Actual source code: matmatmult.c

  1: /*
  2:   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
  3:           C = A * B
  4: */

  6: #include <../src/mat/impls/aij/seq/aij.h>
  7: #include <../src/mat/utils/freespace.h>
  8: #include <petscbt.h>
  9: #include <petsc/private/isimpl.h>
 10: #include <../src/mat/impls/dense/seq/dense.h>

 12: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
 13: {
 14:   PetscFunctionBegin;
 15:   if (C->ops->matmultnumeric) PetscCall((*C->ops->matmultnumeric)(A, B, C));
 16:   else PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A, B, C));
 17:   PetscFunctionReturn(PETSC_SUCCESS);
 18: }

 20: /* Modified from MatCreateSeqAIJWithArrays() */
 21: PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], MatType mtype, Mat mat)
 22: {
 23:   PetscInt    ii;
 24:   Mat_SeqAIJ *aij;
 25:   PetscBool   isseqaij, ofree_a, ofree_ij;

 27:   PetscFunctionBegin;
 28:   PetscCheck(m <= 0 || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
 29:   PetscCall(MatSetSizes(mat, m, n, m, n));

 31:   if (!mtype) {
 32:     PetscCall(PetscObjectBaseTypeCompare((PetscObject)mat, MATSEQAIJ, &isseqaij));
 33:     if (!isseqaij) PetscCall(MatSetType(mat, MATSEQAIJ));
 34:   } else {
 35:     PetscCall(MatSetType(mat, mtype));
 36:   }

 38:   aij      = (Mat_SeqAIJ *)mat->data;
 39:   ofree_a  = aij->free_a;
 40:   ofree_ij = aij->free_ij;
 41:   /* changes the free flags */
 42:   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat, MAT_SKIP_ALLOCATION, NULL));

 44:   PetscCall(PetscFree(aij->ilen));
 45:   PetscCall(PetscFree(aij->imax));
 46:   PetscCall(PetscMalloc1(m, &aij->imax));
 47:   PetscCall(PetscMalloc1(m, &aij->ilen));
 48:   for (ii = 0, aij->nonzerorowcnt = 0, aij->rmax = 0; ii < m; ii++) {
 49:     const PetscInt rnz = i[ii + 1] - i[ii];
 50:     aij->nonzerorowcnt += !!rnz;
 51:     aij->rmax     = PetscMax(aij->rmax, rnz);
 52:     aij->ilen[ii] = aij->imax[ii] = i[ii + 1] - i[ii];
 53:   }
 54:   aij->maxnz = i[m];
 55:   aij->nz    = i[m];

 57:   if (ofree_a) PetscCall(PetscShmgetDeallocateArray((void **)&aij->a));
 58:   if (ofree_ij) PetscCall(PetscShmgetDeallocateArray((void **)&aij->j));
 59:   if (ofree_ij) PetscCall(PetscShmgetDeallocateArray((void **)&aij->i));

 61:   aij->i       = i;
 62:   aij->j       = j;
 63:   aij->a       = a;
 64:   aij->nonew   = -1; /* this indicates that inserting a new value in the matrix that generates a new nonzero is an error */
 65:   aij->free_a  = PETSC_FALSE;
 66:   aij->free_ij = PETSC_FALSE;
 67:   PetscCall(MatCheckCompressedRow(mat, aij->nonzerorowcnt, &aij->compressedrow, aij->i, m, 0.6));
 68:   // Always build the diag info when i, j are set
 69:   PetscFunctionReturn(PETSC_SUCCESS);
 70: }

 72: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
 73: {
 74:   Mat_Product        *product = C->product;
 75:   MatProductAlgorithm alg;
 76:   PetscBool           flg;

 78:   PetscFunctionBegin;
 79:   if (product) {
 80:     alg = product->alg;
 81:   } else {
 82:     alg = "sorted";
 83:   }
 84:   /* sorted */
 85:   PetscCall(PetscStrcmp(alg, "sorted", &flg));
 86:   if (flg) {
 87:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A, B, fill, C));
 88:     PetscFunctionReturn(PETSC_SUCCESS);
 89:   }

 91:   /* scalable */
 92:   PetscCall(PetscStrcmp(alg, "scalable", &flg));
 93:   if (flg) {
 94:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A, B, fill, C));
 95:     PetscFunctionReturn(PETSC_SUCCESS);
 96:   }

 98:   /* scalable_fast */
 99:   PetscCall(PetscStrcmp(alg, "scalable_fast", &flg));
100:   if (flg) {
101:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A, B, fill, C));
102:     PetscFunctionReturn(PETSC_SUCCESS);
103:   }

105:   /* heap */
106:   PetscCall(PetscStrcmp(alg, "heap", &flg));
107:   if (flg) {
108:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A, B, fill, C));
109:     PetscFunctionReturn(PETSC_SUCCESS);
110:   }

112:   /* btheap */
113:   PetscCall(PetscStrcmp(alg, "btheap", &flg));
114:   if (flg) {
115:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A, B, fill, C));
116:     PetscFunctionReturn(PETSC_SUCCESS);
117:   }

119:   /* llcondensed */
120:   PetscCall(PetscStrcmp(alg, "llcondensed", &flg));
121:   if (flg) {
122:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A, B, fill, C));
123:     PetscFunctionReturn(PETSC_SUCCESS);
124:   }

126:   /* rowmerge */
127:   PetscCall(PetscStrcmp(alg, "rowmerge", &flg));
128:   if (flg) {
129:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A, B, fill, C));
130:     PetscFunctionReturn(PETSC_SUCCESS);
131:   }

133: #if defined(PETSC_HAVE_HYPRE)
134:   PetscCall(PetscStrcmp(alg, "hypre", &flg));
135:   if (flg) {
136:     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
137:     PetscFunctionReturn(PETSC_SUCCESS);
138:   }
139: #endif

141:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
142: }

144: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A, Mat B, PetscReal fill, Mat C)
145: {
146:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
147:   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
148:   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
149:   PetscReal          afill;
150:   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
151:   PetscHMapI         ta;
152:   PetscBT            lnkbt;
153:   PetscFreeSpaceList free_space = NULL, current_space = NULL;

155:   PetscFunctionBegin;
156:   /* Get ci and cj */
157:   /* Allocate ci array, arrays for fill computation and */
158:   /* free space for accumulating nonzero column info */
159:   PetscCall(PetscMalloc1(am + 2, &ci));
160:   ci[0] = 0;

162:   /* create and initialize a linked list */
163:   PetscCall(PetscHMapICreateWithSize(bn, &ta));
164:   MatRowMergeMax_SeqAIJ(b, bm, ta);
165:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
166:   PetscCall(PetscHMapIDestroy(&ta));

168:   PetscCall(PetscLLCondensedCreate(Crmax, bn, &lnk, &lnkbt));

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

173:   current_space = free_space;

175:   /* Determine ci and cj */
176:   for (i = 0; i < am; i++) {
177:     anzi = ai[i + 1] - ai[i];
178:     aj   = a->j + ai[i];
179:     for (j = 0; j < anzi; j++) {
180:       brow = aj[j];
181:       bnzj = bi[brow + 1] - bi[brow];
182:       bj   = b->j + bi[brow];
183:       /* add non-zero cols of B into the sorted linked list lnk */
184:       PetscCall(PetscLLCondensedAddSorted(bnzj, bj, lnk, lnkbt));
185:     }
186:     /* add possible missing diagonal entry */
187:     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted(1, &i, lnk, lnkbt));
188:     cnzi = lnk[0];

190:     /* If free space is not available, make more free space */
191:     /* Double the amount of total space in the list */
192:     if (current_space->local_remaining < cnzi) {
193:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
194:       ndouble++;
195:     }

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

200:     current_space->array += cnzi;
201:     current_space->local_used += cnzi;
202:     current_space->local_remaining -= cnzi;

204:     ci[i + 1] = ci[i] + cnzi;
205:   }

207:   /* Column indices are in the list of free space */
208:   /* Allocate space for cj, initialize cj, and */
209:   /* destroy list of free space and other temporary array(s) */
210:   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
211:   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
212:   PetscCall(PetscLLCondensedDestroy(lnk, lnkbt));

214:   /* put together the new symbolic matrix */
215:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
216:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

218:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
219:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
220:   c          = (Mat_SeqAIJ *)C->data;
221:   c->free_a  = PETSC_FALSE;
222:   c->free_ij = PETSC_TRUE;
223:   c->nonew   = 0;

225:   /* fast, needs non-scalable O(bn) array 'abdense' */
226:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

228:   /* set MatInfo */
229:   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
230:   if (afill < 1.0) afill = 1.0;
231:   C->info.mallocs           = ndouble;
232:   C->info.fill_ratio_given  = fill;
233:   C->info.fill_ratio_needed = afill;

235: #if defined(PETSC_USE_INFO)
236:   if (ci[am]) {
237:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
238:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
239:   } else {
240:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
241:   }
242: #endif
243:   PetscFunctionReturn(PETSC_SUCCESS);
244: }

246: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, Mat C)
247: {
248:   PetscLogDouble     flops = 0.0;
249:   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
250:   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
251:   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
252:   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
253:   PetscInt           am = A->rmap->n, cm = C->rmap->n;
254:   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
255:   PetscScalar       *ca, valtmp;
256:   PetscScalar       *ab_dense;
257:   PetscContainer     cab_dense;
258:   const PetscScalar *aa, *ba, *baj;

260:   PetscFunctionBegin;
261:   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
262:   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
263:   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
264:     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
265:     c->a      = ca;
266:     c->free_a = PETSC_TRUE;
267:   } else ca = c->a;

269:   /* TODO this should be done in the symbolic phase */
270:   /* However, this function is so heavily used (sometimes in an hidden way through multnumeric function pointers
271:      that is hard to eradicate) */
272:   PetscCall(PetscObjectQuery((PetscObject)C, "__PETSc__ab_dense", (PetscObject *)&cab_dense));
273:   if (!cab_dense) {
274:     PetscCall(PetscMalloc1(B->cmap->N, &ab_dense));
275:     PetscCall(PetscObjectContainerCompose((PetscObject)C, "__PETSc__ab_dense", ab_dense, PetscCtxDestroyDefault));
276:   } else PetscCall(PetscContainerGetPointer(cab_dense, (void **)&ab_dense));
277:   PetscCall(PetscArrayzero(ab_dense, B->cmap->N));

