Actual source code: mpimatmatmult.c

  1: /*
  2:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
  3:           C = A * B
  4: */
  5: #include <../src/mat/impls/aij/seq/aij.h>
  6: #include <../src/mat/utils/freespace.h>
  7: #include <../src/mat/impls/aij/mpi/mpiaij.h>
  8: #include <petscbt.h>
  9: #include <../src/mat/impls/dense/mpi/mpidense.h>
 10: #include <petsc/private/vecimpl.h>
 11: #include <petsc/private/sfimpl.h>

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

 17: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABt_MPIAIJ_MPIAIJ(Mat C)
 18: {
 19:   Mat_Product *product = C->product;
 20:   Mat          B       = product->B;

 22:   PetscFunctionBegin;
 23:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &product->B));
 24:   PetscCall(MatDestroy(&B));
 25:   PetscCall(MatProductSymbolic_AB_MPIAIJ_MPIAIJ(C));
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
 30: {
 31:   Mat_Product        *product = C->product;
 32:   Mat                 A = product->A, B = product->B;
 33:   MatProductAlgorithm alg  = product->alg;
 34:   PetscReal           fill = product->fill;
 35:   PetscBool           flg;

 37:   PetscFunctionBegin;
 38:   /* scalable */
 39:   PetscCall(PetscStrcmp(alg, "scalable", &flg));
 40:   if (flg) {
 41:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
 42:     PetscFunctionReturn(PETSC_SUCCESS);
 43:   }

 45:   /* nonscalable */
 46:   PetscCall(PetscStrcmp(alg, "nonscalable", &flg));
 47:   if (flg) {
 48:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
 49:     PetscFunctionReturn(PETSC_SUCCESS);
 50:   }

 52:   /* seqmpi */
 53:   PetscCall(PetscStrcmp(alg, "seqmpi", &flg));
 54:   if (flg) {
 55:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A, B, fill, C));
 56:     PetscFunctionReturn(PETSC_SUCCESS);
 57:   }

 59:   /* backend general code */
 60:   PetscCall(PetscStrcmp(alg, "backend", &flg));
 61:   if (flg) {
 62:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
 63:     PetscFunctionReturn(PETSC_SUCCESS);
 64:   }

 66: #if defined(PETSC_HAVE_HYPRE)
 67:   PetscCall(PetscStrcmp(alg, "hypre", &flg));
 68:   if (flg) {
 69:     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
 70:     PetscFunctionReturn(PETSC_SUCCESS);
 71:   }
 72: #endif
 73:   SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
 74: }

 76: PetscErrorCode MatProductCtxDestroy_MPIAIJ_MatMatMult(PetscCtxRt data)
 77: {
 78:   MatProductCtx_APMPI *ptap = *(MatProductCtx_APMPI **)data;

 80:   PetscFunctionBegin;
 81:   PetscCall(PetscFree2(ptap->startsj_s, ptap->startsj_r));
 82:   PetscCall(PetscFree(ptap->bufa));
 83:   PetscCall(MatDestroy(&ptap->P_loc));
 84:   PetscCall(MatDestroy(&ptap->P_oth));
 85:   PetscCall(MatDestroy(&ptap->Pt));
 86:   PetscCall(PetscFree(ptap->api));
 87:   PetscCall(PetscFree(ptap->apj));
 88:   PetscCall(PetscFree(ptap->apa));
 89:   PetscCall(PetscFree(ptap));
 90:   PetscFunctionReturn(PETSC_SUCCESS);
 91: }

 93: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, Mat C)
 94: {
 95:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
 96:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
 97:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
 98:   PetscScalar         *cda, *coa;
 99:   Mat_SeqAIJ          *p_loc, *p_oth;
100:   PetscScalar         *apa, *ca;
101:   PetscInt             cm = C->rmap->n;
102:   MatProductCtx_APMPI *ptap;
103:   PetscInt            *api, *apj, *apJ, i, k;
104:   PetscInt             cstart = C->cmap->rstart;
105:   PetscInt             cdnz, conz, k0, k1;
106:   const PetscScalar   *dummy1, *dummy2, *dummy3, *dummy4;
107:   MPI_Comm             comm;
108:   PetscMPIInt          size;

110:   PetscFunctionBegin;
111:   MatCheckProduct(C, 3);
112:   ptap = (MatProductCtx_APMPI *)C->product->data;
113:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
114:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
115:   PetscCallMPI(MPI_Comm_size(comm, &size));
116:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

118:   /* flag CPU mask for C */
119: #if defined(PETSC_HAVE_DEVICE)
120:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
121:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
122:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
123: #endif

125:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
126:   /* update numerical values of P_oth and P_loc */
127:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
128:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

130:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
131:   /* get data from symbolic products */
132:   p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
133:   p_oth = NULL;
134:   if (size > 1) p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;

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

139:   api = ptap->api;
140:   apj = ptap->apj;
141:   /* trigger copy to CPU */
142:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy1));
143:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy2));
144:   PetscCall(MatSeqAIJGetArrayRead(ptap->P_loc, &dummy3));
145:   if (ptap->P_oth) PetscCall(MatSeqAIJGetArrayRead(ptap->P_oth, &dummy4));
146:   PetscCall(MatSeqAIJGetArrayWrite(c->A, &cda));
147:   PetscCall(MatSeqAIJGetArrayWrite(c->B, &coa));
148:   for (i = 0; i < cm; i++) {
149:     /* compute apa = A[i,:]*P */
150:     AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);

