Actual source code: mpimatmatmult.c

petsc-3.15.0 2021-03-30
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  2: /*
  3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
  4:           C = A * B
  5: */
  6: #include <../src/mat/impls/aij/seq/aij.h>
  7: #include <../src/mat/utils/freespace.h>
  8: #include <../src/mat/impls/aij/mpi/mpiaij.h>
  9: #include <petscbt.h>
 10: #include <../src/mat/impls/dense/mpi/mpidense.h>
 11: #include <petsc/private/vecimpl.h>
 12: #include <petsc/private/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:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
112:   /*-----------------------------------------------------*/
113:   /* update numerical values of P_oth and P_loc */
114:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
115:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

117:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
118:   /*----------------------------------------------------------*/
119:   /* get data from symbolic products */
120:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
121:   p_oth = NULL;
122:   if (size >1) {
123:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
124:   }

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

129:   api = ptap->api;
130:   apj = ptap->apj;
131:   /* trigger copy to CPU */
132:   MatSeqAIJGetArrayRead(a->A,&dummy);
133:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
134:   MatSeqAIJGetArrayRead(a->B,&dummy);
135:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
136:   for (i=0; i<cm; i++) {
137:     /* compute apa = A[i,:]*P */
138:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

140:     /* set values in C */
141:     apJ  = apj + api[i];
142:     cdnz = cd->i[i+1] - cd->i[i];
143:     conz = co->i[i+1] - co->i[i];

145:     /* 1st off-diagonal part of C */
146:     ca = coa + co->i[i];
147:     k  = 0;
148:     for (k0=0; k0<conz; k0++) {
149:       if (apJ[k] >= cstart) break;
150:       ca[k0]      = apa[apJ[k]];
151:       apa[apJ[k++]] = 0.0;
152:     }

154:     /* diagonal part of C */
155:     ca = cda + cd->i[i];
156:     for (k1=0; k1<cdnz; k1++) {
157:       ca[k1]      = apa[apJ[k]];
158:       apa[apJ[k++]] = 0.0;
159:     }

161:     /* 2nd off-diagonal part of C */
162:     ca = coa + co->i[i];
163:     for (; k0<conz; k0++) {
164:       ca[k0]      = apa[apJ[k]];
165:       apa[apJ[k++]] = 0.0;
166:     }
167:   }
168:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
169:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
170:   return(0);
171: }

173: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
174: {
175:   PetscErrorCode     ierr;
176:   MPI_Comm           comm;
177:   PetscMPIInt        size;
178:   Mat_APMPI          *ptap;
179:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
180:   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
181:   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
182:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
183:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
184:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
185:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
186:   PetscBT            lnkbt;
187:   PetscReal          afill;
188:   MatType            mtype;

191:   MatCheckProduct(C,4);
192:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
193:   PetscObjectGetComm((PetscObject)A,&comm);
194:   MPI_Comm_size(comm,&size);

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

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

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

205:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
206:   pi_loc = p_loc->i; pj_loc = p_loc->j;
207:   if (size > 1) {
208:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
209:     pi_oth = p_oth->i; pj_oth = p_oth->j;
210:   } else {
211:     p_oth = NULL;
212:     pi_oth = NULL; pj_oth = NULL;
213:   }

215:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
216:   /*-------------------------------------------------------------------*/
217:   PetscMalloc1(am+2,&api);
218:   ptap->api = api;
219:   api[0]    = 0;

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

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

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

253:     apnz     = lnk[0];
254:     api[i+1] = api[i] + apnz;

256:     /* if free space is not available, double the total space in the list */
257:     if (current_space->local_remaining<apnz) {
258:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
259:       nspacedouble++;
260:     }

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

266:     current_space->array           += apnz;
267:     current_space->local_used      += apnz;
268:     current_space->local_remaining -= apnz;
269:   }

271:   /* Allocate space for apj, initialize apj, and */
272:   /* destroy list of free space and other temporary array(s) */
273:   PetscMalloc1(api[am]+1,&ptap->apj);
274:   apj  = ptap->apj;
275:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
276:   PetscLLDestroy(lnk,lnkbt);

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

281:   /* set and assemble symbolic parallel matrix C */
282:   /*---------------------------------------------*/
283:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
284:   MatSetBlockSizesFromMats(C,A,P);

286:   MatGetType(A,&mtype);
287:   MatSetType(C,mtype);
288:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
289:   MatPreallocateFinalize(dnz,onz);

291:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
292:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
293:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
294:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

296:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
297:   C->ops->productnumeric = MatProductNumeric_AB;

299:   /* attach the supporting struct to C for reuse */
300:   C->product->data    = ptap;
301:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

303:   /* set MatInfo */
304:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
305:   if (afill < 1.0) afill = 1.0;
306:   C->info.mallocs           = nspacedouble;
307:   C->info.fill_ratio_given  = fill;
308:   C->info.fill_ratio_needed = afill;

310: #if defined(PETSC_USE_INFO)
311:   if (api[am]) {
312:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
313:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
314:   } else {
315:     PetscInfo(C,"Empty matrix product\n");
316:   }
317: #endif
318:   return(0);
319: }

321: /* ------------------------------------------------------- */
322: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
323: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);

325: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
326: {
327:   Mat_Product *product = C->product;
328:   Mat         A = product->A,B=product->B;

331:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
332:     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);

334:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
335:   C->ops->productsymbolic = MatProductSymbolic_AB;
336:   return(0);
337: }
338: /* -------------------------------------------------------------------- */
339: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
340: {
341:   Mat_Product *product = C->product;
342:   Mat         A = product->A,B=product->B;

345:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
346:     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);

348:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
349:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
350:   return(0);
351: }

353: /* --------------------------------------------------------------------- */
354: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
355: {
357:   Mat_Product    *product = C->product;

360:   switch (product->type) {
361:   case MATPRODUCT_AB:
362:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
363:     break;
364:   case MATPRODUCT_AtB:
365:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
366:     break;
367:   default:
368:     break;
369:   }
370:   return(0);
371: }
372: /* ------------------------------------------------------- */

374: typedef struct {
375:   Mat          workB,workB1;
376:   MPI_Request  *rwaits,*swaits;
377:   PetscInt     nsends,nrecvs;
378:   MPI_Datatype *stype,*rtype;
379:   PetscInt     blda;
380: } MPIAIJ_MPIDense;

382: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
383: {
384:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
385:   PetscErrorCode  ierr;
386:   PetscInt        i;

389:   MatDestroy(&contents->workB);
390:   MatDestroy(&contents->workB1);
391:   for (i=0; i<contents->nsends; i++) {
392:     MPI_Type_free(&contents->stype[i]);
393:   }
394:   for (i=0; i<contents->nrecvs; i++) {
395:     MPI_Type_free(&contents->rtype[i]);
396:   }
397:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
398:   PetscFree(contents);
399:   return(0);
400: }

402: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
403: {
404:   PetscErrorCode  ierr;
405:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
406:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda;
407:   MPIAIJ_MPIDense *contents;
408:   VecScatter      ctx=aij->Mvctx;
409:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
410:   MPI_Comm        comm;
411:   MPI_Datatype    type1,*stype,*rtype;
412:   const PetscInt  *sindices,*sstarts,*rstarts;
413:   PetscMPIInt     *disp;
414:   PetscBool       cisdense;

417:   MatCheckProduct(C,4);
418:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
419:   PetscObjectGetComm((PetscObject)A,&comm);
420:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
421:   if (!cisdense) {
422:     MatSetType(C,((PetscObject)B)->type_name);
423:   }
424:   MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
425:   MatSetBlockSizesFromMats(C,A,B);
426:   MatSetUp(C);
427:   MatDenseGetLDA(B,&blda);
428:   MatDenseGetLDA(C,&clda);
429:   PetscNew(&contents);

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

434:   /* Create column block of B and C for memory scalability when BN is too large */
435:   /* Estimate Bbn, column size of Bb */
436:   if (nz) {
437:     Bbn1 = 2*Am*BN/nz;
438:     if (!Bbn1) Bbn1 = 1;
439:   } else Bbn1 = BN;