279:   /* clean old values in C */
280:   PetscCall(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:     for (j = 0; j < anzi; j++) {
287:       brow = aj[j];
288:       bnzi = bi[brow + 1] - bi[brow];
289:       bjj  = PetscSafePointerPlusOffset(bj, bi[brow]);
290:       baj  = PetscSafePointerPlusOffset(ba, bi[brow]);
291:       /* perform dense axpy */
292:       valtmp = aa[j];
293:       for (k = 0; k < bnzi; k++) ab_dense[bjj[k]] += valtmp * baj[k];
294:       flops += 2 * bnzi;
295:     }
296:     aj = PetscSafePointerPlusOffset(aj, anzi);
297:     aa = PetscSafePointerPlusOffset(aa, anzi);

299:     cnzi = ci[i + 1] - ci[i];
300:     for (k = 0; k < cnzi; k++) {
301:       ca[k] += ab_dense[cj[k]];
302:       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
303:     }
304:     flops += cnzi;
305:     cj = PetscSafePointerPlusOffset(cj, cnzi);
306:     ca += cnzi;
307:   }
308: #if defined(PETSC_HAVE_DEVICE)
309:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
310: #endif
311:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
312:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
313:   PetscCall(PetscLogFlops(flops));
314:   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
315:   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
316:   PetscFunctionReturn(PETSC_SUCCESS);
317: }

319: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, Mat C)
320: {
321:   PetscLogDouble     flops = 0.0;
322:   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
323:   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
324:   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
325:   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
326:   PetscInt           am = A->rmap->N, cm = C->rmap->N;
327:   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
328:   PetscScalar       *ca = c->a, valtmp;
329:   const PetscScalar *aa, *ba, *baj;
330:   PetscInt           nextb;

332:   PetscFunctionBegin;
333:   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
334:   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
335:   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
336:     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
337:     c->a      = ca;
338:     c->free_a = PETSC_TRUE;
339:   }

341:   /* clean old values in C */
342:   PetscCall(PetscArrayzero(ca, ci[cm]));
343:   /* Traverse A row-wise. */
344:   /* Build the ith row in C by summing over nonzero columns in A, */
345:   /* the rows of B corresponding to nonzeros of A. */
346:   for (i = 0; i < am; i++) {
347:     anzi = ai[i + 1] - ai[i];
348:     cnzi = ci[i + 1] - ci[i];
349:     for (j = 0; j < anzi; j++) {
350:       brow = aj[j];
351:       bnzi = bi[brow + 1] - bi[brow];
352:       bjj  = bj + bi[brow];
353:       baj  = ba + bi[brow];
354:       /* perform sparse axpy */
355:       valtmp = aa[j];
356:       nextb  = 0;
357:       for (k = 0; nextb < bnzi; k++) {
358:         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
359:           ca[k] += valtmp * baj[nextb++];
360:         }
361:       }
362:       flops += 2 * bnzi;
363:     }
364:     aj += anzi;
365:     aa += anzi;
366:     cj += cnzi;
367:     ca += cnzi;
368:   }
369: #if defined(PETSC_HAVE_DEVICE)
370:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
371: #endif
372:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
373:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
374:   PetscCall(PetscLogFlops(flops));
375:   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
376:   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
377:   PetscFunctionReturn(PETSC_SUCCESS);
378: }

380: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A, Mat B, PetscReal fill, Mat C)
381: {
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, *lnk, ndouble = 0, Crmax;
388:   PetscHMapI         ta;
389:   PetscFreeSpaceList free_space = NULL, current_space = NULL;

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

397:   /* create and initialize a linked list */
398:   PetscCall(PetscHMapICreateWithSize(bn, &ta));
399:   MatRowMergeMax_SeqAIJ(b, bm, ta);
400:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
401:   PetscCall(PetscHMapIDestroy(&ta));

403:   PetscCall(PetscLLCondensedCreate_fast(Crmax, &lnk));

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

409:   /* Determine ci and cj */
410:   for (i = 0; i < am; i++) {
411:     anzi = ai[i + 1] - ai[i];
412:     aj   = a->j + ai[i];
413:     for (j = 0; j < anzi; j++) {
414:       brow = aj[j];
415:       bnzj = bi[brow + 1] - bi[brow];
416:       bj   = b->j + bi[brow];
417:       /* add non-zero cols of B into the sorted linked list lnk */
418:       PetscCall(PetscLLCondensedAddSorted_fast(bnzj, bj, lnk));
419:     }
420:     /* add possible missing diagonal entry */
421:     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_fast(1, &i, lnk));
422:     cnzi = lnk[1];

424:     /* If free space is not available, make more free space */
425:     /* Double the amount of total space in the list */
426:     if (current_space->local_remaining < cnzi) {
427:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
428:       ndouble++;
429:     }

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

434:     current_space->array += cnzi;
435:     current_space->local_used += cnzi;
436:     current_space->local_remaining -= cnzi;

438:     ci[i + 1] = ci[i] + cnzi;
439:   }

441:   /* Column indices are in the list of free space */
442:   /* Allocate space for cj, initialize cj, and */
443:   /* destroy list of free space and other temporary array(s) */
444:   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
445:   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
446:   PetscCall(PetscLLCondensedDestroy_fast(lnk));

448:   /* Allocate space for ca */
449:   PetscCall(PetscCalloc1(ci[am] + 1, &ca));

451:   /* put together the new symbolic matrix */
452:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
453:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

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

462:   /* slower, less memory */
463:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;

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

472: #if defined(PETSC_USE_INFO)
473:   if (ci[am]) {
474:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
475:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
476:   } else {
477:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
478:   }
479: #endif
480:   PetscFunctionReturn(PETSC_SUCCESS);
481: }

483: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, PetscReal fill, Mat C)
484: {
485:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
486:   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
487:   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
488:   MatScalar         *ca;
489:   PetscReal          afill;
490:   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
491:   PetscHMapI         ta;
492:   PetscFreeSpaceList free_space = NULL, current_space = NULL;

494:   PetscFunctionBegin;
495:   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
496:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
497:   PetscCall(PetscMalloc1(am + 2, &ci));
498:   ci[0] = 0;

500:   /* create and initialize a linked list */
501:   PetscCall(PetscHMapICreateWithSize(bn, &ta));
502:   MatRowMergeMax_SeqAIJ(b, bm, ta);
503:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
504:   PetscCall(PetscHMapIDestroy(&ta));
505:   PetscCall(PetscLLCondensedCreate_Scalable(Crmax, &lnk));

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

511:   /* Determine ci and cj */
512:   for (i = 0; i < am; i++) {
513:     anzi = ai[i + 1] - ai[i];
514:     aj   = a->j + ai[i];
515:     for (j = 0; j < anzi; j++) {
516:       brow = aj[j];
517:       bnzj = bi[brow + 1] - bi[brow];
518:       bj   = b->j + bi[brow];
519:       /* add non-zero cols of B into the sorted linked list lnk */
520:       PetscCall(PetscLLCondensedAddSorted_Scalable(bnzj, bj, lnk));
521:     }
522:     /* add possible missing diagonal entry */
523:     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_Scalable(1, &i, lnk));

525:     cnzi = lnk[0];

527:     /* If free space is not available, make more free space */
528:     /* Double the amount of total space in the list */
529:     if (current_space->local_remaining < cnzi) {
530:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
531:       ndouble++;
532:     }

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

537:     current_space->array += cnzi;
538:     current_space->local_used += cnzi;
539:     current_space->local_remaining -= cnzi;

541:     ci[i + 1] = ci[i] + cnzi;
542:   }

544:   /* Column indices are in the list of free space */
545:   /* Allocate space for cj, initialize cj, and */
546:   /* destroy list of free space and other temporary array(s) */
547:   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
548:   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
549:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

551:   /* Allocate space for ca */
552:   PetscCall(PetscCalloc1(ci[am] + 1, &ca));

554:   /* put together the new symbolic matrix */
555:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
556:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

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

565:   /* slower, less memory */
566:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;

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

575: #if defined(PETSC_USE_INFO)
576:   if (ci[am]) {
577:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
578:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
579:   } else {
580:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
581:   }
582: #endif
583:   PetscFunctionReturn(PETSC_SUCCESS);
584: }

586: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A, Mat B, PetscReal fill, Mat C)
587: {
588:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
589:   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
590:   PetscInt          *ci, *cj, *bb;
591:   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
592:   PetscReal          afill;
593:   PetscInt           i, j, col, ndouble = 0;
594:   PetscFreeSpaceList free_space = NULL, current_space = NULL;
595:   PetscHeap          h;

597:   PetscFunctionBegin;
598:   /* Get ci and cj - by merging sorted rows using a heap */
599:   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
600:   PetscCall(PetscMalloc1(am + 2, &ci));
601:   ci[0] = 0;

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

607:   PetscCall(PetscHeapCreate(a->rmax, &h));
608:   PetscCall(PetscMalloc1(a->rmax, &bb));

610:   /* Determine ci and cj */
611:   for (i = 0; i < am; i++) {
612:     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 */
613:     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
614:     ci[i + 1]            = ci[i];
615:     /* Populate the min heap */
616:     for (j = 0; j < anzi; j++) {
617:       bb[j] = bi[acol[j]];           /* bb points at the start of the row */
618:       if (bb[j] < bi[acol[j] + 1]) { /* Add if row is nonempty */
619:         PetscCall(PetscHeapAdd(h, j, bj[bb[j]++]));
620:       }
621:     }
622:     /* Pick off the min element, adding it to free space */
623:     PetscCall(PetscHeapPop(h, &j, &col));
624:     while (j >= 0) {
625:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
626:         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
627:         ndouble++;
628:       }
629:       *(current_space->array++) = col;
630:       current_space->local_used++;
631:       current_space->local_remaining--;
632:       ci[i + 1]++;