152:     /* set values in C */
153:     apJ  = PetscSafePointerPlusOffset(apj, api[i]);
154:     cdnz = cd->i[i + 1] - cd->i[i];
155:     conz = co->i[i + 1] - co->i[i];

157:     /* 1st off-diagonal part of C */
158:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
159:     k  = 0;
160:     for (k0 = 0; k0 < conz; k0++) {
161:       if (apJ[k] >= cstart) break;
162:       ca[k0]        = apa[apJ[k]];
163:       apa[apJ[k++]] = 0.0;
164:     }

166:     /* diagonal part of C */
167:     ca = PetscSafePointerPlusOffset(cda, cd->i[i]);
168:     for (k1 = 0; k1 < cdnz; k1++) {
169:       ca[k1]        = apa[apJ[k]];
170:       apa[apJ[k++]] = 0.0;
171:     }

173:     /* 2nd off-diagonal part of C */
174:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
175:     for (; k0 < conz; k0++) {
176:       ca[k0]        = apa[apJ[k]];
177:       apa[apJ[k++]] = 0.0;
178:     }
179:   }
180:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy1));
181:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy2));
182:   PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_loc, &dummy3));
183:   if (ptap->P_oth) PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_oth, &dummy4));
184:   PetscCall(MatSeqAIJRestoreArrayWrite(c->A, &cda));
185:   PetscCall(MatSeqAIJRestoreArrayWrite(c->B, &coa));

187:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
188:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
189:   PetscFunctionReturn(PETSC_SUCCESS);
190: }

192: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, PetscReal fill, Mat C)
193: {
194:   MPI_Comm             comm;
195:   PetscMPIInt          size;
196:   MatProductCtx_APMPI *ptap;
197:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
198:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
199:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
200:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
201:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
202:   PetscInt            *lnk, i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi;
203:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n;
204:   PetscBT              lnkbt;
205:   PetscReal            afill;
206:   MatType              mtype;

208:   PetscFunctionBegin;
209:   MatCheckProduct(C, 4);
210:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
211:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
212:   PetscCallMPI(MPI_Comm_size(comm, &size));

214:   /* create struct MatProductCtx_APMPI and attached it to C later */
215:   PetscCall(PetscNew(&ptap));

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

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

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

236:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
237:   PetscCall(PetscMalloc1(am + 1, &api));
238:   ptap->api = api;
239:   api[0]    = 0;

241:   /* create and initialize a linked list */
242:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));

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

248:   MatPreallocateBegin(comm, am, pn, dnz, onz);
249:   for (i = 0; i < am; i++) {
250:     /* diagonal portion of A */
251:     nzi = adi[i + 1] - adi[i];
252:     for (j = 0; j < nzi; j++) {
253:       row  = *adj++;
254:       pnz  = pi_loc[row + 1] - pi_loc[row];
255:       Jptr = pj_loc + pi_loc[row];
256:       /* add non-zero cols of P into the sorted linked list lnk */
257:       PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
258:     }
259:     /* off-diagonal portion of A */
260:     nzi = aoi[i + 1] - aoi[i];
261:     for (j = 0; j < nzi; j++) {
262:       row  = *aoj++;
263:       pnz  = pi_oth[row + 1] - pi_oth[row];
264:       Jptr = pj_oth + pi_oth[row];
265:       PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
266:     }
267:     /* add possible missing diagonal entry */
268:     if (C->force_diagonals) {
269:       j = i + rstart; /* column index */
270:       PetscCall(PetscLLCondensedAddSorted(1, &j, lnk, lnkbt));
271:     }

273:     apnz       = lnk[0];
274:     api[i + 1] = api[i] + apnz;

276:     /* if free space is not available, double the total space in the list */
277:     if (current_space->local_remaining < apnz) {
278:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
279:       nspacedouble++;
280:     }

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

286:     current_space->array += apnz;
287:     current_space->local_used += apnz;
288:     current_space->local_remaining -= apnz;
289:   }

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

298:   /* malloc apa to store dense row A[i,:]*P */
299:   PetscCall(PetscCalloc1(pN, &ptap->apa));

301:   /* set and assemble symbolic parallel matrix C */
302:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
303:   PetscCall(MatSetBlockSizesFromMats(C, A, P));

305:   PetscCall(MatGetType(A, &mtype));
306:   PetscCall(MatSetType(C, mtype));
307:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
308:   MatPreallocateEnd(dnz, onz);

310:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
311:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
312:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
313:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
314:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

316:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
317:   C->ops->productnumeric = MatProductNumeric_AB;

319:   /* attach the supporting struct to C for reuse */
320:   C->product->data    = ptap;
321:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

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

330: #if defined(PETSC_USE_INFO)
331:   if (api[am]) {
332:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
333:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
334:   } else {
335:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
336:   }
337: #endif
338:   PetscFunctionReturn(PETSC_SUCCESS);
339: }

341: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat, Mat, PetscReal, Mat);
342: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat, Mat, Mat);

344: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
345: {
346:   Mat_Product *product = C->product;
347:   Mat          A = product->A, B = product->B;

349:   PetscFunctionBegin;
350:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
351:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);

353:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
354:   C->ops->productsymbolic = MatProductSymbolic_AB;
355:   PetscFunctionReturn(PETSC_SUCCESS);
356: }

358: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
359: {
360:   Mat_Product *product = C->product;
361:   Mat          A = product->A, B = product->B;

363:   PetscFunctionBegin;
364:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
365:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

367:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
368:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
369:   PetscFunctionReturn(PETSC_SUCCESS);
370: }

372: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
373: {
374:   Mat_Product *product = C->product;

376:   PetscFunctionBegin;
377:   switch (product->type) {
378:   case MATPRODUCT_AB:
379:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
380:     break;
381:   case MATPRODUCT_AtB:
382:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
383:     break;
384:   default:
385:     break;
386:   }
387:   PetscFunctionReturn(PETSC_SUCCESS);
388: }

390: typedef struct {
391:   Mat           workB, workB1;
392:   MPI_Request  *rwaits, *swaits;
393:   PetscInt      nsends, nrecvs;
394:   MPI_Datatype *stype, *rtype;
395:   PetscInt      blda;
396: } MPIAIJ_MPIDense;

398: static PetscErrorCode MatMPIAIJ_MPIDenseDestroy(PetscCtxRt ctx)
399: {
400:   MPIAIJ_MPIDense *contents = *(MPIAIJ_MPIDense **)ctx;
401:   PetscInt         i;

403:   PetscFunctionBegin;
404:   PetscCall(MatDestroy(&contents->workB));
405:   PetscCall(MatDestroy(&contents->workB1));
406:   for (i = 0; i < contents->nsends; i++) PetscCallMPI(MPI_Type_free(&contents->stype[i]));
407:   for (i = 0; i < contents->nrecvs; i++) PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
408:   PetscCall(PetscFree4(contents->stype, contents->rtype, contents->rwaits, contents->swaits));
409:   PetscCall(PetscFree(contents));
410:   PetscFunctionReturn(PETSC_SUCCESS);
411: }

413: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
414: {
415:   Mat_MPIAIJ      *aij = (Mat_MPIAIJ *)A->data;
416:   PetscInt         nz  = aij->B->cmap->n, blda, m, M, n, N;
417:   MPIAIJ_MPIDense *contents;
418:   VecScatter       ctx = aij->Mvctx;
419:   PetscInt         Am = A->rmap->n, Bm = B->rmap->n, BN = B->cmap->N, Bbn, Bbn1, bs, numBb;
420:   MPI_Comm         comm;
421:   MPI_Datatype     type1, *stype, *rtype;
422:   const PetscInt  *sindices, *sstarts, *rstarts;
423:   PetscMPIInt     *disp, nsends, nrecvs, nrows_to, nrows_from;
424:   PetscBool        cisdense;

426:   PetscFunctionBegin;
427:   MatCheckProduct(C, 4);
428:   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
429:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
430:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)C, MATMPIDENSE, &cisdense));
431:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
432:   PetscCall(MatGetLocalSize(C, &m, &n));
433:   PetscCall(MatGetSize(C, &M, &N));
434:   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) PetscCall(MatSetSizes(C, Am, B->cmap->n, A->rmap->N, BN));
435:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
436:   PetscCall(MatSetUp(C));
437:   PetscCall(MatDenseGetLDA(B, &blda));
438:   PetscCall(PetscNew(&contents));

440:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
441:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));

443:   /* Create column block of B and C for memory scalability when BN is too large */
444:   /* Estimate Bbn, column size of Bb */
445:   if (nz) {
446:     Bbn1 = 2 * Am * BN / nz;
447:     if (!Bbn1) Bbn1 = 1;
448:   } else Bbn1 = BN;

450:   bs   = B->cmap->bs;
451:   Bbn1 = Bbn1 / bs * bs; /* Bbn1 is a multiple of bs */
452:   if (Bbn1 > BN) Bbn1 = BN;
453:   PetscCallMPI(MPIU_Allreduce(&Bbn1, &Bbn, 1, MPIU_INT, MPI_MAX, comm));

455:   /* Enable runtime option for Bbn */
456:   PetscOptionsBegin(comm, ((PetscObject)C)->prefix, "MatProduct", "Mat");
457:   PetscCall(PetscOptionsDeprecated("-matmatmult_Bbn", "-matproduct_batch_size", "3.25", NULL));
458:   PetscCall(PetscOptionsInt("-matproduct_batch_size", "Number of columns in Bb", "MatProduct", Bbn, &Bbn, NULL));
459:   PetscOptionsEnd();
460:   Bbn = PetscMin(Bbn, BN);

462:   if (Bbn > 0 && Bbn < BN) {
463:     numBb = BN / Bbn;
464:     Bbn1  = BN - numBb * Bbn;
465:   } else numBb = 0;

467:   if (numBb) {
468:     PetscCall(PetscInfo(C, "use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n", BN, Bbn, numBb));
469:     if (Bbn1) { /* Create workB1 for the remaining columns */
470:       PetscCall(PetscInfo(C, "use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n", BN, Bbn1));
471:       /* Create work matrix used to store off processor rows of B needed for local product */
472:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nz, Bbn1, NULL, &contents->workB1));
473:     } else contents->workB1 = NULL;
474:   }

476:   /* Create work matrix used to store off processor rows of B needed for local product */
477:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nz, Bbn, NULL, &contents->workB));