441:   bs = PetscAbs(B->cmap->bs);
442:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
443:   if (Bbn1 > BN) Bbn1 = BN;
444:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

446:   /* Enable runtime option for Bbn */
447:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
448:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
449:   PetscOptionsEnd();
450:   Bbn  = PetscMin(Bbn,BN);

452:   if (Bbn > 0 && Bbn < BN) {
453:     numBb = BN/Bbn;
454:     Bbn1 = BN - numBb*Bbn;
455:   } else numBb = 0;

457:   if (numBb) {
458:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
459:     if (Bbn1) { /* Create workB1 for the remaining columns */
460:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
461:       /* Create work matrix used to store off processor rows of B needed for local product */
462:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
463:     } else contents->workB1 = NULL;
464:   }

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

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

474:   contents->rtype  = rtype;
475:   contents->nrecvs = nrecvs;
476:   contents->blda   = blda;

478:   PetscMalloc1(Bm+1,&disp);
479:   for (i=0; i<nsends; i++) {
480:     nrows_to = sstarts[i+1]-sstarts[i];
481:     for (j=0; j<nrows_to; j++){
482:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
483:     }
484:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

486:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
487:     MPI_Type_commit(&stype[i]);
488:     MPI_Type_free(&type1);
489:   }

491:   for (i=0; i<nrecvs; i++) {
492:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
493:     nrows_from = rstarts[i+1]-rstarts[i];
494:     disp[0] = 0;
495:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
496:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
497:     MPI_Type_commit(&rtype[i]);
498:     MPI_Type_free(&type1);
499:   }

501:   PetscFree(disp);
502:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
503:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
504:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
505:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
506:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
507:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

509:   C->product->data = contents;
510:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
511:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
512:   return(0);
513: }

515: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
516: /*
517:     Performs an efficient scatter on the rows of B needed by this process; this is
518:     a modification of the VecScatterBegin_() routines.

520:     Input: Bbidx = 0: B = Bb
521:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
522: */
523: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
524: {
525:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
526:   PetscErrorCode    ierr;
527:   const PetscScalar *b;
528:   PetscScalar       *rvalues;
529:   VecScatter        ctx = aij->Mvctx;
530:   const PetscInt    *sindices,*sstarts,*rstarts;
531:   const PetscMPIInt *sprocs,*rprocs;
532:   PetscInt          i,nsends,nrecvs;
533:   MPI_Request       *swaits,*rwaits;
534:   MPI_Comm          comm;
535:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
536:   MPIAIJ_MPIDense   *contents;
537:   Mat               workB;
538:   MPI_Datatype      *stype,*rtype;
539:   PetscInt          blda;

542:   MatCheckProduct(C,4);
543:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
544:   contents = (MPIAIJ_MPIDense*)C->product->data;
545:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
546:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
547:   PetscMPIIntCast(nsends,&nsends_mpi);
548:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
549:   if (Bbidx == 0) {
550:     workB = *outworkB = contents->workB;
551:   } else {
552:     workB = *outworkB = contents->workB1;
553:   }
554:   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);
555:   swaits = contents->swaits;
556:   rwaits = contents->rwaits;

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

563:   /* Post recv, use MPI derived data type to save memory */
564:   PetscObjectGetComm((PetscObject)C,&comm);
565:   rtype = contents->rtype;
566:   for (i=0; i<nrecvs; i++) {
567:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
568:   }

570:   stype = contents->stype;
571:   for (i=0; i<nsends; i++) {
572:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
573:   }

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

578:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
579:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
580:   MatDenseRestoreArrayRead(B,&b);
581:   MatDenseRestoreArray(workB,&rvalues);
582:   return(0);
583: }

585: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
586: {
587:   PetscErrorCode  ierr;
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;
592:   MPIAIJ_MPIDense *contents;

595:   MatCheckProduct(C,3);
596:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
597:   contents = (MPIAIJ_MPIDense*)C->product->data;
598:   /* diagonal block of A times all local rows of B */
599:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
600:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
601:   if (contents->workB->cmap->n == B->cmap->N) {
602:     /* get off processor parts of B needed to complete C=A*B */
603:     MatMPIDenseScatter(A,B,0,C,&workB);

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

612:     for (i=0; i<BN; i+=n) {
613:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
614:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

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

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

623:       MatDenseRestoreSubMatrix(B,&Bb);
624:       MatDenseRestoreSubMatrix(C,&Cb);
625:     }
626:   }
627:   return(0);
628: }

630: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
631: {
632:   PetscErrorCode    ierr;
633:   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
634:   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
635:   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
636:   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
637:   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
638:   Mat_SeqAIJ        *p_loc,*p_oth;
639:   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
640:   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
641:   PetscInt          cm    = C->rmap->n,anz,pnz;
642:   Mat_APMPI         *ptap;
643:   PetscScalar       *apa_sparse;
644:   const PetscScalar *dummy;
645:   PetscInt          *api,*apj,*apJ,i,j,k,row;
646:   PetscInt          cstart = C->cmap->rstart;
647:   PetscInt          cdnz,conz,k0,k1,nextp;
648:   MPI_Comm          comm;
649:   PetscMPIInt       size;

652:   MatCheckProduct(C,3);
653:   ptap = (Mat_APMPI*)C->product->data;
654:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
655:   PetscObjectGetComm((PetscObject)C,&comm);
656:   MPI_Comm_size(comm,&size);
657:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

659:   apa_sparse = ptap->apa;

661:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
662:   /*-----------------------------------------------------*/
663:   /* update numerical values of P_oth and P_loc */
664:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
665:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

667:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
668:   /*----------------------------------------------------------*/
669:   /* get data from symbolic products */
670:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
671:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
672:   if (size >1) {
673:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
674:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
675:   } else {
676:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
677:   }

679:   /* trigger copy to CPU */
680:   MatSeqAIJGetArrayRead(a->A,&dummy);
681:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
682:   MatSeqAIJGetArrayRead(a->B,&dummy);
683:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
684:   api = ptap->api;
685:   apj = ptap->apj;
686:   for (i=0; i<cm; i++) {
687:     apJ = apj + api[i];

689:     /* diagonal portion of A */
690:     anz = adi[i+1] - adi[i];
691:     adj = ad->j + adi[i];
692:     ada = ad->a + adi[i];
693:     for (j=0; j<anz; j++) {
694:       row = adj[j];
695:       pnz = pi_loc[row+1] - pi_loc[row];
696:       pj  = pj_loc + pi_loc[row];
697:       pa  = pa_loc + pi_loc[row];
698:       /* perform sparse axpy */
699:       valtmp = ada[j];
700:       nextp  = 0;
701:       for (k=0; nextp<pnz; k++) {
702:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
703:           apa_sparse[k] += valtmp*pa[nextp++];
704:         }
705:       }
706:       PetscLogFlops(2.0*pnz);
707:     }

709:     /* off-diagonal portion of A */
710:     anz = aoi[i+1] - aoi[i];
711:     aoj = ao->j + aoi[i];
712:     aoa = ao->a + aoi[i];
713:     for (j=0; j<anz; j++) {
714:       row = aoj[j];
715:       pnz = pi_oth[row+1] - pi_oth[row];
716:       pj  = pj_oth + pi_oth[row];
717:       pa  = pa_oth + pi_oth[row];
718:       /* perform sparse axpy */
719:       valtmp = aoa[j];
720:       nextp  = 0;
721:       for (k=0; nextp<pnz; k++) {
722:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
723:           apa_sparse[k] += valtmp*pa[nextp++];
724:         }
725:       }
726:       PetscLogFlops(2.0*pnz);
727:     }

729:     /* set values in C */
730:     cdnz = cd->i[i+1] - cd->i[i];
731:     conz = co->i[i+1] - co->i[i];

733:     /* 1st off-diagonal part of C */
734:     ca = coa + co->i[i];
735:     k  = 0;
736:     for (k0=0; k0<conz; k0++) {
737:       if (apJ[k] >= cstart) break;
738:       ca[k0]        = apa_sparse[k];
739:       apa_sparse[k] = 0.0;
740:       k++;
741:     }