634:       /* stash if anything else remains in this row of B */
635:       if (bb[j] < bi[acol[j] + 1]) PetscCall(PetscHeapStash(h, j, bj[bb[j]++]));
636:       while (1) { /* pop and stash any other rows of B that also had an entry in this column */
637:         PetscInt j2, col2;
638:         PetscCall(PetscHeapPeek(h, &j2, &col2));
639:         if (col2 != col) break;
640:         PetscCall(PetscHeapPop(h, &j2, &col2));
641:         if (bb[j2] < bi[acol[j2] + 1]) PetscCall(PetscHeapStash(h, j2, bj[bb[j2]++]));
642:       }
643:       /* Put any stashed elements back into the min heap */
644:       PetscCall(PetscHeapUnstash(h));
645:       PetscCall(PetscHeapPop(h, &j, &col));
646:     }
647:   }
648:   PetscCall(PetscFree(bb));
649:   PetscCall(PetscHeapDestroy(&h));

651:   /* Column indices are in the list of free space */
652:   /* Allocate space for cj, initialize cj, and */
653:   /* destroy list of free space and other temporary array(s) */
654:   PetscCall(PetscMalloc1(ci[am], &cj));
655:   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));

657:   /* put together the new symbolic matrix */
658:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
659:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

661:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
662:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
663:   c          = (Mat_SeqAIJ *)C->data;
664:   c->free_a  = PETSC_TRUE;
665:   c->free_ij = PETSC_TRUE;
666:   c->nonew   = 0;

668:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

670:   /* set MatInfo */
671:   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
672:   if (afill < 1.0) afill = 1.0;
673:   C->info.mallocs           = ndouble;
674:   C->info.fill_ratio_given  = fill;
675:   C->info.fill_ratio_needed = afill;

677: #if defined(PETSC_USE_INFO)
678:   if (ci[am]) {
679:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
680:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
681:   } else {
682:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
683:   }
684: #endif
685:   PetscFunctionReturn(PETSC_SUCCESS);
686: }

688: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A, Mat B, PetscReal fill, Mat C)
689: {
690:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
691:   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
692:   PetscInt          *ci, *cj, *bb;
693:   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
694:   PetscReal          afill;
695:   PetscInt           i, j, col, ndouble = 0;
696:   PetscFreeSpaceList free_space = NULL, current_space = NULL;
697:   PetscHeap          h;
698:   PetscBT            bt;

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

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

709:   current_space = free_space;

711:   PetscCall(PetscHeapCreate(a->rmax, &h));
712:   PetscCall(PetscMalloc1(a->rmax, &bb));
713:   PetscCall(PetscBTCreate(bn, &bt));

715:   /* Determine ci and cj */
716:   for (i = 0; i < am; i++) {
717:     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 */
718:     const PetscInt *acol = aj + ai[i];           /* column indices of nonzero entries in this row */
719:     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
720:     ci[i + 1]            = ci[i];
721:     /* Populate the min heap */
722:     for (j = 0; j < anzi; j++) {
723:       PetscInt brow = acol[j];
724:       for (bb[j] = bi[brow]; bb[j] < bi[brow + 1]; bb[j]++) {
725:         PetscInt bcol = bj[bb[j]];
726:         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
727:           PetscCall(PetscHeapAdd(h, j, bcol));
728:           bb[j]++;
729:           break;
730:         }
731:       }
732:     }
733:     /* Pick off the min element, adding it to free space */
734:     PetscCall(PetscHeapPop(h, &j, &col));
735:     while (j >= 0) {
736:       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
737:         fptr = NULL;                            /* need PetscBTMemzero */
738:         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
739:         ndouble++;
740:       }
741:       *(current_space->array++) = col;
742:       current_space->local_used++;
743:       current_space->local_remaining--;
744:       ci[i + 1]++;

746:       /* stash if anything else remains in this row of B */
747:       for (; bb[j] < bi[acol[j] + 1]; bb[j]++) {
748:         PetscInt bcol = bj[bb[j]];
749:         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
750:           PetscCall(PetscHeapAdd(h, j, bcol));
751:           bb[j]++;
752:           break;
753:         }
754:       }
755:       PetscCall(PetscHeapPop(h, &j, &col));
756:     }
757:     if (fptr) { /* Clear the bits for this row */
758:       for (; fptr < current_space->array; fptr++) PetscCall(PetscBTClear(bt, *fptr));
759:     } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
760:       PetscCall(PetscBTMemzero(bn, bt));
761:     }
762:   }
763:   PetscCall(PetscFree(bb));
764:   PetscCall(PetscHeapDestroy(&h));
765:   PetscCall(PetscBTDestroy(&bt));

767:   /* Column indices are in the list of free space */
768:   /* Allocate space for cj, initialize cj, and */
769:   /* destroy list of free space and other temporary array(s) */
770:   PetscCall(PetscMalloc1(ci[am], &cj));
771:   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));

773:   /* put together the new symbolic matrix */
774:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
775:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

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

784:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

786:   /* set MatInfo */
787:   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
788:   if (afill < 1.0) afill = 1.0;
789:   C->info.mallocs           = ndouble;
790:   C->info.fill_ratio_given  = fill;
791:   C->info.fill_ratio_needed = afill;

793: #if defined(PETSC_USE_INFO)
794:   if (ci[am]) {
795:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
796:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
797:   } else {
798:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
799:   }
800: #endif
801:   PetscFunctionReturn(PETSC_SUCCESS);
802: }

804: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A, Mat B, PetscReal fill, Mat C)
805: {
806:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
807:   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j, *inputi, *inputj, *inputcol, *inputcol_L1;
808:   PetscInt       *ci, *cj, *outputj, worki_L1[9], worki_L2[9];
809:   PetscInt        c_maxmem, a_maxrownnz = 0, a_rownnz;
810:   const PetscInt  workcol[8] = {0, 1, 2, 3, 4, 5, 6, 7};
811:   const PetscInt  am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
812:   const PetscInt *brow_ptr[8], *brow_end[8];
813:   PetscInt        window[8];
814:   PetscInt        window_min, old_window_min, ci_nnz, outputi_nnz = 0, L1_nrows, L2_nrows;
815:   PetscInt        i, k, ndouble = 0, L1_rowsleft, rowsleft;
816:   PetscReal       afill;
817:   PetscInt       *workj_L1, *workj_L2, *workj_L3;
818:   PetscInt        L1_nnz, L2_nnz;

820:   /* Step 1: Get upper bound on memory required for allocation.
821:              Because of the way virtual memory works,
822:              only the memory pages that are actually needed will be physically allocated. */
823:   PetscFunctionBegin;
824:   PetscCall(PetscMalloc1(am + 1, &ci));
825:   for (i = 0; i < am; i++) {
826:     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 */
827:     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
828:     a_rownnz             = 0;
829:     for (k = 0; k < anzi; ++k) {
830:       a_rownnz += bi[acol[k] + 1] - bi[acol[k]];
831:       if (a_rownnz > bn) {
832:         a_rownnz = bn;
833:         break;
834:       }
835:     }
836:     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
837:   }
838:   /* temporary work areas for merging rows */
839:   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L1));
840:   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L2));
841:   PetscCall(PetscMalloc1(a_maxrownnz, &workj_L3));

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

848:   ci_nnz      = 0;
849:   ci[0]       = 0;
850:   worki_L1[0] = 0;
851:   worki_L2[0] = 0;
852:   for (i = 0; i < am; i++) {
853:     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 */
854:     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
855:     rowsleft             = anzi;
856:     inputcol_L1          = acol;
857:     L2_nnz               = 0;
858:     L2_nrows             = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
859:     worki_L2[1]          = 0;
860:     outputi_nnz          = 0;

862:     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
863:     while (ci_nnz + a_maxrownnz > c_maxmem) {
864:       c_maxmem *= 2;
865:       ndouble++;
866:       PetscCall(PetscRealloc(sizeof(PetscInt) * c_maxmem, &cj));
867:     }

869:     while (rowsleft) {
870:       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
871:       L1_nrows    = 0;
872:       L1_nnz      = 0;
873:       inputcol    = inputcol_L1;
874:       inputi      = bi;
875:       inputj      = bj;

877:       /* The following macro is used to specialize for small rows in A.
878:          This helps with compiler unrolling, improving performance substantially.
879:           Input:  inputj   inputi  inputcol  bn
880:           Output: outputj  outputi_nnz                       */
881: #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \
882:   do { \
883:     window_min  = bn; \
884:     outputi_nnz = 0; \
885:     for (k = 0; k < ANNZ; ++k) { \
886:       brow_ptr[k] = inputj + inputi[inputcol[k]]; \
887:       brow_end[k] = inputj + inputi[inputcol[k] + 1]; \
888:       window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
889:       window_min  = PetscMin(window[k], window_min); \
890:     } \
891:     while (window_min < bn) { \
892:       outputj[outputi_nnz++] = window_min; \
893:       /* advance front and compute new minimum */ \
894:       old_window_min = window_min; \
895:       window_min     = bn; \
896:       for (k = 0; k < ANNZ; ++k) { \
897:         if (window[k] == old_window_min) { \
898:           brow_ptr[k]++; \
899:           window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
900:         } \
901:         window_min = PetscMin(window[k], window_min); \
902:       } \
903:     } \
904:   } while (0)

906:       /************** L E V E L  1 ***************/
907:       /* Merge up to 8 rows of B to L1 work array*/
908:       while (L1_rowsleft) {
909:         outputi_nnz = 0;
910:         if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/
911:         else outputj = cj + ci_nnz;                /* Merge directly to C */

913:         switch (L1_rowsleft) {
914:         case 1:
915:           brow_ptr[0] = inputj + inputi[inputcol[0]];
916:           brow_end[0] = inputj + inputi[inputcol[0] + 1];
917:           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
918:           inputcol += L1_rowsleft;
919:           rowsleft -= L1_rowsleft;
920:           L1_rowsleft = 0;
921:           break;
922:         case 2:
923:           MatMatMultSymbolic_RowMergeMacro(2);
924:           inputcol += L1_rowsleft;
925:           rowsleft -= L1_rowsleft;
926:           L1_rowsleft = 0;
927:           break;
928:         case 3:
929:           MatMatMultSymbolic_RowMergeMacro(3);
930:           inputcol += L1_rowsleft;
931:           rowsleft -= L1_rowsleft;
932:           L1_rowsleft = 0;
933:           break;
934:         case 4:
935:           MatMatMultSymbolic_RowMergeMacro(4);
936:           inputcol += L1_rowsleft;
937:           rowsleft -= L1_rowsleft;
938:           L1_rowsleft = 0;
939:           break;
940:         case 5:
941:           MatMatMultSymbolic_RowMergeMacro(5);
942:           inputcol += L1_rowsleft;
943:           rowsleft -= L1_rowsleft;
944:           L1_rowsleft = 0;
945:           break;
946:         case 6:
947:           MatMatMultSymbolic_RowMergeMacro(6);
948:           inputcol += L1_rowsleft;
949:           rowsleft -= L1_rowsleft;
950:           L1_rowsleft = 0;
951:           break;
952:         case 7:
953:           MatMatMultSymbolic_RowMergeMacro(7);
954:           inputcol += L1_rowsleft;
955:           rowsleft -= L1_rowsleft;
956:           L1_rowsleft = 0;
957:           break;
958:         default:
959:           MatMatMultSymbolic_RowMergeMacro(8);
960:           inputcol += 8;
961:           rowsleft -= 8;
962:           L1_rowsleft -= 8;
963:           break;
964:         }
965:         inputcol_L1 = inputcol;
966:         L1_nnz += outputi_nnz;
967:         worki_L1[++L1_nrows] = L1_nnz;
968:       }

