Actual source code: matmatmult.c

petsc-master 2019-10-13
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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>
  8:  #include <../src/mat/utils/freespace.h>
  9:  #include <petscbt.h>
 10:  #include <petsc/private/isimpl.h>
 11:  #include <../src/mat/impls/dense/seq/dense.h>


 14: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
 15: {

 19:   if (scall == MAT_INITIAL_MATRIX) {
 20:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
 21:     MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
 22:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
 23:   }
 24:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
 25:   MatMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
 26:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
 27:   return(0);
 28: }

 30: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
 31: {

 35:   if (C->ops->matmultnumeric) {
 36:     (*C->ops->matmultnumeric)(A,B,C);
 37:   } else {
 38:     MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A,B,C);
 39:   }
 40:   return(0);
 41: }

 43: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
 44: {
 46: #if !defined(PETSC_HAVE_HYPRE)
 47:   const char     *algTypes[8] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge"};
 48:   PetscInt       nalg = 8;
 49: #else
 50:   const char     *algTypes[9] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge","hypre"};
 51:   PetscInt       nalg = 9;
 52: #endif
 53:   PetscInt       alg = 0; /* set default algorithm */

 56:   PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatMatMult","Mat");
 57:   PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);
 58:   PetscOptionsEnd();
 59:   switch (alg) {
 60:   case 1:
 61:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);
 62:     break;
 63:   case 2:
 64:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);
 65:     break;
 66:   case 3:
 67:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);
 68:     break;
 69:   case 4:
 70:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);
 71:     break;
 72:   case 5:
 73:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);
 74:     break;
 75:   case 6:
 76:     MatMatMult_SeqAIJ_SeqAIJ_Combined(A,B,fill,C);
 77:     break;
 78:   case 7:
 79:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A,B,fill,C);
 80:     break;
 81: #if defined(PETSC_HAVE_HYPRE)
 82:   case 8:
 83:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
 84:     break;
 85: #endif
 86:   default:
 87:     MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A,B,fill,C);
 88:     break;
 89:   }
 90:   return(0);
 91: }

 93: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
 94: {
 95:   PetscErrorCode     ierr;
 96:   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
 97:   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
 98:   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
 99:   PetscReal          afill;
100:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
101:   PetscTable         ta;
102:   PetscBT            lnkbt;
103:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

106:   /* Get ci and cj */
107:   /*---------------*/
108:   /* Allocate ci array, arrays for fill computation and */
109:   /* free space for accumulating nonzero column info */
110:   PetscMalloc1(am+2,&ci);
111:   ci[0] = 0;

113:   /* create and initialize a linked list */
114:   PetscTableCreate(bn,bn,&ta);
115:   MatRowMergeMax_SeqAIJ(b,bm,ta);
116:   PetscTableGetCount(ta,&Crmax);
117:   PetscTableDestroy(&ta);

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

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

124:   current_space = free_space;

126:   /* Determine ci and cj */
127:   for (i=0; i<am; i++) {
128:     anzi = ai[i+1] - ai[i];
129:     aj   = a->j + ai[i];
130:     for (j=0; j<anzi; j++) {
131:       brow = aj[j];
132:       bnzj = bi[brow+1] - bi[brow];
133:       bj   = b->j + bi[brow];
134:       /* add non-zero cols of B into the sorted linked list lnk */
135:       PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);
136:     }
137:     cnzi = lnk[0];

139:     /* If free space is not available, make more free space */
140:     /* Double the amount of total space in the list */
141:     if (current_space->local_remaining<cnzi) {
142:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
143:       ndouble++;
144:     }

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

149:     current_space->array           += cnzi;
150:     current_space->local_used      += cnzi;
151:     current_space->local_remaining -= cnzi;

153:     ci[i+1] = ci[i] + cnzi;
154:   }

156:   /* Column indices are in the list of free space */
157:   /* Allocate space for cj, initialize cj, and */
158:   /* destroy list of free space and other temporary array(s) */
159:   PetscMalloc1(ci[am]+1,&cj);
160:   PetscFreeSpaceContiguous(&free_space,cj);
161:   PetscLLCondensedDestroy(lnk,lnkbt);

163:   /* put together the new symbolic matrix */
164:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
165:   MatSetBlockSizesFromMats(*C,A,B);
166:   MatSetType(*C,((PetscObject)A)->type_name);

168:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
169:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
170:   c                         = (Mat_SeqAIJ*)((*C)->data);
171:   c->free_a                 = PETSC_FALSE;
172:   c->free_ij                = PETSC_TRUE;
173:   c->nonew                  = 0;
174:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; /* fast, needs non-scalable O(bn) array 'abdense' */

176:   /* set MatInfo */
177:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
178:   if (afill < 1.0) afill = 1.0;
179:   c->maxnz                     = ci[am];
180:   c->nz                        = ci[am];
181:   (*C)->info.mallocs           = ndouble;
182:   (*C)->info.fill_ratio_given  = fill;
183:   (*C)->info.fill_ratio_needed = afill;

185: #if defined(PETSC_USE_INFO)
186:   if (ci[am]) {
187:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
188:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
189:   } else {
190:     PetscInfo((*C),"Empty matrix product\n");
191:   }
192: #endif
193:   return(0);
194: }

196: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,Mat C)
197: {
199:   PetscLogDouble flops=0.0;
200:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
201:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
202:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
203:   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
204:   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
205:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
206:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
207:   PetscScalar    *ab_dense;

210:   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
211:     PetscMalloc1(ci[cm]+1,&ca);
212:     c->a      = ca;
213:     c->free_a = PETSC_TRUE;
214:   } else {
215:     ca        = c->a;
216:   }
217:   if (!c->matmult_abdense) {
218:     PetscCalloc1(B->cmap->N,&ab_dense);
219:     c->matmult_abdense = ab_dense;
220:   } else {
221:     ab_dense = c->matmult_abdense;
222:   }

224:   /* clean old values in C */
225:   PetscArrayzero(ca,ci[cm]);
226:   /* Traverse A row-wise. */
227:   /* Build the ith row in C by summing over nonzero columns in A, */
228:   /* the rows of B corresponding to nonzeros of A. */
229:   for (i=0; i<am; i++) {
230:     anzi = ai[i+1] - ai[i];
231:     for (j=0; j<anzi; j++) {
232:       brow = aj[j];
233:       bnzi = bi[brow+1] - bi[brow];
234:       bjj  = bj + bi[brow];
235:       baj  = ba + bi[brow];
236:       /* perform dense axpy */
237:       valtmp = aa[j];
238:       for (k=0; k<bnzi; k++) {
239:         ab_dense[bjj[k]] += valtmp*baj[k];
240:       }
241:       flops += 2*bnzi;
242:     }
243:     aj += anzi; aa += anzi;

245:     cnzi = ci[i+1] - ci[i];
246:     for (k=0; k<cnzi; k++) {
247:       ca[k]          += ab_dense[cj[k]];
248:       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
249:     }
250:     flops += cnzi;
251:     cj    += cnzi; ca += cnzi;
252:   }
253:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
254:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
255:   PetscLogFlops(flops);
256:   return(0);
257: }

259: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
260: {
262:   PetscLogDouble flops=0.0;
263:   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
264:   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
265:   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
266:   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
267:   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
268:   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
269:   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
270:   PetscInt       nextb;

273:   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
274:     PetscMalloc1(ci[cm]+1,&ca);
275:     c->a      = ca;
276:     c->free_a = PETSC_TRUE;
277:   }

