /* max length of buf_si[] */
    1780:   owners_co[0] = 0;
    1781:   for (proc=0; proc<size; proc++) {
    1782:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1783:     if (len_si[proc]) {
    1784:       merge->nsend++;
    1785:       len_si[proc] = 2*(len_si[proc] + 1);
    1786:       len         += len_si[proc];
    1787:     }
    1788:   }

    1790:   /* determine the number and length of messages to receive for coi and coj  */
    1791:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1792:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1794:   /* post the Irecv and Isend of coj */
    1795:   PetscCommGetNewTag(comm,&tagj);
    1796:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1797:   PetscMalloc1(merge->nsend+1,&swaits);
    1798:   for (proc=0, k=0; proc<size; proc++) {
    1799:     if (!len_s[proc]) continue;
    1800:     i    = owners_co[proc];
    1801:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1802:     k++;
    1803:   }

    1805:   /* receives and sends of coj are complete */
    1806:   PetscMalloc1(size,&sstatus);
    1807:   for (i=0; i<merge->nrecv; i++) {
    1808:     PetscMPIInt icompleted;
    1809:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1810:   }
    1811:   PetscFree(rwaits);
    1812:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1814:   /* send and recv coi */
    1815:   /*-------------------*/
    1816:   PetscCommGetNewTag(comm,&tagi);
    1817:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1818:   PetscMalloc1(len+1,&buf_s);
    1819:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1820:   for (proc=0,k=0; proc<size; proc++) {
    1821:     if (!len_s[proc]) continue;
    1822:     /* form outgoing message for i-structure:
    1823:          buf_si[0]:                 nrows to be sent
    1824:                [1:nrows]:           row index (global)
    1825:                [nrows+1:2*nrows+1]: i-structure index
    1826:     */
    1827:     /*-------------------------------------------*/
    1828:     nrows       = len_si[proc]/2 - 1;
    1829:     buf_si_i    = buf_si + nrows+1;
    1830:     buf_si[0]   = nrows;
    1831:     buf_si_i[0] = 0;
    1832:     nrows       = 0;
    1833:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1834:       nzi               = coi[i+1] - coi[i];
    1835:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1836:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1837:       nrows++;
    1838:     }
    1839:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1840:     k++;
    1841:     buf_si += len_si[proc];
    1842:   }
    1843:   i = merge->nrecv;
    1844:   while (i--) {
    1845:     PetscMPIInt icompleted;
    1846:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1847:   }
    1848:   PetscFree(rwaits);
    1849:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1850:   PetscFree(len_si);
    1851:   PetscFree(len_ri);
    1852:   PetscFree(swaits);
    1853:   PetscFree(sstatus);
    1854:   PetscFree(buf_s);

    1856:   /* compute the local portion of C (mpi mat) */
    1857:   /*------------------------------------------*/
    1858:   /* allocate bi array and free space for accumulating nonzero column info */
    1859:   PetscMalloc1(pn+1,&bi);
    1860:   bi[0] = 0;

    1862:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1863:   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
    1864:   PetscFreeSpaceGet(nnz,&free_space);
    1865:   current_space = free_space;

    1867:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1868:   for (k=0; k<merge->nrecv; k++) {
    1869:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1870:     nrows       = *buf_ri_k[k];
    1871:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1872:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure  */
    1873:   }

    1875:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1876:   rmax = 0;
    1877:   for (i=0; i<pn; i++) {
    1878:     /* add pdt[i,:]*AP into lnk */
    1879:     pnz = pdti[i+1] - pdti[i];
    1880:     ptJ = pdtj + pdti[i];
    1881:     for (j=0; j<pnz; j++) {
    1882:       row  = ptJ[j];  /* row of AP == col of Pt */
    1883:       anz  = ai[row+1] - ai[row];
    1884:       Jptr = aj + ai[row];
    1885:       /* add non-zero cols of AP into the sorted linked list lnk */
    1886:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1887:     }

    1889:     /* add received col data into lnk */
    1890:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1891:       if (i == *nextrow[k]) { /* i-th row */
    1892:         nzi  = *(nextci[k]+1) - *nextci[k];
    1893:         Jptr = buf_rj[k] + *nextci[k];
    1894:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    1895:         nextrow[k]++; nextci[k]++;
    1896:       }
    1897:     }
    1898:     nnz = lnk[0];

    1900:     /* if free space is not available, make more free space */
    1901:     if (current_space->local_remaining<nnz) {
    1902:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
    1903:       nspacedouble++;
    1904:     }
    1905:     /* copy data into free space, then initialize lnk */
    1906:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    1907:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    1909:     current_space->array           += nnz;
    1910:     current_space->local_used      += nnz;
    1911:     current_space->local_remaining -= nnz;

    1913:     bi[i+1] = bi[i] + nnz;
    1914:     if (nnz > rmax) rmax = nnz;
    1915:   }
    1916:   PetscFree3(buf_ri_k,nextrow,nextci);

    1918:   PetscMalloc1(bi[pn]+1,&bj);
    1919:   PetscFreeSpaceContiguous(&free_space,bj);
    1920:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    1921:   if (afill_tmp > afill) afill = afill_tmp;
    1922:   PetscLLCondensedDestroy_Scalable(lnk);
    1923:   MatDestroy(&POt);
    1924:   MatDestroy(&PDt);

    1926:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
    1927:   /*----------------------------------------------------------------------------------*/
    1928:   PetscCalloc1(rmax+1,&vals);

    1930:   MatCreate(comm,&Cmpi);
    1931:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    1932:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    1933:   MatSetType(Cmpi,MATMPIAIJ);
    1934:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    1935:   MatPreallocateFinalize(dnz,onz);
    1936:   MatSetBlockSize(Cmpi,1);
    1937:   for (i=0; i<pn; i++) {
    1938:     row  = i + rstart;
    1939:     nnz  = bi[i+1] - bi[i];
    1940:     Jptr = bj + bi[i];
    1941:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
    1942:   }
    1943:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    1944:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
    1945:   PetscFree(vals);

    1947:   merge->bi        = bi;
    1948:   merge->bj        = bj;
    1949:   merge->coi       = coi;
    1950:   merge->coj       = coj;
    1951:   merge->buf_ri    = buf_ri;
    1952:   merge->buf_rj    = buf_rj;
    1953:   merge->owners_co = owners_co;
    1954:   merge->destroy   = Cmpi->ops->destroy;
    1955:   merge->duplicate = Cmpi->ops->duplicate;

    1957:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
    1958:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
    1959:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

    1961:   /* attach the supporting struct to Cmpi for reuse */
    1962:   c = (Mat_MPIAIJ*)Cmpi->data;

    1964:   c->ptap     = ptap;
    1965:   ptap->api   = NULL;
    1966:   ptap->apj   = NULL;
    1967:   ptap->merge = merge;
    1968:   ptap->rmax  = rmax;
    1969:   ptap->apa   = NULL;

    1971:   *C = Cmpi;
    1972: #if defined(PETSC_USE_INFO)
    1973:   if (bi[pn] != 0) {
    1974:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1975:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    1976:   } else {
    1977:     PetscInfo(Cmpi,"Empty matrix product\n");
    1978:   }
    1979: #endif
    1980:   return(0);
    1981: }