Actual source code: mpimatmatmult.c

petsc-3.10.3 2018-12-18
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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>

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

 17: PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
 18: {
 20: #if defined(PETSC_HAVE_HYPRE)
 21:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
 22:   PetscInt       nalg = 4;
 23: #else
 24:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
 25:   PetscInt       nalg = 3;
 26: #endif
 27:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
 28:   MPI_Comm       comm;
 29:   PetscBool      flg;

 32:   if (scall == MAT_INITIAL_MATRIX) {
 33:     PetscObjectGetComm((PetscObject)A,&comm);
 34:     if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(comm,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);

 36:     PetscObjectOptionsBegin((PetscObject)A);
 37:     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
 38:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[1],&alg,&flg);
 39:     PetscOptionsEnd();

 41:     if (!flg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
 42:       MatInfo     Ainfo,Binfo;
 43:       PetscInt    nz_local;
 44:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

 46:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
 47:       MatGetInfo(B,MAT_LOCAL,&Binfo);
 48:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

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

 53:       if (alg_scalable) {
 54:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
 55:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,fill*nz_local);
 56:       }
 57:     }

 59:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
 60:     switch (alg) {
 61:     case 1:
 62:       MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
 63:       break;
 64:     case 2:
 65:       MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);
 66:       break;
 67: #if defined(PETSC_HAVE_HYPRE)
 68:     case 3:
 69:       MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
 70:       break;
 71: #endif
 72:     default:
 73:       MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
 74:       break;
 75:     }
 76:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
 77:   }
 78:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
 79:   (*(*C)->ops->matmultnumeric)(A,B,*C);
 80:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
 81:   return(0);
 82: }

 84: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
 85: {
 87:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
 88:   Mat_PtAPMPI    *ptap = a->ptap;

 91:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
 92:   PetscFree(ptap->bufa);
 93:   MatDestroy(&ptap->P_loc);
 94:   MatDestroy(&ptap->P_oth);
 95:   MatDestroy(&ptap->Pt);
 96:   PetscFree(ptap->api);
 97:   PetscFree(ptap->apj);
 98:   PetscFree(ptap->apa);
 99:   ptap->destroy(A);
100:   PetscFree(ptap);
101:   return(0);
102: }

104: PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
105: {
107:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
108:   Mat_PtAPMPI    *ptap = a->ptap;

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

113:   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
114:   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
115:   return(0);
116: }

118: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
119: {
121:   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
122:   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
123:   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
124:   PetscScalar    *cda=cd->a,*coa=co->a;
125:   Mat_SeqAIJ     *p_loc,*p_oth;
126:   PetscScalar    *apa,*ca;
127:   PetscInt       cm   =C->rmap->n;
128:   Mat_PtAPMPI    *ptap=c->ptap;
129:   PetscInt       *api,*apj,*apJ,i,k;
130:   PetscInt       cstart=C->cmap->rstart;
131:   PetscInt       cdnz,conz,k0,k1;
132:   MPI_Comm       comm;
133:   PetscMPIInt    size;

136:   PetscObjectGetComm((PetscObject)A,&comm);
137:   MPI_Comm_size(comm,&size);

139:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
140:   /*-----------------------------------------------------*/
141:   /* update numerical values of P_oth and P_loc */
142:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
143:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

145:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
146:   /*----------------------------------------------------------*/
147:   /* get data from symbolic products */
148:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
149:   p_oth = NULL;
150:   if (size >1) {
151:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
152:   }

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

157:   api = ptap->api;
158:   apj = ptap->apj;
159:   for (i=0; i<cm; i++) {
160:     /* compute apa = A[i,:]*P */
161:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

163:     /* set values in C */
164:     apJ  = apj + api[i];
165:     cdnz = cd->i[i+1] - cd->i[i];
166:     conz = co->i[i+1] - co->i[i];

168:     /* 1st off-diagoanl part of C */
169:     ca = coa + co->i[i];
170:     k  = 0;
171:     for (k0=0; k0<conz; k0++) {
172:       if (apJ[k] >= cstart) break;
173:       ca[k0]      = apa[apJ[k]];
174:       apa[apJ[k++]] = 0.0;
175:     }

177:     /* diagonal part of C */
178:     ca = cda + cd->i[i];
179:     for (k1=0; k1<cdnz; k1++) {
180:       ca[k1]      = apa[apJ[k]];
181:       apa[apJ[k++]] = 0.0;
182:     }

184:     /* 2nd off-diagoanl part of C */
185:     ca = coa + co->i[i];
186:     for (; k0<conz; k0++) {
187:       ca[k0]      = apa[apJ[k]];
188:       apa[apJ[k++]] = 0.0;
189:     }
190:   }
191:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
193:   return(0);
194: }

196: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat *C)
197: {
198:   PetscErrorCode     ierr;
199:   MPI_Comm           comm;
200:   PetscMPIInt        size;
201:   Mat                Cmpi;
202:   Mat_PtAPMPI        *ptap;
203:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
204:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data,*c;
205:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
206:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
207:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
208:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
209:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
210:   PetscBT            lnkbt;
211:   PetscScalar        *apa;
212:   PetscReal          afill;

215:   PetscObjectGetComm((PetscObject)A,&comm);
216:   MPI_Comm_size(comm,&size);

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

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

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

227:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
228:   pi_loc = p_loc->i; pj_loc = p_loc->j;
229:   if (size > 1) {
230:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
231:     pi_oth = p_oth->i; pj_oth = p_oth->j;
232:   } else {
233:     p_oth = NULL;
234:     pi_oth = NULL; pj_oth = NULL;
235:   }

237:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
238:   /*-------------------------------------------------------------------*/
239:   PetscMalloc1(am+2,&api);
240:   ptap->api = api;
241:   api[0]    = 0;

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

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

250:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
251:   for (i=0; i<am; i++) {
252:     /* diagonal portion of A */
253:     nzi = adi[i+1] - adi[i];
254:     for (j=0; j<nzi; j++) {
255:       row  = *adj++;
256:       pnz  = pi_loc[row+1] - pi_loc[row];
257:       Jptr = pj_loc + pi_loc[row];
258:       /* add non-zero cols of P into the sorted linked list lnk */
259:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
260:     }
261:     /* off-diagonal portion of A */
262:     nzi = aoi[i+1] - aoi[i];
263:     for (j=0; j<nzi; j++) {
264:       row  = *aoj++;
265:       pnz  = pi_oth[row+1] - pi_oth[row];
266:       Jptr = pj_oth + pi_oth[row];
267:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
268:     }

270:     apnz     = lnk[0];
271:     api[i+1] = api[i] + apnz;

273:     /* if free space is not available, double the total space in the list */
274:     if (current_space->local_remaining<apnz) {
275:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
276:       nspacedouble++;
277:     }

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

283:     current_space->array           += apnz;
284:     current_space->local_used      += apnz;
285:     current_space->local_remaining -= apnz;
286:   }

288:   /* Allocate space for apj, initialize apj, and */
289:   /* destroy list of free space and other temporary array(s) */
290:   PetscMalloc1(api[am]+1,&ptap->apj);
291:   apj  = ptap->apj;
292:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
293:   PetscLLDestroy(lnk,lnkbt);

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

298:   ptap->apa = apa;

300:   /* create and assemble symbolic parallel matrix Cmpi */
301:   /*----------------------------------------------------*/
302:   MatCreate(comm,&Cmpi);
303:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
304:   MatSetBlockSizesFromMats(Cmpi,A,P);

306:   MatSetType(Cmpi,MATMPIAIJ);
307:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);

309:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);
310:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
311:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
312:   MatPreallocateFinalize(dnz,onz);