279:   /* clean old values in C */
280:   PetscArrayzero(ca,ci[cm]);
281:   /* Traverse A row-wise. */
282:   /* Build the ith row in C by summing over nonzero columns in A, */
283:   /* the rows of B corresponding to nonzeros of A. */
284:   for (i=0; i<am; i++) {
285:     anzi = ai[i+1] - ai[i];
286:     cnzi = ci[i+1] - ci[i];
287:     for (j=0; j<anzi; j++) {
288:       brow = aj[j];
289:       bnzi = bi[brow+1] - bi[brow];
290:       bjj  = bj + bi[brow];
291:       baj  = ba + bi[brow];
292:       /* perform sparse axpy */
293:       valtmp = aa[j];
294:       nextb  = 0;
295:       for (k=0; nextb<bnzi; k++) {
296:         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
297:           ca[k] += valtmp*baj[nextb++];
298:         }
299:       }
300:       flops += 2*bnzi;
301:     }
302:     aj += anzi; aa += anzi;
303:     cj += cnzi; ca += cnzi;
304:   }

306:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
307:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
308:   PetscLogFlops(flops);
309:   return(0);
310: }

312: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
313: {
314:   PetscErrorCode     ierr;
315:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
316:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
317:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
318:   MatScalar          *ca;
319:   PetscReal          afill;
320:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
321:   PetscTable         ta;
322:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

325:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
326:   /*-----------------------------------------------------------------------------------------*/
327:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
328:   PetscMalloc1(am+2,&ci);
329:   ci[0] = 0;

331:   /* create and initialize a linked list */
332:   PetscTableCreate(bn,bn,&ta);
333:   MatRowMergeMax_SeqAIJ(b,bm,ta);
334:   PetscTableGetCount(ta,&Crmax);
335:   PetscTableDestroy(&ta);

337:   PetscLLCondensedCreate_fast(Crmax,&lnk);

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

343:   /* Determine ci and cj */
344:   for (i=0; i<am; i++) {
345:     anzi = ai[i+1] - ai[i];
346:     aj   = a->j + ai[i];
347:     for (j=0; j<anzi; j++) {
348:       brow = aj[j];
349:       bnzj = bi[brow+1] - bi[brow];
350:       bj   = b->j + bi[brow];
351:       /* add non-zero cols of B into the sorted linked list lnk */
352:       PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);
353:     }
354:     cnzi = lnk[1];

356:     /* If free space is not available, make more free space */
357:     /* Double the amount of total space in the list */
358:     if (current_space->local_remaining<cnzi) {
359:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
360:       ndouble++;
361:     }

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

366:     current_space->array           += cnzi;
367:     current_space->local_used      += cnzi;
368:     current_space->local_remaining -= cnzi;

370:     ci[i+1] = ci[i] + cnzi;
371:   }

373:   /* Column indices are in the list of free space */
374:   /* Allocate space for cj, initialize cj, and */
375:   /* destroy list of free space and other temporary array(s) */
376:   PetscMalloc1(ci[am]+1,&cj);
377:   PetscFreeSpaceContiguous(&free_space,cj);
378:   PetscLLCondensedDestroy_fast(lnk);

380:   /* Allocate space for ca */
381:   PetscCalloc1(ci[am]+1,&ca);

383:   /* put together the new symbolic matrix */
384:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
385:   MatSetBlockSizesFromMats(*C,A,B);
386:   MatSetType(*C,((PetscObject)A)->type_name);

388:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
389:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
390:   c          = (Mat_SeqAIJ*)((*C)->data);
391:   c->free_a  = PETSC_TRUE;
392:   c->free_ij = PETSC_TRUE;
393:   c->nonew   = 0;

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

397:   /* set MatInfo */
398:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
399:   if (afill < 1.0) afill = 1.0;
400:   c->maxnz                     = ci[am];
401:   c->nz                        = ci[am];
402:   (*C)->info.mallocs           = ndouble;
403:   (*C)->info.fill_ratio_given  = fill;
404:   (*C)->info.fill_ratio_needed = afill;

406: #if defined(PETSC_USE_INFO)
407:   if (ci[am]) {
408:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
409:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
410:   } else {
411:     PetscInfo((*C),"Empty matrix product\n");
412:   }
413: #endif
414:   return(0);
415: }


418: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
419: {
420:   PetscErrorCode     ierr;
421:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
422:   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
423:   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
424:   MatScalar          *ca;
425:   PetscReal          afill;
426:   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
427:   PetscTable         ta;
428:   PetscFreeSpaceList free_space=NULL,current_space=NULL;

431:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
432:   /*---------------------------------------------------------------------------------------------*/
433:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
434:   PetscMalloc1(am+2,&ci);
435:   ci[0] = 0;

437:   /* create and initialize a linked list */
438:   PetscTableCreate(bn,bn,&ta);
439:   MatRowMergeMax_SeqAIJ(b,bm,ta);
440:   PetscTableGetCount(ta,&Crmax);
441:   PetscTableDestroy(&ta);
442:   PetscLLCondensedCreate_Scalable(Crmax,&lnk);

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

448:   /* Determine ci and cj */
449:   for (i=0; i<am; i++) {
450:     anzi = ai[i+1] - ai[i];
451:     aj   = a->j + ai[i];
452:     for (j=0; j<anzi; j++) {
453:       brow = aj[j];
454:       bnzj = bi[brow+1] - bi[brow];
455:       bj   = b->j + bi[brow];
456:       /* add non-zero cols of B into the sorted linked list lnk */
457:       PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);
458:     }
459:     cnzi = lnk[0];

461:     /* If free space is not available, make more free space */
462:     /* Double the amount of total space in the list */
463:     if (current_space->local_remaining<cnzi) {
464:       PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);
465:       ndouble++;
466:     }

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

471:     current_space->array           += cnzi;
472:     current_space->local_used      += cnzi;
473:     current_space->local_remaining -= cnzi;

475:     ci[i+1] = ci[i] + cnzi;
476:   }

478:   /* Column indices are in the list of free space */
479:   /* Allocate space for cj, initialize cj, and */
480:   /* destroy list of free space and other temporary array(s) */
481:   PetscMalloc1(ci[am]+1,&cj);
482:   PetscFreeSpaceContiguous(&free_space,cj);
483:   PetscLLCondensedDestroy_Scalable(lnk);

485:   /* Allocate space for ca */
486:   /*-----------------------*/
487:   PetscCalloc1(ci[am]+1,&ca);

489:   /* put together the new symbolic matrix */
490:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);
491:   MatSetBlockSizesFromMats(*C,A,B);
492:   MatSetType(*C,((PetscObject)A)->type_name);

494:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
495:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
496:   c          = (Mat_SeqAIJ*)((*C)->data);
497:   c->free_a  = PETSC_TRUE;
498:   c->free_ij = PETSC_TRUE;
499:   c->nonew   = 0;

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

503:   /* set MatInfo */
504:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
505:   if (afill < 1.0) afill = 1.0;
506:   c->maxnz                     = ci[am];
507:   c->nz                        = ci[am];
508:   (*C)->info.mallocs           = ndouble;
509:   (*C)->info.fill_ratio_given  = fill;
510:   (*C)->info.fill_ratio_needed = afill;

512: #if defined(PETSC_USE_INFO)
513:   if (ci[am]) {
514:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
515:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
516:   } else {
517:     PetscInfo((*C),"Empty matrix product\n");
518:   }
519: #endif
520:   return(0);
521: }

523: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
524: {
525:   PetscErrorCode     ierr;
526:   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
527:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
528:   PetscInt           *ci,*cj,*bb;
529:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
530:   PetscReal          afill;
531:   PetscInt           i,j,col,ndouble = 0;
532:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
533:   PetscHeap          h;