743:     /* diagonal part of C */
744:     ca = cda + cd->i[i];
745:     for (k1=0; k1<cdnz; k1++) {
746:       ca[k1]        = apa_sparse[k];
747:       apa_sparse[k] = 0.0;
748:       k++;
749:     }

751:     /* 2nd off-diagonal part of C */
752:     ca = coa + co->i[i];
753:     for (; k0<conz; k0++) {
754:       ca[k0]        = apa_sparse[k];
755:       apa_sparse[k] = 0.0;
756:       k++;
757:     }
758:   }
759:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
760:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
761:   return(0);
762: }

764: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
765: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
766: {
767:   PetscErrorCode     ierr;
768:   MPI_Comm           comm;
769:   PetscMPIInt        size;
770:   Mat_APMPI          *ptap;
771:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
772:   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
773:   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
774:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
775:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
776:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
777:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
778:   PetscReal          afill;
779:   MatType            mtype;

782:   MatCheckProduct(C,4);
783:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
784:   PetscObjectGetComm((PetscObject)A,&comm);
785:   MPI_Comm_size(comm,&size);

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

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

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

796:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
797:   pi_loc = p_loc->i; pj_loc = p_loc->j;
798:   if (size > 1) {
799:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
800:     pi_oth = p_oth->i; pj_oth = p_oth->j;
801:   } else {
802:     p_oth  = NULL;
803:     pi_oth = NULL; pj_oth = NULL;
804:   }

806:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
807:   /*-------------------------------------------------------------------*/
808:   PetscMalloc1(am+2,&api);
809:   ptap->api = api;
810:   api[0]    = 0;

812:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

814:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
815:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
816:   current_space = free_space;
817:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
818:   for (i=0; i<am; i++) {
819:     /* diagonal portion of A */
820:     nzi = adi[i+1] - adi[i];
821:     for (j=0; j<nzi; j++) {
822:       row  = *adj++;
823:       pnz  = pi_loc[row+1] - pi_loc[row];
824:       Jptr = pj_loc + pi_loc[row];
825:       /* Expand list if it is not long enough */
826:       if (pnz+apnz_max > lsize) {
827:         lsize = pnz+apnz_max;
828:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
829:       }
830:       /* add non-zero cols of P into the sorted linked list lnk */
831:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
832:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
833:       api[i+1] = api[i] + apnz;
834:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
835:     }
836:     /* off-diagonal portion of A */
837:     nzi = aoi[i+1] - aoi[i];
838:     for (j=0; j<nzi; j++) {
839:       row  = *aoj++;
840:       pnz  = pi_oth[row+1] - pi_oth[row];
841:       Jptr = pj_oth + pi_oth[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:     }

854:     /* add missing diagonal entry */
855:     if (C->force_diagonals) {
856:       j = i + rstart; /* column index */
857:       PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
858:     }

860:     apnz     = *lnk;
861:     api[i+1] = api[i] + apnz;
862:     if (apnz > apnz_max) apnz_max = apnz;

864:     /* if free space is not available, double the total space in the list */
865:     if (current_space->local_remaining<apnz) {
866:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
867:       nspacedouble++;
868:     }

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

874:     current_space->array           += apnz;
875:     current_space->local_used      += apnz;
876:     current_space->local_remaining -= apnz;
877:   }

879:   /* Allocate space for apj, initialize apj, and */
880:   /* destroy list of free space and other temporary array(s) */
881:   PetscMalloc1(api[am]+1,&ptap->apj);
882:   apj  = ptap->apj;
883:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
884:   PetscLLCondensedDestroy_Scalable(lnk);

886:   /* create and assemble symbolic parallel matrix C */
887:   /*----------------------------------------------------*/
888:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
889:   MatSetBlockSizesFromMats(C,A,P);
890:   MatGetType(A,&mtype);
891:   MatSetType(C,mtype);
892:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
893:   MatPreallocateFinalize(dnz,onz);

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

898:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
899:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
900:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
901:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

903:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
904:   C->ops->productnumeric = MatProductNumeric_AB;

906:   /* attach the supporting struct to C for reuse */
907:   C->product->data    = ptap;
908:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

910:   /* set MatInfo */
911:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
912:   if (afill < 1.0) afill = 1.0;
913:   C->info.mallocs           = nspacedouble;
914:   C->info.fill_ratio_given  = fill;
915:   C->info.fill_ratio_needed = afill;

917: #if defined(PETSC_USE_INFO)
918:   if (api[am]) {
919:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
920:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
921:   } else {
922:     PetscInfo(C,"Empty matrix product\n");
923:   }
924: #endif
925:   return(0);
926: }

928: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
929: /* Three input arrays are merged to one output array. The size of the    */
930: /* output array is also output. Duplicate entries only show up once.     */
931: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
932:                                PetscInt  size2, PetscInt *in2,
933:                                PetscInt  size3, PetscInt *in3,
934:                                PetscInt *size4, PetscInt *out)
935: {
936:   int i = 0, j = 0, k = 0, l = 0;

938:   /* Traverse all three arrays */
939:   while (i<size1 && j<size2 && k<size3) {
940:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
941:       out[l++] = in1[i++];
942:     }
943:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
944:       out[l++] = in2[j++];
945:     }
946:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
947:       out[l++] = in3[k++];
948:     }
949:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
950:       out[l++] = in1[i];
951:       i++, j++;
952:     }
953:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
954:       out[l++] = in1[i];
955:       i++, k++;
956:     }
957:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
958:       out[l++] = in2[j];
959:       k++, j++;
960:     }
961:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
962:       out[l++] = in1[i];
963:       i++, j++, k++;
964:     }
965:   }

967:   /* Traverse two remaining arrays */
968:   while (i<size1 && j<size2) {
969:     if (in1[i] < in2[j]) {
970:       out[l++] = in1[i++];
971:     }
972:     else if (in1[i] > in2[j]) {
973:       out[l++] = in2[j++];
974:     }
975:     else {
976:       out[l++] = in1[i];
977:       i++, j++;
978:     }
979:   }

981:   while (i<size1 && k<size3) {
982:     if (in1[i] < in3[k]) {
983:       out[l++] = in1[i++];
984:     }
985:     else if (in1[i] > in3[k]) {
986:       out[l++] = in3[k++];
987:     }
988:     else {
989:       out[l++] = in1[i];
990:       i++, k++;
991:     }
992:   }

994:   while (k<size3 && j<size2)  {
995:     if (in3[k] < in2[j]) {
996:       out[l++] = in3[k++];
997:     }
998:     else if (in3[k] > in2[j]) {
999:       out[l++] = in2[j++];
1000:     }
1001:     else {
1002:       out[l++] = in3[k];
1003:       k++, j++;
1004:     }
1005:   }

1007:   /* Traverse one remaining array */
1008:   while (i<size1) out[l++] = in1[i++];
1009:   while (j<size2) out[l++] = in2[j++];
1010:   while (k<size3) out[l++] = in3[k++];

1012:   *size4 = l;
1013: }

1015: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1016: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1017: /* matrix-matrix multiplications.  */
1018: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1019: {
1020:   PetscErrorCode     ierr;
1021:   MPI_Comm           comm;
1022:   PetscMPIInt        size;
1023:   Mat_APMPI          *ptap;
1024:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1025:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
1026:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1027:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
1028:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1029:   PetscInt           adponz, adpdnz;
1030:   PetscInt           *pi_loc,*dnz,*onz;
1031:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1032:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1033:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1034:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1035:   PetscBT            lnkbt;
1036:   PetscReal          afill;
1037:   PetscMPIInt        rank;
1038:   Mat                adpd, aopoth;
1039:   MatType            mtype;
1040:   const char         *prefix;

1043:   MatCheckProduct(C,4);
1044:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1045:   PetscObjectGetComm((PetscObject)A,&comm);
1046:   MPI_Comm_size(comm,&size);
1047:   MPI_Comm_rank(comm, &rank);
1048:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

1050:   /* create struct Mat_APMPI and attached it to C later */
1051:   PetscNew(&ptap);

1053:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1054:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

1056:   /* get P_loc by taking all local rows of P */
1057:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);


1060:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1061:   pi_loc = p_loc->i;

1063:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1064:   PetscMalloc1(am+2,&api);
1065:   PetscMalloc1(am+2,&adpoi);