479:   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
480:   PetscCall(PetscMalloc4(nsends, &stype, nrecvs, &rtype, nrecvs, &contents->rwaits, nsends, &contents->swaits));
481:   contents->stype  = stype;
482:   contents->nsends = nsends;

484:   contents->rtype  = rtype;
485:   contents->nrecvs = nrecvs;
486:   contents->blda   = blda;

488:   PetscCall(PetscMalloc1(Bm + 1, &disp));
489:   for (PetscMPIInt i = 0; i < nsends; i++) {
490:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
491:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j], &disp[j])); /* rowB to be sent */
492:     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, 1, disp, MPIU_SCALAR, &type1));
493:     PetscCallMPI(MPI_Type_create_resized(type1, 0, blda * sizeof(PetscScalar), &stype[i]));
494:     PetscCallMPI(MPI_Type_commit(&stype[i]));
495:     PetscCallMPI(MPI_Type_free(&type1));
496:   }

498:   for (PetscMPIInt i = 0; i < nrecvs; i++) {
499:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
500:     PetscCall(PetscMPIIntCast(rstarts[i + 1] - rstarts[i], &nrows_from));
501:     disp[0] = 0;
502:     PetscCallMPI(MPI_Type_create_indexed_block(1, nrows_from, disp, MPIU_SCALAR, &type1));
503:     PetscCallMPI(MPI_Type_create_resized(type1, 0, nz * sizeof(PetscScalar), &rtype[i]));
504:     PetscCallMPI(MPI_Type_commit(&rtype[i]));
505:     PetscCallMPI(MPI_Type_free(&type1));
506:   }

508:   PetscCall(PetscFree(disp));
509:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
510:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
511:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
512:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
513:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

515:   C->product->data       = contents;
516:   C->product->destroy    = MatMPIAIJ_MPIDenseDestroy;
517:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
518:   PetscFunctionReturn(PETSC_SUCCESS);
519: }

521: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat, Mat, Mat, const PetscBool);

523: /*
524:     Performs an efficient scatter on the rows of B needed by this process; this is
525:     a modification of the VecScatterBegin_() routines.

527:     Input: If Bbidx = 0, uses B = Bb, else B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
528: */

530: static PetscErrorCode MatMPIDenseScatter(Mat A, Mat B, PetscInt Bbidx, Mat C, Mat *outworkB)
531: {
532:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
533:   const PetscScalar *b;
534:   PetscScalar       *rvalues;
535:   VecScatter         ctx = aij->Mvctx;
536:   const PetscInt    *sindices, *sstarts, *rstarts;
537:   const PetscMPIInt *sprocs, *rprocs;
538:   PetscMPIInt        nsends, nrecvs;
539:   MPI_Request       *swaits, *rwaits;
540:   MPI_Comm           comm;
541:   PetscMPIInt        tag = ((PetscObject)ctx)->tag, ncols, nrows, nsends_mpi, nrecvs_mpi;
542:   MPIAIJ_MPIDense   *contents;
543:   Mat                workB;
544:   MPI_Datatype      *stype, *rtype;
545:   PetscInt           blda;

547:   PetscFunctionBegin;
548:   MatCheckProduct(C, 4);
549:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
550:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
551:   PetscCall(PetscMPIIntCast(aij->B->cmap->n, &nrows));
552:   contents = (MPIAIJ_MPIDense *)C->product->data;
553:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
554:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
555:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
556:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
557:   if (Bbidx == 0) workB = *outworkB = contents->workB;
558:   else workB = *outworkB = contents->workB1;
559:   PetscCheck(nrows == workB->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of rows of workB %" PetscInt_FMT " not equal to columns of aij->B %d", workB->cmap->n, nrows);
560:   swaits = contents->swaits;
561:   rwaits = contents->rwaits;

563:   PetscCall(MatDenseGetArrayRead(B, &b));
564:   PetscCall(MatDenseGetLDA(B, &blda));
565:   PetscCheck(blda == contents->blda, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot reuse an input matrix with lda %" PetscInt_FMT " != %" PetscInt_FMT, blda, contents->blda);
566:   PetscCall(MatDenseGetArray(workB, &rvalues));

568:   /* Post recv, use MPI derived data type to save memory */
569:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
570:   rtype = contents->rtype;
571:   for (PetscMPIInt i = 0; i < nrecvs; i++) PetscCallMPI(MPIU_Irecv(rvalues + (rstarts[i] - rstarts[0]), ncols, rtype[i], rprocs[i], tag, comm, rwaits + i));

573:   stype = contents->stype;
574:   for (PetscMPIInt i = 0; i < nsends; i++) PetscCallMPI(MPIU_Isend(b, ncols, stype[i], sprocs[i], tag, comm, swaits + i));

576:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, rwaits, MPI_STATUSES_IGNORE));
577:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, swaits, MPI_STATUSES_IGNORE));

579:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL));
580:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL));
581:   PetscCall(MatDenseRestoreArrayRead(B, &b));
582:   PetscCall(MatDenseRestoreArray(workB, &rvalues));
583:   PetscFunctionReturn(PETSC_SUCCESS);
584: }

586: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A, Mat B, Mat C)
587: {
588:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ *)A->data;
589:   Mat_MPIDense    *bdense = (Mat_MPIDense *)B->data;
590:   Mat_MPIDense    *cdense = (Mat_MPIDense *)C->data;
591:   Mat              workB;
592:   MPIAIJ_MPIDense *contents;