536:   /* Get ci and cj - by merging sorted rows using a heap */
537:   /*---------------------------------------------------------------------------------------------*/
538:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
539:   PetscMalloc1(am+2,&ci);
540:   ci[0] = 0;

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

546:   PetscHeapCreate(a->rmax,&h);
547:   PetscMalloc1(a->rmax,&bb);

549:   /* Determine ci and cj */
550:   for (i=0; i<am; i++) {
551:     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 */
552:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
553:     ci[i+1] = ci[i];
554:     /* Populate the min heap */
555:     for (j=0; j<anzi; j++) {
556:       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
557:       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
558:         PetscHeapAdd(h,j,bj[bb[j]++]);
559:       }
560:     }
561:     /* Pick off the min element, adding it to free space */
562:     PetscHeapPop(h,&j,&col);
563:     while (j >= 0) {
564:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
565:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
566:         ndouble++;
567:       }
568:       *(current_space->array++) = col;
569:       current_space->local_used++;
570:       current_space->local_remaining--;
571:       ci[i+1]++;

573:       /* stash if anything else remains in this row of B */
574:       if (bb[j] < bi[acol[j]+1]) {PetscHeapStash(h,j,bj[bb[j]++]);}
575:       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
576:         PetscInt j2,col2;
577:         PetscHeapPeek(h,&j2,&col2);
578:         if (col2 != col) break;
579:         PetscHeapPop(h,&j2,&col2);
580:         if (bb[j2] < bi[acol[j2]+1]) {PetscHeapStash(h,j2,bj[bb[j2]++]);}
581:       }
582:       /* Put any stashed elements back into the min heap */
583:       PetscHeapUnstash(h);
584:       PetscHeapPop(h,&j,&col);
585:     }
586:   }
587:   PetscFree(bb);
588:   PetscHeapDestroy(&h);

590:   /* Column indices are in the list of free space */
591:   /* Allocate space for cj, initialize cj, and */
592:   /* destroy list of free space and other temporary array(s) */
593:   PetscMalloc1(ci[am],&cj);
594:   PetscFreeSpaceContiguous(&free_space,cj);

596:   /* put together the new symbolic matrix */
597:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
598:   MatSetBlockSizesFromMats(*C,A,B);
599:   MatSetType(*C,((PetscObject)A)->type_name);

601:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
602:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
603:   c          = (Mat_SeqAIJ*)((*C)->data);
604:   c->free_a  = PETSC_TRUE;
605:   c->free_ij = PETSC_TRUE;
606:   c->nonew   = 0;

608:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

610:   /* set MatInfo */
611:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
612:   if (afill < 1.0) afill = 1.0;
613:   c->maxnz                     = ci[am];
614:   c->nz                        = ci[am];
615:   (*C)->info.mallocs           = ndouble;
616:   (*C)->info.fill_ratio_given  = fill;
617:   (*C)->info.fill_ratio_needed = afill;

619: #if defined(PETSC_USE_INFO)
620:   if (ci[am]) {
621:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
622:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
623:   } else {
624:     PetscInfo((*C),"Empty matrix product\n");
625:   }
626: #endif
627:   return(0);
628: }

630: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
631: {
632:   PetscErrorCode     ierr;
633:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
634:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
635:   PetscInt           *ci,*cj,*bb;
636:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
637:   PetscReal          afill;
638:   PetscInt           i,j,col,ndouble = 0;
639:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
640:   PetscHeap          h;
641:   PetscBT            bt;

644:   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
645:   /*---------------------------------------------------------------------------------------------*/
646:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
647:   PetscMalloc1(am+2,&ci);
648:   ci[0] = 0;

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

653:   current_space = free_space;

655:   PetscHeapCreate(a->rmax,&h);
656:   PetscMalloc1(a->rmax,&bb);
657:   PetscBTCreate(bn,&bt);

659:   /* Determine ci and cj */
660:   for (i=0; i<am; i++) {
661:     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 */
662:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
663:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
664:     ci[i+1] = ci[i];
665:     /* Populate the min heap */
666:     for (j=0; j<anzi; j++) {
667:       PetscInt brow = acol[j];
668:       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
669:         PetscInt bcol = bj[bb[j]];
670:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
671:           PetscHeapAdd(h,j,bcol);
672:           bb[j]++;
673:           break;
674:         }
675:       }
676:     }
677:     /* Pick off the min element, adding it to free space */
678:     PetscHeapPop(h,&j,&col);
679:     while (j >= 0) {
680:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
681:         fptr = NULL;                      /* need PetscBTMemzero */
682:         PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);
683:         ndouble++;
684:       }
685:       *(current_space->array++) = col;
686:       current_space->local_used++;
687:       current_space->local_remaining--;
688:       ci[i+1]++;

690:       /* stash if anything else remains in this row of B */
691:       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
692:         PetscInt bcol = bj[bb[j]];
693:         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
694:           PetscHeapAdd(h,j,bcol);
695:           bb[j]++;
696:           break;
697:         }
698:       }
699:       PetscHeapPop(h,&j,&col);
700:     }
701:     if (fptr) {                 /* Clear the bits for this row */
702:       for (; fptr<current_space->array; fptr++) {PetscBTClear(bt,*fptr);}
703:     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
704:       PetscBTMemzero(bn,bt);
705:     }
706:   }
707:   PetscFree(bb);
708:   PetscHeapDestroy(&h);
709:   PetscBTDestroy(&bt);

711:   /* Column indices are in the list of free space */
712:   /* Allocate space for cj, initialize cj, and */
713:   /* destroy list of free space and other temporary array(s) */
714:   PetscMalloc1(ci[am],&cj);
715:   PetscFreeSpaceContiguous(&free_space,cj);

717:   /* put together the new symbolic matrix */
718:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
719:   MatSetBlockSizesFromMats(*C,A,B);
720:   MatSetType(*C,((PetscObject)A)->type_name);

722:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
723:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
724:   c          = (Mat_SeqAIJ*)((*C)->data);
725:   c->free_a  = PETSC_TRUE;
726:   c->free_ij = PETSC_TRUE;
727:   c->nonew   = 0;

729:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

731:   /* set MatInfo */
732:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
733:   if (afill < 1.0) afill = 1.0;
734:   c->maxnz                     = ci[am];
735:   c->nz                        = ci[am];
736:   (*C)->info.mallocs           = ndouble;
737:   (*C)->info.fill_ratio_given  = fill;
738:   (*C)->info.fill_ratio_needed = afill;

740: #if defined(PETSC_USE_INFO)
741:   if (ci[am]) {
742:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
743:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
744:   } else {
745:     PetscInfo((*C),"Empty matrix product\n");
746:   }
747: #endif
748:   return(0);
749: }


752: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A,Mat B,PetscReal fill,Mat *C)
753: {
754:   PetscErrorCode     ierr;
755:   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
756:   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j,*inputi,*inputj,*inputcol,*inputcol_L1;
757:   PetscInt           *ci,*cj,*outputj,worki_L1[9],worki_L2[9];
758:   PetscInt           c_maxmem,a_maxrownnz=0,a_rownnz;
759:   const PetscInt     workcol[8]={0,1,2,3,4,5,6,7};
760:   const PetscInt     am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
761:   const PetscInt     *brow_ptr[8],*brow_end[8];
762:   PetscInt           window[8];
763:   PetscInt           window_min,old_window_min,ci_nnz,outputi_nnz=0,L1_nrows,L2_nrows;
764:   PetscInt           i,k,ndouble=0,L1_rowsleft,rowsleft;
765:   PetscReal          afill;
766:   PetscInt           *workj_L1,*workj_L2,*workj_L3;
767:   PetscInt           L1_nnz,L2_nnz;

