Actual source code: matmatmult.c

petsc-3.6.4 2016-04-12
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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: 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,nlnk_max,*lnk,ndouble=0;
 69:   PetscBT            lnkbt;
 70:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

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

 80:   /* create and initialize a linked list */
 81:   nlnk_max = a->rmax*b->rmax;
 82:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
 83:   PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);

 85:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
 86:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);

 88:   current_space = free_space;

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

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

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

113:     current_space->array           += cnzi;
114:     current_space->local_used      += cnzi;
115:     current_space->local_remaining -= cnzi;

117:     ci[i+1] = ci[i] + cnzi;
118:   }

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

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

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

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

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

161: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
162: {
164:   PetscLogDouble flops=0.0;
165:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
166:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
167:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
168:   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
169:   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
170:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
171:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
172:   PetscScalar    *ab_dense;

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

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

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

226: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
227: {
229:   PetscLogDouble flops=0.0;
230:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
231:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
232:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
233:   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
234:   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
235:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
236:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
237:   PetscInt       nextb;

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

267:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
268:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
269:   PetscLogFlops(flops);
270:   return(0);
271: }

275: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
276: {
277:   PetscErrorCode     ierr;
278:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
279:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
280:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
281:   MatScalar          *ca;
282:   PetscReal          afill;
283:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
284:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

287:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
288:   /*-----------------------------------------------------------------------------------------*/
289:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
290:   PetscMalloc1(am+2,&ci);
291:   ci[0] = 0;

293:   /* create and initialize a linked list */
294:   nlnk_max = a->rmax*b->rmax;
295:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
296:   PetscLLCondensedCreate_fast(nlnk_max,&lnk);

298:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
299:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
300:   current_space = free_space;

302:   /* Determine ci and cj */
303:   for (i=0; i<am; i++) {
304:     anzi = ai[i+1] - ai[i];
305:     aj   = a->j + ai[i];
306:     for (j=0; j<anzi; j++) {
307:       brow = aj[j];
308:       bnzj = bi[brow+1] - bi[brow];
309:       bj   = b->j + bi[brow];
310:       /* add non-zero cols of B into the sorted linked list lnk */
311:       PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);
312:     }
313:     cnzi = lnk[1];

315:     /* If free space is not available, make more free space */
316:     /* Double the amount of total space in the list */
317:     if (current_space->local_remaining<cnzi) {
318:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
319:       ndouble++;
320:     }

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

325:     current_space->array           += cnzi;
326:     current_space->local_used      += cnzi;
327:     current_space->local_remaining -= cnzi;

329:     ci[i+1] = ci[i] + cnzi;
330:   }

332:   /* Column indices are in the list of free space */
333:   /* Allocate space for cj, initialize cj, and */
334:   /* destroy list of free space and other temporary array(s) */
335:   PetscMalloc1(ci[am]+1,&cj);
336:   PetscFreeSpaceContiguous(&free_space,cj);
337:   PetscLLCondensedDestroy_fast(lnk);

339:   /* Allocate space for ca */
340:   PetscMalloc1(ci[am]+1,&ca);
341:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

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

347:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
348:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
349:   c          = (Mat_SeqAIJ*)((*C)->data);
350:   c->free_a  = PETSC_TRUE;
351:   c->free_ij = PETSC_TRUE;
352:   c->nonew   = 0;

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

356:   /* set MatInfo */
357:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
358:   if (afill < 1.0) afill = 1.0;
359:   c->maxnz                     = ci[am];
360:   c->nz                        = ci[am];
361:   (*C)->info.mallocs           = ndouble;
362:   (*C)->info.fill_ratio_given  = fill;
363:   (*C)->info.fill_ratio_needed = afill;

365: #if defined(PETSC_USE_INFO)
366:   if (ci[am]) {
367:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
368:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
369:   } else {
370:     PetscInfo((*C),"Empty matrix product\n");
371:   }
372: #endif
373:   return(0);
374: }


379: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
380: {
381:   PetscErrorCode     ierr;
382:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
383:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
384:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
385:   MatScalar          *ca;
386:   PetscReal          afill;
387:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
388:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

391:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
392:   /*---------------------------------------------------------------------------------------------*/
393:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
394:   PetscMalloc1(am+2,&ci);
395:   ci[0] = 0;

397:   /* create and initialize a linked list */
398:   nlnk_max = a->rmax*b->rmax;
399:   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
400:   PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);

402:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
403:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
404:   current_space = free_space;