1067:   adpoi[0]    = 0;
1068:   ptap->api = api;
1069:   api[0] = 0;

1071:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1072:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
1073:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

1075:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1076:   MatGetOptionsPrefix(A,&prefix);
1077:   MatProductCreate(a->A,p->A,NULL,&adpd);
1078:   MatGetOptionsPrefix(A,&prefix);
1079:   MatSetOptionsPrefix(adpd,prefix);
1080:   MatAppendOptionsPrefix(adpd,"inner_diag_");

1082:   MatProductSetType(adpd,MATPRODUCT_AB);
1083:   MatProductSetAlgorithm(adpd,"sorted");
1084:   MatProductSetFill(adpd,fill);
1085:   MatProductSetFromOptions(adpd);

1087:   adpd->force_diagonals = C->force_diagonals;
1088:   MatProductSymbolic(adpd);

1090:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1091:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1092:   p_off = (Mat_SeqAIJ*)((p->B)->data);
1093:   poff_i = p_off->i; poff_j = p_off->j;

1095:   /* j_temp stores indices of a result row before they are added to the linked list */
1096:   PetscMalloc1(pN+2,&j_temp);


1099:   /* Symbolic calc of the A_diag * p_loc_off */
1100:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1101:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
1102:   current_space = free_space_diag;

1104:   for (i=0; i<am; i++) {
1105:     /* A_diag * P_loc_off */
1106:     nzi = adi[i+1] - adi[i];
1107:     for (j=0; j<nzi; j++) {
1108:       row  = *adj++;
1109:       pnz  = poff_i[row+1] - poff_i[row];
1110:       Jptr = poff_j + poff_i[row];
1111:       for (i1 = 0; i1 < pnz; i1++) {
1112:         j_temp[i1] = p->garray[Jptr[i1]];
1113:       }
1114:       /* add non-zero cols of P into the sorted linked list lnk */
1115:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
1116:     }

1118:     adponz     = lnk[0];
1119:     adpoi[i+1] = adpoi[i] + adponz;

1121:     /* if free space is not available, double the total space in the list */
1122:     if (current_space->local_remaining<adponz) {
1123:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
1124:       nspacedouble++;
1125:     }

1127:     /* Copy data into free space, then initialize lnk */
1128:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

1130:     current_space->array           += adponz;
1131:     current_space->local_used      += adponz;
1132:     current_space->local_remaining -= adponz;
1133:   }

1135:   /* Symbolic calc of A_off * P_oth */
1136:   MatSetOptionsPrefix(a->B,prefix);
1137:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
1138:   MatCreate(PETSC_COMM_SELF,&aopoth);
1139:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
1140:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1141:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

1143:   /* Allocate space for apj, adpj, aopj, ... */
1144:   /* destroy lists of free space and other temporary array(s) */

1146:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
1147:   PetscMalloc1(adpoi[am]+2, &adpoj);

1149:   /* Copy from linked list to j-array */
1150:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
1151:   PetscLLDestroy(lnk,lnkbt);

1153:   adpoJ = adpoj;
1154:   adpdJ = adpdj;
1155:   aopJ = aopothj;
1156:   apj  = ptap->apj;
1157:   apJ = apj; /* still empty */

1159:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1160:   /* A_diag * P_loc_diag to get A*P */
1161:   for (i = 0; i < am; i++) {
1162:     aopnz  =  aopothi[i+1] -  aopothi[i];
1163:     adponz = adpoi[i+1] - adpoi[i];
1164:     adpdnz = adpdi[i+1] - adpdi[i];

1166:     /* Correct indices from A_diag*P_diag */
1167:     for (i1 = 0; i1 < adpdnz; i1++) {
1168:       adpdJ[i1] += p_colstart;
1169:     }
1170:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1171:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1172:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

1174:     aopJ += aopnz;
1175:     adpoJ += adponz;
1176:     adpdJ += adpdnz;
1177:     apJ += apnz;
1178:     api[i+1] = api[i] + apnz;
1179:   }

1181:   /* malloc apa to store dense row A[i,:]*P */
1182:   PetscCalloc1(pN+2,&ptap->apa);

1184:   /* create and assemble symbolic parallel matrix C */
1185:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
1186:   MatSetBlockSizesFromMats(C,A,P);
1187:   MatGetType(A,&mtype);
1188:   MatSetType(C,mtype);
1189:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1190:   MatPreallocateFinalize(dnz,onz);

1192:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
1193:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1194:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1195:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1197:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1198:   C->ops->productnumeric = MatProductNumeric_AB;

1200:   /* attach the supporting struct to C for reuse */
1201:   C->product->data    = ptap;
1202:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

1204:   /* set MatInfo */
1205:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1206:   if (afill < 1.0) afill = 1.0;
1207:   C->info.mallocs           = nspacedouble;
1208:   C->info.fill_ratio_given  = fill;
1209:   C->info.fill_ratio_needed = afill;

1211: #if defined(PETSC_USE_INFO)
1212:   if (api[am]) {
1213:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1214:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1215:   } else {
1216:     PetscInfo(C,"Empty matrix product\n");
1217:   }
1218: #endif

1220:   MatDestroy(&aopoth);
1221:   MatDestroy(&adpd);
1222:   PetscFree(j_temp);
1223:   PetscFree(adpoj);
1224:   PetscFree(adpoi);
1225:   return(0);
1226: }

1228: /*-------------------------------------------------------------------------*/
1229: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1230: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1231: {
1233:   Mat_APMPI      *ptap;
1234:   Mat            Pt;

1237:   MatCheckProduct(C,3);
1238:   ptap = (Mat_APMPI*)C->product->data;
1239:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1240:   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");

1242:   Pt   = ptap->Pt;
1243:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
1244:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
1245:   return(0);
1246: }

1248: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1249: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1250: {
1251:   PetscErrorCode      ierr;
1252:   Mat_APMPI           *ptap;
1253:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1254:   MPI_Comm            comm;
1255:   PetscMPIInt         size,rank;
1256:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1257:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1258:   PetscInt            *lnk,i,k,nsend,rstart;
1259:   PetscBT             lnkbt;
1260:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1261:   PETSC_UNUSED PetscMPIInt icompleted=0;
1262:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1263:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1264:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1265:   MPI_Request         *swaits,*rwaits;
1266:   MPI_Status          *sstatus,rstatus;
1267:   PetscLayout         rowmap;
1268:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1269:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1270:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1271:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1272:   PetscTable          ta;
1273:   MatType             mtype;
1274:   const char          *prefix;

1277:   PetscObjectGetComm((PetscObject)A,&comm);
1278:   MPI_Comm_size(comm,&size);
1279:   MPI_Comm_rank(comm,&rank);

1281:   /* create symbolic parallel matrix C */
1282:   MatGetType(A,&mtype);
1283:   MatSetType(C,mtype);

1285:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1287:   /* create struct Mat_APMPI and attached it to C later */
1288:   PetscNew(&ptap);
1289:   ptap->reuse = MAT_INITIAL_MATRIX;

1291:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1292:   /* --------------------------------- */
1293:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
1294:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

1296:   /* (1) compute symbolic A_loc */
1297:   /* ---------------------------*/
1298:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

1300:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1301:   /* ------------------------------------ */
1302:   MatGetOptionsPrefix(A,&prefix);
1303:   MatSetOptionsPrefix(ptap->Ro,prefix);
1304:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
1305:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
1306:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

1308:   /* (3) send coj of C_oth to other processors  */
1309:   /* ------------------------------------------ */
1310:   /* determine row ownership */
1311:   PetscLayoutCreate(comm,&rowmap);
1312:   rowmap->n  = pn;
1313:   rowmap->bs = 1;
1314:   PetscLayoutSetUp(rowmap);
1315:   owners = rowmap->range;

1317:   /* determine the number of messages to send, their lengths */
1318:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
1319:   PetscArrayzero(len_s,size);
1320:   PetscArrayzero(len_si,size);

1322:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1323:   coi   = c_oth->i; coj = c_oth->j;
1324:   con   = ptap->C_oth->rmap->n;
1325:   proc  = 0;
1326:   for (i=0; i<con; i++) {
1327:     while (prmap[i] >= owners[proc+1]) proc++;
1328:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1329:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1330:   }