769:   /* Step 1: Get upper bound on memory required for allocation.
770:              Because of the way virtual memory works,
771:              only the memory pages that are actually needed will be physically allocated. */
773:   PetscMalloc1(am+1,&ci);
774:   for (i=0; i<am; i++) {
775:     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 */
776:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
777:     a_rownnz = 0;
778:     for (k=0; k<anzi; ++k) {
779:       a_rownnz += bi[acol[k]+1] - bi[acol[k]];
780:       if (a_rownnz > bn) {
781:         a_rownnz = bn;
782:         break;
783:       }
784:     }
785:     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
786:   }
787:   /* temporary work areas for merging rows */
788:   PetscMalloc1(a_maxrownnz*8,&workj_L1);
789:   PetscMalloc1(a_maxrownnz*8,&workj_L2);
790:   PetscMalloc1(a_maxrownnz,&workj_L3);

792:   /* This should be enough for almost all matrices. If not, memory is reallocated later. */
793:   c_maxmem = 8*(ai[am]+bi[bm]);
794:   /* Step 2: Populate pattern for C */
795:   PetscMalloc1(c_maxmem,&cj);

797:   ci_nnz       = 0;
798:   ci[0]        = 0;
799:   worki_L1[0]  = 0;
800:   worki_L2[0]  = 0;
801:   for (i=0; i<am; i++) {
802:     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 */
803:     const PetscInt *acol = aj + ai[i];      /* column indices of nonzero entries in this row */
804:     rowsleft             = anzi;
805:     inputcol_L1          = acol;
806:     L2_nnz               = 0;
807:     L2_nrows             = 1;  /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
808:     worki_L2[1]          = 0;
809:     outputi_nnz          = 0;

811:     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
812:     while (ci_nnz+a_maxrownnz > c_maxmem) {
813:       c_maxmem *= 2;
814:       ndouble++;
815:       PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);
816:     }

818:     while (rowsleft) {
819:       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
820:       L1_nrows    = 0;
821:       L1_nnz      = 0;
822:       inputcol    = inputcol_L1;
823:       inputi      = bi;
824:       inputj      = bj;

826:       /* The following macro is used to specialize for small rows in A.
827:          This helps with compiler unrolling, improving performance substantially.
828:           Input:  inputj   inputi  inputcol  bn
829:           Output: outputj  outputi_nnz                       */
830:        #define MatMatMultSymbolic_RowMergeMacro(ANNZ)                        \
831:          window_min  = bn;                                                   \
832:          outputi_nnz = 0;                                                    \
833:          for (k=0; k<ANNZ; ++k) {                                            \
834:            brow_ptr[k] = inputj + inputi[inputcol[k]];                       \
835:            brow_end[k] = inputj + inputi[inputcol[k]+1];                     \
836:            window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn;   \
837:            window_min  = PetscMin(window[k], window_min);                    \
838:          }                                                                   \
839:          while (window_min < bn) {                                           \
840:            outputj[outputi_nnz++] = window_min;                              \
841:            /* advance front and compute new minimum */                       \
842:            old_window_min = window_min;                                      \
843:            window_min = bn;                                                  \
844:            for (k=0; k<ANNZ; ++k) {                                          \
845:              if (window[k] == old_window_min) {                              \
846:                brow_ptr[k]++;                                                \
847:                window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
848:              }                                                               \
849:              window_min = PetscMin(window[k], window_min);                   \
850:            }                                                                 \
851:          }

853:       /************** L E V E L  1 ***************/
854:       /* Merge up to 8 rows of B to L1 work array*/
855:       while (L1_rowsleft) {
856:         outputi_nnz = 0;
857:         if (anzi > 8)  outputj = workj_L1 + L1_nnz;     /* Level 1 rowmerge*/
858:         else           outputj = cj + ci_nnz;           /* Merge directly to C */

860:         switch (L1_rowsleft) {
861:         case 1:  brow_ptr[0] = inputj + inputi[inputcol[0]];
862:                  brow_end[0] = inputj + inputi[inputcol[0]+1];
863:                  for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
864:                  inputcol    += L1_rowsleft;
865:                  rowsleft    -= L1_rowsleft;
866:                  L1_rowsleft  = 0;
867:                  break;
868:         case 2:  MatMatMultSymbolic_RowMergeMacro(2);
869:                  inputcol    += L1_rowsleft;
870:                  rowsleft    -= L1_rowsleft;
871:                  L1_rowsleft  = 0;
872:                  break;
873:         case 3: MatMatMultSymbolic_RowMergeMacro(3);
874:                  inputcol    += L1_rowsleft;
875:                  rowsleft    -= L1_rowsleft;
876:                  L1_rowsleft  = 0;
877:                  break;
878:         case 4:  MatMatMultSymbolic_RowMergeMacro(4);
879:                  inputcol    += L1_rowsleft;
880:                  rowsleft    -= L1_rowsleft;
881:                  L1_rowsleft  = 0;
882:                  break;
883:         case 5:  MatMatMultSymbolic_RowMergeMacro(5);
884:                  inputcol    += L1_rowsleft;
885:                  rowsleft    -= L1_rowsleft;
886:                  L1_rowsleft  = 0;
887:                  break;
888:         case 6:  MatMatMultSymbolic_RowMergeMacro(6);
889:                  inputcol    += L1_rowsleft;
890:                  rowsleft    -= L1_rowsleft;
891:                  L1_rowsleft  = 0;
892:                  break;
893:         case 7:  MatMatMultSymbolic_RowMergeMacro(7);
894:                  inputcol    += L1_rowsleft;
895:                  rowsleft    -= L1_rowsleft;
896:                  L1_rowsleft  = 0;
897:                  break;
898:         default: MatMatMultSymbolic_RowMergeMacro(8);
899:                  inputcol    += 8;
900:                  rowsleft    -= 8;
901:                  L1_rowsleft -= 8;
902:                  break;
903:         }
904:         inputcol_L1           = inputcol;
905:         L1_nnz               += outputi_nnz;
906:         worki_L1[++L1_nrows]  = L1_nnz;
907:       }

909:       /********************** L E V E L  2 ************************/
910:       /* Merge from L1 work array to either C or to L2 work array */
911:       if (anzi > 8) {
912:         inputi      = worki_L1;
913:         inputj      = workj_L1;
914:         inputcol    = workcol;
915:         outputi_nnz = 0;

917:         if (anzi <= 64) outputj = cj + ci_nnz;        /* Merge from L1 work array to C */
918:         else            outputj = workj_L2 + L2_nnz;  /* Merge from L1 work array to L2 work array */

920:         switch (L1_nrows) {
921:         case 1:  brow_ptr[0] = inputj + inputi[inputcol[0]];
922:                  brow_end[0] = inputj + inputi[inputcol[0]+1];
923:                  for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
924:                  break;
925:         case 2:  MatMatMultSymbolic_RowMergeMacro(2); break;
926:         case 3:  MatMatMultSymbolic_RowMergeMacro(3); break;
927:         case 4:  MatMatMultSymbolic_RowMergeMacro(4); break;
928:         case 5:  MatMatMultSymbolic_RowMergeMacro(5); break;
929:         case 6:  MatMatMultSymbolic_RowMergeMacro(6); break;
930:         case 7:  MatMatMultSymbolic_RowMergeMacro(7); break;
931:         case 8:  MatMatMultSymbolic_RowMergeMacro(8); break;
932:         default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
933:         }
934:         L2_nnz               += outputi_nnz;
935:         worki_L2[++L2_nrows]  = L2_nnz;