970:       /********************** L E V E L  2 ************************/
971:       /* Merge from L1 work array to either C or to L2 work array */
972:       if (anzi > 8) {
973:         inputi      = worki_L1;
974:         inputj      = workj_L1;
975:         inputcol    = workcol;
976:         outputi_nnz = 0;

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

981:         switch (L1_nrows) {
982:         case 1:
983:           brow_ptr[0] = inputj + inputi[inputcol[0]];
984:           brow_end[0] = inputj + inputi[inputcol[0] + 1];
985:           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
986:           break;
987:         case 2:
988:           MatMatMultSymbolic_RowMergeMacro(2);
989:           break;
990:         case 3:
991:           MatMatMultSymbolic_RowMergeMacro(3);
992:           break;
993:         case 4:
994:           MatMatMultSymbolic_RowMergeMacro(4);
995:           break;
996:         case 5:
997:           MatMatMultSymbolic_RowMergeMacro(5);
998:           break;
999:         case 6:
1000:           MatMatMultSymbolic_RowMergeMacro(6);
1001:           break;
1002:         case 7:
1003:           MatMatMultSymbolic_RowMergeMacro(7);
1004:           break;
1005:         case 8:
1006:           MatMatMultSymbolic_RowMergeMacro(8);
1007:           break;
1008:         default:
1009:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
1010:         }
1011:         L2_nnz += outputi_nnz;
1012:         worki_L2[++L2_nrows] = L2_nnz;

1014:         /************************ L E V E L  3 **********************/
1015:         /* Merge from L2 work array to either C or to L2 work array */
1016:         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
1017:           inputi      = worki_L2;
1018:           inputj      = workj_L2;
1019:           inputcol    = workcol;
1020:           outputi_nnz = 0;
1021:           if (rowsleft) outputj = workj_L3;
1022:           else outputj = cj + ci_nnz;
1023:           switch (L2_nrows) {
1024:           case 1:
1025:             brow_ptr[0] = inputj + inputi[inputcol[0]];
1026:             brow_end[0] = inputj + inputi[inputcol[0] + 1];
1027:             for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1028:             break;
1029:           case 2:
1030:             MatMatMultSymbolic_RowMergeMacro(2);
1031:             break;
1032:           case 3:
1033:             MatMatMultSymbolic_RowMergeMacro(3);
1034:             break;
1035:           case 4:
1036:             MatMatMultSymbolic_RowMergeMacro(4);
1037:             break;
1038:           case 5:
1039:             MatMatMultSymbolic_RowMergeMacro(5);
1040:             break;
1041:           case 6:
1042:             MatMatMultSymbolic_RowMergeMacro(6);
1043:             break;
1044:           case 7:
1045:             MatMatMultSymbolic_RowMergeMacro(7);
1046:             break;
1047:           case 8:
1048:             MatMatMultSymbolic_RowMergeMacro(8);
1049:             break;
1050:           default:
1051:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
1052:           }
1053:           L2_nrows    = 1;
1054:           L2_nnz      = outputi_nnz;
1055:           worki_L2[1] = outputi_nnz;
1056:           /* Copy to workj_L2 */
1057:           if (rowsleft) {
1058:             for (k = 0; k < outputi_nnz; ++k) workj_L2[k] = outputj[k];
1059:           }
1060:         }
1061:       }
1062:     } /* while (rowsleft) */
1063: #undef MatMatMultSymbolic_RowMergeMacro

1065:     /* terminate current row */
1066:     ci_nnz += outputi_nnz;
1067:     ci[i + 1] = ci_nnz;
1068:   }

1070:   /* Step 3: Create the new symbolic matrix */
1071:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1072:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

1074:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1075:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1076:   c          = (Mat_SeqAIJ *)C->data;
1077:   c->free_a  = PETSC_TRUE;
1078:   c->free_ij = PETSC_TRUE;
1079:   c->nonew   = 0;

1081:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

1083:   /* set MatInfo */
1084:   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
1085:   if (afill < 1.0) afill = 1.0;
1086:   C->info.mallocs           = ndouble;
1087:   C->info.fill_ratio_given  = fill;
1088:   C->info.fill_ratio_needed = afill;

1090: #if defined(PETSC_USE_INFO)
1091:   if (ci[am]) {
1092:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1093:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1094:   } else {
1095:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1096:   }
1097: #endif

1099:   /* Step 4: Free temporary work areas */
1100:   PetscCall(PetscFree(workj_L1));
1101:   PetscCall(PetscFree(workj_L2));
1102:   PetscCall(PetscFree(workj_L3));
1103:   PetscFunctionReturn(PETSC_SUCCESS);
1104: }

1106: /* concatenate unique entries and then sort */
1107: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, PetscReal fill, Mat C)
1108: {
1109:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
1110:   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
1111:   PetscInt       *ci, *cj, bcol;
1112:   PetscInt        am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
1113:   PetscReal       afill;
1114:   PetscInt        i, j, ndouble = 0;
1115:   PetscSegBuffer  seg, segrow;
1116:   char           *seen;

1118:   PetscFunctionBegin;
1119:   PetscCall(PetscMalloc1(am + 1, &ci));
1120:   ci[0] = 0;

1122:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1123:   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), (PetscInt)(fill * (ai[am] + bi[bm])), &seg));
1124:   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 100, &segrow));
1125:   PetscCall(PetscCalloc1(bn, &seen));

1127:   /* Determine ci and cj */
1128:   for (i = 0; i < am; i++) {
1129:     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 */
1130:     const PetscInt *acol = PetscSafePointerPlusOffset(aj, ai[i]); /* column indices of nonzero entries in this row */
1131:     PetscInt packlen     = 0, *PETSC_RESTRICT crow;

1133:     /* Pack segrow */
1134:     for (j = 0; j < anzi; j++) {
1135:       PetscInt brow = acol[j], bjstart = bi[brow], bjend = bi[brow + 1], k;
1136:       for (k = bjstart; k < bjend; k++) {
1137:         bcol = bj[k];
1138:         if (!seen[bcol]) { /* new entry */
1139:           PetscInt *PETSC_RESTRICT slot;
1140:           PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1141:           *slot      = bcol;
1142:           seen[bcol] = 1;
1143:           packlen++;
1144:         }
1145:       }
1146:     }

1148:     /* Check i-th diagonal entry */
1149:     if (C->force_diagonals && !seen[i]) {
1150:       PetscInt *PETSC_RESTRICT slot;
1151:       PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1152:       *slot   = i;
1153:       seen[i] = 1;
1154:       packlen++;
1155:     }

1157:     PetscCall(PetscSegBufferGetInts(seg, packlen, &crow));
1158:     PetscCall(PetscSegBufferExtractTo(segrow, crow));
1159:     PetscCall(PetscSortInt(packlen, crow));
1160:     ci[i + 1] = ci[i] + packlen;
1161:     for (j = 0; j < packlen; j++) seen[crow[j]] = 0;
1162:   }
1163:   PetscCall(PetscSegBufferDestroy(&segrow));
1164:   PetscCall(PetscFree(seen));

1166:   /* Column indices are in the segmented buffer */
1167:   PetscCall(PetscSegBufferExtractAlloc(seg, &cj));
1168:   PetscCall(PetscSegBufferDestroy(&seg));

1170:   /* put together the new symbolic matrix */
1171:   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1172:   PetscCall(MatSetBlockSizesFromMats(C, A, B));

1174:   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1175:   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1176:   c          = (Mat_SeqAIJ *)C->data;
1177:   c->free_a  = PETSC_TRUE;
1178:   c->free_ij = PETSC_TRUE;
1179:   c->nonew   = 0;

1181:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;

1183:   /* set MatInfo */
1184:   afill = (PetscReal)ci[am] / PetscMax(ai[am] + bi[bm], 1) + 1.e-5;
1185:   if (afill < 1.0) afill = 1.0;
1186:   C->info.mallocs           = ndouble;
1187:   C->info.fill_ratio_given  = fill;
1188:   C->info.fill_ratio_needed = afill;

1190: #if defined(PETSC_USE_INFO)
1191:   if (ci[am]) {
1192:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1193:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1194:   } else {
1195:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1196:   }
1197: #endif
1198:   PetscFunctionReturn(PETSC_SUCCESS);
1199: }

1201: static PetscErrorCode MatProductCtxDestroy_SeqAIJ_MatMatMultTrans(void **data)
1202: {
1203:   MatProductCtx_MatMatTransMult *abt = *(MatProductCtx_MatMatTransMult **)data;

1205:   PetscFunctionBegin;
1206:   PetscCall(MatTransposeColoringDestroy(&abt->matcoloring));
1207:   PetscCall(MatDestroy(&abt->Bt_den));
1208:   PetscCall(MatDestroy(&abt->ABt_den));
1209:   PetscCall(PetscFree(abt));
1210:   PetscFunctionReturn(PETSC_SUCCESS);
1211: }

1213: PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1214: {
1215:   Mat                            Bt;
1216:   MatProductCtx_MatMatTransMult *abt;
1217:   Mat_Product                   *product = C->product;
1218:   char                          *alg;

1220:   PetscFunctionBegin;
1221:   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1222:   PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");