314:   ptap->destroy        = Cmpi->ops->destroy;
315:   ptap->duplicate      = Cmpi->ops->duplicate;
316:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
317:   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
318:   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatMatMult;

320:   /* attach the supporting struct to Cmpi for reuse */
321:   c       = (Mat_MPIAIJ*)Cmpi->data;
322:   c->ptap = ptap;

324:   *C = Cmpi;

326:   /* set MatInfo */
327:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
328:   if (afill < 1.0) afill = 1.0;
329:   Cmpi->info.mallocs           = nspacedouble;
330:   Cmpi->info.fill_ratio_given  = fill;
331:   Cmpi->info.fill_ratio_needed = afill;

333: #if defined(PETSC_USE_INFO)
334:   if (api[am]) {
335:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
336:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
337:   } else {
338:     PetscInfo(Cmpi,"Empty matrix product\n");
339:   }
340: #endif
341:   return(0);
342: }

344: PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
345: {

349:   if (scall == MAT_INITIAL_MATRIX) {
350:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
351:     MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);
352:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
353:   }
354:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
355:   MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);
356:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
357:   return(0);
358: }

360: typedef struct {
361:   Mat         workB;
362:   PetscScalar *rvalues,*svalues;
363:   MPI_Request *rwaits,*swaits;
364: } MPIAIJ_MPIDense;

366: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
367: {
368:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
369:   PetscErrorCode  ierr;

372:   MatDestroy(&contents->workB);
373:   PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);
374:   PetscFree(contents);
375:   return(0);
376: }

378:  #include <petsc/private/vecscatterimpl.h>
379: /*
380:     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
381:   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option

383:   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C

385:   Developer Notes: This directly accesses information inside the VecScatter associated with the matrix-vector product
386:    for this matrix. This is not desirable..

388: */
389: PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
390: {
391:   PetscErrorCode         ierr;
392:   PetscBool              flg;
393:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
394:   PetscInt               nz   = aij->B->cmap->n;
395:   PetscContainer         container;
396:   MPIAIJ_MPIDense        *contents;
397:   VecScatter             ctx   = aij->Mvctx;
398:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
399:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;

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

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

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

411:   PetscNew(&contents);
412:   /* Create work matrix used to store off processor rows of B needed for local product */
413:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
414:   /* Create work arrays needed */
415:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
416:                       B->cmap->N*to->starts[to->n],&contents->svalues,
417:                       from->n,&contents->rwaits,
418:                       to->n,&contents->swaits);

420:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
421:   PetscContainerSetPointer(container,contents);
422:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
423:   PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);
424:   PetscContainerDestroy(&container);

426:   (*C->ops->matmultnumeric)(A,B,C);
427:   return(0);
428: }

430: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
431: {
432:   PetscErrorCode         ierr;
433:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
434:   PetscInt               nz   = aij->B->cmap->n;
435:   PetscContainer         container;
436:   MPIAIJ_MPIDense        *contents;
437:   VecScatter             ctx   = aij->Mvctx;
438:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
439:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
440:   PetscInt               m     = A->rmap->n,n=B->cmap->n;

443:   MatCreate(PetscObjectComm((PetscObject)B),C);
444:   MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);
445:   MatSetBlockSizesFromMats(*C,A,B);
446:   MatSetType(*C,MATMPIDENSE);
447:   MatMPIDenseSetPreallocation(*C,NULL);
448:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
449:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);

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

453:   PetscNew(&contents);
454:   /* Create work matrix used to store off processor rows of B needed for local product */
455:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
456:   /* Create work arrays needed */
457:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
458:                       B->cmap->N*to->starts[to->n],&contents->svalues,
459:                       from->n,&contents->rwaits,
460:                       to->n,&contents->swaits);

462:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
463:   PetscContainerSetPointer(container,contents);
464:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
465:   PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);
466:   PetscContainerDestroy(&container);
467:   return(0);
468: }

470: /*
471:     Performs an efficient scatter on the rows of B needed by this process; this is
472:     a modification of the VecScatterBegin_() routines.
473: */
474: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
475: {
476:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
477:   PetscErrorCode         ierr;
478:   PetscScalar            *b,*w,*svalues,*rvalues;
479:   VecScatter             ctx   = aij->Mvctx;
480:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
481:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
482:   PetscInt               i,j,k;
483:   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
484:   PetscMPIInt            *sprocs,*rprocs,nrecvs;
485:   MPI_Request            *swaits,*rwaits;
486:   MPI_Comm               comm;
487:   PetscMPIInt            tag  = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
488:   MPI_Status             status;
489:   MPIAIJ_MPIDense        *contents;
490:   PetscContainer         container;
491:   Mat                    workB;

494:   PetscObjectGetComm((PetscObject)A,&comm);
495:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
496:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
497:   PetscContainerGetPointer(container,(void**)&contents);

499:   workB = *outworkB = contents->workB;
500:   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
501:   sindices = to->indices;
502:   sstarts  = to->starts;
503:   sprocs   = to->procs;
504:   swaits   = contents->swaits;
505:   svalues  = contents->svalues;

507:   rindices = from->indices;
508:   rstarts  = from->starts;
509:   rprocs   = from->procs;
510:   rwaits   = contents->rwaits;
511:   rvalues  = contents->rvalues;

513:   MatDenseGetArray(B,&b);
514:   MatDenseGetArray(workB,&w);

516:   for (i=0; i<from->n; i++) {
517:     MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);
518:   }

520:   for (i=0; i<to->n; i++) {
521:     /* pack a message at a time */
522:     for (j=0; j<sstarts[i+1]-sstarts[i]; j++) {
523:       for (k=0; k<ncols; k++) {
524:         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
525:       }
526:     }
527:     MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);
528:   }

530:   nrecvs = from->n;
531:   while (nrecvs) {
532:     MPI_Waitany(from->n,rwaits,&imdex,&status);
533:     nrecvs--;
534:     /* unpack a message at a time */
535:     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++) {
536:       for (k=0; k<ncols; k++) {
537:         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
538:       }
539:     }
540:   }
541:   if (to->n) {MPI_Waitall(to->n,swaits,to->sstatus);}

543:   MatDenseRestoreArray(B,&b);
544:   MatDenseRestoreArray(workB,&w);
545:   MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);
546:   MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);
547:   return(0);
548: }
549: extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);

551: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
552: {
554:   Mat_MPIAIJ     *aij    = (Mat_MPIAIJ*)A->data;
555:   Mat_MPIDense   *bdense = (Mat_MPIDense*)B->data;
556:   Mat_MPIDense   *cdense = (Mat_MPIDense*)C->data;
557:   Mat            workB;

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

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

566:   /* off-diagonal block of A times nonlocal rows of B */
567:   MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);
568:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
569:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
570:   return(0);
571: }

573: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
574: {
576:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
577:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
578:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
579:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
580:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
581:   Mat_SeqAIJ     *p_loc,*p_oth;
582:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
583:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
584:   PetscInt       cm          = C->rmap->n,anz,pnz;
585:   Mat_PtAPMPI    *ptap       = c->ptap;
586:   PetscScalar    *apa_sparse = ptap->apa;
587:   PetscInt       *api,*apj,*apJ,i,j,k,row;
588:   PetscInt       cstart = C->cmap->rstart;
589:   PetscInt       cdnz,conz,k0,k1,nextp;
590:   MPI_Comm       comm;
591:   PetscMPIInt    size;

594:   PetscObjectGetComm((PetscObject)A,&comm);
595:   MPI_Comm_size(comm,&size);

597:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
598:   /*-----------------------------------------------------*/
599:   /* update numerical values of P_oth and P_loc */
600:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
601:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

603:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
604:   /*----------------------------------------------------------*/
605:   /* get data from symbolic products */
606:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
607:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
608:   if (size >1) {
609:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
610:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
611:   } else {
612:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
613:   }

615:   api = ptap->api;
616:   apj = ptap->apj;
617:   for (i=0; i<cm; i++) {
618:     apJ = apj + api[i];

620:     /* diagonal portion of A */
621:     anz = adi[i+1] - adi[i];
622:     adj = ad->j + adi[i];
623:     ada = ad->a + adi[i];
624:     for (j=0; j<anz; j++) {
625:       row = adj[j];
626:       pnz = pi_loc[row+1] - pi_loc[row];
627:       pj  = pj_loc + pi_loc[row];
628:       pa  = pa_loc + pi_loc[row];
629:       /* perform sparse axpy */
630:       valtmp = ada[j];
631:       nextp  = 0;
632:       for (k=0; nextp<pnz; k++) {
633:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
634:           apa_sparse[k] += valtmp*pa[nextp++];
635:         }
636:       }
637:       PetscLogFlops(2.0*pnz);
638:     }

640:     /* off-diagonal portion of A */
641:     anz = aoi[i+1] - aoi[i];
642:     aoj = ao->j + aoi[i];
643:     aoa = ao->a + aoi[i];
644:     for (j=0; j<anz; j++) {
645:       row = aoj[j];
646:       pnz = pi_oth[row+1] - pi_oth[row];
647:       pj  = pj_oth + pi_oth[row];
648:       pa  = pa_oth + pi_oth[row];
649:       /* perform sparse axpy */
650:       valtmp = aoa[j];
651:       nextp  = 0;
652:       for (k=0; nextp<pnz; k++) {
653:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
654:           apa_sparse[k] += valtmp*pa[nextp++];
655:         }
656:       }
657:       PetscLogFlops(2.0*pnz);
658:     }

660:     /* set values in C */
661:     cdnz = cd->i[i+1] - cd->i[i];
662:     conz = co->i[i+1] - co->i[i];

664:     /* 1st off-diagoanl part of C */
665:     ca = coa + co->i[i];
666:     k  = 0;
667:     for (k0=0; k0<conz; k0++) {
668:       if (apJ[k] >= cstart) break;
669:       ca[k0]        = apa_sparse[k];
670:       apa_sparse[k] = 0.0;
671:       k++;
672:     }

674:     /* diagonal part of C */
675:     ca = cda + cd->i[i];
676:     for (k1=0; k1<cdnz; k1++) {
677:       ca[k1]        = apa_sparse[k];
678:       apa_sparse[k] = 0.0;
679:       k++;
680:     }

682:     /* 2nd off-diagoanl part of C */
683:     ca = coa + co->i[i];
684:     for (; k0<conz; k0++) {
685:       ca[k0]        = apa_sparse[k];
686:       apa_sparse[k] = 0.0;
687:       k++;
688:     }
689:   }
690:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
691:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
692:   return(0);
693: }

695: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
696: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
697: {
698:   PetscErrorCode     ierr;
699:   MPI_Comm           comm;
700:   PetscMPIInt        size;
701:   Mat                Cmpi;
702:   Mat_PtAPMPI        *ptap;
703:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
704:   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
705:   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
706:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
707:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
708:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
709:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
710:   PetscReal          afill;
711:   PetscScalar        *apa;

714:   PetscObjectGetComm((PetscObject)A,&comm);
715:   MPI_Comm_size(comm,&size);

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

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

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

726:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
727:   pi_loc = p_loc->i; pj_loc = p_loc->j;
728:   if (size > 1) {
729:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
730:     pi_oth = p_oth->i; pj_oth = p_oth->j;
731:   } else {
732:     p_oth  = NULL;
733:     pi_oth = NULL; pj_oth = NULL;
734:   }

736:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
737:   /*-------------------------------------------------------------------*/
738:   PetscMalloc1(am+2,&api);
739:   ptap->api = api;
740:   api[0]    = 0;

742:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

744:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
745:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
746:   current_space = free_space;
747:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
748:   for (i=0; i<am; i++) {
749:     /* diagonal portion of A */
750:     nzi = adi[i+1] - adi[i];
751:     for (j=0; j<nzi; j++) {
752:       row  = *adj++;
753:       pnz  = pi_loc[row+1] - pi_loc[row];
754:       Jptr = pj_loc + pi_loc[row];
755:       /* Expand list if it is not long enough */
756:       if (pnz+apnz_max > lsize) {
757:         lsize = pnz+apnz_max;
758:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
759:       }
760:       /* add non-zero cols of P into the sorted linked list lnk */
761:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
762:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
763:       api[i+1] = api[i] + apnz;
764:       if (apnz > apnz_max) apnz_max = apnz;
765:     }
766:     /* off-diagonal portion of A */
767:     nzi = aoi[i+1] - aoi[i];
768:     for (j=0; j<nzi; j++) {
769:       row  = *aoj++;
770:       pnz  = pi_oth[row+1] - pi_oth[row];
771:       Jptr = pj_oth + pi_oth[row];
772:       /* Expand list if it is not long enough */
773:       if (pnz+apnz_max > lsize) {
774:         lsize = pnz + apnz_max;
775:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
776:       }
777:       /* add non-zero cols of P into the sorted linked list lnk */
778:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
779:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
780:       api[i+1] = api[i] + apnz;
781:       if (apnz > apnz_max) apnz_max = apnz;
782:     }
783:     apnz     = *lnk;
784:     api[i+1] = api[i] + apnz;
785:     if (apnz > apnz_max) apnz_max = apnz;

787:     /* if free space is not available, double the total space in the list */
788:     if (current_space->local_remaining<apnz) {
789:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
790:       nspacedouble++;
791:     }

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

797:     current_space->array           += apnz;
798:     current_space->local_used      += apnz;
799:     current_space->local_remaining -= apnz;
800:   }

802:   /* Allocate space for apj, initialize apj, and */
803:   /* destroy list of free space and other temporary array(s) */
804:   PetscMalloc1(api[am]+1,&ptap->apj);
805:   apj  = ptap->apj;
806:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
807:   PetscLLCondensedDestroy_Scalable(lnk);

809:   /* create and assemble symbolic parallel matrix Cmpi */
810:   /*----------------------------------------------------*/
811:   MatCreate(comm,&Cmpi);
812:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
813:   MatSetBlockSizesFromMats(Cmpi,A,P);
814:   MatSetType(Cmpi,MATMPIAIJ);
815:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);

817:   /* malloc apa for assembly Cmpi */
818:   PetscCalloc1(apnz_max,&apa);
819:   ptap->apa = apa;

821:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);
822:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
823:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
824:   MatPreallocateFinalize(dnz,onz);

826:   ptap->destroy             = Cmpi->ops->destroy;
827:   ptap->duplicate           = Cmpi->ops->duplicate;
828:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
829:   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
830:   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;

832:   /* attach the supporting struct to Cmpi for reuse */
833:   c       = (Mat_MPIAIJ*)Cmpi->data;
834:   c->ptap = ptap;
835:   *C = Cmpi;

837:   /* set MatInfo */
838:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
839:   if (afill < 1.0) afill = 1.0;
840:   Cmpi->info.mallocs           = nspacedouble;
841:   Cmpi->info.fill_ratio_given  = fill;
842:   Cmpi->info.fill_ratio_needed = afill;

844: #if defined(PETSC_USE_INFO)
845:   if (api[am]) {
846:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
847:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
848:   } else {
849:     PetscInfo(Cmpi,"Empty matrix product\n");
850:   }
851: #endif
852:   return(0);
853: }