1332:   len          = 0; /* max length of buf_si[], see (4) */
1333:   owners_co[0] = 0;
1334:   nsend        = 0;
1335:   for (proc=0; proc<size; proc++) {
1336:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1337:     if (len_s[proc]) {
1338:       nsend++;
1339:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1340:       len         += len_si[proc];
1341:     }
1342:   }

1344:   /* determine the number and length of messages to receive for coi and coj  */
1345:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
1346:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

1348:   /* post the Irecv and Isend of coj */
1349:   PetscCommGetNewTag(comm,&tagj);
1350:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
1351:   PetscMalloc1(nsend+1,&swaits);
1352:   for (proc=0, k=0; proc<size; proc++) {
1353:     if (!len_s[proc]) continue;
1354:     i    = owners_co[proc];
1355:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1356:     k++;
1357:   }

1359:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1360:   /* ---------------------------------------- */
1361:   MatSetOptionsPrefix(ptap->Rd,prefix);
1362:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
1363:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
1364:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
1365:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

1367:   /* receives coj are complete */
1368:   for (i=0; i<nrecv; i++) {
1369:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1370:   }
1371:   PetscFree(rwaits);
1372:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1374:   /* add received column indices into ta to update Crmax */
1375:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

1377:   /* create and initialize a linked list */
1378:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
1379:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

1381:   for (k=0; k<nrecv; k++) {/* k-th received message */
1382:     Jptr = buf_rj[k];
1383:     for (j=0; j<len_r[k]; j++) {
1384:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1385:     }
1386:   }
1387:   PetscTableGetCount(ta,&Crmax);
1388:   PetscTableDestroy(&ta);

1390:   /* (4) send and recv coi */
1391:   /*-----------------------*/
1392:   PetscCommGetNewTag(comm,&tagi);
1393:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
1394:   PetscMalloc1(len+1,&buf_s);
1395:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1396:   for (proc=0,k=0; proc<size; proc++) {
1397:     if (!len_s[proc]) continue;
1398:     /* form outgoing message for i-structure:
1399:          buf_si[0]:                 nrows to be sent
1400:                [1:nrows]:           row index (global)
1401:                [nrows+1:2*nrows+1]: i-structure index
1402:     */
1403:     /*-------------------------------------------*/
1404:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1405:     buf_si_i    = buf_si + nrows+1;
1406:     buf_si[0]   = nrows;
1407:     buf_si_i[0] = 0;
1408:     nrows       = 0;
1409:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1410:       nzi = coi[i+1] - coi[i];
1411:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1412:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1413:       nrows++;
1414:     }
1415:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1416:     k++;
1417:     buf_si += len_si[proc];
1418:   }
1419:   for (i=0; i<nrecv; i++) {
1420:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1421:   }
1422:   PetscFree(rwaits);
1423:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1425:   PetscFree4(len_s,len_si,sstatus,owners_co);
1426:   PetscFree(len_ri);
1427:   PetscFree(swaits);
1428:   PetscFree(buf_s);

1430:   /* (5) compute the local portion of C      */
1431:   /* ------------------------------------------ */
1432:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1433:   PetscFreeSpaceGet(Crmax,&free_space);
1434:   current_space = free_space;

1436:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
1437:   for (k=0; k<nrecv; k++) {
1438:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1439:     nrows       = *buf_ri_k[k];
1440:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1441:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1442:   }

1444:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
1445:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
1446:   for (i=0; i<pn; i++) { /* for each local row of C */
1447:     /* add C_loc into C */
1448:     nzi  = c_loc->i[i+1] - c_loc->i[i];
1449:     Jptr = c_loc->j + c_loc->i[i];
1450:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

1452:     /* add received col data into lnk */
1453:     for (k=0; k<nrecv; k++) { /* k-th received message */
1454:       if (i == *nextrow[k]) { /* i-th row */
1455:         nzi  = *(nextci[k]+1) - *nextci[k];
1456:         Jptr = buf_rj[k] + *nextci[k];
1457:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1458:         nextrow[k]++; nextci[k]++;
1459:       }
1460:     }

1462:     /* add missing diagonal entry */
1463:     if (C->force_diagonals) {
1464:       k = i + owners[rank]; /* column index */
1465:       PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
1466:     }

1468:     nzi = lnk[0];

1470:     /* copy data into free space, then initialize lnk */
1471:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
1472:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
1473:   }
1474:   PetscFree3(buf_ri_k,nextrow,nextci);
1475:   PetscLLDestroy(lnk,lnkbt);
1476:   PetscFreeSpaceDestroy(free_space);

1478:   /* local sizes and preallocation */
1479:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
1480:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
1481:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
1482:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1483:   MatPreallocateFinalize(dnz,onz);

1485:   /* add C_loc and C_oth to C */
1486:   MatGetOwnershipRange(C,&rstart,NULL);
1487:   for (i=0; i<pn; i++) {
1488:     ncols = c_loc->i[i+1] - c_loc->i[i];
1489:     cols  = c_loc->j + c_loc->i[i];
1490:     row   = rstart + i;
1491:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);

1493:     if (C->force_diagonals) {
1494:       MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
1495:     }
1496:   }
1497:   for (i=0; i<con; i++) {
1498:     ncols = c_oth->i[i+1] - c_oth->i[i];
1499:     cols  = c_oth->j + c_oth->i[i];
1500:     row   = prmap[i];
1501:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
1502:   }
1503:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1504:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1505:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1507:   /* members in merge */
1508:   PetscFree(id_r);
1509:   PetscFree(len_r);
1510:   PetscFree(buf_ri[0]);
1511:   PetscFree(buf_ri);
1512:   PetscFree(buf_rj[0]);
1513:   PetscFree(buf_rj);
1514:   PetscLayoutDestroy(&rowmap);

1516:   /* attach the supporting struct to C for reuse */
1517:   C->product->data    = ptap;
1518:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1519:   return(0);
1520: }

1522: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1523: {
1524:   PetscErrorCode    ierr;
1525:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1526:   Mat_SeqAIJ        *c_seq;
1527:   Mat_APMPI         *ptap;
1528:   Mat               A_loc,C_loc,C_oth;
1529:   PetscInt          i,rstart,rend,cm,ncols,row;
1530:   const PetscInt    *cols;
1531:   const PetscScalar *vals;

1534:   MatCheckProduct(C,3);
1535:   ptap = (Mat_APMPI*)C->product->data;
1536:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1537:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1538:   MatZeroEntries(C);

1540:   if (ptap->reuse == MAT_REUSE_MATRIX) {
1541:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1542:     /* 1) get R = Pd^T, Ro = Po^T */
1543:     /*----------------------------*/
1544:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
1545:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

1547:     /* 2) compute numeric A_loc */
1548:     /*--------------------------*/
1549:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
1550:   }

1552:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1553:   A_loc = ptap->A_loc;
1554:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
1555:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
1556:   C_loc = ptap->C_loc;
1557:   C_oth = ptap->C_oth;

1559:   /* add C_loc and C_oth to C */
1560:   MatGetOwnershipRange(C,&rstart,&rend);

1562:   /* C_loc -> C */
1563:   cm    = C_loc->rmap->N;
1564:   c_seq = (Mat_SeqAIJ*)C_loc->data;
1565:   cols = c_seq->j;
1566:   vals = c_seq->a;
1567:   for (i=0; i<cm; i++) {
1568:     ncols = c_seq->i[i+1] - c_seq->i[i];
1569:     row = rstart + i;
1570:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1571:     cols += ncols; vals += ncols;
1572:   }

1574:   /* Co -> C, off-processor part */
1575:   cm    = C_oth->rmap->N;
1576:   c_seq = (Mat_SeqAIJ*)C_oth->data;
1577:   cols  = c_seq->j;
1578:   vals  = c_seq->a;
1579:   for (i=0; i<cm; i++) {
1580:     ncols = c_seq->i[i+1] - c_seq->i[i];
1581:     row = p->garray[i];
1582:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1583:     cols += ncols; vals += ncols;
1584:   }
1585:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1586:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1587:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1589:   ptap->reuse = MAT_REUSE_MATRIX;
1590:   return(0);
1591: }