406:   /* Determine ci and cj */
407:   for (i=0; i<am; i++) {
408:     anzi = ai[i+1] - ai[i];
409:     aj   = a->j + ai[i];
410:     for (j=0; j<anzi; j++) {
411:       brow = aj[j];
412:       bnzj = bi[brow+1] - bi[brow];
413:       bj   = b->j + bi[brow];
414:       /* add non-zero cols of B into the sorted linked list lnk */
415:       PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);
416:     }
417:     cnzi = lnk[0];

419:     /* If free space is not available, make more free space */
420:     /* Double the amount of total space in the list */
421:     if (current_space->local_remaining<cnzi) {
422:       PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);
423:       ndouble++;
424:     }

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

429:     current_space->array           += cnzi;
430:     current_space->local_used      += cnzi;
431:     current_space->local_remaining -= cnzi;

433:     ci[i+1] = ci[i] + cnzi;
434:   }

436:   /* Column indices are in the list of free space */
437:   /* Allocate space for cj, initialize cj, and */
438:   /* destroy list of free space and other temporary array(s) */
439:   PetscMalloc1(ci[am]+1,&cj);
440:   PetscFreeSpaceContiguous(&free_space,cj);
441:   PetscLLCondensedDestroy_Scalable(lnk);

443:   /* Allocate space for ca */
444:   /*-----------------------*/
445:   PetscMalloc1(ci[am]+1,&ca);
446:   PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));

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

452:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
453:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
454:   c          = (Mat_SeqAIJ*)((*C)->data);
455:   c->free_a  = PETSC_TRUE;
456:   c->free_ij = PETSC_TRUE;
457:   c->nonew   = 0;

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

461:   /* set MatInfo */
462:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
463:   if (afill < 1.0) afill = 1.0;
464:   c->maxnz                     = ci[am];
465:   c->nz                        = ci[am];
466:   (*C)->info.mallocs           = ndouble;
467:   (*C)->info.fill_ratio_given  = fill;
468:   (*C)->info.fill_ratio_needed = afill;

470: #if defined(PETSC_USE_INFO)
471:   if (ci[am]) {
472:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
473:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
474:   } else {
475:     PetscInfo((*C),"Empty matrix product\n");
476:   }
477: #endif
478:   return(0);
479: }

483: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
484: {
485:   PetscErrorCode     ierr;
486:   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
487:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
488:   PetscInt           *ci,*cj,*bb;
489:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
490:   PetscReal          afill;
491:   PetscInt           i,j,col,ndouble = 0;
492:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
493:   PetscHeap          h;

496:   /* Get ci and cj - by merging sorted rows using a heap */
497:   /*---------------------------------------------------------------------------------------------*/
498:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
499:   PetscMalloc1(am+2,&ci);
500:   ci[0] = 0;

502:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
503:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
504:   current_space = free_space;

506:   PetscHeapCreate(a->rmax,&h);
507:   PetscMalloc1(a->rmax,&bb);

509:   /* Determine ci and cj */
510:   for (i=0; i<am; i++) {
511:     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 */
512:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
513:     ci[i+1] = ci[i];
514:     /* Populate the min heap */
515:     for (j=0; j<anzi; j++) {
516:       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
517:       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
518:         PetscHeapAdd(h,j,bj[bb[j]++]);
519:       }
520:     }
521:     /* Pick off the min element, adding it to free space */
522:     PetscHeapPop(h,&j,&col);
523:     while (j >= 0) {
524:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
525:         PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);
526:         ndouble++;
527:       }
528:       *(current_space->array++) = col;
529:       current_space->local_used++;
530:       current_space->local_remaining--;
531:       ci[i+1]++;

533:       /* stash if anything else remains in this row of B */
534:       if (bb[j] < bi[acol[j]+1]) {PetscHeapStash(h,j,bj[bb[j]++]);}
535:       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
536:         PetscInt j2,col2;
537:         PetscHeapPeek(h,&j2,&col2);
538:         if (col2 != col) break;
539:         PetscHeapPop(h,&j2,&col2);
540:         if (bb[j2] < bi[acol[j2]+1]) {PetscHeapStash(h,j2,bj[bb[j2]++]);}
541:       }
542:       /* Put any stashed elements back into the min heap */
543:       PetscHeapUnstash(h);
544:       PetscHeapPop(h,&j,&col);
545:     }
546:   }
547:   PetscFree(bb);
548:   PetscHeapDestroy(&h);

550:   /* Column indices are in the list of free space */
551:   /* Allocate space for cj, initialize cj, and */
552:   /* destroy list of free space and other temporary array(s) */
553:   PetscMalloc1(ci[am],&cj);
554:   PetscFreeSpaceContiguous(&free_space,cj);