855: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
856: /* Three input arrays are merged to one output array. The size of the    */
857: /* output array is also output. Duplicate entries only show up once.     */
858: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
859:                                PetscInt  size2, PetscInt *in2,
860:                                PetscInt  size3, PetscInt *in3,
861:                                PetscInt *size4, PetscInt *out)
862: {
863:   int i = 0, j = 0, k = 0, l = 0;

865:   /* Traverse all three arrays */
866:   while (i<size1 && j<size2 && k<size3) {
867:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
868:       out[l++] = in1[i++];
869:     }
870:     else if(in2[j] < in1[i] && in2[j] < in3[k]) {
871:       out[l++] = in2[j++];
872:     }
873:     else if(in3[k] < in1[i] && in3[k] < in2[j]) {
874:       out[l++] = in3[k++];
875:     }
876:     else if(in1[i] == in2[j] && in1[i] < in3[k]) {
877:       out[l++] = in1[i];
878:       i++, j++;
879:     }
880:     else if(in1[i] == in3[k] && in1[i] < in2[j]) {
881:       out[l++] = in1[i];
882:       i++, k++;
883:     }
884:     else if(in3[k] == in2[j] && in2[j] < in1[i])  {
885:       out[l++] = in2[j];
886:       k++, j++;
887:     }
888:     else if(in1[i] == in2[j] && in1[i] == in3[k]) {
889:       out[l++] = in1[i];
890:       i++, j++, k++;
891:     }
892:   }

894:   /* Traverse two remaining arrays */
895:   while (i<size1 && j<size2) {
896:     if (in1[i] < in2[j]) {
897:       out[l++] = in1[i++];
898:     }
899:     else if(in1[i] > in2[j]) {
900:       out[l++] = in2[j++];
901:     }
902:     else {
903:       out[l++] = in1[i];
904:       i++, j++;
905:     }
906:   }

908:   while (i<size1 && k<size3) {
909:     if (in1[i] < in3[k]) {
910:       out[l++] = in1[i++];
911:     }
912:     else if(in1[i] > in3[k]) {
913:       out[l++] = in3[k++];
914:     }
915:     else {
916:       out[l++] = in1[i];
917:       i++, k++;
918:     }
919:   }

921:   while (k<size3 && j<size2)  {
922:     if (in3[k] < in2[j]) {
923:       out[l++] = in3[k++];
924:     }
925:     else if(in3[k] > in2[j]) {
926:       out[l++] = in2[j++];
927:     }
928:     else {
929:       out[l++] = in3[k];
930:       k++, j++;
931:     }
932:   }

934:   /* Traverse one remaining array */
935:   while (i<size1) out[l++] = in1[i++];
936:   while (j<size2) out[l++] = in2[j++];
937:   while (k<size3) out[l++] = in3[k++];

939:   *size4 = l;
940: }

942: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
943: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
944: /* matrix-matrix multiplications.  */
947: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat *C)
948: {
949:   PetscErrorCode     ierr;
950:   MPI_Comm           comm;
951:   PetscMPIInt        size;
952:   Mat                Cmpi;
953:   Mat_PtAPMPI        *ptap;
954:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
955:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data;
956:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
957:   Mat_MPIAIJ         *p        =(Mat_MPIAIJ*)P->data;
958:   Mat_MPIAIJ         *c;
959:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
960:   PetscInt           adponz, adpdnz;
961:   PetscInt           *pi_loc,*dnz,*onz;
962:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
963:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
964:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
965:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
966:   PetscBT            lnkbt;
967:   PetscScalar        *apa;
968:   PetscReal          afill;
969:   PetscMPIInt        rank;
970:   Mat                adpd, aopoth;

973:   PetscObjectGetComm((PetscObject)A,&comm);
974:   MPI_Comm_size(comm,&size);
975:   MPI_Comm_rank(comm, &rank);
976:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

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

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

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


988:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
989:   pi_loc = p_loc->i;

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

995:   adpoi[0]    = 0;
996:   ptap->api = api;
997:   api[0] = 0;

999:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1000:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
1001:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

1003:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1004:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->A, p->A, fill, &adpd);
1005:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1006:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1007:   p_off = (Mat_SeqAIJ*)((p->B)->data);
1008:   poff_i = p_off->i; poff_j = p_off->j;

1010:   /* j_temp stores indices of a result row before they are added to the linked list */
1011:   PetscMalloc1(pN+2,&j_temp);


1014:   /* Symbolic calc of the A_diag * p_loc_off */
1015:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1016:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
1017:   current_space = free_space_diag;

1019:   for (i=0; i<am; i++) {
1020:     /* A_diag * P_loc_off */
1021:     nzi = adi[i+1] - adi[i];
1022:     for (j=0; j<nzi; j++) {
1023:       row  = *adj++;
1024:       pnz  = poff_i[row+1] - poff_i[row];
1025:       Jptr = poff_j + poff_i[row];
1026:       for(i1 = 0; i1 < pnz; i1++) {
1027:         j_temp[i1] = p->garray[Jptr[i1]];
1028:       }
1029:       /* add non-zero cols of P into the sorted linked list lnk */
1030:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
1031:     }

1033:     adponz     = lnk[0];
1034:     adpoi[i+1] = adpoi[i] + adponz;

1036:     /* if free space is not available, double the total space in the list */
1037:     if (current_space->local_remaining<adponz) {
1038:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
1039:       nspacedouble++;
1040:     }

1042:     /* Copy data into free space, then initialize lnk */
1043:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

1045:     current_space->array           += adponz;
1046:     current_space->local_used      += adponz;
1047:     current_space->local_remaining -= adponz;
1048:   }

1050:   /* Symbolic calc of A_off * P_oth */
1051:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, &aopoth);
1052:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1053:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

1055:   /* Allocate space for apj, adpj, aopj, ... */
1056:   /* destroy lists of free space and other temporary array(s) */

1058:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
1059:   PetscMalloc1(adpoi[am]+2, &adpoj);

1061:   /* Copy from linked list to j-array */
1062:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
1063:   PetscLLDestroy(lnk,lnkbt);

1065:   adpoJ = adpoj;
1066:   adpdJ = adpdj;
1067:   aopJ = aopothj;
1068:   apj  = ptap->apj;
1069:   apJ = apj; /* still empty */

1071:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1072:   /* A_diag * P_loc_diag to get A*P */
1073:   for (i = 0; i < am; i++) {
1074:     aopnz  =  aopothi[i+1] -  aopothi[i];
1075:     adponz = adpoi[i+1] - adpoi[i];
1076:     adpdnz = adpdi[i+1] - adpdi[i];

1078:     /* Correct indices from A_diag*P_diag */
1079:     for(i1 = 0; i1 < adpdnz; i1++) {
1080:       adpdJ[i1] += p_colstart;
1081:     }
1082:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1083:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1084:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

1086:     aopJ += aopnz;
1087:     adpoJ += adponz;
1088:     adpdJ += adpdnz;
1089:     apJ += apnz;
1090:     api[i+1] = api[i] + apnz;
1091:   }

1093:   /* malloc apa to store dense row A[i,:]*P */
1094:   PetscCalloc1(pN+2,&apa);

1096:   ptap->apa = apa;
1097:   /* create and assemble symbolic parallel matrix Cmpi */
1098:   MatCreate(comm,&Cmpi);
1099:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
1100:   MatSetBlockSizesFromMats(Cmpi,A,P);

1102:   MatSetType(Cmpi,MATMPIAIJ);
1103:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);


1106:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);
1107:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
1108:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
1109:   MatPreallocateFinalize(dnz,onz);


1112:   ptap->destroy        = Cmpi->ops->destroy;
1113:   ptap->duplicate      = Cmpi->ops->duplicate;
1114:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1115:   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
1116:   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatMatMult;