594:   PetscFunctionBegin;
595:   MatCheckProduct(C, 3);
596:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
597:   contents = (MPIAIJ_MPIDense *)C->product->data;
598:   /* diagonal block of A times all local rows of B */
599:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
600:   PetscCall(MatMatMult(aij->A, bdense->A, MAT_REUSE_MATRIX, PETSC_CURRENT, &cdense->A));
601:   if (contents->workB->cmap->n == B->cmap->N) {
602:     /* get off processor parts of B needed to complete C=A*B */
603:     PetscCall(MatMPIDenseScatter(A, B, 0, C, &workB));

605:     /* off-diagonal block of A times nonlocal rows of B */
606:     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
607:   } else {
608:     Mat       Bb, Cb;
609:     PetscInt  BN = B->cmap->N, n = contents->workB->cmap->n;
610:     PetscBool ccpu;

612:     PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
613:     /* Prevent from unneeded copies back and forth from the GPU
614:        when getting and restoring the submatrix
615:        We need a proper GPU code for AIJ * dense in parallel */
616:     PetscCall(MatBoundToCPU(C, &ccpu));
617:     PetscCall(MatBindToCPU(C, PETSC_TRUE));
618:     for (PetscInt i = 0; i < BN; i += n) {
619:       PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Bb));
620:       PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Cb));

622:       /* get off processor parts of B needed to complete C=A*B */
623:       PetscCall(MatMPIDenseScatter(A, Bb, (i + n) > BN, C, &workB));

625:       /* off-diagonal block of A times nonlocal rows of B */
626:       cdense = (Mat_MPIDense *)Cb->data;
627:       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
628:       PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
629:       PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
630:     }
631:     PetscCall(MatBindToCPU(C, ccpu));
632:   }
633:   PetscFunctionReturn(PETSC_SUCCESS);
634: }

636: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
637: {
638:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
639:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
640:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
641:   PetscInt            *adi = ad->i, *adj, *aoi = ao->i, *aoj;
642:   PetscScalar         *ada, *aoa, *cda = cd->a, *coa = co->a;
643:   Mat_SeqAIJ          *p_loc, *p_oth;
644:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
645:   PetscScalar         *pa_loc, *pa_oth, *pa, valtmp, *ca;
646:   PetscInt             cm = C->rmap->n, anz, pnz;
647:   MatProductCtx_APMPI *ptap;
648:   PetscScalar         *apa_sparse;
649:   const PetscScalar   *dummy;
650:   PetscInt            *api, *apj, *apJ, i, j, k, row;
651:   PetscInt             cstart = C->cmap->rstart;
652:   PetscInt             cdnz, conz, k0, k1, nextp;
653:   MPI_Comm             comm;
654:   PetscMPIInt          size;

656:   PetscFunctionBegin;
657:   MatCheckProduct(C, 3);
658:   ptap = (MatProductCtx_APMPI *)C->product->data;
659:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
660:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
661:   PetscCallMPI(MPI_Comm_size(comm, &size));
662:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

664:   /* flag CPU mask for C */
665: #if defined(PETSC_HAVE_DEVICE)
666:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
667:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
668:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
669: #endif
670:   apa_sparse = ptap->apa;

672:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
673:   /* update numerical values of P_oth and P_loc */
674:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
675:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

677:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
678:   /* get data from symbolic products */
679:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
680:   pi_loc = p_loc->i;
681:   pj_loc = p_loc->j;
682:   pa_loc = p_loc->a;
683:   if (size > 1) {
684:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
685:     pi_oth = p_oth->i;
686:     pj_oth = p_oth->j;
687:     pa_oth = p_oth->a;
688:   } else {
689:     p_oth  = NULL;
690:     pi_oth = NULL;
691:     pj_oth = NULL;
692:     pa_oth = NULL;
693:   }

695:   /* trigger copy to CPU */
696:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
697:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
698:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
699:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
700:   api = ptap->api;
701:   apj = ptap->apj;
702:   for (i = 0; i < cm; i++) {
703:     apJ = apj + api[i];

705:     /* diagonal portion of A */
706:     anz = adi[i + 1] - adi[i];
707:     adj = ad->j + adi[i];
708:     ada = ad->a + adi[i];
709:     for (j = 0; j < anz; j++) {
710:       row = adj[j];
711:       pnz = pi_loc[row + 1] - pi_loc[row];
712:       pj  = pj_loc + pi_loc[row];
713:       pa  = pa_loc + pi_loc[row];
714:       /* perform sparse axpy */
715:       valtmp = ada[j];
716:       nextp  = 0;
717:       for (k = 0; nextp < pnz; k++) {
718:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
719:           apa_sparse[k] += valtmp * pa[nextp++];
720:         }
721:       }
722:       PetscCall(PetscLogFlops(2.0 * pnz));
723:     }

725:     /* off-diagonal portion of A */
726:     anz = aoi[i + 1] - aoi[i];
727:     aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
728:     aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
729:     for (j = 0; j < anz; j++) {
730:       row = aoj[j];
731:       pnz = pi_oth[row + 1] - pi_oth[row];
732:       pj  = pj_oth + pi_oth[row];
733:       pa  = pa_oth + pi_oth[row];
734:       /* perform sparse axpy */
735:       valtmp = aoa[j];
736:       nextp  = 0;
737:       for (k = 0; nextp < pnz; k++) {
738:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
739:           apa_sparse[k] += valtmp * pa[nextp++];
740:         }
741:       }
742:       PetscCall(PetscLogFlops(2.0 * pnz));
743:     }

