Actual source code: matmatmult.c

petsc-3.7.3 2016-08-01
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  2: /*
  3:   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
  4:           C = A * B
  5: */

  7: #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
  8: #include <../src/mat/utils/freespace.h>
  9: #include <../src/mat/utils/petscheap.h>
 10: #include <petscbt.h>
 11: #include <petsc/private/isimpl.h>
 12: #include <../src/mat/impls/dense/seq/dense.h>

 14: static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);

 18: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
 19: {
 21:   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
 22:   PetscInt       alg=0; /* set default algorithm */

 25:   if (scall == MAT_INITIAL_MATRIX) {
 26:     PetscObjectOptionsBegin((PetscObject)A);
 27:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,6,algTypes[0],&alg,NULL);
 28:     PetscOptionsEnd();
 29:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
 30:     switch (alg) {
 31:     case 1:
 32:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);
 33:       break;
 34:     case 2:
 35:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);
 36:       break;
 37:     case 3:
 38:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);
 39:       break;
 40:     case 4:
 41:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);
 42:       break;
 43:     case 5:
 44:       MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);
 45:       break;
 46:     default:
 47:       MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
 48:      break;
 49:     }
 50:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
 51:   }

 53:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
 54:   (*(*C)->ops->matmultnumeric)(A,B,*C);
 55:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
 56:   return(0);
 57: }

 61: static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
 62: {
 63:   PetscErrorCode     ierr;
 64:   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
 65:   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
 66:   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
 67:   PetscReal          afill;
 68:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
 69:   PetscTable         ta;
 70:   PetscBT            lnkbt;
 71:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

 74:   /* Get ci and cj */
 75:   /*---------------*/
 76:   /* Allocate ci array, arrays for fill computation and */
 77:   /* free space for accumulating nonzero column info */
 78:   PetscMalloc1(am+2,&ci);
 79:   ci[0] = 0;

 81:   /* create and initialize a linked list */
 82:   PetscTableCreate(bn,bn,&ta);
 83:   MatRowMergeMax_SeqAIJ(b,bm,ta);
 84:   PetscTableGetCount(ta,&Crmax);
 85:   PetscTableDestroy(&ta);

 87:   PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);

 89:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
 90:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);

 92:   current_space = free_space;

 94:   /* Determine ci and cj */
 95:   for (i=0; i<am; i++) {
 96:     anzi = ai[i+1] - ai[i];
 97:     aj   = a->j + ai[i];
 98:     for (j=0; j<anzi; j++) {
 99:       brow = aj[j];
100:       bnzj = bi[brow+1] - bi[brow];
101:       bj   = b->j + bi[brow];
102:       /* add non-zero cols of B into the sorted linked list lnk */
103:       PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);
104:     }
105:     cnzi = lnk[0];

107:     /* If free space is not available, make more free space */
108:     /* Double the amount of total space in the list */
109:     if (current_space->local_remaining<cnzi) {
110:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
111:       ndouble++;
112:     }

114:     /* Copy data into free space, then initialize lnk */
115:     PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);

117:     current_space->array           += cnzi;
118:     current_space->local_used      += cnzi;
119:     current_space->local_remaining -= cnzi;

121:     ci[i+1] = ci[i] + cnzi;
122:   }

124:   /* Column indices are in the list of free space */
125:   /* Allocate space for cj, initialize cj, and */
126:   /* destroy list of free space and other temporary array(s) */
127:   PetscMalloc1(ci[am]+1,&cj);
128:   PetscFreeSpaceContiguous(&free_space,cj);
129:   PetscLLCondensedDestroy(lnk,lnkbt);

131:   /* put together the new symbolic matrix */
132:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
133:   MatSetBlockSizesFromMats(*C,A,B);

135:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
136:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
137:   c                         = (Mat_SeqAIJ*)((*C)->data);
138:   c->free_a                 = PETSC_FALSE;
139:   c->free_ij                = PETSC_TRUE;
140:   c->nonew                  = 0;
141:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */

143:   /* set MatInfo */
144:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
145:   if (afill < 1.0) afill = 1.0;
146:   c->maxnz                     = ci[am];
147:   c->nz                        = ci[am];
148:   (*C)->info.mallocs           = ndouble;
149:   (*C)->info.fill_ratio_given  = fill;
150:   (*C)->info.fill_ratio_needed = afill;

152: #if defined(PETSC_USE_INFO)
153:   if (ci[am]) {
154:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
155:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
156:   } else {
157:     PetscInfo((*C),"Empty matrix product\n");
158:   }
159: #endif
160:   return(0);
161: }

165: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
166: {
168:   PetscLogDouble flops=0.0;
169:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
170:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
171:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
172:   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
173:   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
174:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
175:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
176:   PetscScalar    *ab_dense;

179:   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
180:     PetscMalloc1(ci[cm]+1,&ca);
181:     c->a      = ca;
182:     c->free_a = PETSC_TRUE;
183:   } else {
184:     ca        = c->a;
185:   }
186:   if (!c->matmult_abdense) {
187:     PetscCalloc1(B->cmap->N,&ab_dense);
188:     c->matmult_abdense = ab_dense;
189:   } else {
190:     ab_dense = c->matmult_abdense;
191:   }