1118:   /* attach the supporting struct to Cmpi for reuse */
1119:   c       = (Mat_MPIAIJ*)Cmpi->data;
1120:   c->ptap = ptap;
1121:   *C = Cmpi;

1123:   /* set MatInfo */
1124:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1125:   if (afill < 1.0) afill = 1.0;
1126:   Cmpi->info.mallocs           = nspacedouble;
1127:   Cmpi->info.fill_ratio_given  = fill;
1128:   Cmpi->info.fill_ratio_needed = afill;

1130: #if defined(PETSC_USE_INFO)
1131:   if (api[am]) {
1132:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1133:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1134:   } else {
1135:     PetscInfo(Cmpi,"Empty matrix product\n");
1136:   }
1137: #endif

1139:   MatDestroy(&aopoth);
1140:   MatDestroy(&adpd);
1141:   PetscFree(j_temp);
1142:   PetscFree(adpoj);
1143:   PetscFree(adpoi);
1144:   return(0);
1145: }


1148: /*-------------------------------------------------------------------------*/
1149: PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C)
1150: {
1152:   const char     *algTypes[3] = {"scalable","nonscalable","matmatmult"};
1153:   PetscInt       aN=A->cmap->N,alg=1; /* set default algorithm */
1154:   PetscBool      flg;

1157:   if (scall == MAT_INITIAL_MATRIX) {
1158:     PetscObjectOptionsBegin((PetscObject)A);
1159:     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
1160:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,3,algTypes[1],&alg,&flg);
1161:     PetscOptionsEnd();

1163:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,P,A,0,0);
1164:     switch (alg) {
1165:     case 1:
1166:       if (!flg && aN > 100000) { /* may switch to scalable algorithm as default */
1167:         MatInfo     Ainfo,Pinfo;
1168:         PetscInt    nz_local;
1169:         PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
1170:         MPI_Comm    comm;

1172:         MatGetInfo(A,MAT_LOCAL,&Ainfo);
1173:         MatGetInfo(P,MAT_LOCAL,&Pinfo);
1174:         nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated); /* estimated local nonzero entries */

1176:         if (aN > fill*nz_local) alg_scalable_loc = PETSC_TRUE;
1177:         PetscObjectGetComm((PetscObject)A,&comm);
1178:         MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

1180:         if (alg_scalable) {
1181:           alg  = 0; /* scalable algorithm would slower than nonscalable algorithm */
1182:           MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);
1183:           break;
1184:         }
1185:       }
1186:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(P,A,fill,C);
1187:       break;
1188:     case 2:
1189:     {
1190:       Mat         Pt;
1191:       Mat_PtAPMPI *ptap;
1192:       Mat_MPIAIJ  *c;
1193:       MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);
1194:       MatMatMult(Pt,A,MAT_INITIAL_MATRIX,fill,C);
1195:       c        = (Mat_MPIAIJ*)(*C)->data;
1196:       ptap     = c->ptap;
1197:       ptap->Pt = Pt;
1198:       (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
1199:       return(0);
1200:     }
1201:       break;
1202:     default: /* scalable algorithm */
1203:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);
1204:       break;
1205:     }
1206:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,P,A,0,0);
1207:   }
1208:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,P,A,0,0);
1209:   (*(*C)->ops->mattransposemultnumeric)(P,A,*C);
1210:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,P,A,0,0);
1211:   return(0);
1212: }

1214: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1215: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1216: {
1218:   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
1219:   Mat_PtAPMPI    *ptap= c->ptap;
1220:   Mat            Pt=ptap->Pt;

1223:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
1224:   MatMatMultNumeric(Pt,A,C);
1225:   return(0);
1226: }

1228: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat,MatDuplicateOption,Mat*);

1230: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1231: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat *C)
1232: {
1233:   PetscErrorCode      ierr;
1234:   Mat_PtAPMPI         *ptap;
1235:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
1236:   MPI_Comm            comm;
1237:   PetscMPIInt         size,rank;
1238:   Mat                 Cmpi;
1239:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1240:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1241:   PetscInt            *lnk,i,k,nsend;
1242:   PetscBT             lnkbt;
1243:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
1244:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1245:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1246:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1247:   MPI_Request         *swaits,*rwaits;
1248:   MPI_Status          *sstatus,rstatus;
1249:   PetscLayout         rowmap;
1250:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1251:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1252:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1253:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1254:   PetscTable          ta;

1257:   PetscObjectGetComm((PetscObject)A,&comm);
1258:   MPI_Comm_size(comm,&size);
1259:   MPI_Comm_rank(comm,&rank);

1261:   /* create symbolic parallel matrix Cmpi */
1262:   MatCreate(comm,&Cmpi);
1263:   MatSetType(Cmpi,MATMPIAIJ);

1265:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1267:   /* create struct Mat_PtAPMPI and attached it to C later */
1268:   PetscNew(&ptap);
1269:   ptap->reuse = MAT_INITIAL_MATRIX;

1271:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1272:   /* --------------------------------- */
1273:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
1274:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

1276:   /* (1) compute symbolic A_loc */
1277:   /* ---------------------------*/
1278:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

1280:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1281:   /* ------------------------------------ */
1282:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,&ptap->C_oth);

1284:   /* (3) send coj of C_oth to other processors  */
1285:   /* ------------------------------------------ */
1286:   /* determine row ownership */
1287:   PetscLayoutCreate(comm,&rowmap);
1288:   rowmap->n  = pn;
1289:   rowmap->bs = 1;
1290:   PetscLayoutSetUp(rowmap);
1291:   owners = rowmap->range;

1293:   /* determine the number of messages to send, their lengths */
1294:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
1295:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));
1296:   PetscMemzero(len_si,size*sizeof(PetscMPIInt));

1298:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1299:   coi   = c_oth->i; coj = c_oth->j;
1300:   con   = ptap->C_oth->rmap->n;
1301:   proc  = 0;
1302:   for (i=0; i<con; i++) {
1303:     while (prmap[i] >= owners[proc+1]) proc++;
1304:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1305:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1306:   }

1308:   len          = 0; /* max length of buf_si[], see (4) */
1309:   owners_co[0] = 0;
1310:   nsend        = 0;
1311:   for (proc=0; proc<size; proc++) {
1312:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1313:     if (len_s[proc]) {
1314:       nsend++;
1315:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1316:       len         += len_si[proc];
1317:     }
1318:   }

1320:   /* determine the number and length of messages to receive for coi and coj  */
1321:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
1322:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

1324:   /* post the Irecv and Isend of coj */
1325:   PetscCommGetNewTag(comm,&tagj);
1326:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
1327:   PetscMalloc1(nsend+1,&swaits);
1328:   for (proc=0, k=0; proc<size; proc++) {
1329:     if (!len_s[proc]) continue;
1330:     i    = owners_co[proc];
1331:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1332:     k++;
1333:   }

1335:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1336:   /* ---------------------------------------- */
1337:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,&ptap->C_loc);
1338:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

1340:   /* receives coj are complete */
1341:   for (i=0; i<nrecv; i++) {
1342:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1343:   }
1344:   PetscFree(rwaits);
1345:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1347:   /* add received column indices into ta to update Crmax */
1348:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

1350:   /* create and initialize a linked list */
1351:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
1352:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

1354:   for (k=0; k<nrecv; k++) {/* k-th received message */
1355:     Jptr = buf_rj[k];
1356:     for (j=0; j<len_r[k]; j++) {
1357:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1358:     }
1359:   }
1360:   PetscTableGetCount(ta,&Crmax);
1361:   PetscTableDestroy(&ta);