745:     /* set values in C */
746:     cdnz = cd->i[i + 1] - cd->i[i];
747:     conz = co->i[i + 1] - co->i[i];

749:     /* 1st off-diagonal part of C */
750:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
751:     k  = 0;
752:     for (k0 = 0; k0 < conz; k0++) {
753:       if (apJ[k] >= cstart) break;
754:       ca[k0]        = apa_sparse[k];
755:       apa_sparse[k] = 0.0;
756:       k++;
757:     }

759:     /* diagonal part of C */
760:     ca = cda + cd->i[i];
761:     for (k1 = 0; k1 < cdnz; k1++) {
762:       ca[k1]        = apa_sparse[k];
763:       apa_sparse[k] = 0.0;
764:       k++;
765:     }

767:     /* 2nd off-diagonal part of C */
768:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
769:     for (; k0 < conz; k0++) {
770:       ca[k0]        = apa_sparse[k];
771:       apa_sparse[k] = 0.0;
772:       k++;
773:     }
774:   }
775:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
776:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
781: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A, Mat P, PetscReal fill, Mat C)
782: {
783:   MPI_Comm             comm;
784:   PetscMPIInt          size;
785:   MatProductCtx_APMPI *ptap;
786:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
787:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
788:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
789:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
790:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
791:   PetscInt             i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi, *lnk, apnz_max = 1;
792:   PetscInt             am = A->rmap->n, pn = P->cmap->n, pm = P->rmap->n, lsize = pn + 20;
793:   PetscReal            afill;
794:   MatType              mtype;

796:   PetscFunctionBegin;
797:   MatCheckProduct(C, 4);
798:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
799:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
800:   PetscCallMPI(MPI_Comm_size(comm, &size));

802:   /* create struct MatProductCtx_APMPI and attached it to C later */
803:   PetscCall(PetscNew(&ptap));

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

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

811:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
812:   pi_loc = p_loc->i;
813:   pj_loc = p_loc->j;
814:   if (size > 1) {
815:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
816:     pi_oth = p_oth->i;
817:     pj_oth = p_oth->j;
818:   } else {
819:     p_oth  = NULL;
820:     pi_oth = NULL;
821:     pj_oth = NULL;
822:   }

824:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
825:   PetscCall(PetscMalloc1(am + 1, &api));
826:   ptap->api = api;
827:   api[0]    = 0;

829:   PetscCall(PetscLLCondensedCreate_Scalable(lsize, &lnk));

831:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
832:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
833:   current_space = free_space;
834:   MatPreallocateBegin(comm, am, pn, dnz, onz);
835:   for (i = 0; i < am; i++) {
836:     /* diagonal portion of A */
837:     nzi = adi[i + 1] - adi[i];
838:     for (j = 0; j < nzi; j++) {
839:       row  = *adj++;
840:       pnz  = pi_loc[row + 1] - pi_loc[row];
841:       Jptr = pj_loc + pi_loc[row];
842:       /* Expand list if it is not long enough */
843:       if (pnz + apnz_max > lsize) {
844:         lsize = pnz + apnz_max;
845:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
846:       }
847:       /* add non-zero cols of P into the sorted linked list lnk */
848:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
849:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
850:       api[i + 1] = api[i] + apnz;
851:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
852:     }
853:     /* off-diagonal portion of A */
854:     nzi = aoi[i + 1] - aoi[i];
855:     for (j = 0; j < nzi; j++) {
856:       row  = *aoj++;
857:       pnz  = pi_oth[row + 1] - pi_oth[row];
858:       Jptr = pj_oth + pi_oth[row];
859:       /* Expand list if it is not long enough */
860:       if (pnz + apnz_max > lsize) {
861:         lsize = pnz + apnz_max;
862:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
863:       }
864:       /* add non-zero cols of P into the sorted linked list lnk */
865:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
866:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
867:       api[i + 1] = api[i] + apnz;
868:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
869:     }

871:     /* add missing diagonal entry */
872:     if (C->force_diagonals) {
873:       j = i + rstart; /* column index */
874:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
875:     }

877:     apnz       = *lnk;
878:     api[i + 1] = api[i] + apnz;
879:     if (apnz > apnz_max) apnz_max = apnz;

881:     /* if free space is not available, double the total space in the list */
882:     if (current_space->local_remaining < apnz) {
883:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
884:       nspacedouble++;
885:     }

887:     /* Copy data into free space, then initialize lnk */
888:     PetscCall(PetscLLCondensedClean_Scalable(apnz, current_space->array, lnk));
889:     PetscCall(MatPreallocateSet(i + rstart, apnz, current_space->array, dnz, onz));

891:     current_space->array += apnz;
892:     current_space->local_used += apnz;
893:     current_space->local_remaining -= apnz;
894:   }

896:   /* Allocate space for apj, initialize apj, and */
897:   /* destroy list of free space and other temporary array(s) */
898:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
899:   apj = ptap->apj;
900:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
901:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