937:         /************************ L E V E L  3 **********************/
938:         /* Merge from L2 work array to either C or to L2 work array */
939:         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
940:           inputi      = worki_L2;
941:           inputj      = workj_L2;
942:           inputcol    = workcol;
943:           outputi_nnz = 0;
944:           if (rowsleft) outputj = workj_L3;
945:           else          outputj = cj + ci_nnz;
946:           switch (L2_nrows) {
947:           case 1:  brow_ptr[0] = inputj + inputi[inputcol[0]];
948:                    brow_end[0] = inputj + inputi[inputcol[0]+1];
949:                    for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
950:                    break;
951:           case 2:  MatMatMultSymbolic_RowMergeMacro(2); break;
952:           case 3:  MatMatMultSymbolic_RowMergeMacro(3); break;
953:           case 4:  MatMatMultSymbolic_RowMergeMacro(4); break;
954:           case 5:  MatMatMultSymbolic_RowMergeMacro(5); break;
955:           case 6:  MatMatMultSymbolic_RowMergeMacro(6); break;
956:           case 7:  MatMatMultSymbolic_RowMergeMacro(7); break;
957:           case 8:  MatMatMultSymbolic_RowMergeMacro(8); break;
958:           default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
959:           }
960:           L2_nrows    = 1;
961:           L2_nnz      = outputi_nnz;
962:           worki_L2[1] = outputi_nnz;
963:           /* Copy to workj_L2 */
964:           if (rowsleft) {
965:             for (k=0; k<outputi_nnz; ++k)  workj_L2[k] = outputj[k];
966:           }
967:         }
968:       }
969:     }  /* while (rowsleft) */
970: #undef MatMatMultSymbolic_RowMergeMacro

972:     /* terminate current row */
973:     ci_nnz += outputi_nnz;
974:     ci[i+1] = ci_nnz;
975:   }

977:   /* Step 3: Create the new symbolic matrix */
978:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
979:   MatSetBlockSizesFromMats(*C,A,B);
980:   MatSetType(*C,((PetscObject)A)->type_name);

982:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
983:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
984:   c          = (Mat_SeqAIJ*)((*C)->data);
985:   c->free_a  = PETSC_TRUE;
986:   c->free_ij = PETSC_TRUE;
987:   c->nonew   = 0;

989:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

991:   /* set MatInfo */
992:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
993:   if (afill < 1.0) afill = 1.0;
994:   c->maxnz                     = ci[am];
995:   c->nz                        = ci[am];
996:   (*C)->info.mallocs           = ndouble;
997:   (*C)->info.fill_ratio_given  = fill;
998:   (*C)->info.fill_ratio_needed = afill;

1000: #if defined(PETSC_USE_INFO)
1001:   if (ci[am]) {
1002:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
1003:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1004:   } else {
1005:     PetscInfo((*C),"Empty matrix product\n");
1006:   }
1007: #endif

1009:   /* Step 4: Free temporary work areas */
1010:   PetscFree(workj_L1);
1011:   PetscFree(workj_L2);
1012:   PetscFree(workj_L3);
1013:   return(0);
1014: }

1016: /* concatenate unique entries and then sort */
1017: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,PetscReal fill,Mat *C)
1018: {
1019:   PetscErrorCode     ierr;
1020:   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
1021:   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
1022:   PetscInt           *ci,*cj;
1023:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
1024:   PetscReal          afill;
1025:   PetscInt           i,j,ndouble = 0;
1026:   PetscSegBuffer     seg,segrow;
1027:   char               *seen;

1030:   PetscMalloc1(am+1,&ci);
1031:   ci[0] = 0;

1033:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1034:   PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);
1035:   PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);
1036:   PetscCalloc1(bn,&seen);

1038:   /* Determine ci and cj */
1039:   for (i=0; i<am; i++) {
1040:     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 */
1041:     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
1042:     PetscInt packlen = 0,*PETSC_RESTRICT crow;
1043:     /* Pack segrow */
1044:     for (j=0; j<anzi; j++) {
1045:       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
1046:       for (k=bjstart; k<bjend; k++) {
1047:         PetscInt bcol = bj[k];
1048:         if (!seen[bcol]) { /* new entry */
1049:           PetscInt *PETSC_RESTRICT slot;
1050:           PetscSegBufferGetInts(segrow,1,&slot);
1051:           *slot = bcol;
1052:           seen[bcol] = 1;
1053:           packlen++;
1054:         }
1055:       }
1056:     }
1057:     PetscSegBufferGetInts(seg,packlen,&crow);
1058:     PetscSegBufferExtractTo(segrow,crow);
1059:     PetscSortInt(packlen,crow);
1060:     ci[i+1] = ci[i] + packlen;
1061:     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
1062:   }
1063:   PetscSegBufferDestroy(&segrow);
1064:   PetscFree(seen);

1066:   /* Column indices are in the segmented buffer */
1067:   PetscSegBufferExtractAlloc(seg,&cj);
1068:   PetscSegBufferDestroy(&seg);

1070:   /* put together the new symbolic matrix */
1071:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
1072:   MatSetBlockSizesFromMats(*C,A,B);
1073:   MatSetType(*C,((PetscObject)A)->type_name);

1075:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1076:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1077:   c          = (Mat_SeqAIJ*)((*C)->data);
1078:   c->free_a  = PETSC_TRUE;
1079:   c->free_ij = PETSC_TRUE;
1080:   c->nonew   = 0;

1082:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

1084:   /* set MatInfo */
1085:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
1086:   if (afill < 1.0) afill = 1.0;
1087:   c->maxnz                     = ci[am];
1088:   c->nz                        = ci[am];
1089:   (*C)->info.mallocs           = ndouble;
1090:   (*C)->info.fill_ratio_given  = fill;
1091:   (*C)->info.fill_ratio_needed = afill;

1093: #if defined(PETSC_USE_INFO)
1094:   if (ci[am]) {
1095:     PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);
1096:     PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1097:   } else {
1098:     PetscInfo((*C),"Empty matrix product\n");
1099:   }
1100: #endif
1101:   return(0);
1102: }

1104: /* This routine is not used. Should be removed! */
1105: PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1106: {

1110:   if (scall == MAT_INITIAL_MATRIX) {
1111:     PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);
1112:     MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
1113:     PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);
1114:   }
1115:   PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);
1116:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
1117:   PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);
1118:   return(0);
1119: }

1121: PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
1122: {
1123:   PetscErrorCode      ierr;
1124:   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
1125:   Mat_MatMatTransMult *abt=a->abt;

1128:   (abt->destroy)(A);
1129:   MatTransposeColoringDestroy(&abt->matcoloring);
1130:   MatDestroy(&abt->Bt_den);
1131:   MatDestroy(&abt->ABt_den);
1132:   PetscFree(abt);
1133:   return(0);
1134: }

1136: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1137: {
1138:   PetscErrorCode      ierr;
1139:   Mat                 Bt;
1140:   PetscInt            *bti,*btj;
1141:   Mat_MatMatTransMult *abt;
1142:   Mat_SeqAIJ          *c;

1145:   /* create symbolic Bt */
1146:   MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);
1147:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);
1148:   MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));
1149:   MatSetType(Bt,((PetscObject)A)->type_name);

1151:   /* get symbolic C=A*Bt */
1152:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);

1154:   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
1155:   PetscNew(&abt);
1156:   c      = (Mat_SeqAIJ*)(*C)->data;
1157:   c->abt = abt;

1159:   abt->usecoloring = PETSC_FALSE;
1160:   abt->destroy     = (*C)->ops->destroy;
1161:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;