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

560:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
561:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
562:   c          = (Mat_SeqAIJ*)((*C)->data);
563:   c->free_a  = PETSC_TRUE;
564:   c->free_ij = PETSC_TRUE;
565:   c->nonew   = 0;

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

569:   /* set MatInfo */
570:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
571:   if (afill < 1.0) afill = 1.0;
572:   c->maxnz                     = ci[am];
573:   c->nz                        = ci[am];
574:   (*C)->info.mallocs           = ndouble;
575:   (*C)->info.fill_ratio_given  = fill;
576:   (*C)->info.fill_ratio_needed = afill;

578: #if defined(PETSC_USE_INFO)
579:   if (ci[am]) {
580:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
581:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
582:   } else {
583:     PetscInfo((*C),"Empty matrix product\n");
584:   }
585: #endif
586:   return(0);
587: }

591: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
592: {
593:   PetscErrorCode     ierr;
594:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
595:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
596:   PetscInt           *ci,*cj,*bb;
597:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
598:   PetscReal          afill;
599:   PetscInt           i,j,col,ndouble = 0;
600:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
601:   PetscHeap          h;
602:   PetscBT            bt;

605:   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
606:   /*---------------------------------------------------------------------------------------------*/
607:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
608:   PetscMalloc1(am+2,&ci);
609:   ci[0] = 0;

611:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
612:   PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);

614:   current_space = free_space;

616:   PetscHeapCreate(a->rmax,&h);
617:   PetscMalloc1(a->rmax,&bb);
618:   PetscBTCreate(bn,&bt);

620:   /* Determine ci and cj */
621:   for (i=0; i<am; i++) {
622:     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 */
623:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
624:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
625:     ci[i+1] = ci[i];
626:     /* Populate the min heap */
627:     for (j=0; j<anzi; j++) {
628:       PetscInt brow = acol[j];
629:       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
630:         PetscInt bcol = bj[bb[j]];
631:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
632:           PetscHeapAdd(h,j,bcol);
633:           bb[j]++;
634:           break;
635:         }
636:       }
637:     }
638:     /* Pick off the min element, adding it to free space */
639:     PetscHeapPop(h,&j,&col);
640:     while (j >= 0) {
641:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
642:         fptr = NULL;                      /* need PetscBTMemzero */
643:         PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);
644:         ndouble++;
645:       }
646:       *(current_space->array++) = col;
647:       current_space->local_used++;
648:       current_space->local_remaining--;
649:       ci[i+1]++;

651:       /* stash if anything else remains in this row of B */
652:       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
653:         PetscInt bcol = bj[bb[j]];
654:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
655:           PetscHeapAdd(h,j,bcol);
656:           bb[j]++;
657:           break;
658:         }
659:       }
660:       PetscHeapPop(h,&j,&col);
661:     }
662:     if (fptr) {                 /* Clear the bits for this row */
663:       for (; fptr<current_space->array; fptr++) {PetscBTClear(bt,*fptr);}
664:     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
665:       PetscBTMemzero(bn,bt);
666:     }
667:   }
668:   PetscFree(bb);
669:   PetscHeapDestroy(&h);
670:   PetscBTDestroy(&bt);

672:   /* Column indices are in the list of free space */
673:   /* Allocate space for cj, initialize cj, and */
674:   /* destroy list of free space and other temporary array(s) */
675:   PetscMalloc1(ci[am],&cj);
676:   PetscFreeSpaceContiguous(&free_space,cj);

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

682:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
683:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
684:   c          = (Mat_SeqAIJ*)((*C)->data);
685:   c->free_a  = PETSC_TRUE;
686:   c->free_ij = PETSC_TRUE;
687:   c->nonew   = 0;

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

691:   /* set MatInfo */
692:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
693:   if (afill < 1.0) afill = 1.0;
694:   c->maxnz                     = ci[am];
695:   c->nz                        = ci[am];
696:   (*C)->info.mallocs           = ndouble;
697:   (*C)->info.fill_ratio_given  = fill;
698:   (*C)->info.fill_ratio_needed = afill;

700: #if defined(PETSC_USE_INFO)
701:   if (ci[am]) {
702:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
703:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
704:   } else {
705:     PetscInfo((*C),"Empty matrix product\n");
706:   }
707: #endif
708:   return(0);
709: }

713: /* concatenate unique entries and then sort */
714: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
715: {
716:   PetscErrorCode     ierr;
717:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
718:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
719:   PetscInt           *ci,*cj;
720:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
721:   PetscReal          afill;
722:   PetscInt           i,j,ndouble = 0;
723:   PetscSegBuffer     seg,segrow;
724:   char               *seen;