193:   /* clean old values in C */
194:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
195:   /* Traverse A row-wise. */
196:   /* Build the ith row in C by summing over nonzero columns in A, */
197:   /* the rows of B corresponding to nonzeros of A. */
198:   for (i=0; i<am; i++) {
199:     anzi = ai[i+1] - ai[i];
200:     for (j=0; j<anzi; j++) {
201:       brow = aj[j];
202:       bnzi = bi[brow+1] - bi[brow];
203:       bjj  = bj + bi[brow];
204:       baj  = ba + bi[brow];
205:       /* perform dense axpy */
206:       valtmp = aa[j];
207:       for (k=0; k<bnzi; k++) {
208:         ab_dense[bjj[k]] += valtmp*baj[k];
209:       }
210:       flops += 2*bnzi;
211:     }
212:     aj += anzi; aa += anzi;

214:     cnzi = ci[i+1] - ci[i];
215:     for (k=0; k<cnzi; k++) {
216:       ca[k]          += ab_dense[cj[k]];
217:       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
218:     }
219:     flops += cnzi;
220:     cj    += cnzi; ca += cnzi;
221:   }
222:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
223:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
224:   PetscLogFlops(flops);
225:   return(0);
226: }

230: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
231: {
233:   PetscLogDouble flops=0.0;
234:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
235:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
236:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
237:   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
238:   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
239:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
240:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
241:   PetscInt       nextb;

244:   /* clean old values in C */
245:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
246:   /* Traverse A row-wise. */
247:   /* Build the ith row in C by summing over nonzero columns in A, */
248:   /* the rows of B corresponding to nonzeros of A. */
249:   for (i=0; i<am; i++) {
250:     anzi = ai[i+1] - ai[i];
251:     cnzi = ci[i+1] - ci[i];
252:     for (j=0; j<anzi; j++) {
253:       brow = aj[j];
254:       bnzi = bi[brow+1] - bi[brow];
255:       bjj  = bj + bi[brow];
256:       baj  = ba + bi[brow];
257:       /* perform sparse axpy */
258:       valtmp = aa[j];
259:       nextb  = 0;
260:       for (k=0; nextb<bnzi; k++) {
261:         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
262:           ca[k] += valtmp*baj[nextb++];
263:         }
264:       }
265:       flops += 2*bnzi;
266:     }
267:     aj += anzi; aa += anzi;
268:     cj += cnzi; ca += cnzi;
269:   }

271:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
272:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
273:   PetscLogFlops(flops);
274:   return(0);
275: }

279: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
280: {
281:   PetscErrorCode     ierr;
282:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
283:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
284:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
285:   MatScalar          *ca;
286:   PetscReal          afill;
287:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
288:   PetscTable         ta;
289:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

292:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
293:   /*-----------------------------------------------------------------------------------------*/
294:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
295:   PetscMalloc1(am+2,&ci);
296:   ci[0] = 0;

298:   /* create and initialize a linked list */
299:   PetscTableCreate(bn,bn,&ta);
300:   MatRowMergeMax_SeqAIJ(b,bm,ta);
301:   PetscTableGetCount(ta,&Crmax);
302:   PetscTableDestroy(&ta);

304:   PetscLLCondensedCreate_fast(Crmax,&lnk);

306:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
307:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
308:   current_space = free_space;

310:   /* Determine ci and cj */
311:   for (i=0; i<am; i++) {
312:     anzi = ai[i+1] - ai[i];
313:     aj   = a->j + ai[i];
314:     for (j=0; j<anzi; j++) {
315:       brow = aj[j];
316:       bnzj = bi[brow+1] - bi[brow];
317:       bj   = b->j + bi[brow];
318:       /* add non-zero cols of B into the sorted linked list lnk */
319:       PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);
320:     }
321:     cnzi = lnk[1];

323:     /* If free space is not available, make more free space */
324:     /* Double the amount of total space in the list */
325:     if (current_space->local_remaining<cnzi) {
326:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
327:       ndouble++;
328:     }

330:     /* Copy data into free space, then initialize lnk */
331:     PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);

333:     current_space->array           += cnzi;
334:     current_space->local_used      += cnzi;
335:     current_space->local_remaining -= cnzi;

337:     ci[i+1] = ci[i] + cnzi;
338:   }

340:   /* Column indices are in the list of free space */
341:   /* Allocate space for cj, initialize cj, and */
342:   /* destroy list of free space and other temporary array(s) */
343:   PetscMalloc1(ci[am]+1,&cj);
344:   PetscFreeSpaceContiguous(&free_space,cj);
345:   PetscLLCondensedDestroy_fast(lnk);

347:   /* Allocate space for ca */
348:   PetscMalloc1(ci[am]+1,&ca);
349:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

351:   /* put together the new symbolic matrix */
352:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
353:   MatSetBlockSizesFromMats(*C,A,B);

355:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
356:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
357:   c          = (Mat_SeqAIJ*)((*C)->data);
358:   c->free_a  = PETSC_TRUE;
359:   c->free_ij = PETSC_TRUE;
360:   c->nonew   = 0;

362:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */

364:   /* set MatInfo */
365:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
366:   if (afill < 1.0) afill = 1.0;
367:   c->maxnz                     = ci[am];
368:   c->nz                        = ci[am];
369:   (*C)->info.mallocs           = ndouble;
370:   (*C)->info.fill_ratio_given  = fill;
371:   (*C)->info.fill_ratio_needed = afill;

373: #if defined(PETSC_USE_INFO)
374:   if (ci[am]) {
375:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
376:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
377:   } else {
378:     PetscInfo((*C),"Empty matrix product\n");
379:   }
380: #endif
381:   return(0);
382: }