1163:   PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);
1164:   if (abt->usecoloring) {
1165:     /* Create MatTransposeColoring from symbolic C=A*B^T */
1166:     MatTransposeColoring matcoloring;
1167:     MatColoring          coloring;
1168:     ISColoring           iscoloring;
1169:     Mat                  Bt_dense,C_dense;
1170:     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
1171:     /* inode causes memory problem, don't know why */
1172:     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");

1174:     MatColoringCreate(*C,&coloring);
1175:     MatColoringSetDistance(coloring,2);
1176:     MatColoringSetType(coloring,MATCOLORINGSL);
1177:     MatColoringSetFromOptions(coloring);
1178:     MatColoringApply(coloring,&iscoloring);
1179:     MatColoringDestroy(&coloring);
1180:     MatTransposeColoringCreate(*C,iscoloring,&matcoloring);

1182:     abt->matcoloring = matcoloring;

1184:     ISColoringDestroy(&iscoloring);

1186:     /* Create Bt_dense and C_dense = A*Bt_dense */
1187:     MatCreate(PETSC_COMM_SELF,&Bt_dense);
1188:     MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
1189:     MatSetType(Bt_dense,MATSEQDENSE);
1190:     MatSeqDenseSetPreallocation(Bt_dense,NULL);

1192:     Bt_dense->assembled = PETSC_TRUE;
1193:     abt->Bt_den   = Bt_dense;

1195:     MatCreate(PETSC_COMM_SELF,&C_dense);
1196:     MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);
1197:     MatSetType(C_dense,MATSEQDENSE);
1198:     MatSeqDenseSetPreallocation(C_dense,NULL);

1200:     Bt_dense->assembled = PETSC_TRUE;
1201:     abt->ABt_den  = C_dense;

1203: #if defined(PETSC_USE_INFO)
1204:     {
1205:       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
1206:       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));
1207:     }
1208: #endif
1209:   }
1210:   /* clean up */
1211:   MatDestroy(&Bt);
1212:   MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);
1213:   return(0);
1214: }

1216: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1217: {
1218:   PetscErrorCode      ierr;
1219:   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1220:   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
1221:   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
1222:   PetscLogDouble      flops=0.0;
1223:   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
1224:   Mat_MatMatTransMult *abt = c->abt;

1227:   /* clear old values in C */
1228:   if (!c->a) {
1229:     PetscCalloc1(ci[cm]+1,&ca);
1230:     c->a      = ca;
1231:     c->free_a = PETSC_TRUE;
1232:   } else {
1233:     ca =  c->a;
1234:     PetscArrayzero(ca,ci[cm]+1);
1235:   }

1237:   if (abt->usecoloring) {
1238:     MatTransposeColoring matcoloring = abt->matcoloring;
1239:     Mat                  Bt_dense,C_dense = abt->ABt_den;

1241:     /* Get Bt_dense by Apply MatTransposeColoring to B */
1242:     Bt_dense = abt->Bt_den;
1243:     MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);

1245:     /* C_dense = A*Bt_dense */
1246:     MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);

1248:     /* Recover C from C_dense */
1249:     MatTransColoringApplyDenToSp(matcoloring,C_dense,C);
1250:     return(0);
1251:   }

1253:   for (i=0; i<cm; i++) {
1254:     anzi = ai[i+1] - ai[i];
1255:     acol = aj + ai[i];
1256:     aval = aa + ai[i];
1257:     cnzi = ci[i+1] - ci[i];
1258:     ccol = cj + ci[i];
1259:     cval = ca + ci[i];
1260:     for (j=0; j<cnzi; j++) {
1261:       brow = ccol[j];
1262:       bnzj = bi[brow+1] - bi[brow];
1263:       bcol = bj + bi[brow];
1264:       bval = ba + bi[brow];

1266:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1267:       nexta = 0; nextb = 0;
1268:       while (nexta<anzi && nextb<bnzj) {
1269:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1270:         if (nexta == anzi) break;
1271:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1272:         if (nextb == bnzj) break;
1273:         if (acol[nexta] == bcol[nextb]) {
1274:           cval[j] += aval[nexta]*bval[nextb];
1275:           nexta++; nextb++;
1276:           flops += 2;
1277:         }
1278:       }
1279:     }
1280:   }
1281:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1282:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1283:   PetscLogFlops(flops);
1284:   return(0);
1285: }

1287: PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(Mat A)
1288: {
1289:   PetscErrorCode      ierr;
1290:   Mat_SeqAIJ          *a = (Mat_SeqAIJ*)A->data;
1291:   Mat_MatTransMatMult *atb = a->atb;

1294:   if (atb) {
1295:     MatDestroy(&atb->At);
1296:     (*atb->destroy)(A);
1297:   }
1298:   PetscFree(atb);
1299:   return(0);
1300: }

1302: PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1303: {
1304:   PetscErrorCode      ierr;
1305:   const char          *algTypes[2] = {"matmatmult","outerproduct"};
1306:   PetscInt            alg=0; /* set default algorithm */
1307:   Mat                 At;
1308:   Mat_MatTransMatMult *atb;
1309:   Mat_SeqAIJ          *c;

1312:   if (scall == MAT_INITIAL_MATRIX) {
1313:     PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatTransposeMatMult","Mat");
1314:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,2,algTypes[0],&alg,NULL);
1315:     PetscOptionsEnd();

1317:     switch (alg) {
1318:     case 1:
1319:       MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
1320:       break;
1321:     default:
1322:       PetscNew(&atb);
1323:       MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);
1324:       MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_INITIAL_MATRIX,fill,C);

1326:       c                  = (Mat_SeqAIJ*)(*C)->data;
1327:       c->atb             = atb;
1328:       atb->At            = At;
1329:       atb->destroy       = (*C)->ops->destroy;
1330:       (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult;

1332:       break;
1333:     }
1334:   }
1335:   if (alg) {
1336:     (*(*C)->ops->mattransposemultnumeric)(A,B,*C);
1337:   } else if (!alg && scall == MAT_REUSE_MATRIX) {
1338:     c   = (Mat_SeqAIJ*)(*C)->data;
1339:     atb = c->atb;
1340:     At  = atb->At;
1341:     MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);
1342:     MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_REUSE_MATRIX,fill,C);
1343:   }
1344:   return(0);
1345: }

1347: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1348: {
1350:   Mat            At;
1351:   PetscInt       *ati,*atj;

1354:   /* create symbolic At */
1355:   MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
1356:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);
1357:   MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));
1358:   MatSetType(At,((PetscObject)A)->type_name);

1360:   /* get symbolic C=At*B */
1361:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);

1363:   /* clean up */
1364:   MatDestroy(&At);
1365:   MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);

1367:   (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ;
1368:   return(0);
1369: }

1371: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1372: {
1374:   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1375:   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1376:   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1377:   PetscLogDouble flops=0.0;
1378:   MatScalar      *aa  =a->a,*ba,*ca,*caj;

1381:   if (!c->a) {
1382:     PetscCalloc1(ci[cm]+1,&ca);

1384:     c->a      = ca;
1385:     c->free_a = PETSC_TRUE;
1386:   } else {
1387:     ca   = c->a;
1388:     PetscArrayzero(ca,ci[cm]);
1389:   }

1391:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1392:   for (i=0; i<am; i++) {
1393:     bj   = b->j + bi[i];
1394:     ba   = b->a + bi[i];
1395:     bnzi = bi[i+1] - bi[i];
1396:     anzi = ai[i+1] - ai[i];
1397:     for (j=0; j<anzi; j++) {
1398:       nextb = 0;
1399:       crow  = *aj++;
1400:       cjj   = cj + ci[crow];
1401:       caj   = ca + ci[crow];
1402:       /* perform sparse axpy operation.  Note cjj includes bj. */
1403:       for (k=0; nextb<bnzi; k++) {
1404:         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1405:           caj[k] += (*aa)*(*(ba+nextb));
1406:           nextb++;
1407:         }
1408:       }
1409:       flops += 2*bnzi;
1410:       aa++;
1411:     }
1412:   }