1593: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1594: {
1595:   PetscErrorCode      ierr;
1596:   Mat_Merge_SeqsToMPI *merge;
1597:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1598:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1599:   Mat_APMPI           *ptap;
1600:   PetscInt            *adj;
1601:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1602:   MatScalar           *ada,*ca,valtmp;
1603:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1604:   MPI_Comm            comm;
1605:   PetscMPIInt         size,rank,taga,*len_s;
1606:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1607:   PetscInt            **buf_ri,**buf_rj;
1608:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1609:   MPI_Request         *s_waits,*r_waits;
1610:   MPI_Status          *status;
1611:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1612:   const PetscScalar   *dummy;
1613:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1614:   Mat                 A_loc;
1615:   Mat_SeqAIJ          *a_loc;

1618:   MatCheckProduct(C,3);
1619:   ptap = (Mat_APMPI*)C->product->data;
1620:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1621:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1622:   PetscObjectGetComm((PetscObject)C,&comm);
1623:   MPI_Comm_size(comm,&size);
1624:   MPI_Comm_rank(comm,&rank);

1626:   merge = ptap->merge;

1628:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1629:   /*------------------------------------------*/
1630:   /* get data from symbolic products */
1631:   coi    = merge->coi; coj = merge->coj;
1632:   PetscCalloc1(coi[pon]+1,&coa);
1633:   bi     = merge->bi; bj = merge->bj;
1634:   owners = merge->rowmap->range;
1635:   PetscCalloc1(bi[cm]+1,&ba);

1637:   /* get A_loc by taking all local rows of A */
1638:   A_loc = ptap->A_loc;
1639:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1640:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1641:   ai    = a_loc->i;
1642:   aj    = a_loc->j;

1644:   /* trigger copy to CPU */
1645:   MatSeqAIJGetArrayRead(p->A,&dummy);
1646:   MatSeqAIJRestoreArrayRead(p->A,&dummy);
1647:   MatSeqAIJGetArrayRead(p->B,&dummy);
1648:   MatSeqAIJRestoreArrayRead(p->B,&dummy);
1649:   for (i=0; i<am; i++) {
1650:     anz = ai[i+1] - ai[i];
1651:     adj = aj + ai[i];
1652:     ada = a_loc->a + ai[i];

1654:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1655:     /*-------------------------------------------------------------*/
1656:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1657:     pnz = po->i[i+1] - po->i[i];
1658:     poJ = po->j + po->i[i];
1659:     pA  = po->a + po->i[i];
1660:     for (j=0; j<pnz; j++) {
1661:       row = poJ[j];
1662:       cj  = coj + coi[row];
1663:       ca  = coa + coi[row];
1664:       /* perform sparse axpy */
1665:       nexta  = 0;
1666:       valtmp = pA[j];
1667:       for (k=0; nexta<anz; k++) {
1668:         if (cj[k] == adj[nexta]) {
1669:           ca[k] += valtmp*ada[nexta];
1670:           nexta++;
1671:         }
1672:       }
1673:       PetscLogFlops(2.0*anz);
1674:     }

1676:     /* put the value into Cd (diagonal part) */
1677:     pnz = pd->i[i+1] - pd->i[i];
1678:     pdJ = pd->j + pd->i[i];
1679:     pA  = pd->a + pd->i[i];
1680:     for (j=0; j<pnz; j++) {
1681:       row = pdJ[j];
1682:       cj  = bj + bi[row];
1683:       ca  = ba + bi[row];
1684:       /* perform sparse axpy */
1685:       nexta  = 0;
1686:       valtmp = pA[j];
1687:       for (k=0; nexta<anz; k++) {
1688:         if (cj[k] == adj[nexta]) {
1689:           ca[k] += valtmp*ada[nexta];
1690:           nexta++;
1691:         }
1692:       }
1693:       PetscLogFlops(2.0*anz);
1694:     }
1695:   }

1697:   /* 3) send and recv matrix values coa */
1698:   /*------------------------------------*/
1699:   buf_ri = merge->buf_ri;
1700:   buf_rj = merge->buf_rj;
1701:   len_s  = merge->len_s;
1702:   PetscCommGetNewTag(comm,&taga);
1703:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

1705:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1706:   for (proc=0,k=0; proc<size; proc++) {
1707:     if (!len_s[proc]) continue;
1708:     i    = merge->owners_co[proc];
1709:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1710:     k++;
1711:   }
1712:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1713:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

1715:   PetscFree2(s_waits,status);
1716:   PetscFree(r_waits);
1717:   PetscFree(coa);

1719:   /* 4) insert local Cseq and received values into Cmpi */
1720:   /*----------------------------------------------------*/
1721:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1722:   for (k=0; k<merge->nrecv; k++) {
1723:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1724:     nrows       = *(buf_ri_k[k]);
1725:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1726:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1727:   }

1729:   for (i=0; i<cm; i++) {
1730:     row  = owners[rank] + i; /* global row index of C_seq */
1731:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1732:     ba_i = ba + bi[i];
1733:     bnz  = bi[i+1] - bi[i];
1734:     /* add received vals into ba */
1735:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1736:       /* i-th row */
1737:       if (i == *nextrow[k]) {
1738:         cnz    = *(nextci[k]+1) - *nextci[k];
1739:         cj     = buf_rj[k] + *(nextci[k]);
1740:         ca     = abuf_r[k] + *(nextci[k]);
1741:         nextcj = 0;
1742:         for (j=0; nextcj<cnz; j++) {
1743:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1744:             ba_i[j] += ca[nextcj++];
1745:           }
1746:         }
1747:         nextrow[k]++; nextci[k]++;
1748:         PetscLogFlops(2.0*cnz);
1749:       }
1750:     }
1751:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1752:   }
1753:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1754:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1756:   PetscFree(ba);
1757:   PetscFree(abuf_r[0]);
1758:   PetscFree(abuf_r);
1759:   PetscFree3(buf_ri_k,nextrow,nextci);
1760:   return(0);
1761: }

1763: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1764: {
1765:   PetscErrorCode      ierr;
1766:   Mat                 A_loc;
1767:   Mat_APMPI           *ptap;
1768:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1769:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1770:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1771:   PetscInt            nnz;
1772:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1773:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1774:   MPI_Comm            comm;
1775:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1776:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1777:   PetscInt            len,proc,*dnz,*onz,*owners;
1778:   PetscInt            nzi,*bi,*bj;
1779:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1780:   MPI_Request         *swaits,*rwaits;
1781:   MPI_Status          *sstatus,rstatus;
1782:   Mat_Merge_SeqsToMPI *merge;
1783:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1784:   PetscReal           afill  =1.0,afill_tmp;
1785:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1786:   Mat_SeqAIJ          *a_loc;
1787:   PetscTable          ta;
1788:   MatType             mtype;

1791:   PetscObjectGetComm((PetscObject)A,&comm);
1792:   /* check if matrix local sizes are compatible */
1793:   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);

1795:   MPI_Comm_size(comm,&size);
1796:   MPI_Comm_rank(comm,&rank);

1798:   /* create struct Mat_APMPI and attached it to C later */
1799:   PetscNew(&ptap);

1801:   /* get A_loc by taking all local rows of A */
1802:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

1804:   ptap->A_loc = A_loc;
1805:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1806:   ai          = a_loc->i;
1807:   aj          = a_loc->j;

1809:   /* determine symbolic Co=(p->B)^T*A - send to others */
1810:   /*----------------------------------------------------*/
1811:   MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
1812:   MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
1813:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1814:                          >= (num of nonzero rows of C_seq) - pn */
1815:   PetscMalloc1(pon+1,&coi);
1816:   coi[0] = 0;

1818:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1819:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1820:   PetscFreeSpaceGet(nnz,&free_space);
1821:   current_space = free_space;

1823:   /* create and initialize a linked list */
1824:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
1825:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1826:   PetscTableGetCount(ta,&Armax);