727:   PetscMalloc1(am+1,&ci);
728:   ci[0] = 0;

730:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
731:   PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);
732:   PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);
733:   PetscMalloc1(bn,&seen);
734:   PetscMemzero(seen,bn*sizeof(char));

736:   /* Determine ci and cj */
737:   for (i=0; i<am; i++) {
738:     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 */
739:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
740:     PetscInt packlen = 0,*PETSC_RESTRICT crow;
741:     /* Pack segrow */
742:     for (j=0; j<anzi; j++) {
743:       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
744:       for (k=bjstart; k<bjend; k++) {
745:         PetscInt bcol = bj[k];
746:         if (!seen[bcol]) { /* new entry */
747:           PetscInt *PETSC_RESTRICT slot;
748:           PetscSegBufferGetInts(segrow,1,&slot);
749:           *slot = bcol;
750:           seen[bcol] = 1;
751:           packlen++;
752:         }
753:       }
754:     }
755:     PetscSegBufferGetInts(seg,packlen,&crow);
756:     PetscSegBufferExtractTo(segrow,crow);
757:     PetscSortInt(packlen,crow);
758:     ci[i+1] = ci[i] + packlen;
759:     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
760:   }
761:   PetscSegBufferDestroy(&segrow);
762:   PetscFree(seen);

764:   /* Column indices are in the segmented buffer */
765:   PetscSegBufferExtractAlloc(seg,&cj);
766:   PetscSegBufferDestroy(&seg);

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

772:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
773:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
774:   c          = (Mat_SeqAIJ*)((*C)->data);
775:   c->free_a  = PETSC_TRUE;
776:   c->free_ij = PETSC_TRUE;
777:   c->nonew   = 0;

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

781:   /* set MatInfo */
782:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
783:   if (afill < 1.0) afill = 1.0;
784:   c->maxnz                     = ci[am];
785:   c->nz                        = ci[am];
786:   (*C)->info.mallocs           = ndouble;
787:   (*C)->info.fill_ratio_given  = fill;
788:   (*C)->info.fill_ratio_needed = afill;

790: #if defined(PETSC_USE_INFO)
791:   if (ci[am]) {
792:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
793:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
794:   } else {
795:     PetscInfo((*C),"Empty matrix product\n");
796:   }
797: #endif
798:   return(0);
799: }

801: /* This routine is not used. Should be removed! */
804: PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
805: {

809:   if (scall == MAT_INITIAL_MATRIX) {
810:     PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);
811:     MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
812:     PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);
813:   }
814:   PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);
815:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
816:   PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);
817:   return(0);
818: }

822: PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
823: {
824:   PetscErrorCode      ierr;
825:   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
826:   Mat_MatMatTransMult *abt=a->abt;

829:   (abt->destroy)(A);
830:   MatTransposeColoringDestroy(&abt->matcoloring);
831:   MatDestroy(&abt->Bt_den);
832:   MatDestroy(&abt->ABt_den);
833:   PetscFree(abt);
834:   return(0);
835: }

839: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
840: {
841:   PetscErrorCode      ierr;
842:   Mat                 Bt;
843:   PetscInt            *bti,*btj;
844:   Mat_MatMatTransMult *abt;
845:   Mat_SeqAIJ          *c;

848:   /* create symbolic Bt */
849:   MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);
850:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);
851:   MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

853:   /* get symbolic C=A*Bt */
854:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);

856:   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
857:   PetscNew(&abt);
858:   c      = (Mat_SeqAIJ*)(*C)->data;
859:   c->abt = abt;

861:   abt->usecoloring = PETSC_FALSE;
862:   abt->destroy     = (*C)->ops->destroy;
863:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;

865:   PetscOptionsGetBool(NULL,"-matmattransmult_color",&abt->usecoloring,NULL);
866:   if (abt->usecoloring) {
867:     /* Create MatTransposeColoring from symbolic C=A*B^T */
868:     MatTransposeColoring matcoloring;
869:     MatColoring          coloring;
870:     ISColoring           iscoloring;
871:     Mat                  Bt_dense,C_dense;
872:     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
873:     /* inode causes memory problem, don't know why */
874:     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");

876:     MatColoringCreate(*C,&coloring);
877:     MatColoringSetDistance(coloring,2);
878:     MatColoringSetType(coloring,MATCOLORINGSL);
879:     MatColoringSetFromOptions(coloring);
880:     MatColoringApply(coloring,&iscoloring);
881:     MatColoringDestroy(&coloring);
882:     MatTransposeColoringCreate(*C,iscoloring,&matcoloring);