1414:   /* Assemble the final matrix and clean up */
1415:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1416:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1417:   PetscLogFlops(flops);
1418:   return(0);
1419: }

1421: PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1422: {

1426:   if (scall == MAT_INITIAL_MATRIX) {
1427:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
1428:     MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
1429:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
1430:   }
1431:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
1432:   MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
1433:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
1434:   return(0);
1435: }

1437: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1438: {

1442:   MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);

1444:   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1445:   return(0);
1446: }

1448: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1449: {
1450:   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1451:   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1452:   PetscErrorCode    ierr;
1453:   PetscScalar       *c,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1454:   const PetscScalar *aa,*b,*b1,*b2,*b3,*b4,*av;
1455:   const PetscInt    *aj;
1456:   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1457:   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;

1460:   if (!cm || !cn) return(0);
1461:   MatSeqAIJGetArrayRead(A,&av);
1462:   MatDenseGetArray(C,&c);
1463:   MatDenseGetArrayRead(B,&b);
1464:   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1465:   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1466:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1467:     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1468:       r1 = r2 = r3 = r4 = 0.0;
1469:       n  = a->i[i+1] - a->i[i];
1470:       aj = a->j + a->i[i];
1471:       aa = av + a->i[i];
1472:       for (j=0; j<n; j++) {
1473:         aatmp = aa[j]; ajtmp = aj[j];
1474:         r1 += aatmp*b1[ajtmp];
1475:         r2 += aatmp*b2[ajtmp];
1476:         r3 += aatmp*b3[ajtmp];
1477:         r4 += aatmp*b4[ajtmp];
1478:       }
1479:       c1[i] += r1;
1480:       c2[i] += r2;
1481:       c3[i] += r3;
1482:       c4[i] += r4;
1483:     }
1484:     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1485:     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1486:   }
1487:   for (; col<cn; col++) {   /* over extra columns of C */
1488:     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1489:       r1 = 0.0;
1490:       n  = a->i[i+1] - a->i[i];
1491:       aj = a->j + a->i[i];
1492:       aa = av + a->i[i];
1493:       for (j=0; j<n; j++) {
1494:         r1 += aa[j]*b1[aj[j]];
1495:       }
1496:       c1[i] += r1;
1497:     }
1498:     b1 += bm;
1499:     c1 += am;
1500:   }
1501:   PetscLogFlops(cn*(2.0*a->nz));
1502:   MatDenseRestoreArray(C,&c);
1503:   MatDenseRestoreArrayRead(B,&b);
1504:   MatSeqAIJRestoreArrayRead(A,&av);
1505:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1506:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1507:   return(0);
1508: }

1510: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1511: {

1515:   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);
1516:   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);
1517:   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);

1519:   MatZeroEntries(C);
1520:   MatMatMultNumericAdd_SeqAIJ_SeqDense(A,B,C);
1521:   return(0);
1522: }

1524: PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1525: {
1527:   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1528:   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1529:   PetscInt       *bi      = b->i,*bj=b->j;
1530:   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1531:   MatScalar      *btval,*btval_den,*ba=b->a;
1532:   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;

1535:   btval_den=btdense->v;
1536:   PetscArrayzero(btval_den,m*n);
1537:   for (k=0; k<ncolors; k++) {
1538:     ncolumns = coloring->ncolumns[k];
1539:     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1540:       col   = *(columns + colorforcol[k] + l);
1541:       btcol = bj + bi[col];
1542:       btval = ba + bi[col];
1543:       anz   = bi[col+1] - bi[col];
1544:       for (j=0; j<anz; j++) {
1545:         brow            = btcol[j];
1546:         btval_den[brow] = btval[j];
1547:       }
1548:     }
1549:     btval_den += m;
1550:   }
1551:   return(0);
1552: }

1554: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1555: {
1556:   PetscErrorCode    ierr;
1557:   Mat_SeqAIJ        *csp = (Mat_SeqAIJ*)Csp->data;
1558:   const PetscScalar *ca_den,*ca_den_ptr;
1559:   PetscScalar       *ca=csp->a;
1560:   PetscInt          k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1561:   PetscInt          brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1562:   PetscInt          nrows,*row,*idx;
1563:   PetscInt          *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;

1566:   MatDenseGetArrayRead(Cden,&ca_den);

1568:   if (brows > 0) {
1569:     PetscInt *lstart,row_end,row_start;
1570:     lstart = matcoloring->lstart;
1571:     PetscArrayzero(lstart,ncolors);

1573:     row_end = brows;
1574:     if (row_end > m) row_end = m;
1575:     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1576:       ca_den_ptr = ca_den;
1577:       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1578:         nrows = matcoloring->nrows[k];
1579:         row   = rows  + colorforrow[k];
1580:         idx   = den2sp + colorforrow[k];
1581:         for (l=lstart[k]; l<nrows; l++) {
1582:           if (row[l] >= row_end) {
1583:             lstart[k] = l;
1584:             break;
1585:           } else {
1586:             ca[idx[l]] = ca_den_ptr[row[l]];
1587:           }
1588:         }
1589:         ca_den_ptr += m;
1590:       }
1591:       row_end += brows;
1592:       if (row_end > m) row_end = m;
1593:     }
1594:   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1595:     ca_den_ptr = ca_den;
1596:     for (k=0; k<ncolors; k++) {
1597:       nrows = matcoloring->nrows[k];
1598:       row   = rows  + colorforrow[k];
1599:       idx   = den2sp + colorforrow[k];
1600:       for (l=0; l<nrows; l++) {
1601:         ca[idx[l]] = ca_den_ptr[row[l]];
1602:       }
1603:       ca_den_ptr += m;
1604:     }
1605:   }

1607:   MatDenseRestoreArrayRead(Cden,&ca_den);
1608: #if defined(PETSC_USE_INFO)
1609:   if (matcoloring->brows > 0) {
1610:     PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);
1611:   } else {
1612:     PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");
1613:   }
1614: #endif
1615:   return(0);
1616: }

1618: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1619: {
1621:   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1622:   const PetscInt *is,*ci,*cj,*row_idx;
1623:   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1624:   IS             *isa;
1625:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1626:   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1627:   PetscInt       *colorforcol,*columns,*columns_i,brows;
1628:   PetscBool      flg;

1631:   ISColoringGetIS(iscoloring,PETSC_USE_POINTER,PETSC_IGNORE,&isa);

1633:   /* bs >1 is not being tested yet! */
1634:   Nbs       = mat->cmap->N/bs;
1635:   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1636:   c->N      = Nbs;
1637:   c->m      = c->M;
1638:   c->rstart = 0;
1639:   c->brows  = 100;

1641:   c->ncolors = nis;
1642:   PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);
1643:   PetscMalloc1(csp->nz+1,&rows);
1644:   PetscMalloc1(csp->nz+1,&den2sp);

1646:   brows = c->brows;
1647:   PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);
1648:   if (flg) c->brows = brows;
1649:   if (brows > 0) {
1650:     PetscMalloc1(nis+1,&c->lstart);
1651:   }

1653:   colorforrow[0] = 0;
1654:   rows_i         = rows;
1655:   den2sp_i       = den2sp;

1657:   PetscMalloc1(nis+1,&colorforcol);
1658:   PetscMalloc1(Nbs+1,&columns);

1660:   colorforcol[0] = 0;
1661:   columns_i      = columns;