1828:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

1830:   for (i=0; i<pon; i++) {
1831:     pnz = poti[i+1] - poti[i];
1832:     ptJ = potj + poti[i];
1833:     for (j=0; j<pnz; j++) {
1834:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1835:       anz  = ai[row+1] - ai[row];
1836:       Jptr = aj + ai[row];
1837:       /* add non-zero cols of AP into the sorted linked list lnk */
1838:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1839:     }
1840:     nnz = lnk[0];

1842:     /* If free space is not available, double the total space in the list */
1843:     if (current_space->local_remaining<nnz) {
1844:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
1845:       nspacedouble++;
1846:     }

1848:     /* Copy data into free space, and zero out denserows */
1849:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

1851:     current_space->array           += nnz;
1852:     current_space->local_used      += nnz;
1853:     current_space->local_remaining -= nnz;

1855:     coi[i+1] = coi[i] + nnz;
1856:   }

1858:   PetscMalloc1(coi[pon]+1,&coj);
1859:   PetscFreeSpaceContiguous(&free_space,coj);
1860:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

1862:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1863:   if (afill_tmp > afill) afill = afill_tmp;

1865:   /* send j-array (coj) of Co to other processors */
1866:   /*----------------------------------------------*/
1867:   /* determine row ownership */
1868:   PetscNew(&merge);
1869:   PetscLayoutCreate(comm,&merge->rowmap);

1871:   merge->rowmap->n  = pn;
1872:   merge->rowmap->bs = 1;

1874:   PetscLayoutSetUp(merge->rowmap);
1875:   owners = merge->rowmap->range;

1877:   /* determine the number of messages to send, their lengths */
1878:   PetscCalloc1(size,&len_si);
1879:   PetscCalloc1(size,&merge->len_s);

1881:   len_s        = merge->len_s;
1882:   merge->nsend = 0;

1884:   PetscMalloc1(size+2,&owners_co);

1886:   proc = 0;
1887:   for (i=0; i<pon; i++) {
1888:     while (prmap[i] >= owners[proc+1]) proc++;
1889:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1890:     len_s[proc] += coi[i+1] - coi[i];
1891:   }

1893:   len          = 0; /* max length of buf_si[] */
1894:   owners_co[0] = 0;
1895:   for (proc=0; proc<size; proc++) {
1896:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1897:     if (len_si[proc]) {
1898:       merge->nsend++;
1899:       len_si[proc] = 2*(len_si[proc] + 1);
1900:       len         += len_si[proc];
1901:     }
1902:   }

1904:   /* determine the number and length of messages to receive for coi and coj  */
1905:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1906:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

1908:   /* post the Irecv and Isend of coj */
1909:   PetscCommGetNewTag(comm,&tagj);
1910:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1911:   PetscMalloc1(merge->nsend+1,&swaits);
1912:   for (proc=0, k=0; proc<size; proc++) {
1913:     if (!len_s[proc]) continue;
1914:     i    = owners_co[proc];
1915:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1916:     k++;
1917:   }

1919:   /* receives and sends of coj are complete */
1920:   PetscMalloc1(size,&sstatus);
1921:   for (i=0; i<merge->nrecv; i++) {
1922:     PETSC_UNUSED PetscMPIInt icompleted;
1923:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1924:   }
1925:   PetscFree(rwaits);
1926:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

1928:   /* add received column indices into table to update Armax */
1929:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1930:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1931:     Jptr = buf_rj[k];
1932:     for (j=0; j<merge->len_r[k]; j++) {
1933:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1934:     }
1935:   }
1936:   PetscTableGetCount(ta,&Armax);
1937:   /* 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); */

1939:   /* send and recv coi */
1940:   /*-------------------*/
1941:   PetscCommGetNewTag(comm,&tagi);
1942:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1943:   PetscMalloc1(len+1,&buf_s);
1944:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1945:   for (proc=0,k=0; proc<size; proc++) {
1946:     if (!len_s[proc]) continue;
1947:     /* form outgoing message for i-structure:
1948:          buf_si[0]:                 nrows to be sent
1949:                [1:nrows]:           row index (global)
1950:                [nrows+1:2*nrows+1]: i-structure index
1951:     */
1952:     /*-------------------------------------------*/
1953:     nrows       = len_si[proc]/2 - 1;
1954:     buf_si_i    = buf_si + nrows+1;
1955:     buf_si[0]   = nrows;
1956:     buf_si_i[0] = 0;
1957:     nrows       = 0;
1958:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1959:       nzi               = coi[i+1] - coi[i];
1960:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1961:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1962:       nrows++;
1963:     }
1964:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1965:     k++;
1966:     buf_si += len_si[proc];
1967:   }
1968:   i = merge->nrecv;
1969:   while (i--) {
1970:     PETSC_UNUSED PetscMPIInt icompleted;
1971:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1972:   }
1973:   PetscFree(rwaits);
1974:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1975:   PetscFree(len_si);
1976:   PetscFree(len_ri);
1977:   PetscFree(swaits);
1978:   PetscFree(sstatus);
1979:   PetscFree(buf_s);

1981:   /* compute the local portion of C (mpi mat) */
1982:   /*------------------------------------------*/
1983:   /* allocate bi array and free space for accumulating nonzero column info */
1984:   PetscMalloc1(pn+1,&bi);
1985:   bi[0] = 0;

1987:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1988:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1989:   PetscFreeSpaceGet(nnz,&free_space);
1990:   current_space = free_space;

1992:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1993:   for (k=0; k<merge->nrecv; k++) {
1994:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1995:     nrows       = *buf_ri_k[k];
1996:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1997:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1998:   }

2000:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
2001:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
2002:   rmax = 0;
2003:   for (i=0; i<pn; i++) {
2004:     /* add pdt[i,:]*AP into lnk */
2005:     pnz = pdti[i+1] - pdti[i];
2006:     ptJ = pdtj + pdti[i];
2007:     for (j=0; j<pnz; j++) {
2008:       row  = ptJ[j];  /* row of AP == col of Pt */
2009:       anz  = ai[row+1] - ai[row];
2010:       Jptr = aj + ai[row];
2011:       /* add non-zero cols of AP into the sorted linked list lnk */
2012:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
2013:     }

2015:     /* add received col data into lnk */
2016:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2017:       if (i == *nextrow[k]) { /* i-th row */
2018:         nzi  = *(nextci[k]+1) - *nextci[k];
2019:         Jptr = buf_rj[k] + *nextci[k];
2020:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
2021:         nextrow[k]++; nextci[k]++;
2022:       }
2023:     }

2025:     /* add missing diagonal entry */
2026:     if (C->force_diagonals) {
2027:       k = i + owners[rank]; /* column index */
2028:       PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
2029:     }

2031:     nnz = lnk[0];

2033:     /* if free space is not available, make more free space */
2034:     if (current_space->local_remaining<nnz) {
2035:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
2036:       nspacedouble++;
2037:     }
2038:     /* copy data into free space, then initialize lnk */
2039:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
2040:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

2042:     current_space->array           += nnz;
2043:     current_space->local_used      += nnz;
2044:     current_space->local_remaining -= nnz;

2046:     bi[i+1] = bi[i] + nnz;
2047:     if (nnz > rmax) rmax = nnz;
2048:   }
2049:   PetscFree3(buf_ri_k,nextrow,nextci);

2051:   PetscMalloc1(bi[pn]+1,&bj);
2052:   PetscFreeSpaceContiguous(&free_space,bj);
2053:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2054:   if (afill_tmp > afill) afill = afill_tmp;
2055:   PetscLLCondensedDestroy_Scalable(lnk);
2056:   PetscTableDestroy(&ta);
2057:   MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
2058:   MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);

2060:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2061:   /*-------------------------------------------------------------------------------*/
2062:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
2063:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
2064:   MatGetType(A,&mtype);
2065:   MatSetType(C,mtype);
2066:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
2067:   MatPreallocateFinalize(dnz,onz);
2068:   MatSetBlockSize(C,1);
2069:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
2070:   for (i=0; i<pn; i++) {
2071:     row  = i + rstart;
2072:     nnz  = bi[i+1] - bi[i];
2073:     Jptr = bj + bi[i];
2074:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
2075:   }
2076:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
2077:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
2078:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
2079:   merge->bi        = bi;
2080:   merge->bj        = bj;
2081:   merge->coi       = coi;
2082:   merge->coj       = coj;
2083:   merge->buf_ri    = buf_ri;
2084:   merge->buf_rj    = buf_rj;
2085:   merge->owners_co = owners_co;