1363:   /* (4) send and recv coi */
1364:   /*-----------------------*/
1365:   PetscCommGetNewTag(comm,&tagi);
1366:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
1367:   PetscMalloc1(len+1,&buf_s);
1368:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1369:   for (proc=0,k=0; proc<size; proc++) {
1370:     if (!len_s[proc]) continue;
1371:     /* form outgoing message for i-structure:
1372:          buf_si[0]:                 nrows to be sent
1373:                [1:nrows]:           row index (global)
1374:                [nrows+1:2*nrows+1]: i-structure index
1375:     */
1376:     /*-------------------------------------------*/
1377:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1378:     buf_si_i    = buf_si + nrows+1;
1379:     buf_si[0]   = nrows;
1380:     buf_si_i[0] = 0;
1381:     nrows       = 0;
1382:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1383:       nzi = coi[i+1] - coi[i];
1384:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1385:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1386:       nrows++;
1387:     }
1388:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1389:     k++;
1390:     buf_si += len_si[proc];
1391:   }
1392:   for (i=0; i<nrecv; i++) {
1393:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1394:   }
1395:   PetscFree(rwaits);
1396:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1398:   PetscFree4(len_s,len_si,sstatus,owners_co);
1399:   PetscFree(len_ri);
1400:   PetscFree(swaits);
1401:   PetscFree(buf_s);

1403:   /* (5) compute the local portion of Cmpi      */
1404:   /* ------------------------------------------ */
1405:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
1406:   PetscFreeSpaceGet(Crmax,&free_space);
1407:   current_space = free_space;

1409:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
1410:   for (k=0; k<nrecv; k++) {
1411:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1412:     nrows       = *buf_ri_k[k];
1413:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1414:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1415:   }

1417:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
1418:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
1419:   for (i=0; i<pn; i++) {
1420:     /* add C_loc into Cmpi */
1421:     nzi  = c_loc->i[i+1] - c_loc->i[i];
1422:     Jptr = c_loc->j + c_loc->i[i];
1423:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

1425:     /* add received col data into lnk */
1426:     for (k=0; k<nrecv; k++) { /* k-th received message */
1427:       if (i == *nextrow[k]) { /* i-th row */
1428:         nzi  = *(nextci[k]+1) - *nextci[k];
1429:         Jptr = buf_rj[k] + *nextci[k];
1430:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1431:         nextrow[k]++; nextci[k]++;
1432:       }
1433:     }
1434:     nzi = lnk[0];

1436:     /* copy data into free space, then initialize lnk */
1437:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
1438:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
1439:   }
1440:   PetscFree3(buf_ri_k,nextrow,nextci);
1441:   PetscLLDestroy(lnk,lnkbt);
1442:   PetscFreeSpaceDestroy(free_space);

1444:   /* local sizes and preallocation */
1445:   MatSetSizes(Cmpi,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
1446:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));
1447:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
1448:   MatPreallocateFinalize(dnz,onz);

1450:   /* members in merge */
1451:   PetscFree(id_r);
1452:   PetscFree(len_r);
1453:   PetscFree(buf_ri[0]);
1454:   PetscFree(buf_ri);
1455:   PetscFree(buf_rj[0]);
1456:   PetscFree(buf_rj);
1457:   PetscLayoutDestroy(&rowmap);

1459:   /* attach the supporting struct to Cmpi for reuse */
1460:   c = (Mat_MPIAIJ*)Cmpi->data;
1461:   c->ptap         = ptap;
1462:   ptap->duplicate = Cmpi->ops->duplicate;
1463:   ptap->destroy   = Cmpi->ops->destroy;

1465:   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
1466:   Cmpi->assembled        = PETSC_FALSE;
1467:   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1468:   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
1469:   *C                     = Cmpi;
1470:   return(0);
1471: }

1473: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1474: {
1475:   PetscErrorCode    ierr;
1476:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1477:   Mat_SeqAIJ        *c_seq;
1478:   Mat_PtAPMPI       *ptap = c->ptap;
1479:   Mat               A_loc,C_loc,C_oth;
1480:   PetscInt          i,rstart,rend,cm,ncols,row;
1481:   const PetscInt    *cols;
1482:   const PetscScalar *vals;

1485:   MatZeroEntries(C);

1487:   if (ptap->reuse == MAT_REUSE_MATRIX) {
1488:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1489:     /* 1) get R = Pd^T, Ro = Po^T */
1490:     /*----------------------------*/
1491:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
1492:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

1494:     /* 2) compute numeric A_loc */
1495:     /*--------------------------*/
1496:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
1497:   }

1499:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1500:   A_loc = ptap->A_loc;
1501:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
1502:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
1503:   C_loc = ptap->C_loc;
1504:   C_oth = ptap->C_oth;

1506:   /* add C_loc and Co to to C */
1507:   MatGetOwnershipRange(C,&rstart,&rend);

1509:   /* C_loc -> C */
1510:   cm    = C_loc->rmap->N;
1511:   c_seq = (Mat_SeqAIJ*)C_loc->data;
1512:   cols = c_seq->j;
1513:   vals = c_seq->a;
1514:   for (i=0; i<cm; i++) {
1515:     ncols = c_seq->i[i+1] - c_seq->i[i];
1516:     row = rstart + i;
1517:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1518:     cols += ncols; vals += ncols;
1519:   }

1521:   /* Co -> C, off-processor part */
1522:   cm    = C_oth->rmap->N;
1523:   c_seq = (Mat_SeqAIJ*)C_oth->data;
1524:   cols  = c_seq->j;
1525:   vals  = c_seq->a;
1526:   for (i=0; i<cm; i++) {
1527:     ncols = c_seq->i[i+1] - c_seq->i[i];
1528:     row = p->garray[i];
1529:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1530:     cols += ncols; vals += ncols;
1531:   }
1532:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1533:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1535:   ptap->reuse = MAT_REUSE_MATRIX;
1536:   return(0);
1537: }

1539: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1540: {
1541:   PetscErrorCode      ierr;
1542:   Mat_Merge_SeqsToMPI *merge;
1543:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1544:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1545:   Mat_PtAPMPI         *ptap;
1546:   PetscInt            *adj;
1547:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1548:   MatScalar           *ada,*ca,valtmp;
1549:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1550:   MPI_Comm            comm;
1551:   PetscMPIInt         size,rank,taga,*len_s;
1552:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1553:   PetscInt            **buf_ri,**buf_rj;
1554:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1555:   MPI_Request         *s_waits,*r_waits;
1556:   MPI_Status          *status;
1557:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1558:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1559:   Mat                 A_loc;
1560:   Mat_SeqAIJ          *a_loc;

1563:   PetscObjectGetComm((PetscObject)C,&comm);
1564:   MPI_Comm_size(comm,&size);
1565:   MPI_Comm_rank(comm,&rank);

1567:   ptap  = c->ptap;
1568:   merge = ptap->merge;

1570:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1571:   /*------------------------------------------*/
1572:   /* get data from symbolic products */
1573:   coi    = merge->coi; coj = merge->coj;
1574:   PetscCalloc1(coi[pon]+1,&coa);
1575:   bi     = merge->bi; bj = merge->bj;
1576:   owners = merge->rowmap->range;
1577:   PetscCalloc1(bi[cm]+1,&ba);

1579:   /* get A_loc by taking all local rows of A */
1580:   A_loc = ptap->A_loc;
1581:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1582:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1583:   ai    = a_loc->i;
1584:   aj    = a_loc->j;

1586:   for (i=0; i<am; i++) {
1587:     anz = ai[i+1] - ai[i];
1588:     adj = aj + ai[i];
1589:     ada = a_loc->a + ai[i];