1663:   /* get column-wise storage of mat */
1664:   MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);

1666:   cm   = c->m;
1667:   PetscMalloc1(cm+1,&rowhit);
1668:   PetscMalloc1(cm+1,&idxhit);
1669:   for (i=0; i<nis; i++) { /* loop over color */
1670:     ISGetLocalSize(isa[i],&n);
1671:     ISGetIndices(isa[i],&is);

1673:     c->ncolumns[i] = n;
1674:     if (n) {
1675:       PetscArraycpy(columns_i,is,n);
1676:     }
1677:     colorforcol[i+1] = colorforcol[i] + n;
1678:     columns_i       += n;

1680:     /* fast, crude version requires O(N*N) work */
1681:     PetscArrayzero(rowhit,cm);

1683:     for (j=0; j<n; j++) { /* loop over columns*/
1684:       col     = is[j];
1685:       row_idx = cj + ci[col];
1686:       m       = ci[col+1] - ci[col];
1687:       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1688:         idxhit[*row_idx]   = spidx[ci[col] + k];
1689:         rowhit[*row_idx++] = col + 1;
1690:       }
1691:     }
1692:     /* count the number of hits */
1693:     nrows = 0;
1694:     for (j=0; j<cm; j++) {
1695:       if (rowhit[j]) nrows++;
1696:     }
1697:     c->nrows[i]      = nrows;
1698:     colorforrow[i+1] = colorforrow[i] + nrows;

1700:     nrows = 0;
1701:     for (j=0; j<cm; j++) { /* loop over rows */
1702:       if (rowhit[j]) {
1703:         rows_i[nrows]   = j;
1704:         den2sp_i[nrows] = idxhit[j];
1705:         nrows++;
1706:       }
1707:     }
1708:     den2sp_i += nrows;

1710:     ISRestoreIndices(isa[i],&is);
1711:     rows_i += nrows;
1712:   }
1713:   MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);
1714:   PetscFree(rowhit);
1715:   ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&isa);
1716:   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);

1718:   c->colorforrow = colorforrow;
1719:   c->rows        = rows;
1720:   c->den2sp      = den2sp;
1721:   c->colorforcol = colorforcol;
1722:   c->columns     = columns;

1724:   PetscFree(idxhit);
1725:   return(0);
1726: }

1728: /* The combine method has done the symbolic and numeric in the first phase, and so we just return here */
1729: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,Mat C)
1730: {
1732:   /* Empty function */
1733:   return(0);
1734: }

1736: /* This algorithm combines the symbolic and numeric phase of matrix-matrix multiplication. */
1737: PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,PetscReal fill,Mat *C)
1738: {
1739:   PetscErrorCode     ierr;
1740:   PetscLogDouble     flops=0.0;
1741:   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
1742:   const PetscInt     *ai=a->i,*bi=b->i;
1743:   PetscInt           *ci,*cj,*cj_i;
1744:   PetscScalar        *ca,*ca_i;
1745:   PetscInt           b_maxmemrow,c_maxmem,a_col;
1746:   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
1747:   PetscInt           i,k,ndouble=0;
1748:   PetscReal          afill;
1749:   PetscScalar        *c_row_val_dense;
1750:   PetscBool          *c_row_idx_flags;
1751:   PetscInt           *aj_i=a->j;
1752:   PetscScalar        *aa_i=a->a;


1756:   /* Step 1: Determine upper bounds on memory for C and allocate memory */
1757:   /* This should be enough for almost all matrices. If still more memory is needed, it is reallocated later. */
1758:   c_maxmem    = 8*(ai[am]+bi[bm]);
1759:   b_maxmemrow = PetscMin(bi[bm],bn);
1760:   PetscMalloc1(am+1,&ci);
1761:   PetscCalloc1(bn,&c_row_val_dense);
1762:   PetscCalloc1(bn,&c_row_idx_flags);
1763:   PetscMalloc1(c_maxmem,&cj);
1764:   PetscMalloc1(c_maxmem,&ca);
1765:   ca_i  = ca;
1766:   cj_i  = cj;
1767:   ci[0] = 0;
1768:   for (i=0; i<am; i++) {
1769:     /* Step 2: Initialize the dense row vector for C  */
1770:     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 */
1771:     PetscInt       cnzi = 0;
1772:     PetscInt       *bj_i;
1773:     PetscScalar    *ba_i;
1774:     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory
1775:        Usually, there is enough memory in the first place, so this is not executed. */
1776:     while (ci[i] + b_maxmemrow > c_maxmem) {
1777:       c_maxmem *= 2;
1778:       ndouble++;
1779:       PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);
1780:       PetscRealloc(sizeof(PetscScalar)*c_maxmem,&ca);
1781:     }

1783:     /* Step 3: Do the numerical calculations */
1784:     for (a_col=0; a_col<anzi; a_col++) {          /* iterate over all non zero values in a row of A */
1785:       PetscInt       a_col_index = aj_i[a_col];
1786:       const PetscInt bnzi        = bi[a_col_index+1] - bi[a_col_index];
1787:       flops += 2*bnzi;
1788:       bj_i   = b->j + bi[a_col_index];   /* points to the current row in bj */
1789:       ba_i   = b->a + bi[a_col_index];   /* points to the current row in ba */
1790:       for (k=0; k<bnzi; ++k) { /* iterate over all non zeros of this row in B */
1791:         if (c_row_idx_flags[bj_i[k]] == PETSC_FALSE) {
1792:           cj_i[cnzi++]             = bj_i[k];
1793:           c_row_idx_flags[bj_i[k]] = PETSC_TRUE;
1794:         }
1795:         c_row_val_dense[bj_i[k]] += aa_i[a_col] * ba_i[k];
1796:       }
1797:     }

1799:     /* Sort array */
1800:     PetscSortInt(cnzi,cj_i);
1801:     /* Step 4 */
1802:     for (k=0; k<cnzi; k++) {
1803:       ca_i[k]                  = c_row_val_dense[cj_i[k]];
1804:       c_row_val_dense[cj_i[k]] = 0.;
1805:       c_row_idx_flags[cj_i[k]] = PETSC_FALSE;
1806:     }
1807:     /* terminate current row */
1808:     aa_i   += anzi;
1809:     aj_i   += anzi;
1810:     ca_i   += cnzi;
1811:     cj_i   += cnzi;
1812:     ci[i+1] = ci[i] + cnzi;
1813:     flops  += cnzi;
1814:   }

1816:   /* Step 5 */
1817:   /* Create the new matrix */
1818:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);
1819:   MatSetBlockSizesFromMats(*C,A,B);
1820:   MatSetType(*C,((PetscObject)A)->type_name);

1822:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1823:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1824:   c          = (Mat_SeqAIJ*)((*C)->data);
1825:   c->a       = ca;
1826:   c->free_a  = PETSC_TRUE;
1827:   c->free_ij = PETSC_TRUE;
1828:   c->nonew   = 0;

1830:   /* set MatInfo */
1831:   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
1832:   if (afill < 1.0) afill = 1.0;
1833:   c->maxnz                     = ci[am];
1834:   c->nz                        = ci[am];
1835:   (*C)->info.mallocs           = ndouble;
1836:   (*C)->info.fill_ratio_given  = fill;
1837:   (*C)->info.fill_ratio_needed = afill;
1838:   (*C)->ops->matmultnumeric    = MatMatMultNumeric_SeqAIJ_SeqAIJ_Combined;

1840:   PetscFree(c_row_val_dense);
1841:   PetscFree(c_row_idx_flags);

1843:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
1844:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);
1845:   PetscLogFlops(flops);
1846:   return(0);
1847: }