387: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
388: {
389:   PetscErrorCode     ierr;
390:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
391:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
392:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
393:   MatScalar          *ca;
394:   PetscReal          afill;
395:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
396:   PetscTable         ta;
397:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

400:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
401:   /*---------------------------------------------------------------------------------------------*/
402:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
403:   PetscMalloc1(am+2,&ci);
404:   ci[0] = 0;

406:   /* create and initialize a linked list */
407:   PetscTableCreate(bn,bn,&ta);
408:   MatRowMergeMax_SeqAIJ(b,bm,ta);
409:   PetscTableGetCount(ta,&Crmax);
410:   PetscTableDestroy(&ta);
411:   PetscLLCondensedCreate_Scalable(Crmax,&lnk);

413:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
414:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
415:   current_space = free_space;

417:   /* Determine ci and cj */
418:   for (i=0; i<am; i++) {
419:     anzi = ai[i+1] - ai[i];
420:     aj   = a->j + ai[i];
421:     for (j=0; j<anzi; j++) {
422:       brow = aj[j];
423:       bnzj = bi[brow+1] - bi[brow];
424:       bj   = b->j + bi[brow];
425:       /* add non-zero cols of B into the sorted linked list lnk */
426:       PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);
427:     }
428:     cnzi = lnk[0];

430:     /* If free space is not available, make more free space */
431:     /* Double the amount of total space in the list */
432:     if (current_space->local_remaining<cnzi) {
433:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
434:       ndouble++;
435:     }

437:     /* Copy data into free space, then initialize lnk */
438:     PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);

440:     current_space->array           += cnzi;
441:     current_space->local_used      += cnzi;
442:     current_space->local_remaining -= cnzi;

444:     ci[i+1] = ci[i] + cnzi;
445:   }

447:   /* Column indices are in the list of free space */
448:   /* Allocate space for cj, initialize cj, and */
449:   /* destroy list of free space and other temporary array(s) */
450:   PetscMalloc1(ci[am]+1,&cj);
451:   PetscFreeSpaceContiguous(&free_space,cj);
452:   PetscLLCondensedDestroy_Scalable(lnk);

454:   /* Allocate space for ca */
455:   /*-----------------------*/
456:   PetscMalloc1(ci[am]+1,&ca);
457:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

459:   /* put together the new symbolic matrix */
460:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
461:   MatSetBlockSizesFromMats(*C,A,B);

463:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
464:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
465:   c          = (Mat_SeqAIJ*)((*C)->data);
466:   c->free_a  = PETSC_TRUE;
467:   c->free_ij = PETSC_TRUE;
468:   c->nonew   = 0;

470:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */

472:   /* set MatInfo */
473:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
474:   if (afill < 1.0) afill = 1.0;
475:   c->maxnz                     = ci[am];
476:   c->nz                        = ci[am];
477:   (*C)->info.mallocs           = ndouble;
478:   (*C)->info.fill_ratio_given  = fill;
479:   (*C)->info.fill_ratio_needed = afill;

481: #if defined(PETSC_USE_INFO)
482:   if (ci[am]) {
483:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
484:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
485:   } else {
486:     PetscInfo((*C),"Empty matrix product\n");
487:   }
488: #endif
489:   return(0);
490: }

494: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
495: {
496:   PetscErrorCode     ierr;
497:   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
498:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
499:   PetscInt           *ci,*cj,*bb;
500:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
501:   PetscReal          afill;
502:   PetscInt           i,j,col,ndouble = 0;
503:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
504:   PetscHeap          h;

507:   /* Get ci and cj - by merging sorted rows using a heap */
508:   /*---------------------------------------------------------------------------------------------*/
509:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
510:   PetscMalloc1(am+2,&ci);
511:   ci[0] = 0;

513:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
514:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);
515:   current_space = free_space;

517:   PetscHeapCreate(a->rmax,&h);
518:   PetscMalloc1(a->rmax,&bb);

520:   /* Determine ci and cj */
521:   for (i=0; i<am; i++) {
522:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
523:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
524:     ci[i+1] = ci[i];
525:     /* Populate the min heap */
526:     for (j=0; j<anzi; j++) {
527:       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
528:       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
529:         PetscHeapAdd(h,j,bj[bb[j]++]);
530:       }
531:     }
532:     /* Pick off the min element, adding it to free space */
533:     PetscHeapPop(h,&j,&col);
534:     while (j >= 0) {
535:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
536:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
537:         ndouble++;
538:       }
539:       *(current_space->array++) = col;
540:       current_space->local_used++;
541:       current_space->local_remaining--;
542:       ci[i+1]++;

544:       /* stash if anything else remains in this row of B */
545:       if (bb[j] < bi[acol[j]+1]) {PetscHeapStash(h,j,bj[bb[j]++]);}
546:       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
547:         PetscInt j2,col2;
548:         PetscHeapPeek(h,&j2,&col2);
549:         if (col2 != col) break;
550:         PetscHeapPop(h,&j2,&col2);
551:         if (bb[j2] < bi[acol[j2]+1]) {PetscHeapStash(h,j2,bj[bb[j2]++]);}
552:       }
553:       /* Put any stashed elements back into the min heap */
554:       PetscHeapUnstash(h);
555:       PetscHeapPop(h,&j,&col);
556:     }
557:   }
558:   PetscFree(bb);
559:   PetscHeapDestroy(&h);

561:   /* Column indices are in the list of free space */
562:   /* Allocate space for cj, initialize cj, and */
563:   /* destroy list of free space and other temporary array(s) */
564:   PetscMalloc1(ci[am],&cj);
565:   PetscFreeSpaceContiguous(&free_space,cj);