1224:   /* create symbolic Bt */
1225:   PetscCall(MatTransposeSymbolic(B, &Bt));
1226:   PetscCall(MatSetBlockSizes(Bt, A->cmap->bs, B->cmap->bs));
1227:   PetscCall(MatSetType(Bt, ((PetscObject)A)->type_name));

1229:   /* get symbolic C=A*Bt */
1230:   PetscCall(PetscStrallocpy(product->alg, &alg));
1231:   PetscCall(MatProductSetAlgorithm(C, "sorted")); /* set algorithm for C = A*Bt */
1232:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(A, Bt, fill, C));
1233:   PetscCall(MatProductSetAlgorithm(C, alg)); /* resume original algorithm for ABt product */
1234:   PetscCall(PetscFree(alg));

1236:   /* create a supporting struct for reuse intermediate dense matrices with matcoloring */
1237:   PetscCall(PetscNew(&abt));

1239:   product->data    = abt;
1240:   product->destroy = MatProductCtxDestroy_SeqAIJ_MatMatMultTrans;

1242:   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ;

1244:   abt->usecoloring = PETSC_FALSE;
1245:   PetscCall(PetscStrcmp(product->alg, "color", &abt->usecoloring));
1246:   if (abt->usecoloring) {
1247:     /* Create MatTransposeColoring from symbolic C=A*B^T */
1248:     MatTransposeColoring matcoloring;
1249:     MatColoring          coloring;
1250:     ISColoring           iscoloring;
1251:     Mat                  Bt_dense, C_dense;

1253:     /* inode causes memory problem */
1254:     PetscCall(MatSetOption(C, MAT_USE_INODES, PETSC_FALSE));

1256:     PetscCall(MatColoringCreate(C, &coloring));
1257:     PetscCall(MatColoringSetDistance(coloring, 2));
1258:     PetscCall(MatColoringSetType(coloring, MATCOLORINGSL));
1259:     PetscCall(MatColoringSetFromOptions(coloring));
1260:     PetscCall(MatColoringApply(coloring, &iscoloring));
1261:     PetscCall(MatColoringDestroy(&coloring));
1262:     PetscCall(MatTransposeColoringCreate(C, iscoloring, &matcoloring));

1264:     abt->matcoloring = matcoloring;

1266:     PetscCall(ISColoringDestroy(&iscoloring));

1268:     /* Create Bt_dense and C_dense = A*Bt_dense */
1269:     PetscCall(MatCreate(PETSC_COMM_SELF, &Bt_dense));
1270:     PetscCall(MatSetSizes(Bt_dense, A->cmap->n, matcoloring->ncolors, A->cmap->n, matcoloring->ncolors));
1271:     PetscCall(MatSetType(Bt_dense, MATSEQDENSE));
1272:     PetscCall(MatSeqDenseSetPreallocation(Bt_dense, NULL));

1274:     Bt_dense->assembled = PETSC_TRUE;
1275:     abt->Bt_den         = Bt_dense;

1277:     PetscCall(MatCreate(PETSC_COMM_SELF, &C_dense));
1278:     PetscCall(MatSetSizes(C_dense, A->rmap->n, matcoloring->ncolors, A->rmap->n, matcoloring->ncolors));
1279:     PetscCall(MatSetType(C_dense, MATSEQDENSE));
1280:     PetscCall(MatSeqDenseSetPreallocation(C_dense, NULL));

1282:     Bt_dense->assembled = PETSC_TRUE;
1283:     abt->ABt_den        = C_dense;

1285: #if defined(PETSC_USE_INFO)
1286:     {
1287:       Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
1288:       PetscCall(PetscInfo(C, "Use coloring of C=A*B^T; B^T: %" PetscInt_FMT " %" PetscInt_FMT ", Bt_dense: %" PetscInt_FMT ",%" PetscInt_FMT "; Cnz %" PetscInt_FMT " / (cm*ncolors %" PetscInt_FMT ") = %g\n", B->cmap->n, B->rmap->n, Bt_dense->rmap->n,
1289:                           Bt_dense->cmap->n, c->nz, A->rmap->n * matcoloring->ncolors, (double)(((PetscReal)c->nz) / ((PetscReal)(A->rmap->n * matcoloring->ncolors)))));
1290:     }
1291: #endif
1292:   }
1293:   /* clean up */
1294:   PetscCall(MatDestroy(&Bt));
1295:   PetscFunctionReturn(PETSC_SUCCESS);
1296: }

1298: PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1299: {
1300:   Mat_SeqAIJ                    *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1301:   PetscInt                      *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, anzi, bnzj, nexta, nextb, *acol, *bcol, brow;
1302:   PetscInt                       cm = C->rmap->n, *ci = c->i, *cj = c->j, i, j, cnzi, *ccol;
1303:   PetscLogDouble                 flops = 0.0;
1304:   MatScalar                     *aa = a->a, *aval, *ba = b->a, *bval, *ca, *cval;
1305:   MatProductCtx_MatMatTransMult *abt;
1306:   Mat_Product                   *product = C->product;

1308:   PetscFunctionBegin;
1309:   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1310:   abt = (MatProductCtx_MatMatTransMult *)product->data;
1311:   PetscCheck(abt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1312:   /* clear old values in C */
1313:   if (!c->a) {
1314:     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1315:     c->a      = ca;
1316:     c->free_a = PETSC_TRUE;
1317:   } else {
1318:     ca = c->a;
1319:     PetscCall(PetscArrayzero(ca, ci[cm] + 1));
1320:   }

1322:   if (abt->usecoloring) {
1323:     MatTransposeColoring matcoloring = abt->matcoloring;
1324:     Mat                  Bt_dense, C_dense = abt->ABt_den;

1326:     /* Get Bt_dense by Apply MatTransposeColoring to B */
1327:     Bt_dense = abt->Bt_den;
1328:     PetscCall(MatTransColoringApplySpToDen(matcoloring, B, Bt_dense));

1330:     /* C_dense = A*Bt_dense */
1331:     PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(A, Bt_dense, C_dense));

1333:     /* Recover C from C_dense */
1334:     PetscCall(MatTransColoringApplyDenToSp(matcoloring, C_dense, C));
1335:     PetscFunctionReturn(PETSC_SUCCESS);
1336:   }

1338:   for (i = 0; i < cm; i++) {
1339:     anzi = ai[i + 1] - ai[i];
1340:     acol = PetscSafePointerPlusOffset(aj, ai[i]);
1341:     aval = PetscSafePointerPlusOffset(aa, ai[i]);
1342:     cnzi = ci[i + 1] - ci[i];
1343:     ccol = PetscSafePointerPlusOffset(cj, ci[i]);
1344:     cval = ca + ci[i];
1345:     for (j = 0; j < cnzi; j++) {
1346:       brow = ccol[j];
1347:       bnzj = bi[brow + 1] - bi[brow];
1348:       bcol = bj + bi[brow];
1349:       bval = ba + bi[brow];

1351:       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1352:       nexta = 0;
1353:       nextb = 0;
1354:       while (nexta < anzi && nextb < bnzj) {
1355:         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1356:         if (nexta == anzi) break;
1357:         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1358:         if (nextb == bnzj) break;
1359:         if (acol[nexta] == bcol[nextb]) {
1360:           cval[j] += aval[nexta] * bval[nextb];
1361:           nexta++;
1362:           nextb++;
1363:           flops += 2;
1364:         }
1365:       }
1366:     }
1367:   }
1368:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1369:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1370:   PetscCall(PetscLogFlops(flops));
1371:   PetscFunctionReturn(PETSC_SUCCESS);
1372: }

1374: PetscErrorCode MatProductCtxDestroy_SeqAIJ_MatTransMatMult(void **data)
1375: {
1376:   MatProductCtx_MatTransMatMult *atb = *(MatProductCtx_MatTransMatMult **)data;

1378:   PetscFunctionBegin;
1379:   PetscCall(MatDestroy(&atb->At));
1380:   if (atb->destroy) PetscCall((*atb->destroy)(&atb->data));
1381:   PetscCall(PetscFree(atb));
1382:   PetscFunctionReturn(PETSC_SUCCESS);
1383: }

1385: PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1386: {
1387:   Mat          At      = NULL;
1388:   Mat_Product *product = C->product;
1389:   PetscBool    flg, def, square;

1391:   PetscFunctionBegin;
1392:   MatCheckProduct(C, 4);
1393:   square = (PetscBool)(A == B && A->symmetric == PETSC_BOOL3_TRUE);
1394:   /* outerproduct */
1395:   PetscCall(PetscStrcmp(product->alg, "outerproduct", &flg));
1396:   if (flg) {
1397:     /* create symbolic At */
1398:     if (!square) {
1399:       PetscCall(MatTransposeSymbolic(A, &At));
1400:       PetscCall(MatSetBlockSizes(At, A->cmap->bs, B->cmap->bs));
1401:       PetscCall(MatSetType(At, ((PetscObject)A)->type_name));
1402:     }
1403:     /* get symbolic C=At*B */
1404:     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1405:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));

1407:     /* clean up */
1408:     if (!square) PetscCall(MatDestroy(&At));

1410:     C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; /* outerproduct */
1411:     PetscCall(MatProductSetAlgorithm(C, "outerproduct"));
1412:     PetscFunctionReturn(PETSC_SUCCESS);
1413:   }

1415:   /* matmatmult */
1416:   PetscCall(PetscStrcmp(product->alg, "default", &def));
1417:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
1418:   if (flg || def) {
1419:     MatProductCtx_MatTransMatMult *atb;

1421:     PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1422:     PetscCall(PetscNew(&atb));
1423:     if (!square) PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
1424:     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1425:     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1426:     PetscCall(MatProductSetAlgorithm(C, "at*b"));
1427:     product->data    = atb;
1428:     product->destroy = MatProductCtxDestroy_SeqAIJ_MatTransMatMult;
1429:     atb->At          = At;

1431:     C->ops->mattransposemultnumeric = NULL; /* see MatProductNumeric_AtB_SeqAIJ_SeqAIJ */
1432:     PetscFunctionReturn(PETSC_SUCCESS);
1433:   }

1435:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
1436: }

1438: PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1439: {
1440:   Mat_SeqAIJ    *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1441:   PetscInt       am = A->rmap->n, anzi, *ai = a->i, *aj = a->j, *bi = b->i, *bj, bnzi, nextb;
1442:   PetscInt       cm = C->rmap->n, *ci = c->i, *cj = c->j, crow, *cjj, i, j, k;
1443:   PetscLogDouble flops = 0.0;
1444:   MatScalar     *aa    = a->a, *ba, *ca, *caj;