884:     abt->matcoloring = matcoloring;

886:     ISColoringDestroy(&iscoloring);

888:     /* Create Bt_dense and C_dense = A*Bt_dense */
889:     MatCreate(PETSC_COMM_SELF,&Bt_dense);
890:     MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
891:     MatSetType(Bt_dense,MATSEQDENSE);
892:     MatSeqDenseSetPreallocation(Bt_dense,NULL);

894:     Bt_dense->assembled = PETSC_TRUE;
895:     abt->Bt_den   = Bt_dense;

897:     MatCreate(PETSC_COMM_SELF,&C_dense);
898:     MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);
899:     MatSetType(C_dense,MATSEQDENSE);
900:     MatSeqDenseSetPreallocation(C_dense,NULL);

902:     Bt_dense->assembled = PETSC_TRUE;
903:     abt->ABt_den  = C_dense;

905: #if defined(PETSC_USE_INFO)
906:     {
907:       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
908:       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));
909:     }
910: #endif
911:   }
912:   /* clean up */
913:   MatDestroy(&Bt);
914:   MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);
915:   return(0);
916: }

920: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
921: {
922:   PetscErrorCode      ierr;
923:   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
924:   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
925:   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
926:   PetscLogDouble      flops=0.0;
927:   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
928:   Mat_MatMatTransMult *abt = c->abt;

931:   /* clear old values in C */
932:   if (!c->a) {
933:     PetscMalloc1(ci[cm]+1,&ca);
934:     c->a      = ca;
935:     c->free_a = PETSC_TRUE;
936:   } else {
937:     ca =  c->a;
938:   }
939:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

941:   if (abt->usecoloring) {
942:     MatTransposeColoring matcoloring = abt->matcoloring;
943:     Mat                  Bt_dense,C_dense = abt->ABt_den;

945:     /* Get Bt_dense by Apply MatTransposeColoring to B */
946:     Bt_dense = abt->Bt_den;
947:     MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);

949:     /* C_dense = A*Bt_dense */
950:     MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);

952:     /* Recover C from C_dense */
953:     MatTransColoringApplyDenToSp(matcoloring,C_dense,C);
954:     return(0);
955:   }

957:   for (i=0; i<cm; i++) {
958:     anzi = ai[i+1] - ai[i];
959:     acol = aj + ai[i];
960:     aval = aa + ai[i];
961:     cnzi = ci[i+1] - ci[i];
962:     ccol = cj + ci[i];
963:     cval = ca + ci[i];
964:     for (j=0; j<cnzi; j++) {
965:       brow = ccol[j];
966:       bnzj = bi[brow+1] - bi[brow];
967:       bcol = bj + bi[brow];
968:       bval = ba + bi[brow];

970:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
971:       nexta = 0; nextb = 0;
972:       while (nexta<anzi && nextb<bnzj) {
973:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
974:         if (nexta == anzi) break;
975:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
976:         if (nextb == bnzj) break;
977:         if (acol[nexta] == bcol[nextb]) {
978:           cval[j] += aval[nexta]*bval[nextb];
979:           nexta++; nextb++;
980:           flops += 2;
981:         }
982:       }
983:     }
984:   }
985:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
986:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
987:   PetscLogFlops(flops);
988:   return(0);
989: }

993: PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
994: {

998:   if (scall == MAT_INITIAL_MATRIX) {
999:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);
1000:     MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
1001:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);
1002:   }
1003:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);
1004:   MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
1005:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);
1006:   return(0);
1007: }

1011: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1012: {
1014:   Mat            At;
1015:   PetscInt       *ati,*atj;

1018:   /* create symbolic At */
1019:   MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
1020:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);
1021:   MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));

1023:   /* get symbolic C=At*B */
1024:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);

1026:   /* clean up */
1027:   MatDestroy(&At);
1028:   MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);
1029:   return(0);
1030: }

1034: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1035: {
1037:   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1038:   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1039:   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1040:   PetscLogDouble flops=0.0;
1041:   MatScalar      *aa  =a->a,*ba,*ca,*caj;

1044:   if (!c->a) {
1045:     PetscMalloc1(ci[cm]+1,&ca);

1047:     c->a      = ca;
1048:     c->free_a = PETSC_TRUE;
1049:   } else {
1050:     ca = c->a;
1051:   }
1052:   /* clear old values in C */
1053:   PetscMemzero(ca,ci[cm]*sizeof(MatScalar));