567:   /* put together the new symbolic matrix */
568:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
569:   MatSetBlockSizesFromMats(*C,A,B);

571:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
572:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
573:   c          = (Mat_SeqAIJ*)((*C)->data);
574:   c->free_a  = PETSC_TRUE;
575:   c->free_ij = PETSC_TRUE;
576:   c->nonew   = 0;

578:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

580:   /* set MatInfo */
581:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
582:   if (afill < 1.0) afill = 1.0;
583:   c->maxnz                     = ci[am];
584:   c->nz                        = ci[am];
585:   (*C)->info.mallocs           = ndouble;
586:   (*C)->info.fill_ratio_given  = fill;
587:   (*C)->info.fill_ratio_needed = afill;

589: #if defined(PETSC_USE_INFO)
590:   if (ci[am]) {
591:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
592:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
593:   } else {
594:     PetscInfo((*C),"Empty matrix product\n");
595:   }
596: #endif
597:   return(0);
598: }

602: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
603: {
604:   PetscErrorCode     ierr;
605:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
606:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
607:   PetscInt           *ci,*cj,*bb;
608:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
609:   PetscReal          afill;
610:   PetscInt           i,j,col,ndouble = 0;
611:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
612:   PetscHeap          h;
613:   PetscBT            bt;

616:   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
617:   /*---------------------------------------------------------------------------------------------*/
618:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
619:   PetscMalloc1(am+2,&ci);
620:   ci[0] = 0;

622:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
623:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);

625:   current_space = free_space;

627:   PetscHeapCreate(a->rmax,&h);
628:   PetscMalloc1(a->rmax,&bb);
629:   PetscBTCreate(bn,&bt);

631:   /* Determine ci and cj */
632:   for (i=0; i<am; i++) {
633:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
634:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
635:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
636:     ci[i+1] = ci[i];
637:     /* Populate the min heap */
638:     for (j=0; j<anzi; j++) {
639:       PetscInt brow = acol[j];
640:       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
641:         PetscInt bcol = bj[bb[j]];
642:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
643:           PetscHeapAdd(h,j,bcol);
644:           bb[j]++;
645:           break;
646:         }
647:       }
648:     }
649:     /* Pick off the min element, adding it to free space */
650:     PetscHeapPop(h,&j,&col);
651:     while (j >= 0) {
652:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
653:         fptr = NULL;                      /* need PetscBTMemzero */
654:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
655:         ndouble++;
656:       }
657:       *(current_space->array++) = col;
658:       current_space->local_used++;
659:       current_space->local_remaining--;
660:       ci[i+1]++;

662:       /* stash if anything else remains in this row of B */
663:       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
664:         PetscInt bcol = bj[bb[j]];
665:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
666:           PetscHeapAdd(h,j,bcol);
667:           bb[j]++;
668:           break;
669:         }
670:       }
671:       PetscHeapPop(h,&j,&col);
672:     }
673:     if (fptr) {                 /* Clear the bits for this row */
674:       for (; fptr<current_space->array; fptr++) {PetscBTClear(bt,*fptr);}
675:     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
676:       PetscBTMemzero(bn,bt);
677:     }
678:   }
679:   PetscFree(bb);
680:   PetscHeapDestroy(&h);
681:   PetscBTDestroy(&bt);

683:   /* Column indices are in the list of free space */
684:   /* Allocate space for cj, initialize cj, and */
685:   /* destroy list of free space and other temporary array(s) */
686:   PetscMalloc1(ci[am],&cj);
687:   PetscFreeSpaceContiguous(&free_space,cj);

689:   /* put together the new symbolic matrix */
690:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
691:   MatSetBlockSizesFromMats(*C,A,B);

693:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
694:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
695:   c          = (Mat_SeqAIJ*)((*C)->data);
696:   c->free_a  = PETSC_TRUE;
697:   c->free_ij = PETSC_TRUE;
698:   c->nonew   = 0;

700:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

702:   /* set MatInfo */
703:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
704:   if (afill < 1.0) afill = 1.0;
705:   c->maxnz                     = ci[am];
706:   c->nz                        = ci[am];
707:   (*C)->info.mallocs           = ndouble;
708:   (*C)->info.fill_ratio_given  = fill;
709:   (*C)->info.fill_ratio_needed = afill;

711: #if defined(PETSC_USE_INFO)
712:   if (ci[am]) {
713:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
714:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
715:   } else {
716:     PetscInfo((*C),"Empty matrix product\n");
717:   }
718: #endif
719:   return(0);
720: }

724: /* concatenate unique entries and then sort */
725: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
726: {
727:   PetscErrorCode     ierr;
728:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
729:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
730:   PetscInt           *ci,*cj;
731:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
732:   PetscReal          afill;
733:   PetscInt           i,j,ndouble = 0;
734:   PetscSegBuffer     seg,segrow;
735:   char               *seen;

738:   PetscMalloc1(am+1,&ci);
739:   ci[0] = 0;

741:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
742:   PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);
743:   PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);
744:   PetscMalloc1(bn,&seen);
745:   PetscMemzero(seen,bn*sizeof(char));