1446:   PetscFunctionBegin;
1447:   if (!c->a) {
1448:     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));

1450:     c->a      = ca;
1451:     c->free_a = PETSC_TRUE;
1452:   } else {
1453:     ca = c->a;
1454:     PetscCall(PetscArrayzero(ca, ci[cm]));
1455:   }

1457:   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1458:   for (i = 0; i < am; i++) {
1459:     bj   = b->j + bi[i];
1460:     ba   = b->a + bi[i];
1461:     bnzi = bi[i + 1] - bi[i];
1462:     anzi = ai[i + 1] - ai[i];
1463:     for (j = 0; j < anzi; j++) {
1464:       nextb = 0;
1465:       crow  = *aj++;
1466:       cjj   = cj + ci[crow];
1467:       caj   = ca + ci[crow];
1468:       /* perform sparse axpy operation.  Note cjj includes bj. */
1469:       for (k = 0; nextb < bnzi; k++) {
1470:         if (cjj[k] == *(bj + nextb)) { /* ccol == bcol */
1471:           caj[k] += (*aa) * (*(ba + nextb));
1472:           nextb++;
1473:         }
1474:       }
1475:       flops += 2 * bnzi;
1476:       aa++;
1477:     }
1478:   }

1480:   /* Assemble the final matrix and clean up */
1481:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1482:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1483:   PetscCall(PetscLogFlops(flops));
1484:   PetscFunctionReturn(PETSC_SUCCESS);
1485: }

1487: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
1488: {
1489:   PetscFunctionBegin;
1490:   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
1491:   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1492:   PetscFunctionReturn(PETSC_SUCCESS);
1493: }

1495: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A, Mat B, Mat C, const PetscBool add)
1496: {
1497:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1498:   PetscScalar       *c, r1, r2, r3, r4, *c1, *c2, *c3, *c4;
1499:   const PetscScalar *aa, *b, *b1, *b2, *b3, *b4, *av;
1500:   const PetscInt    *aj;
1501:   PetscInt           cm = C->rmap->n, cn = B->cmap->n, bm, am = A->rmap->n;
1502:   PetscInt           clda;
1503:   PetscInt           am4, bm4, col, i, j, n;

1505:   PetscFunctionBegin;
1506:   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
1507:   PetscCall(MatSeqAIJGetArrayRead(A, &av));
1508:   if (add) {
1509:     PetscCall(MatDenseGetArray(C, &c));
1510:   } else {
1511:     PetscCall(MatDenseGetArrayWrite(C, &c));
1512:   }
1513:   PetscCall(MatDenseGetArrayRead(B, &b));
1514:   PetscCall(MatDenseGetLDA(B, &bm));
1515:   PetscCall(MatDenseGetLDA(C, &clda));
1516:   am4 = 4 * clda;
1517:   bm4 = 4 * bm;
1518:   if (b) {
1519:     b1 = b;
1520:     b2 = b1 + bm;
1521:     b3 = b2 + bm;
1522:     b4 = b3 + bm;
1523:   } else b1 = b2 = b3 = b4 = NULL;
1524:   c1 = c;
1525:   c2 = c1 + clda;
1526:   c3 = c2 + clda;
1527:   c4 = c3 + clda;
1528:   for (col = 0; col < (cn / 4) * 4; col += 4) { /* over columns of C */
1529:     for (i = 0; i < am; i++) {                  /* over rows of A in those columns */
1530:       r1 = r2 = r3 = r4 = 0.0;
1531:       n                 = a->i[i + 1] - a->i[i];
1532:       aj                = PetscSafePointerPlusOffset(a->j, a->i[i]);
1533:       aa                = PetscSafePointerPlusOffset(av, a->i[i]);
1534:       for (j = 0; j < n; j++) {
1535:         const PetscScalar aatmp = aa[j];
1536:         const PetscInt    ajtmp = aj[j];
1537:         r1 += aatmp * b1[ajtmp];
1538:         r2 += aatmp * b2[ajtmp];
1539:         r3 += aatmp * b3[ajtmp];
1540:         r4 += aatmp * b4[ajtmp];
1541:       }
1542:       if (add) {
1543:         c1[i] += r1;
1544:         c2[i] += r2;
1545:         c3[i] += r3;
1546:         c4[i] += r4;
1547:       } else {
1548:         c1[i] = r1;
1549:         c2[i] = r2;
1550:         c3[i] = r3;
1551:         c4[i] = r4;
1552:       }
1553:     }
1554:     if (b) {
1555:       b1 += bm4;
1556:       b2 += bm4;
1557:       b3 += bm4;
1558:       b4 += bm4;
1559:     }
1560:     c1 += am4;
1561:     c2 += am4;
1562:     c3 += am4;
1563:     c4 += am4;
1564:   }
1565:   /* process remaining columns */
1566:   if (col != cn) {
1567:     PetscInt rc = cn - col;

1569:     if (rc == 1) {
1570:       for (i = 0; i < am; i++) {
1571:         r1 = 0.0;
1572:         n  = a->i[i + 1] - a->i[i];
1573:         aj = PetscSafePointerPlusOffset(a->j, a->i[i]);
1574:         aa = PetscSafePointerPlusOffset(av, a->i[i]);
1575:         for (j = 0; j < n; j++) r1 += aa[j] * b1[aj[j]];
1576:         if (add) c1[i] += r1;
1577:         else c1[i] = r1;
1578:       }
1579:     } else if (rc == 2) {
1580:       for (i = 0; i < am; i++) {
1581:         r1 = r2 = 0.0;
1582:         n       = a->i[i + 1] - a->i[i];
1583:         aj      = PetscSafePointerPlusOffset(a->j, a->i[i]);
1584:         aa      = PetscSafePointerPlusOffset(av, a->i[i]);
1585:         for (j = 0; j < n; j++) {
1586:           const PetscScalar aatmp = aa[j];
1587:           const PetscInt    ajtmp = aj[j];
1588:           r1 += aatmp * b1[ajtmp];
1589:           r2 += aatmp * b2[ajtmp];
1590:         }
1591:         if (add) {
1592:           c1[i] += r1;
1593:           c2[i] += r2;
1594:         } else {
1595:           c1[i] = r1;
1596:           c2[i] = r2;
1597:         }
1598:       }
1599:     } else {
1600:       for (i = 0; i < am; i++) {
1601:         r1 = r2 = r3 = 0.0;
1602:         n            = a->i[i + 1] - a->i[i];
1603:         aj           = PetscSafePointerPlusOffset(a->j, a->i[i]);
1604:         aa           = PetscSafePointerPlusOffset(av, a->i[i]);
1605:         for (j = 0; j < n; j++) {
1606:           const PetscScalar aatmp = aa[j];
1607:           const PetscInt    ajtmp = aj[j];
1608:           r1 += aatmp * b1[ajtmp];
1609:           r2 += aatmp * b2[ajtmp];
1610:           r3 += aatmp * b3[ajtmp];
1611:         }
1612:         if (add) {
1613:           c1[i] += r1;
1614:           c2[i] += r2;
1615:           c3[i] += r3;
1616:         } else {
1617:           c1[i] = r1;
1618:           c2[i] = r2;
1619:           c3[i] = r3;
1620:         }
1621:       }
1622:     }
1623:   }
1624:   PetscCall(PetscLogFlops(cn * (2.0 * a->nz)));
1625:   if (add) {
1626:     PetscCall(MatDenseRestoreArray(C, &c));
1627:   } else {
1628:     PetscCall(MatDenseRestoreArrayWrite(C, &c));
1629:   }
1630:   PetscCall(MatDenseRestoreArrayRead(B, &b));
1631:   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
1632:   PetscFunctionReturn(PETSC_SUCCESS);
1633: }

1635: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A, Mat B, Mat C)
1636: {
1637:   PetscFunctionBegin;
1638:   PetscCheck(B->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in A %" PetscInt_FMT " not equal rows in B %" PetscInt_FMT, A->cmap->n, B->rmap->n);
1639:   PetscCheck(A->rmap->n == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number rows in C %" PetscInt_FMT " not equal rows in A %" PetscInt_FMT, C->rmap->n, A->rmap->n);
1640:   PetscCheck(B->cmap->n == C->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in B %" PetscInt_FMT " not equal columns in C %" PetscInt_FMT, B->cmap->n, C->cmap->n);

1642:   PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(A, B, C, PETSC_FALSE));
1643:   PetscFunctionReturn(PETSC_SUCCESS);
1644: }

1646: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AB(Mat C)
1647: {
1648:   PetscFunctionBegin;
1649:   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqDense;
1650:   C->ops->productsymbolic = MatProductSymbolic_AB;
1651:   PetscFunctionReturn(PETSC_SUCCESS);
1652: }

1654: PETSC_INTERN PetscErrorCode MatTMatTMultSymbolic_SeqAIJ_SeqDense(Mat, Mat, PetscReal, Mat);

1656: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(Mat C)
1657: {
1658:   PetscFunctionBegin;
1659:   C->ops->transposematmultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1660:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
1661:   PetscFunctionReturn(PETSC_SUCCESS);
1662: }

1664: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(Mat C)
1665: {
1666:   PetscFunctionBegin;
1667:   C->ops->mattransposemultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1668:   C->ops->productsymbolic          = MatProductSymbolic_ABt;
1669:   PetscFunctionReturn(PETSC_SUCCESS);
1670: }

1672: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat C)
1673: {
1674:   Mat_Product *product = C->product;

1676:   PetscFunctionBegin;
1677:   switch (product->type) {
1678:   case MATPRODUCT_AB:
1679:     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AB(C));
1680:     break;
1681:   case MATPRODUCT_AtB:
1682:     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(C));
1683:     break;
1684:   case MATPRODUCT_ABt:
1685:     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(C));
1686:     break;
1687:   default:
1688:     break;
1689:   }
1690:   PetscFunctionReturn(PETSC_SUCCESS);
1691: }

1693: static PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(Mat C)
1694: {
1695:   Mat_Product *product = C->product;
1696:   Mat          A       = product->A;
1697:   PetscBool    baij;