1055:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1056:   for (i=0; i<am; i++) {
1057:     bj   = b->j + bi[i];
1058:     ba   = b->a + bi[i];
1059:     bnzi = bi[i+1] - bi[i];
1060:     anzi = ai[i+1] - ai[i];
1061:     for (j=0; j<anzi; j++) {
1062:       nextb = 0;
1063:       crow  = *aj++;
1064:       cjj   = cj + ci[crow];
1065:       caj   = ca + ci[crow];
1066:       /* perform sparse axpy operation.  Note cjj includes bj. */
1067:       for (k=0; nextb<bnzi; k++) {
1068:         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1069:           caj[k] += (*aa)*(*(ba+nextb));
1070:           nextb++;
1071:         }
1072:       }
1073:       flops += 2*bnzi;
1074:       aa++;
1075:     }
1076:   }

1078:   /* Assemble the final matrix and clean up */
1079:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1080:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1081:   PetscLogFlops(flops);
1082:   return(0);
1083: }

1087: PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1088: {

1092:   if (scall == MAT_INITIAL_MATRIX) {
1093:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
1094:     MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
1095:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
1096:   }
1097:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
1098:   MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
1099:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
1100:   return(0);
1101: }

1105: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1106: {

1110:   MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);

1112:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1113:   return(0);
1114: }

1118: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1119: {
1120:   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1121:   PetscErrorCode    ierr;
1122:   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1123:   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1124:   const PetscInt    *aj;
1125:   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=B->rmap->n,am=A->rmap->n;
1126:   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;

1129:   if (!cm || !cn) return(0);
1130:   if (bm != 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,bm);
1131:   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);
1132:   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);
1133:   MatDenseGetArray(B,&b);
1134:   MatDenseGetArray(C,&c);
1135:   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1136:   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1137:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1138:     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1139:       r1 = r2 = r3 = r4 = 0.0;
1140:       n  = a->i[i+1] - a->i[i];
1141:       aj = a->j + a->i[i];
1142:       aa = a->a + a->i[i];
1143:       for (j=0; j<n; j++) {
1144:         aatmp = aa[j]; ajtmp = aj[j];
1145:         r1 += aatmp*b1[ajtmp];
1146:         r2 += aatmp*b2[ajtmp];
1147:         r3 += aatmp*b3[ajtmp];
1148:         r4 += aatmp*b4[ajtmp];
1149:       }
1150:       c1[i] = r1;
1151:       c2[i] = r2;
1152:       c3[i] = r3;
1153:       c4[i] = r4;
1154:     }
1155:     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1156:     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1157:   }
1158:   for (; col<cn; col++) {   /* over extra columns of C */
1159:     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1160:       r1 = 0.0;
1161:       n  = a->i[i+1] - a->i[i];
1162:       aj = a->j + a->i[i];
1163:       aa = a->a + a->i[i];
1164:       for (j=0; j<n; j++) {
1165:         r1 += aa[j]*b1[aj[j]];
1166:       }
1167:       c1[i] = r1;
1168:     }
1169:     b1 += bm;
1170:     c1 += am;
1171:   }
1172:   PetscLogFlops(cn*(2.0*a->nz));
1173:   MatDenseRestoreArray(B,&b);
1174:   MatDenseRestoreArray(C,&c);
1175:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1176:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1177:   return(0);
1178: }

1180: /*
1181:    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1182: */
1185: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1186: {
1187:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1189:   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1190:   MatScalar      *aa;
1191:   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1192:   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;

1195:   if (!cm || !cn) return(0);
1196:   MatDenseGetArray(B,&b);
1197:   MatDenseGetArray(C,&c);
1198:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;

1200:   if (a->compressedrow.use) { /* use compressed row format */
1201:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1202:       colam = col*am;
1203:       arm   = a->compressedrow.nrows;
1204:       ii    = a->compressedrow.i;
1205:       ridx  = a->compressedrow.rindex;
1206:       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1207:         r1 = r2 = r3 = r4 = 0.0;
1208:         n  = ii[i+1] - ii[i];
1209:         aj = a->j + ii[i];
1210:         aa = a->a + ii[i];
1211:         for (j=0; j<n; j++) {
1212:           r1 += (*aa)*b1[*aj];
1213:           r2 += (*aa)*b2[*aj];
1214:           r3 += (*aa)*b3[*aj];
1215:           r4 += (*aa++)*b4[*aj++];
1216:         }
1217:         c[colam       + ridx[i]] += r1;
1218:         c[colam + am  + ridx[i]] += r2;
1219:         c[colam + am2 + ridx[i]] += r3;
1220:         c[colam + am3 + ridx[i]] += r4;
1221:       }
1222:       b1 += bm4;
1223:       b2 += bm4;
1224:       b3 += bm4;
1225:       b4 += bm4;
1226:     }
1227:     for (; col<cn; col++) {     /* over extra columns of C */
1228:       colam = col*am;
1229:       arm   = a->compressedrow.nrows;
1230:       ii    = a->compressedrow.i;
1231:       ridx  = a->compressedrow.rindex;
1232:       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1233:         r1 = 0.0;
1234:         n  = ii[i+1] - ii[i];
1235:         aj = a->j + ii[i];
1236:         aa = a->a + ii[i];