903:   /* create and assemble symbolic parallel matrix C */
904:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
905:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
906:   PetscCall(MatGetType(A, &mtype));
907:   PetscCall(MatSetType(C, mtype));
908:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
909:   MatPreallocateEnd(dnz, onz);

911:   /* malloc apa for assembly C */
912:   PetscCall(PetscCalloc1(apnz_max, &ptap->apa));

914:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
915:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
916:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
917:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
918:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

920:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
921:   C->ops->productnumeric = MatProductNumeric_AB;

923:   /* attach the supporting struct to C for reuse */
924:   C->product->data    = ptap;
925:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

927:   /* set MatInfo */
928:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
929:   if (afill < 1.0) afill = 1.0;
930:   C->info.mallocs           = nspacedouble;
931:   C->info.fill_ratio_given  = fill;
932:   C->info.fill_ratio_needed = afill;

934: #if defined(PETSC_USE_INFO)
935:   if (api[am]) {
936:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
937:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
938:   } else {
939:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
940:   }
941: #endif
942:   PetscFunctionReturn(PETSC_SUCCESS);
943: }

945: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
946: /* Three input arrays are merged to one output array. The size of the    */
947: /* output array is also output. Duplicate entries only show up once.     */
948: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
949: {
950:   int i = 0, j = 0, k = 0, l = 0;

952:   /* Traverse all three arrays */
953:   while (i < size1 && j < size2 && k < size3) {
954:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
955:       out[l++] = in1[i++];
956:     } else if (in2[j] < in1[i] && in2[j] < in3[k]) {
957:       out[l++] = in2[j++];
958:     } else if (in3[k] < in1[i] && in3[k] < in2[j]) {
959:       out[l++] = in3[k++];
960:     } else if (in1[i] == in2[j] && in1[i] < in3[k]) {
961:       out[l++] = in1[i];
962:       i++, j++;
963:     } else if (in1[i] == in3[k] && in1[i] < in2[j]) {
964:       out[l++] = in1[i];
965:       i++, k++;
966:     } else if (in3[k] == in2[j] && in2[j] < in1[i]) {
967:       out[l++] = in2[j];
968:       k++, j++;
969:     } else if (in1[i] == in2[j] && in1[i] == in3[k]) {
970:       out[l++] = in1[i];
971:       i++, j++, k++;
972:     }
973:   }

975:   /* Traverse two remaining arrays */
976:   while (i < size1 && j < size2) {
977:     if (in1[i] < in2[j]) {
978:       out[l++] = in1[i++];
979:     } else if (in1[i] > in2[j]) {
980:       out[l++] = in2[j++];
981:     } else {
982:       out[l++] = in1[i];
983:       i++, j++;
984:     }
985:   }

987:   while (i < size1 && k < size3) {
988:     if (in1[i] < in3[k]) {
989:       out[l++] = in1[i++];
990:     } else if (in1[i] > in3[k]) {
991:       out[l++] = in3[k++];
992:     } else {
993:       out[l++] = in1[i];
994:       i++, k++;
995:     }
996:   }

998:   while (k < size3 && j < size2) {
999:     if (in3[k] < in2[j]) {
1000:       out[l++] = in3[k++];
1001:     } else if (in3[k] > in2[j]) {
1002:       out[l++] = in2[j++];
1003:     } else {
1004:       out[l++] = in3[k];
1005:       k++, j++;
1006:     }
1007:   }

1009:   /* Traverse one remaining array */
1010:   while (i < size1) out[l++] = in1[i++];
1011:   while (j < size2) out[l++] = in2[j++];
1012:   while (k < size3) out[l++] = in3[k++];

1014:   *size4 = l;
1015: }

1017: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1018: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1019: /* matrix-matrix multiplications.  */
1020: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1021: {
1022:   MPI_Comm             comm;
1023:   PetscMPIInt          size;
1024:   MatProductCtx_APMPI *ptap;
1025:   PetscFreeSpaceList   free_space_diag = NULL, current_space = NULL;
1026:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
1027:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1028:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1029:   Mat_SeqAIJ          *adpd_seq, *p_off, *aopoth_seq;
1030:   PetscInt             adponz, adpdnz;
1031:   PetscInt            *pi_loc, *dnz, *onz;
1032:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1033:   PetscInt            *lnk, i, i1 = 0, pnz, row, *adpoi, *adpoj, *api, *adpoJ, *aopJ, *apJ, *Jptr, aopnz, nspacedouble = 0, j, nzi, *apj, apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1034:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1035:   PetscBT              lnkbt;
1036:   PetscReal            afill;
1037:   PetscMPIInt          rank;
1038:   Mat                  adpd, aopoth;
1039:   MatType              mtype;
1040:   const char          *prefix;

1042:   PetscFunctionBegin;
1043:   MatCheckProduct(C, 4);
1044:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1045:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1046:   PetscCallMPI(MPI_Comm_size(comm, &size));
1047:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1048:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1050:   /* create struct MatProductCtx_APMPI and attached it to C later */
1051:   PetscCall(PetscNew(&ptap));

1053:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1054:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1056:   /* get P_loc by taking all local rows of P */
1057:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1059:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1060:   pi_loc = p_loc->i;

1062:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1063:   PetscCall(PetscMalloc1(am + 1, &api));
1064:   PetscCall(PetscMalloc1(am + 1, &adpoi));

1066:   adpoi[0]  = 0;
1067:   ptap->api = api;
1068:   api[0]    = 0;