1699:   PetscFunctionBegin;
1700:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &baij));
1701:   if (!baij) { /* A is seqsbaij */
1702:     PetscBool sbaij;
1703:     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &sbaij));
1704:     PetscCheck(sbaij, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "Mat must be either seqbaij or seqsbaij format");

1706:     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqSBAIJ_SeqDense;
1707:   } else { /* A is seqbaij */
1708:     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqBAIJ_SeqDense;
1709:   }

1711:   C->ops->productsymbolic = MatProductSymbolic_AB;
1712:   PetscFunctionReturn(PETSC_SUCCESS);
1713: }

1715: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense(Mat C)
1716: {
1717:   Mat_Product *product = C->product;

1719:   PetscFunctionBegin;
1720:   MatCheckProduct(C, 1);
1721:   PetscCheck(product->A, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing A");
1722:   if (product->type == MATPRODUCT_AB || (product->type == MATPRODUCT_AtB && product->A->symmetric == PETSC_BOOL3_TRUE)) PetscCall(MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(C));
1723:   else if (product->type == MATPRODUCT_AtB) {
1724:     PetscBool flg;

1726:     PetscCall(PetscObjectTypeCompare((PetscObject)product->A, MATSEQBAIJ, &flg));
1727:     if (flg) {
1728:       C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_SeqBAIJ_SeqDense;
1729:       C->ops->productsymbolic          = MatProductSymbolic_AtB;
1730:     }
1731:   }
1732:   PetscFunctionReturn(PETSC_SUCCESS);
1733: }

1735: static PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ_AB(Mat C)
1736: {
1737:   PetscFunctionBegin;
1738:   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqAIJ;
1739:   C->ops->productsymbolic = MatProductSymbolic_AB;
1740:   PetscFunctionReturn(PETSC_SUCCESS);
1741: }

1743: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ(Mat C)
1744: {
1745:   Mat_Product *product = C->product;

1747:   PetscFunctionBegin;
1748:   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_SeqDense_SeqAIJ_AB(C));
1749:   PetscFunctionReturn(PETSC_SUCCESS);
1750: }

1752: PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring, Mat B, Mat Btdense)
1753: {
1754:   Mat_SeqAIJ   *b       = (Mat_SeqAIJ *)B->data;
1755:   Mat_SeqDense *btdense = (Mat_SeqDense *)Btdense->data;
1756:   PetscInt     *bi = b->i, *bj = b->j;
1757:   PetscInt      m = Btdense->rmap->n, n = Btdense->cmap->n, j, k, l, col, anz, *btcol, brow, ncolumns;
1758:   MatScalar    *btval, *btval_den, *ba = b->a;
1759:   PetscInt     *columns = coloring->columns, *colorforcol = coloring->colorforcol, ncolors = coloring->ncolors;

1761:   PetscFunctionBegin;
1762:   btval_den = btdense->v;
1763:   PetscCall(PetscArrayzero(btval_den, m * n));
1764:   for (k = 0; k < ncolors; k++) {
1765:     ncolumns = coloring->ncolumns[k];
1766:     for (l = 0; l < ncolumns; l++) { /* insert a row of B to a column of Btdense */
1767:       col   = *(columns + colorforcol[k] + l);
1768:       btcol = bj + bi[col];
1769:       btval = ba + bi[col];
1770:       anz   = bi[col + 1] - bi[col];
1771:       for (j = 0; j < anz; j++) {
1772:         brow            = btcol[j];
1773:         btval_den[brow] = btval[j];
1774:       }
1775:     }
1776:     btval_den += m;
1777:   }
1778:   PetscFunctionReturn(PETSC_SUCCESS);
1779: }

1781: PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
1782: {
1783:   Mat_SeqAIJ        *csp = (Mat_SeqAIJ *)Csp->data;
1784:   const PetscScalar *ca_den, *ca_den_ptr;
1785:   PetscScalar       *ca = csp->a;
1786:   PetscInt           k, l, m = Cden->rmap->n, ncolors = matcoloring->ncolors;
1787:   PetscInt           brows = matcoloring->brows, *den2sp = matcoloring->den2sp;
1788:   PetscInt           nrows, *row, *idx;
1789:   PetscInt          *rows = matcoloring->rows, *colorforrow = matcoloring->colorforrow;

1791:   PetscFunctionBegin;
1792:   PetscCall(MatDenseGetArrayRead(Cden, &ca_den));

1794:   if (brows > 0) {
1795:     PetscInt *lstart, row_end, row_start;
1796:     lstart = matcoloring->lstart;
1797:     PetscCall(PetscArrayzero(lstart, ncolors));

1799:     row_end = brows;
1800:     if (row_end > m) row_end = m;
1801:     for (row_start = 0; row_start < m; row_start += brows) { /* loop over row blocks of Csp */
1802:       ca_den_ptr = ca_den;
1803:       for (k = 0; k < ncolors; k++) { /* loop over colors (columns of Cden) */
1804:         nrows = matcoloring->nrows[k];
1805:         row   = rows + colorforrow[k];
1806:         idx   = den2sp + colorforrow[k];
1807:         for (l = lstart[k]; l < nrows; l++) {
1808:           if (row[l] >= row_end) {
1809:             lstart[k] = l;
1810:             break;
1811:           } else {
1812:             ca[idx[l]] = ca_den_ptr[row[l]];
1813:           }
1814:         }
1815:         ca_den_ptr += m;
1816:       }
1817:       row_end += brows;
1818:       if (row_end > m) row_end = m;
1819:     }
1820:   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1821:     ca_den_ptr = ca_den;
1822:     for (k = 0; k < ncolors; k++) {
1823:       nrows = matcoloring->nrows[k];
1824:       row   = rows + colorforrow[k];
1825:       idx   = den2sp + colorforrow[k];
1826:       for (l = 0; l < nrows; l++) ca[idx[l]] = ca_den_ptr[row[l]];
1827:       ca_den_ptr += m;
1828:     }
1829:   }

1831:   PetscCall(MatDenseRestoreArrayRead(Cden, &ca_den));
1832: #if defined(PETSC_USE_INFO)
1833:   if (matcoloring->brows > 0) {
1834:     PetscCall(PetscInfo(Csp, "Loop over %" PetscInt_FMT " row blocks for den2sp\n", brows));
1835:   } else {
1836:     PetscCall(PetscInfo(Csp, "Loop over colors/columns of Cden, inefficient for large sparse matrix product \n"));
1837:   }
1838: #endif
1839:   PetscFunctionReturn(PETSC_SUCCESS);
1840: }

1842: PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat, ISColoring iscoloring, MatTransposeColoring c)
1843: {
1844:   PetscInt        i, n, nrows, Nbs, j, k, m, ncols, col, cm;
1845:   const PetscInt *is, *ci, *cj, *row_idx;
1846:   PetscInt        nis = iscoloring->n, *rowhit, bs = 1;
1847:   IS             *isa;
1848:   Mat_SeqAIJ     *csp = (Mat_SeqAIJ *)mat->data;
1849:   PetscInt       *colorforrow, *rows, *rows_i, *idxhit, *spidx, *den2sp, *den2sp_i;
1850:   PetscInt       *colorforcol, *columns, *columns_i, brows;
1851:   PetscBool       flg;

1853:   PetscFunctionBegin;
1854:   PetscCall(ISColoringGetIS(iscoloring, PETSC_USE_POINTER, PETSC_IGNORE, &isa));

1856:   /* bs > 1 is not being tested yet! */
1857:   Nbs       = mat->cmap->N / bs;
1858:   c->M      = mat->rmap->N / bs; /* set total rows, columns and local rows */
1859:   c->N      = Nbs;
1860:   c->m      = c->M;
1861:   c->rstart = 0;
1862:   c->brows  = 100;

1864:   c->ncolors = nis;
1865:   PetscCall(PetscMalloc3(nis, &c->ncolumns, nis, &c->nrows, nis + 1, &colorforrow));
1866:   PetscCall(PetscMalloc1(csp->nz + 1, &rows));
1867:   PetscCall(PetscMalloc1(csp->nz + 1, &den2sp));

1869:   brows = c->brows;
1870:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-matden2sp_brows", &brows, &flg));
1871:   if (flg) c->brows = brows;
1872:   if (brows > 0) PetscCall(PetscMalloc1(nis + 1, &c->lstart));

1874:   colorforrow[0] = 0;
1875:   rows_i         = rows;
1876:   den2sp_i       = den2sp;

1878:   PetscCall(PetscMalloc1(nis + 1, &colorforcol));
1879:   PetscCall(PetscMalloc1(Nbs + 1, &columns));

1881:   colorforcol[0] = 0;
1882:   columns_i      = columns;

1884:   /* get column-wise storage of mat */
1885:   PetscCall(MatGetColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));

1887:   cm = c->m;
1888:   PetscCall(PetscMalloc1(cm + 1, &rowhit));
1889:   PetscCall(PetscMalloc1(cm + 1, &idxhit));
1890:   for (i = 0; i < nis; i++) { /* loop over color */
1891:     PetscCall(ISGetLocalSize(isa[i], &n));
1892:     PetscCall(ISGetIndices(isa[i], &is));

1894:     c->ncolumns[i] = n;
1895:     if (n) PetscCall(PetscArraycpy(columns_i, is, n));
1896:     colorforcol[i + 1] = colorforcol[i] + n;
1897:     columns_i += n;

1899:     /* fast, crude version requires O(N*N) work */
1900:     PetscCall(PetscArrayzero(rowhit, cm));

1902:     for (j = 0; j < n; j++) { /* loop over columns*/
1903:       col     = is[j];
1904:       row_idx = cj + ci[col];
1905:       m       = ci[col + 1] - ci[col];
1906:       for (k = 0; k < m; k++) { /* loop over columns marking them in rowhit */
1907:         idxhit[*row_idx]   = spidx[ci[col] + k];
1908:         rowhit[*row_idx++] = col + 1;
1909:       }
1910:     }
1911:     /* count the number of hits */
1912:     nrows = 0;
1913:     for (j = 0; j < cm; j++) {
1914:       if (rowhit[j]) nrows++;
1915:     }
1916:     c->nrows[i]        = nrows;
1917:     colorforrow[i + 1] = colorforrow[i] + nrows;