747:   /* Determine ci and cj */
748:   for (i=0; i<am; i++) {
749:     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
750:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
751:     PetscInt packlen = 0,*PETSC_RESTRICT crow;
752:     /* Pack segrow */
753:     for (j=0; j<anzi; j++) {
754:       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
755:       for (k=bjstart; k<bjend; k++) {
756:         PetscInt bcol = bj[k];
757:         if (!seen[bcol]) { /* new entry */
758:           PetscInt *PETSC_RESTRICT slot;
759:           PetscSegBufferGetInts(segrow,1,&slot);
760:           *slot = bcol;
761:           seen[bcol] = 1;
762:           packlen++;
763:         }
764:       }
765:     }
766:     PetscSegBufferGetInts(seg,packlen,&crow);
767:     PetscSegBufferExtractTo(segrow,crow);
768:     PetscSortInt(packlen,crow);
769:     ci[i+1] = ci[i] + packlen;
770:     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
771:   }
772:   PetscSegBufferDestroy(&segrow);
773:   PetscFree(seen);

775:   /* Column indices are in the segmented buffer */
776:   PetscSegBufferExtractAlloc(seg,&cj);
777:   PetscSegBufferDestroy(&seg);

779:   /* put together the new symbolic matrix */
780:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
781:   MatSetBlockSizesFromMats(*C,A,B);

783:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
784:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
785:   c          = (Mat_SeqAIJ*)((*C)->data);
786:   c->free_a  = PETSC_TRUE;
787:   c->free_ij = PETSC_TRUE;
788:   c->nonew   = 0;

790:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;

792:   /* set MatInfo */
793:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
794:   if (afill < 1.0) afill = 1.0;
795:   c->maxnz                     = ci[am];
796:   c->nz                        = ci[am];
797:   (*C)->info.mallocs           = ndouble;
798:   (*C)->info.fill_ratio_given  = fill;
799:   (*C)->info.fill_ratio_needed = afill;

801: #if defined(PETSC_USE_INFO)
802:   if (ci[am]) {
803:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
804:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
805:   } else {
806:     PetscInfo((*C),"Empty matrix product\n");
807:   }
808: #endif
809:   return(0);
810: }

812: /* This routine is not used. Should be removed! */
815: PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
816: {

820:   if (scall == MAT_INITIAL_MATRIX) {
821:     PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);
822:     MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
823:     PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);
824:   }
825:   PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);
826:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
827:   PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);
828:   return(0);
829: }

833: PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
834: {
835:   PetscErrorCode      ierr;
836:   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
837:   Mat_MatMatTransMult *abt=a->abt;

840:   (abt->destroy)(A);
841:   MatTransposeColoringDestroy(&abt->matcoloring);
842:   MatDestroy(&abt->Bt_den);
843:   MatDestroy(&abt->ABt_den);
844:   PetscFree(abt);
845:   return(0);
846: }

850: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
851: {
852:   PetscErrorCode      ierr;
853:   Mat                 Bt;
854:   PetscInt            *bti,*btj;
855:   Mat_MatMatTransMult *abt;
856:   Mat_SeqAIJ          *c;

859:   /* create symbolic Bt */
860:   MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);
861:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);
862:   MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

864:   /* get symbolic C=A*Bt */
865:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);

867:   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
868:   PetscNew(&abt);
869:   c      = (Mat_SeqAIJ*)(*C)->data;
870:   c->abt = abt;

872:   abt->usecoloring = PETSC_FALSE;
873:   abt->destroy     = (*C)->ops->destroy;
874:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;

876:   PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);
877:   if (abt->usecoloring) {
878:     /* Create MatTransposeColoring from symbolic C=A*B^T */
879:     MatTransposeColoring matcoloring;
880:     MatColoring          coloring;
881:     ISColoring           iscoloring;
882:     Mat                  Bt_dense,C_dense;
883:     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
884:     /* inode causes memory problem, don't know why */
885:     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");

887:     MatColoringCreate(*C,&coloring);
888:     MatColoringSetDistance(coloring,2);
889:     MatColoringSetType(coloring,MATCOLORINGSL);
890:     MatColoringSetFromOptions(coloring);
891:     MatColoringApply(coloring,&iscoloring);
892:     MatColoringDestroy(&coloring);
893:     MatTransposeColoringCreate(*C,iscoloring,&matcoloring);

895:     abt->matcoloring = matcoloring;

897:     ISColoringDestroy(&iscoloring);

899:     /* Create Bt_dense and C_dense = A*Bt_dense */
900:     MatCreate(PETSC_COMM_SELF,&Bt_dense);
901:     MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
902:     MatSetType(Bt_dense,MATSEQDENSE);
903:     MatSeqDenseSetPreallocation(Bt_dense,NULL);

905:     Bt_dense->assembled = PETSC_TRUE;
906:     abt->Bt_den   = Bt_dense;

908:     MatCreate(PETSC_COMM_SELF,&C_dense);
909:     MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);
910:     MatSetType(C_dense,MATSEQDENSE);
911:     MatSeqDenseSetPreallocation(C_dense,NULL);

913:     Bt_dense->assembled = PETSC_TRUE;
914:     abt->ABt_den  = C_dense;

916: #if defined(PETSC_USE_INFO)
917:     {
918:       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
919:       PetscInfo7(*C,"Use coloring of C=A*B^T; B^T: %D %D, Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",B->cmap->n,B->rmap->n,Bt_dense->rmap->n,Bt_dense->cmap->n,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));
920:     }
921: #endif
922:   }
923:   /* clean up */
924:   MatDestroy(&Bt);
925:   MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);
926:   return(0);
927: }

931: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
932: {
933:   PetscErrorCode      ierr;
934:   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
935:   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
936:   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
937:   PetscLogDouble      flops=0.0;
938:   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
939:   Mat_MatMatTransMult *abt = c->abt;