1591:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1592:     /*-------------------------------------------------------------*/
1593:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1594:     pnz = po->i[i+1] - po->i[i];
1595:     poJ = po->j + po->i[i];
1596:     pA  = po->a + po->i[i];
1597:     for (j=0; j<pnz; j++) {
1598:       row = poJ[j];
1599:       cj  = coj + coi[row];
1600:       ca  = coa + coi[row];
1601:       /* perform sparse axpy */
1602:       nexta  = 0;
1603:       valtmp = pA[j];
1604:       for (k=0; nexta<anz; k++) {
1605:         if (cj[k] == adj[nexta]) {
1606:           ca[k] += valtmp*ada[nexta];
1607:           nexta++;
1608:         }
1609:       }
1610:       PetscLogFlops(2.0*anz);
1611:     }

1613:     /* put the value into Cd (diagonal part) */
1614:     pnz = pd->i[i+1] - pd->i[i];
1615:     pdJ = pd->j + pd->i[i];
1616:     pA  = pd->a + pd->i[i];
1617:     for (j=0; j<pnz; j++) {
1618:       row = pdJ[j];
1619:       cj  = bj + bi[row];
1620:       ca  = ba + bi[row];
1621:       /* perform sparse axpy */
1622:       nexta  = 0;
1623:       valtmp = pA[j];
1624:       for (k=0; nexta<anz; k++) {
1625:         if (cj[k] == adj[nexta]) {
1626:           ca[k] += valtmp*ada[nexta];
1627:           nexta++;
1628:         }
1629:       }
1630:       PetscLogFlops(2.0*anz);
1631:     }
1632:   }

1634:   /* 3) send and recv matrix values coa */
1635:   /*------------------------------------*/
1636:   buf_ri = merge->buf_ri;
1637:   buf_rj = merge->buf_rj;
1638:   len_s  = merge->len_s;
1639:   PetscCommGetNewTag(comm,&taga);
1640:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

1642:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1643:   for (proc=0,k=0; proc<size; proc++) {
1644:     if (!len_s[proc]) continue;
1645:     i    = merge->owners_co[proc];
1646:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1647:     k++;
1648:   }
1649:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1650:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

1652:   PetscFree2(s_waits,status);
1653:   PetscFree(r_waits);
1654:   PetscFree(coa);

1656:   /* 4) insert local Cseq and received values into Cmpi */
1657:   /*----------------------------------------------------*/
1658:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1659:   for (k=0; k<merge->nrecv; k++) {
1660:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1661:     nrows       = *(buf_ri_k[k]);
1662:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1663:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1664:   }

1666:   for (i=0; i<cm; i++) {
1667:     row  = owners[rank] + i; /* global row index of C_seq */
1668:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1669:     ba_i = ba + bi[i];
1670:     bnz  = bi[i+1] - bi[i];
1671:     /* add received vals into ba */
1672:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1673:       /* i-th row */
1674:       if (i == *nextrow[k]) {
1675:         cnz    = *(nextci[k]+1) - *nextci[k];
1676:         cj     = buf_rj[k] + *(nextci[k]);
1677:         ca     = abuf_r[k] + *(nextci[k]);
1678:         nextcj = 0;
1679:         for (j=0; nextcj<cnz; j++) {
1680:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1681:             ba_i[j] += ca[nextcj++];
1682:           }
1683:         }
1684:         nextrow[k]++; nextci[k]++;
1685:         PetscLogFlops(2.0*cnz);
1686:       }
1687:     }
1688:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1689:   }
1690:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1691:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1693:   PetscFree(ba);
1694:   PetscFree(abuf_r[0]);
1695:   PetscFree(abuf_r);
1696:   PetscFree3(buf_ri_k,nextrow,nextci);
1697:   return(0);
1698: }

1700: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C)
1701: {
1702:   PetscErrorCode      ierr;
1703:   Mat                 Cmpi,A_loc,POt,PDt;
1704:   Mat_PtAPMPI         *ptap;
1705:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1706:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data,*c;
1707:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1708:   PetscInt            nnz;
1709:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1710:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1711:   MPI_Comm            comm;
1712:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1713:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1714:   PetscInt            len,proc,*dnz,*onz,*owners;
1715:   PetscInt            nzi,*bi,*bj;
1716:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1717:   MPI_Request         *swaits,*rwaits;
1718:   MPI_Status          *sstatus,rstatus;
1719:   Mat_Merge_SeqsToMPI *merge;
1720:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1721:   PetscReal           afill  =1.0,afill_tmp;
1722:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1723:   PetscScalar         *vals;
1724:   Mat_SeqAIJ          *a_loc,*pdt,*pot;
1725:   PetscTable          ta;

1728:   PetscObjectGetComm((PetscObject)A,&comm);
1729:   /* check if matrix local sizes are compatible */
1730:   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);

1732:   MPI_Comm_size(comm,&size);
1733:   MPI_Comm_rank(comm,&rank);

1735:   /* create struct Mat_PtAPMPI and attached it to C later */
1736:   PetscNew(&ptap);

1738:   /* get A_loc by taking all local rows of A */
1739:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

1741:   ptap->A_loc = A_loc;
1742:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1743:   ai          = a_loc->i;
1744:   aj          = a_loc->j;

1746:   /* determine symbolic Co=(p->B)^T*A - send to others */
1747:   /*----------------------------------------------------*/
1748:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
1749:   pdt  = (Mat_SeqAIJ*)PDt->data;
1750:   pdti = pdt->i; pdtj = pdt->j;

1752:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
1753:   pot  = (Mat_SeqAIJ*)POt->data;
1754:   poti = pot->i; potj = pot->j;

1756:   /* then, compute symbolic Co = (p->B)^T*A */
1757:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1758:                          >= (num of nonzero rows of C_seq) - pn */
1759:   PetscMalloc1(pon+1,&coi);
1760:   coi[0] = 0;

1762:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1763:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1764:   PetscFreeSpaceGet(nnz,&free_space);
1765:   current_space = free_space;

1767:   /* create and initialize a linked list */
1768:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
1769:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1770:   PetscTableGetCount(ta,&Armax);

1772:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

1774:   for (i=0; i<pon; i++) {
1775:     pnz = poti[i+1] - poti[i];
1776:     ptJ = potj + poti[i];
1777:     for (j=0; j<pnz; j++) {
1778:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1779:       anz  = ai[row+1] - ai[row];
1780:       Jptr = aj + ai[row];
1781:       /* add non-zero cols of AP into the sorted linked list lnk */
1782:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1783:     }
1784:     nnz = lnk[0];

1786:     /* If free space is not available, double the total space in the list */
1787:     if (current_space->local_remaining<nnz) {
1788:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
1789:       nspacedouble++;
1790:     }

1792:     /* Copy data into free space, and zero out denserows */
1793:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

1795:     current_space->array           += nnz;
1796:     current_space->local_used      += nnz;
1797:     current_space->local_remaining -= nnz;

1799:     coi[i+1] = coi[i] + nnz;
1800:   }

1802:   PetscMalloc1(coi[pon]+1,&coj);
1803:   PetscFreeSpaceContiguous(&free_space,coj);
1804:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

1806:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1807:   if (afill_tmp > afill) afill = afill_tmp;

1809:   /* send j-array (coj) of Co to other processors */
1810:   /*----------------------------------------------*/
1811:   /* determine row ownership */
1812:   PetscNew(&merge);
1813:   PetscLayoutCreate(comm,&merge->rowmap);

1815:   merge->rowmap->n  = pn;
1816:   merge->rowmap->bs = 1;

1818:   PetscLayoutSetUp(merge->rowmap);
1819:   owners = merge->rowmap->range;

1821:   /* determine the number of messages to send, their lengths */
1822:   PetscCalloc1(size,&len_si);
1823:   PetscMalloc1(size,&merge->len_s);