1919:     nrows = 0;
1920:     for (j = 0; j < cm; j++) { /* loop over rows */
1921:       if (rowhit[j]) {
1922:         rows_i[nrows]   = j;
1923:         den2sp_i[nrows] = idxhit[j];
1924:         nrows++;
1925:       }
1926:     }
1927:     den2sp_i += nrows;

1929:     PetscCall(ISRestoreIndices(isa[i], &is));
1930:     rows_i += nrows;
1931:   }
1932:   PetscCall(MatRestoreColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1933:   PetscCall(PetscFree(rowhit));
1934:   PetscCall(ISColoringRestoreIS(iscoloring, PETSC_USE_POINTER, &isa));
1935:   PetscCheck(csp->nz == colorforrow[nis], PETSC_COMM_SELF, PETSC_ERR_PLIB, "csp->nz %" PetscInt_FMT " != colorforrow[nis] %" PetscInt_FMT, csp->nz, colorforrow[nis]);

1937:   c->colorforrow = colorforrow;
1938:   c->rows        = rows;
1939:   c->den2sp      = den2sp;
1940:   c->colorforcol = colorforcol;
1941:   c->columns     = columns;

1943:   PetscCall(PetscFree(idxhit));
1944:   PetscFunctionReturn(PETSC_SUCCESS);
1945: }

1947: static PetscErrorCode MatProductNumeric_AtB_SeqAIJ_SeqAIJ(Mat C)
1948: {
1949:   Mat_Product *product = C->product;
1950:   Mat          A = product->A, B = product->B;

1952:   PetscFunctionBegin;
1953:   if (C->ops->mattransposemultnumeric) {
1954:     /* Alg: "outerproduct" */
1955:     PetscCall((*C->ops->mattransposemultnumeric)(A, B, C));
1956:   } else {
1957:     /* Alg: "matmatmult" -- C = At*B */
1958:     MatProductCtx_MatTransMatMult *atb = (MatProductCtx_MatTransMatMult *)product->data;

1960:     PetscCheck(atb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1961:     if (atb->At) {
1962:       /* At is computed in MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ();
1963:          user may have called MatProductReplaceMats() to get this A=product->A */
1964:       PetscCall(MatTransposeSetPrecursor(A, atb->At));
1965:       PetscCall(MatTranspose(A, MAT_REUSE_MATRIX, &atb->At));
1966:     }
1967:     PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ(atb->At ? atb->At : A, B, C));
1968:   }
1969:   PetscFunctionReturn(PETSC_SUCCESS);
1970: }

1972: static PetscErrorCode MatProductSymbolic_AtB_SeqAIJ_SeqAIJ(Mat C)
1973: {
1974:   Mat_Product *product = C->product;
1975:   Mat          A = product->A, B = product->B;
1976:   PetscReal    fill = product->fill;

1978:   PetscFunctionBegin;
1979:   PetscCall(MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A, B, fill, C));

1981:   C->ops->productnumeric = MatProductNumeric_AtB_SeqAIJ_SeqAIJ;
1982:   PetscFunctionReturn(PETSC_SUCCESS);
1983: }

1985: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AB(Mat C)
1986: {
1987:   Mat_Product *product = C->product;
1988:   PetscInt     alg     = 0; /* default algorithm */
1989:   PetscBool    flg     = PETSC_FALSE;
1990: #if !defined(PETSC_HAVE_HYPRE)
1991:   const char *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
1992:   PetscInt    nalg        = 7;
1993: #else
1994:   const char *algTypes[8] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge", "hypre"};
1995:   PetscInt    nalg        = 8;
1996: #endif

1998:   PetscFunctionBegin;
1999:   /* Set default algorithm */
2000:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2001:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2003:   /* Get runtime option */
2004:   if (product->api_user) {
2005:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2006:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[0], &alg, &flg));
2007:     PetscOptionsEnd();
2008:   } else {
2009:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2010:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AB", algTypes, nalg, algTypes[0], &alg, &flg));
2011:     PetscOptionsEnd();
2012:   }
2013:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2015:   C->ops->productsymbolic = MatProductSymbolic_AB;
2016:   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqAIJ;
2017:   PetscFunctionReturn(PETSC_SUCCESS);
2018: }

2020: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AtB(Mat C)
2021: {
2022:   Mat_Product *product     = C->product;
2023:   PetscInt     alg         = 0; /* default algorithm */
2024:   PetscBool    flg         = PETSC_FALSE;
2025:   const char  *algTypes[3] = {"default", "at*b", "outerproduct"};
2026:   PetscInt     nalg        = 3;

2028:   PetscFunctionBegin;
2029:   /* Get runtime option */
2030:   if (product->api_user) {
2031:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2032:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2033:     PetscOptionsEnd();
2034:   } else {
2035:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2036:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AtB", algTypes, nalg, algTypes[alg], &alg, &flg));
2037:     PetscOptionsEnd();
2038:   }
2039:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2041:   C->ops->productsymbolic = MatProductSymbolic_AtB_SeqAIJ_SeqAIJ;
2042:   PetscFunctionReturn(PETSC_SUCCESS);
2043: }

2045: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABt(Mat C)
2046: {
2047:   Mat_Product *product     = C->product;
2048:   PetscInt     alg         = 0; /* default algorithm */
2049:   PetscBool    flg         = PETSC_FALSE;
2050:   const char  *algTypes[2] = {"default", "color"};
2051:   PetscInt     nalg        = 2;

2053:   PetscFunctionBegin;
2054:   /* Set default algorithm */
2055:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2056:   if (!flg) {
2057:     alg = 1;
2058:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2059:   }

2061:   /* Get runtime option */
2062:   if (product->api_user) {
2063:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatTransposeMult", "Mat");
2064:     PetscCall(PetscOptionsEList("-matmattransmult_via", "Algorithmic approach", "MatMatTransposeMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2065:     PetscOptionsEnd();
2066:   } else {
2067:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABt", "Mat");
2068:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABt", algTypes, nalg, algTypes[alg], &alg, &flg));
2069:     PetscOptionsEnd();
2070:   }
2071:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2073:   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ;
2074:   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2075:   PetscFunctionReturn(PETSC_SUCCESS);
2076: }

2078: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_PtAP(Mat C)
2079: {
2080:   Mat_Product *product = C->product;
2081:   PetscBool    flg     = PETSC_FALSE;
2082:   PetscInt     alg     = 0; /* default algorithm -- alg=1 should be default!!! */
2083: #if !defined(PETSC_HAVE_HYPRE)
2084:   const char *algTypes[2] = {"scalable", "rap"};
2085:   PetscInt    nalg        = 2;
2086: #else
2087:   const char *algTypes[3] = {"scalable", "rap", "hypre"};
2088:   PetscInt    nalg        = 3;
2089: #endif

2091:   PetscFunctionBegin;
2092:   /* Set default algorithm */
2093:   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2094:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2096:   /* Get runtime option */
2097:   if (product->api_user) {
2098:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2099:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2100:     PetscOptionsEnd();
2101:   } else {
2102:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2103:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_PtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2104:     PetscOptionsEnd();
2105:   }
2106:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2108:   C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ;
2109:   PetscFunctionReturn(PETSC_SUCCESS);
2110: }

2112: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_RARt(Mat C)
2113: {
2114:   Mat_Product *product     = C->product;
2115:   PetscBool    flg         = PETSC_FALSE;
2116:   PetscInt     alg         = 0; /* default algorithm */
2117:   const char  *algTypes[3] = {"r*a*rt", "r*art", "coloring_rart"};
2118:   PetscInt     nalg        = 3;

2120:   PetscFunctionBegin;
2121:   /* Set default algorithm */
2122:   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2123:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2125:   /* Get runtime option */
2126:   if (product->api_user) {
2127:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatRARt", "Mat");
2128:     PetscCall(PetscOptionsEList("-matrart_via", "Algorithmic approach", "MatRARt", algTypes, nalg, algTypes[0], &alg, &flg));
2129:     PetscOptionsEnd();
2130:   } else {
2131:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_RARt", "Mat");
2132:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_RARt", algTypes, nalg, algTypes[0], &alg, &flg));
2133:     PetscOptionsEnd();
2134:   }
2135:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2137:   C->ops->productsymbolic = MatProductSymbolic_RARt_SeqAIJ_SeqAIJ;
2138:   PetscFunctionReturn(PETSC_SUCCESS);
2139: }

2141: /* ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm */
2142: static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABC(Mat C)
2143: {
2144:   Mat_Product *product     = C->product;
2145:   PetscInt     alg         = 0; /* default algorithm */
2146:   PetscBool    flg         = PETSC_FALSE;
2147:   const char  *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
2148:   PetscInt     nalg        = 7;

2150:   PetscFunctionBegin;
2151:   /* Set default algorithm */
2152:   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2153:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2155:   /* Get runtime option */
2156:   if (product->api_user) {
2157:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2158:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2159:     PetscOptionsEnd();
2160:   } else {
2161:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2162:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2163:     PetscOptionsEnd();
2164:   }
2165:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2167:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ;
2168:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2169:   PetscFunctionReturn(PETSC_SUCCESS);
2170: }

2172: PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat C)
2173: {
2174:   Mat_Product *product = C->product;

2176:   PetscFunctionBegin;
2177:   switch (product->type) {
2178:   case MATPRODUCT_AB:
2179:     PetscCall(MatProductSetFromOptions_SeqAIJ_AB(C));
2180:     break;
2181:   case MATPRODUCT_AtB:
2182:     PetscCall(MatProductSetFromOptions_SeqAIJ_AtB(C));
2183:     break;
2184:   case MATPRODUCT_ABt:
2185:     PetscCall(MatProductSetFromOptions_SeqAIJ_ABt(C));
2186:     break;
2187:   case MATPRODUCT_PtAP:
2188:     PetscCall(MatProductSetFromOptions_SeqAIJ_PtAP(C));
2189:     break;
2190:   case MATPRODUCT_RARt:
2191:     PetscCall(MatProductSetFromOptions_SeqAIJ_RARt(C));
2192:     break;
2193:   case MATPRODUCT_ABC:
2194:     PetscCall(MatProductSetFromOptions_SeqAIJ_ABC(C));
2195:     break;
2196:   default:
2197:     break;
2198:   }
2199:   PetscFunctionReturn(PETSC_SUCCESS);
2200: }