1238:         for (j=0; j<n; j++) {
1239:           r1 += (*aa++)*b1[*aj++];
1240:         }
1241:         c[colam + ridx[i]] += r1;
1242:       }
1243:       b1 += bm;
1244:     }
1245:   } else {
1246:     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1247:       colam = col*am;
1248:       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1249:         r1 = r2 = r3 = r4 = 0.0;
1250:         n  = a->i[i+1] - a->i[i];
1251:         aj = a->j + a->i[i];
1252:         aa = a->a + a->i[i];
1253:         for (j=0; j<n; j++) {
1254:           r1 += (*aa)*b1[*aj];
1255:           r2 += (*aa)*b2[*aj];
1256:           r3 += (*aa)*b3[*aj];
1257:           r4 += (*aa++)*b4[*aj++];
1258:         }
1259:         c[colam + i]       += r1;
1260:         c[colam + am + i]  += r2;
1261:         c[colam + am2 + i] += r3;
1262:         c[colam + am3 + i] += r4;
1263:       }
1264:       b1 += bm4;
1265:       b2 += bm4;
1266:       b3 += bm4;
1267:       b4 += bm4;
1268:     }
1269:     for (; col<cn; col++) {     /* over extra columns of C */
1270:       colam = col*am;
1271:       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1272:         r1 = 0.0;
1273:         n  = a->i[i+1] - a->i[i];
1274:         aj = a->j + a->i[i];
1275:         aa = a->a + a->i[i];

1277:         for (j=0; j<n; j++) {
1278:           r1 += (*aa++)*b1[*aj++];
1279:         }
1280:         c[colam + i] += r1;
1281:       }
1282:       b1 += bm;
1283:     }
1284:   }
1285:   PetscLogFlops(cn*2.0*a->nz);
1286:   MatDenseRestoreArray(B,&b);
1287:   MatDenseRestoreArray(C,&c);
1288:   return(0);
1289: }

1293: PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1294: {
1296:   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1297:   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1298:   PetscInt       *bi      = b->i,*bj=b->j;
1299:   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1300:   MatScalar      *btval,*btval_den,*ba=b->a;
1301:   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;

1304:   btval_den=btdense->v;
1305:   PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));
1306:   for (k=0; k<ncolors; k++) {
1307:     ncolumns = coloring->ncolumns[k];
1308:     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1309:       col   = *(columns + colorforcol[k] + l);
1310:       btcol = bj + bi[col];
1311:       btval = ba + bi[col];
1312:       anz   = bi[col+1] - bi[col];
1313:       for (j=0; j<anz; j++) {
1314:         brow            = btcol[j];
1315:         btval_den[brow] = btval[j];
1316:       }
1317:     }
1318:     btval_den += m;
1319:   }
1320:   return(0);
1321: }

1325: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1326: {
1328:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1329:   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1330:   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1331:   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1332:   PetscInt       nrows,*row,*idx;
1333:   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;

1336:   MatDenseGetArray(Cden,&ca_den);

1338:   if (brows > 0) {
1339:     PetscInt *lstart,row_end,row_start;
1340:     lstart = matcoloring->lstart;
1341:     PetscMemzero(lstart,ncolors*sizeof(PetscInt));

1343:     row_end = brows;
1344:     if (row_end > m) row_end = m;
1345:     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1346:       ca_den_ptr = ca_den;
1347:       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1348:         nrows = matcoloring->nrows[k];
1349:         row   = rows  + colorforrow[k];
1350:         idx   = den2sp + colorforrow[k];
1351:         for (l=lstart[k]; l<nrows; l++) {
1352:           if (row[l] >= row_end) {
1353:             lstart[k] = l;
1354:             break;
1355:           } else {
1356:             ca[idx[l]] = ca_den_ptr[row[l]];
1357:           }
1358:         }
1359:         ca_den_ptr += m;
1360:       }
1361:       row_end += brows;
1362:       if (row_end > m) row_end = m;
1363:     }
1364:   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1365:     ca_den_ptr = ca_den;
1366:     for (k=0; k<ncolors; k++) {
1367:       nrows = matcoloring->nrows[k];
1368:       row   = rows  + colorforrow[k];
1369:       idx   = den2sp + colorforrow[k];
1370:       for (l=0; l<nrows; l++) {
1371:         ca[idx[l]] = ca_den_ptr[row[l]];
1372:       }
1373:       ca_den_ptr += m;
1374:     }
1375:   }