1825:   len_s        = merge->len_s;
1826:   merge->nsend = 0;

1828:   PetscMalloc1(size+2,&owners_co);
1829:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

1831:   proc = 0;
1832:   for (i=0; i<pon; i++) {
1833:     while (prmap[i] >= owners[proc+1]) proc++;
1834:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1835:     len_s[proc] += coi[i+1] - coi[i];
1836:   }

1838:   len          = 0; /* max length of buf_si[] */
1839:   owners_co[0] = 0;
1840:   for (proc=0; proc<size; proc++) {
1841:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1842:     if (len_si[proc]) {
1843:       merge->nsend++;
1844:       len_si[proc] = 2*(len_si[proc] + 1);
1845:       len         += len_si[proc];
1846:     }
1847:   }

1849:   /* determine the number and length of messages to receive for coi and coj  */
1850:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1851:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

1853:   /* post the Irecv and Isend of coj */
1854:   PetscCommGetNewTag(comm,&tagj);
1855:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1856:   PetscMalloc1(merge->nsend+1,&swaits);
1857:   for (proc=0, k=0; proc<size; proc++) {
1858:     if (!len_s[proc]) continue;
1859:     i    = owners_co[proc];
1860:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1861:     k++;
1862:   }

1864:   /* receives and sends of coj are complete */
1865:   PetscMalloc1(size,&sstatus);
1866:   for (i=0; i<merge->nrecv; i++) {
1867:     PetscMPIInt icompleted;
1868:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1869:   }
1870:   PetscFree(rwaits);
1871:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

1873:   /* add received column indices into table to update Armax */
1874:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/examples/tutorials/ex56.c! */
1875:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1876:     Jptr = buf_rj[k];
1877:     for (j=0; j<merge->len_r[k]; j++) {
1878:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1879:     }
1880:   }
1881:   PetscTableGetCount(ta,&Armax);
1882:   /* 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); */

1884:   /* send and recv coi */
1885:   /*-------------------*/
1886:   PetscCommGetNewTag(comm,&tagi);
1887:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1888:   PetscMalloc1(len+1,&buf_s);
1889:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1890:   for (proc=0,k=0; proc<size; proc++) {
1891:     if (!len_s[proc]) continue;
1892:     /* form outgoing message for i-structure:
1893:          buf_si[0]:                 nrows to be sent
1894:                [1:nrows]:           row index (global)
1895:                [nrows+1:2*nrows+1]: i-structure index
1896:     */
1897:     /*-------------------------------------------*/
1898:     nrows       = len_si[proc]/2 - 1;
1899:     buf_si_i    = buf_si + nrows+1;
1900:     buf_si[0]   = nrows;
1901:     buf_si_i[0] = 0;
1902:     nrows       = 0;
1903:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1904:       nzi               = coi[i+1] - coi[i];
1905:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1906:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1907:       nrows++;
1908:     }
1909:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1910:     k++;
1911:     buf_si += len_si[proc];
1912:   }
1913:   i = merge->nrecv;
1914:   while (i--) {
1915:     PetscMPIInt icompleted;
1916:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1917:   }
1918:   PetscFree(rwaits);
1919:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1920:   PetscFree(len_si);
1921:   PetscFree(len_ri);
1922:   PetscFree(swaits);
1923:   PetscFree(sstatus);
1924:   PetscFree(buf_s);

1926:   /* compute the local portion of C (mpi mat) */
1927:   /*------------------------------------------*/
1928:   /* allocate bi array and free space for accumulating nonzero column info */
1929:   PetscMalloc1(pn+1,&bi);
1930:   bi[0] = 0;

1932:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1933:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1934:   PetscFreeSpaceGet(nnz,&free_space);
1935:   current_space = free_space;

1937:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1938:   for (k=0; k<merge->nrecv; k++) {
1939:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1940:     nrows       = *buf_ri_k[k];
1941:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1942:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure  */
1943:   }

1945:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
1946:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
1947:   rmax = 0;
1948:   for (i=0; i<pn; i++) {
1949:     /* add pdt[i,:]*AP into lnk */
1950:     pnz = pdti[i+1] - pdti[i];
1951:     ptJ = pdtj + pdti[i];
1952:     for (j=0; j<pnz; j++) {
1953:       row  = ptJ[j];  /* row of AP == col of Pt */
1954:       anz  = ai[row+1] - ai[row];
1955:       Jptr = aj + ai[row];
1956:       /* add non-zero cols of AP into the sorted linked list lnk */
1957:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1958:     }

1960:     /* add received col data into lnk */
1961:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1962:       if (i == *nextrow[k]) { /* i-th row */
1963:         nzi  = *(nextci[k]+1) - *nextci[k];
1964:         Jptr = buf_rj[k] + *nextci[k];
1965:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
1966:         nextrow[k]++; nextci[k]++;
1967:       }
1968:     }
1969:     nnz = lnk[0];

1971:     /* if free space is not available, make more free space */
1972:     if (current_space->local_remaining<nnz) {
1973:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
1974:       nspacedouble++;
1975:     }
1976:     /* copy data into free space, then initialize lnk */
1977:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
1978:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

1980:     current_space->array           += nnz;
1981:     current_space->local_used      += nnz;
1982:     current_space->local_remaining -= nnz;

1984:     bi[i+1] = bi[i] + nnz;
1985:     if (nnz > rmax) rmax = nnz;
1986:   }
1987:   PetscFree3(buf_ri_k,nextrow,nextci);

1989:   PetscMalloc1(bi[pn]+1,&bj);
1990:   PetscFreeSpaceContiguous(&free_space,bj);
1991:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
1992:   if (afill_tmp > afill) afill = afill_tmp;
1993:   PetscLLCondensedDestroy_Scalable(lnk);
1994:   PetscTableDestroy(&ta);

1996:   MatDestroy(&POt);
1997:   MatDestroy(&PDt);

1999:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
2000:   /*----------------------------------------------------------------------------------*/
2001:   PetscCalloc1(rmax+1,&vals);

2003:   MatCreate(comm,&Cmpi);
2004:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
2005:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
2006:   MatSetType(Cmpi,MATMPIAIJ);
2007:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
2008:   MatPreallocateFinalize(dnz,onz);
2009:   MatSetBlockSize(Cmpi,1);
2010:   for (i=0; i<pn; i++) {
2011:     row  = i + rstart;
2012:     nnz  = bi[i+1] - bi[i];
2013:     Jptr = bj + bi[i];
2014:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
2015:   }
2016:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
2017:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
2018:   PetscFree(vals);

2020:   merge->bi        = bi;
2021:   merge->bj        = bj;
2022:   merge->coi       = coi;
2023:   merge->coj       = coj;
2024:   merge->buf_ri    = buf_ri;
2025:   merge->buf_rj    = buf_rj;
2026:   merge->owners_co = owners_co;

2028:   /* attach the supporting struct to Cmpi for reuse */
2029:   c = (Mat_MPIAIJ*)Cmpi->data;

2031:   c->ptap     = ptap;
2032:   ptap->api   = NULL;
2033:   ptap->apj   = NULL;
2034:   ptap->merge = merge;
2035:   ptap->apa   = NULL;
2036:   ptap->destroy   = Cmpi->ops->destroy;
2037:   ptap->duplicate = Cmpi->ops->duplicate;

2039:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2040:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
2041:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

2043:   *C = Cmpi;
2044: #if defined(PETSC_USE_INFO)
2045:   if (bi[pn] != 0) {
2046:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
2047:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
2048:   } else {
2049:     PetscInfo(Cmpi,"Empty matrix product\n");
2050:   }
2051: #endif
2052:   return(0);
2053: }