942:   /* clear old values in C */
943:   if (!c->a) {
944:     PetscMalloc1(ci[cm]+1,&ca);
945:     c->a      = ca;
946:     c->free_a = PETSC_TRUE;
947:   } else {
948:     ca =  c->a;
949:   }
950:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

952:   if (abt->usecoloring) {
953:     MatTransposeColoring matcoloring = abt->matcoloring;
954:     Mat                  Bt_dense,C_dense = abt->ABt_den;

956:     /* Get Bt_dense by Apply MatTransposeColoring to B */
957:     Bt_dense = abt->Bt_den;
958:     MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);

960:     /* C_dense = A*Bt_dense */
961:     MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);

963:     /* Recover C from C_dense */
964:     MatTransColoringApplyDenToSp(matcoloring,C_dense,C);
965:     return(0);
966:   }

968:   for (i=0; i<cm; i++) {
969:     anzi = ai[i+1] - ai[i];
970:     acol = aj + ai[i];
971:     aval = aa + ai[i];
972:     cnzi = ci[i+1] - ci[i];
973:     ccol = cj + ci[i];
974:     cval = ca + ci[i];
975:     for (j=0; j<cnzi; j++) {
976:       brow = ccol[j];
977:       bnzj = bi[brow+1] - bi[brow];
978:       bcol = bj + bi[brow];
979:       bval = ba + bi[brow];

981:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
982:       nexta = 0; nextb = 0;
983:       while (nexta<anzi && nextb<bnzj) {
984:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
985:         if (nexta == anzi) break;
986:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
987:         if (nextb == bnzj) break;
988:         if (acol[nexta] == bcol[nextb]) {
989:           cval[j] += aval[nexta]*bval[nextb];
990:           nexta++; nextb++;
991:           flops += 2;
992:         }
993:       }
994:     }
995:   }
996:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
997:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
998:   PetscLogFlops(flops);
999:   return(0);
1000: }

1004: PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1005: {

1009:   if (scall == MAT_INITIAL_MATRIX) {
1010:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);
1011:     MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
1012:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);
1013:   }
1014:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);
1015:   MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
1016:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);
1017:   return(0);
1018: }

1022: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1023: {
1025:   Mat            At;
1026:   PetscInt       *ati,*atj;

1029:   /* create symbolic At */
1030:   MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
1031:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);
1032:   MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

1034:   /* get symbolic C=At*B */
1035:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);

1037:   /* clean up */
1038:   MatDestroy(&At);
1039:   MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);
1040:   return(0);
1041: }

1045: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1046: {
1048:   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1049:   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1050:   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1051:   PetscLogDouble flops=0.0;
1052:   MatScalar      *aa  =a->a,*ba,*ca,*caj;

1055:   if (!c->a) {
1056:     PetscMalloc1(ci[cm]+1,&ca);

1058:     c->a      = ca;
1059:     c->free_a = PETSC_TRUE;
1060:   } else {
1061:     ca = c->a;
1062:   }
1063:   /* clear old values in C */
1064:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

1066:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1067:   for (i=0; i<am; i++) {
1068:     bj   = b->j + bi[i];
1069:     ba   = b->a + bi[i];
1070:     bnzi = bi[i+1] - bi[i];
1071:     anzi = ai[i+1] - ai[i];
1072:     for (j=0; j<anzi; j++) {
1073:       nextb = 0;
1074:       crow  = *aj++;
1075:       cjj   = cj + ci[crow];
1076:       caj   = ca + ci[crow];
1077:       /* perform sparse axpy operation.  Note cjj includes bj. */
1078:       for (k=0; nextb<bnzi; k++) {
1079:         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1080:           caj[k] += (*aa)*(*(ba+nextb));
1081:           nextb++;
1082:         }
1083:       }
1084:       flops += 2*bnzi;
1085:       aa++;
1086:     }
1087:   }

1089:   /* Assemble the final matrix and clean up */
1090:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1091:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1092:   PetscLogFlops(flops);
1093:   return(0);
1094: }

1098: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1099: {

1103:   if (scall == MAT_INITIAL_MATRIX) {
1104:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
1105:     MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
1106:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
1107:   }
1108:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
1109:   MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
1110:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
1111:   return(0);
1112: }

1116: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1117: {

1121:   MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);

1123:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1124:   return(0);
1125: }

1129: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1130: {
1131:   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1132:   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1133:   PetscErrorCode    ierr;
1134:   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1135:   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1136:   const PetscInt    *aj;
1137:   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1138:   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;

1141:   if (!cm || !cn) return(0);
1142:   if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n);
1143:   if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n);
1144:   if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n);
1145:   b = bd->v;
1146:   MatDenseGetArray(C,&c);
1147:   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1148:   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1149:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1150:     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1151:       r1 = r2 = r3 = r4 = 0.0;
1152:       n  = a->i[i+1] - a->i[i];
1153:       aj = a->j + a->i[i];
1154:       aa = a->a + a->i[i];
1155:       for (j=0; j<n; j++) {
1156:         aatmp = aa[j]; ajtmp = aj[j];
1157:         r1 += aatmp*b1[ajtmp];
1158:         r2 += aatmp*b2[ajtmp];
1159:         r3 += aatmp*b3[ajtmp];
1160:         r4 += aatmp*b4[ajtmp];
1161:       }
1162:       c1[i] = r1;
1163:       c2[i] = r2;
1164:       c3[i] = r3;
1165:       c4[i] = r4;
1166:     }
1167:     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1168:     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1169:   }
1170:   for (; col<cn; col++) {   /* over extra columns of C */
1171:     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1172:       r1 = 0.0;
1173:       n  = a->i[i+1] - a->i[i];
1174:       aj = a->j + a->i[i];
1175:       aa = a->a + a->i[i];
1176:       for (j=0; j<n; j++) {
1177:         r1 += aa[j]*b1[aj[j]];
1178:       }
1179:       c1[i] = r1;
1180:     }
1181:     b1 += bm;
1182:     c1 += am;
1183:   }
1184:   PetscLogFlops(cn*(2.0*a->nz));
1185:   MatDenseRestoreArray(C,&c);
1186:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1187:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1188:   return(0);
1189: }