1377:   MatDenseRestoreArray(Cden,&ca_den);
1378: #if defined(PETSC_USE_INFO)
1379:   if (matcoloring->brows > 0) {
1380:     PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);
1381:   } else {
1382:     PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");
1383:   }
1384: #endif
1385:   return(0);
1386: }

1390: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1391: {
1393:   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1394:   const PetscInt *is,*ci,*cj,*row_idx;
1395:   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1396:   IS             *isa;
1397:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1398:   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1399:   PetscInt       *colorforcol,*columns,*columns_i,brows;
1400:   PetscBool      flg;

1403:   ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);

1405:   /* bs >1 is not being tested yet! */
1406:   Nbs       = mat->cmap->N/bs;
1407:   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1408:   c->N      = Nbs;
1409:   c->m      = c->M;
1410:   c->rstart = 0;
1411:   c->brows  = 100;

1413:   c->ncolors = nis;
1414:   PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);
1415:   PetscMalloc1(csp->nz+1,&rows);
1416:   PetscMalloc1(csp->nz+1,&den2sp);

1418:   brows = c->brows;
1419:   PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);
1420:   if (flg) c->brows = brows;
1421:   if (brows > 0) {
1422:     PetscMalloc1(nis+1,&c->lstart);
1423:   }

1425:   colorforrow[0] = 0;
1426:   rows_i         = rows;
1427:   den2sp_i       = den2sp;

1429:   PetscMalloc1(nis+1,&colorforcol);
1430:   PetscMalloc1(Nbs+1,&columns);

1432:   colorforcol[0] = 0;
1433:   columns_i      = columns;

1435:   /* get column-wise storage of mat */
1436:   MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);

1438:   cm   = c->m;
1439:   PetscMalloc1(cm+1,&rowhit);
1440:   PetscMalloc1(cm+1,&idxhit);
1441:   for (i=0; i<nis; i++) { /* loop over color */
1442:     ISGetLocalSize(isa[i],&n);
1443:     ISGetIndices(isa[i],&is);

1445:     c->ncolumns[i] = n;
1446:     if (n) {
1447:       PetscMemcpy(columns_i,is,n*sizeof(PetscInt));
1448:     }
1449:     colorforcol[i+1] = colorforcol[i] + n;
1450:     columns_i       += n;

1452:     /* fast, crude version requires O(N*N) work */
1453:     PetscMemzero(rowhit,cm*sizeof(PetscInt));

1455:     for (j=0; j<n; j++) { /* loop over columns*/
1456:       col     = is[j];
1457:       row_idx = cj + ci[col];
1458:       m       = ci[col+1] - ci[col];
1459:       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1460:         idxhit[*row_idx]   = spidx[ci[col] + k];
1461:         rowhit[*row_idx++] = col + 1;
1462:       }
1463:     }
1464:     /* count the number of hits */
1465:     nrows = 0;
1466:     for (j=0; j<cm; j++) {
1467:       if (rowhit[j]) nrows++;
1468:     }
1469:     c->nrows[i]      = nrows;
1470:     colorforrow[i+1] = colorforrow[i] + nrows;

1472:     nrows = 0;
1473:     for (j=0; j<cm; j++) { /* loop over rows */
1474:       if (rowhit[j]) {
1475:         rows_i[nrows]   = j;
1476:         den2sp_i[nrows] = idxhit[j];
1477:         nrows++;
1478:       }
1479:     }
1480:     den2sp_i += nrows;

1482:     ISRestoreIndices(isa[i],&is);
1483:     rows_i += nrows;
1484:   }
1485:   MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);
1486:   PetscFree(rowhit);
1487:   ISColoringRestoreIS(iscoloring,&isa);
1488:   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);

1490:   c->colorforrow = colorforrow;
1491:   c->rows        = rows;
1492:   c->den2sp      = den2sp;
1493:   c->colorforcol = colorforcol;
1494:   c->columns     = columns;

1496:   PetscFree(idxhit);
1497:   return(0);
1498: }