2087:   /* attach the supporting struct to C for reuse */
2088:   C->product->data    = ptap;
2089:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2090:   ptap->merge         = merge;

2092:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2094: #if defined(PETSC_USE_INFO)
2095:   if (bi[pn] != 0) {
2096:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
2097:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
2098:   } else {
2099:     PetscInfo(C,"Empty matrix product\n");
2100:   }
2101: #endif
2102:   return(0);
2103: }

2105: /* ---------------------------------------------------------------- */
2106: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2107: {
2109:   Mat_Product    *product = C->product;
2110:   Mat            A=product->A,B=product->B;
2111:   PetscReal      fill=product->fill;
2112:   PetscBool      flg;

2115:   /* scalable */
2116:   PetscStrcmp(product->alg,"scalable",&flg);
2117:   if (flg) {
2118:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
2119:     goto next;
2120:   }

2122:   /* nonscalable */
2123:   PetscStrcmp(product->alg,"nonscalable",&flg);
2124:   if (flg) {
2125:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
2126:     goto next;
2127:   }

2129:   /* matmatmult */
2130:   PetscStrcmp(product->alg,"at*b",&flg);
2131:   if (flg) {
2132:     Mat       At;
2133:     Mat_APMPI *ptap;

2135:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
2136:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
2137:     ptap = (Mat_APMPI*)C->product->data;
2138:     if (ptap) {
2139:       ptap->Pt = At;
2140:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2141:     }
2142:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2143:     goto next;
2144:   }

2146:   /* backend general code */
2147:   PetscStrcmp(product->alg,"backend",&flg);
2148:   if (flg) {
2149:     MatProductSymbolic_MPIAIJBACKEND(C);
2150:     return(0);
2151:   }

2153:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

2155: next:
2156:   C->ops->productnumeric = MatProductNumeric_AtB;
2157:   return(0);
2158: }

2160: /* ---------------------------------------------------------------- */
2161: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2162: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2163: {
2165:   Mat_Product    *product = C->product;
2166:   Mat            A=product->A,B=product->B;
2167: #if defined(PETSC_HAVE_HYPRE)
2168:   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2169:   PetscInt       nalg = 5;
2170: #else
2171:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2172:   PetscInt       nalg = 4;
2173: #endif
2174:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2175:   PetscBool      flg;
2176:   MPI_Comm       comm;

2179:   /* Check matrix local sizes */
2180:   PetscObjectGetComm((PetscObject)C,&comm);
2181:   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);

2183:   /* Set "nonscalable" as default algorithm */
2184:   PetscStrcmp(C->product->alg,"default",&flg);
2185:   if (flg) {
2186:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

2188:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2189:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2190:       MatInfo     Ainfo,Binfo;
2191:       PetscInt    nz_local;
2192:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2194:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
2195:       MatGetInfo(B,MAT_LOCAL,&Binfo);
2196:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2198:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2199:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2201:       if (alg_scalable) {
2202:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2203:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2204:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2205:       }
2206:     }
2207:   }

2209:   /* Get runtime option */
2210:   if (product->api_user) {
2211:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
2212:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2213:     PetscOptionsEnd();
2214:   } else {
2215:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
2216:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2217:     PetscOptionsEnd();
2218:   }
2219:   if (flg) {
2220:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2221:   }

2223:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2224:   return(0);
2225: }

2227: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2228: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2229: {
2231:   Mat_Product    *product = C->product;
2232:   Mat            A=product->A,B=product->B;
2233:   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2234:   PetscInt       nalg = 4;
2235:   PetscInt       alg = 1; /* set default algorithm  */
2236:   PetscBool      flg;
2237:   MPI_Comm       comm;

2240:   /* Check matrix local sizes */
2241:   PetscObjectGetComm((PetscObject)C,&comm);
2242:   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);

2244:   /* Set default algorithm */
2245:   PetscStrcmp(C->product->alg,"default",&flg);
2246:   if (flg) {
2247:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2248:   }

2250:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2251:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2252:     MatInfo     Ainfo,Binfo;
2253:     PetscInt    nz_local;
2254:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2256:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
2257:     MatGetInfo(B,MAT_LOCAL,&Binfo);
2258:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2260:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2261:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2263:     if (alg_scalable) {
2264:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2265:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2266:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2267:     }
2268:   }

2270:   /* Get runtime option */
2271:   if (product->api_user) {
2272:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
2273:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2274:     PetscOptionsEnd();
2275:   } else {
2276:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
2277:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2278:     PetscOptionsEnd();
2279:   }
2280:   if (flg) {
2281:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2282:   }

2284:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2285:   return(0);
2286: }

2288: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2289: {
2291:   Mat_Product    *product = C->product;
2292:   Mat            A=product->A,P=product->B;
2293:   MPI_Comm       comm;
2294:   PetscBool      flg;
2295:   PetscInt       alg=1; /* set default algorithm */
2296: #if !defined(PETSC_HAVE_HYPRE)
2297:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2298:   PetscInt       nalg=5;
2299: #else
2300:   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2301:   PetscInt       nalg=6;
2302: #endif
2303:   PetscInt       pN=P->cmap->N;

2306:   /* Check matrix local sizes */
2307:   PetscObjectGetComm((PetscObject)C,&comm);
2308:   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);
2309:   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);

2311:   /* Set "nonscalable" as default algorithm */
2312:   PetscStrcmp(C->product->alg,"default",&flg);
2313:   if (flg) {
2314:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

2316:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2317:     if (pN > 100000) {
2318:       MatInfo     Ainfo,Pinfo;
2319:       PetscInt    nz_local;
2320:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2322:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
2323:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
2324:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2326:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2327:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2329:       if (alg_scalable) {
2330:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2331:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2332:       }
2333:     }
2334:   }

2336:   /* Get runtime option */
2337:   if (product->api_user) {
2338:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
2339:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2340:     PetscOptionsEnd();
2341:   } else {
2342:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
2343:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2344:     PetscOptionsEnd();
2345:   }
2346:   if (flg) {
2347:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2348:   }

2350:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2351:   return(0);
2352: }

2354: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2355: {
2356:   Mat_Product *product = C->product;
2357:   Mat         A = product->A,R=product->B;

2360:   /* Check matrix local sizes */
2361:   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);

2363:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2364:   return(0);
2365: }

2367: /*
2368:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2369: */
2370: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2371: {
2373:   Mat_Product    *product = C->product;
2374:   PetscBool      flg = PETSC_FALSE;
2375:   PetscInt       alg = 1; /* default algorithm */
2376:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2377:   PetscInt       nalg = 3;

2380:   /* Set default algorithm */
2381:   PetscStrcmp(C->product->alg,"default",&flg);
2382:   if (flg) {
2383:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2384:   }

2386:   /* Get runtime option */
2387:   if (product->api_user) {
2388:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
2389:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2390:     PetscOptionsEnd();
2391:   } else {
2392:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
2393:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
2394:     PetscOptionsEnd();
2395:   }
2396:   if (flg) {
2397:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2398:   }

2400:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2401:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2402:   return(0);
2403: }

2405: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2406: {
2408:   Mat_Product    *product = C->product;

2411:   switch (product->type) {
2412:   case MATPRODUCT_AB:
2413:     MatProductSetFromOptions_MPIAIJ_AB(C);
2414:     break;
2415:   case MATPRODUCT_AtB:
2416:     MatProductSetFromOptions_MPIAIJ_AtB(C);
2417:     break;
2418:   case MATPRODUCT_PtAP:
2419:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
2420:     break;
2421:   case MATPRODUCT_RARt:
2422:     MatProductSetFromOptions_MPIAIJ_RARt(C);
2423:     break;
2424:   case MATPRODUCT_ABC:
2425:     MatProductSetFromOptions_MPIAIJ_ABC(C);
2426:     break;
2427:   default:
2428:     break;
2429:   }
2430:   return(0);
2431: }