1191: /*
1192:    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1193: */
1196: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1197: {
1198:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1199:   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
1201:   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1202:   MatScalar      *aa;
1203:   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1204:   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;

1207:   if (!cm || !cn) return(0);
1208:   b = bd->v;
1209:   MatDenseGetArray(C,&c);
1210:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;

1212:   if (a->compressedrow.use) { /* use compressed row format */
1213:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1214:       colam = col*am;
1215:       arm   = a->compressedrow.nrows;
1216:       ii    = a->compressedrow.i;
1217:       ridx  = a->compressedrow.rindex;
1218:       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1219:         r1 = r2 = r3 = r4 = 0.0;
1220:         n  = ii[i+1] - ii[i];
1221:         aj = a->j + ii[i];
1222:         aa = a->a + ii[i];
1223:         for (j=0; j<n; j++) {
1224:           r1 += (*aa)*b1[*aj];
1225:           r2 += (*aa)*b2[*aj];
1226:           r3 += (*aa)*b3[*aj];
1227:           r4 += (*aa++)*b4[*aj++];
1228:         }
1229:         c[colam       + ridx[i]] += r1;
1230:         c[colam + am  + ridx[i]] += r2;
1231:         c[colam + am2 + ridx[i]] += r3;
1232:         c[colam + am3 + ridx[i]] += r4;
1233:       }
1234:       b1 += bm4;
1235:       b2 += bm4;
1236:       b3 += bm4;
1237:       b4 += bm4;
1238:     }
1239:     for (; col<cn; col++) {     /* over extra columns of C */
1240:       colam = col*am;
1241:       arm   = a->compressedrow.nrows;
1242:       ii    = a->compressedrow.i;
1243:       ridx  = a->compressedrow.rindex;
1244:       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1245:         r1 = 0.0;
1246:         n  = ii[i+1] - ii[i];
1247:         aj = a->j + ii[i];
1248:         aa = a->a + ii[i];

1250:         for (j=0; j<n; j++) {
1251:           r1 += (*aa++)*b1[*aj++];
1252:         }
1253:         c[colam + ridx[i]] += r1;
1254:       }
1255:       b1 += bm;
1256:     }
1257:   } else {
1258:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1259:       colam = col*am;
1260:       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1261:         r1 = r2 = r3 = r4 = 0.0;
1262:         n  = a->i[i+1] - a->i[i];
1263:         aj = a->j + a->i[i];
1264:         aa = a->a + a->i[i];
1265:         for (j=0; j<n; j++) {
1266:           r1 += (*aa)*b1[*aj];
1267:           r2 += (*aa)*b2[*aj];
1268:           r3 += (*aa)*b3[*aj];
1269:           r4 += (*aa++)*b4[*aj++];
1270:         }
1271:         c[colam + i]       += r1;
1272:         c[colam + am + i]  += r2;
1273:         c[colam + am2 + i] += r3;
1274:         c[colam + am3 + i] += r4;
1275:       }
1276:       b1 += bm4;
1277:       b2 += bm4;
1278:       b3 += bm4;
1279:       b4 += bm4;
1280:     }
1281:     for (; col<cn; col++) {     /* over extra columns of C */
1282:       colam = col*am;
1283:       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1284:         r1 = 0.0;
1285:         n  = a->i[i+1] - a->i[i];
1286:         aj = a->j + a->i[i];
1287:         aa = a->a + a->i[i];

1289:         for (j=0; j<n; j++) {
1290:           r1 += (*aa++)*b1[*aj++];
1291:         }
1292:         c[colam + i] += r1;
1293:       }
1294:       b1 += bm;
1295:     }
1296:   }
1297:   PetscLogFlops(cn*2.0*a->nz);
1298:   MatDenseRestoreArray(C,&c);
1299:   return(0);
1300: }

1304: PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1305: {
1307:   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1308:   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1309:   PetscInt       *bi      = b->i,*bj=b->j;
1310:   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1311:   MatScalar      *btval,*btval_den,*ba=b->a;
1312:   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;

1315:   btval_den=btdense->v;
1316:   PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));
1317:   for (k=0; k<ncolors; k++) {
1318:     ncolumns = coloring->ncolumns[k];
1319:     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1320:       col   = *(columns + colorforcol[k] + l);
1321:       btcol = bj + bi[col];
1322:       btval = ba + bi[col];
1323:       anz   = bi[col+1] - bi[col];
1324:       for (j=0; j<anz; j++) {
1325:         brow            = btcol[j];
1326:         btval_den[brow] = btval[j];
1327:       }
1328:     }
1329:     btval_den += m;
1330:   }
1331:   return(0);
1332: }

1336: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1337: {
1339:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1340:   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1341:   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1342:   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1343:   PetscInt       nrows,*row,*idx;
1344:   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;

1347:   MatDenseGetArray(Cden,&ca_den);

1349:   if (brows > 0) {
1350:     PetscInt *lstart,row_end,row_start;
1351:     lstart = matcoloring->lstart;
1352:     PetscMemzero(lstart,ncolors*sizeof(PetscInt));

1354:     row_end = brows;
1355:     if (row_end > m) row_end = m;
1356:     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1357:       ca_den_ptr = ca_den;
1358:       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1359:         nrows = matcoloring->nrows[k];
1360:         row   = rows  + colorforrow[k];
1361:         idx   = den2sp + colorforrow[k];
1362:         for (l=lstart[k]; l<nrows; l++) {
1363:           if (row[l] >= row_end) {
1364:             lstart[k] = l;
1365:             break;
1366:           } else {
1367:             ca[idx[l]] = ca_den_ptr[row[l]];
1368:           }
1369:         }
1370:         ca_den_ptr += m;
1371:       }
1372:       row_end += brows;
1373:       if (row_end > m) row_end = m;
1374:     }
1375:   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1376:     ca_den_ptr = ca_den;
1377:     for (k=0; k<ncolors; k++) {
1378:       nrows = matcoloring->nrows[k];
1379:       row   = rows  + colorforrow[k];
1380:       idx   = den2sp + colorforrow[k];
1381:       for (l=0; l<nrows; l++) {
1382:         ca[idx[l]] = ca_den_ptr[row[l]];
1383:       }
1384:       ca_den_ptr += m;
1385:     }
1386:   }

1388:   MatDenseRestoreArray(Cden,&ca_den);
1389: #if defined(PETSC_USE_INFO)
1390:   if (matcoloring->brows > 0) {
1391:     PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);
1392:   } else {
1393:     PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");
1394:   }
1395: #endif
1396:   return(0);
1397: }

1401: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1402: {
1404:   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1405:   const PetscInt *is,*ci,*cj,*row_idx;
1406:   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1407:   IS             *isa;
1408:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1409:   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1410:   PetscInt       *colorforcol,*columns,*columns_i,brows;
1411:   PetscBool      flg;

1414:   ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);

1416:   /* bs >1 is not being tested yet! */
1417:   Nbs       = mat->cmap->N/bs;
1418:   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1419:   c->N      = Nbs;
1420:   c->m      = c->M;
1421:   c->rstart = 0;
1422:   c->brows  = 100;

1424:   c->ncolors = nis;
1425:   PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);
1426:   PetscMalloc1(csp->nz+1,&rows);
1427:   PetscMalloc1(csp->nz+1,&den2sp);

1429:   brows = c->brows;
1430:   PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);
1431:   if (flg) c->brows = brows;
1432:   if (brows > 0) {
1433:     PetscMalloc1(nis+1,&c->lstart);
1434:   }

1436:   colorforrow[0] = 0;
1437:   rows_i         = rows;
1438:   den2sp_i       = den2sp;

1440:   PetscMalloc1(nis+1,&colorforcol);
1441:   PetscMalloc1(Nbs+1,&columns);

1443:   colorforcol[0] = 0;
1444:   columns_i      = columns;

1446:   /* get column-wise storage of mat */
1447:   MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);

1449:   cm   = c->m;
1450:   PetscMalloc1(cm+1,&rowhit);
1451:   PetscMalloc1(cm+1,&idxhit);
1452:   for (i=0; i<nis; i++) { /* loop over color */
1453:     ISGetLocalSize(isa[i],&n);
1454:     ISGetIndices(isa[i],&is);

1456:     c->ncolumns[i] = n;
1457:     if (n) {
1458:       PetscMemcpy(columns_i,is,n*sizeof(PetscInt));
1459:     }
1460:     colorforcol[i+1] = colorforcol[i] + n;
1461:     columns_i       += n;

1463:     /* fast, crude version requires O(N*N) work */
1464:     PetscMemzero(rowhit,cm*sizeof(PetscInt));

1466:     for (j=0; j<n; j++) { /* loop over columns*/
1467:       col     = is[j];
1468:       row_idx = cj + ci[col];
1469:       m       = ci[col+1] - ci[col];
1470:       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1471:         idxhit[*row_idx]   = spidx[ci[col] + k];
1472:         rowhit[*row_idx++] = col + 1;
1473:       }
1474:     }
1475:     /* count the number of hits */
1476:     nrows = 0;
1477:     for (j=0; j<cm; j++) {
1478:       if (rowhit[j]) nrows++;
1479:     }
1480:     c->nrows[i]      = nrows;
1481:     colorforrow[i+1] = colorforrow[i] + nrows;

1483:     nrows = 0;
1484:     for (j=0; j<cm; j++) { /* loop over rows */
1485:       if (rowhit[j]) {
1486:         rows_i[nrows]   = j;
1487:         den2sp_i[nrows] = idxhit[j];
1488:         nrows++;
1489:       }
1490:     }
1491:     den2sp_i += nrows;

1493:     ISRestoreIndices(isa[i],&is);
1494:     rows_i += nrows;
1495:   }
1496:   MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);
1497:   PetscFree(rowhit);
1498:   ISColoringRestoreIS(iscoloring,&isa);
1499:   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);

1501:   c->colorforrow = colorforrow;
1502:   c->rows        = rows;
1503:   c->den2sp      = den2sp;
1504:   c->colorforcol = colorforcol;
1505:   c->columns     = columns;

1507:   PetscFree(idxhit);
1508:   return(0);
1509: }