1070:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1071:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1072:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1074:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1075:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1076:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1077:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1078:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1079:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1081:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1082:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1083:   PetscCall(MatProductSetFill(adpd, fill));
1084:   PetscCall(MatProductSetFromOptions(adpd));

1086:   adpd->force_diagonals = C->force_diagonals;
1087:   PetscCall(MatProductSymbolic(adpd));

1089:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1090:   adpdi    = adpd_seq->i;
1091:   adpdj    = adpd_seq->j;
1092:   p_off    = (Mat_SeqAIJ *)p->B->data;
1093:   poff_i   = p_off->i;
1094:   poff_j   = p_off->j;

1096:   /* j_temp stores indices of a result row before they are added to the linked list */
1097:   PetscCall(PetscMalloc1(pN, &j_temp));

1099:   /* Symbolic calc of the A_diag * p_loc_off */
1100:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1101:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1102:   current_space = free_space_diag;

1104:   for (i = 0; i < am; i++) {
1105:     /* A_diag * P_loc_off */
1106:     nzi = adi[i + 1] - adi[i];
1107:     for (j = 0; j < nzi; j++) {
1108:       row  = *adj++;
1109:       pnz  = poff_i[row + 1] - poff_i[row];
1110:       Jptr = poff_j + poff_i[row];
1111:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1112:       /* add non-zero cols of P into the sorted linked list lnk */
1113:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1114:     }

1116:     adponz       = lnk[0];
1117:     adpoi[i + 1] = adpoi[i] + adponz;

1119:     /* if free space is not available, double the total space in the list */
1120:     if (current_space->local_remaining < adponz) {
1121:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1122:       nspacedouble++;
1123:     }

1125:     /* Copy data into free space, then initialize lnk */
1126:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1128:     current_space->array += adponz;
1129:     current_space->local_used += adponz;
1130:     current_space->local_remaining -= adponz;
1131:   }

1133:   /* Symbolic calc of A_off * P_oth */
1134:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1135:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1136:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1137:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1138:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1139:   aopothi    = aopoth_seq->i;
1140:   aopothj    = aopoth_seq->j;

1142:   /* Allocate space for apj, adpj, aopj, ... */
1143:   /* destroy lists of free space and other temporary array(s) */

1145:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1146:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

1148:   /* Copy from linked list to j-array */
1149:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1150:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1152:   adpoJ = adpoj;
1153:   adpdJ = adpdj;
1154:   aopJ  = aopothj;
1155:   apj   = ptap->apj;
1156:   apJ   = apj; /* still empty */

1158:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1159:   /* A_diag * P_loc_diag to get A*P */
1160:   for (i = 0; i < am; i++) {
1161:     aopnz  = aopothi[i + 1] - aopothi[i];
1162:     adponz = adpoi[i + 1] - adpoi[i];
1163:     adpdnz = adpdi[i + 1] - adpdi[i];

1165:     /* Correct indices from A_diag*P_diag */
1166:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1167:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1168:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1169:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1171:     aopJ += aopnz;
1172:     adpoJ += adponz;
1173:     adpdJ += adpdnz;
1174:     apJ += apnz;
1175:     api[i + 1] = api[i] + apnz;
1176:   }

1178:   /* malloc apa to store dense row A[i,:]*P */
1179:   PetscCall(PetscCalloc1(pN, &ptap->apa));

1181:   /* create and assemble symbolic parallel matrix C */
1182:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1183:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1184:   PetscCall(MatGetType(A, &mtype));
1185:   PetscCall(MatSetType(C, mtype));
1186:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1187:   MatPreallocateEnd(dnz, onz);

1189:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1190:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1191:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1192:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1193:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1195:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1196:   C->ops->productnumeric = MatProductNumeric_AB;

1198:   /* attach the supporting struct to C for reuse */
1199:   C->product->data    = ptap;
1200:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

1202:   /* set MatInfo */
1203:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1204:   if (afill < 1.0) afill = 1.0;
1205:   C->info.mallocs           = nspacedouble;
1206:   C->info.fill_ratio_given  = fill;
1207:   C->info.fill_ratio_needed = afill;

1209: #if defined(PETSC_USE_INFO)
1210:   if (api[am]) {
1211:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1212:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1213:   } else {
1214:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1215:   }
1216: #endif

1218:   PetscCall(MatDestroy(&aopoth));
1219:   PetscCall(MatDestroy(&adpd));
1220:   PetscCall(PetscFree(j_temp));
1221:   PetscCall(PetscFree(adpoj));
1222:   PetscCall(PetscFree(adpoi));
1223:   PetscFunctionReturn(PETSC_SUCCESS);
1224: }

1226: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1227: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1228: {
1229:   MatProductCtx_APMPI *ptap;
1230:   Mat                  Pt;

1232:   PetscFunctionBegin;
1233:   MatCheckProduct(C, 3);
1234:   ptap = (MatProductCtx_APMPI *)C->product->data;
1235:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1236:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1238:   Pt = ptap->Pt;
1239:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1240:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1241:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1242:   PetscFunctionReturn(PETSC_SUCCESS);
1243: }

1245: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1246: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1247: {
1248:   MatProductCtx_APMPI     *ptap;
1249:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1250:   MPI_Comm                 comm;
1251:   PetscMPIInt              size, rank;
1252:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1253:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1254:   PetscInt                *lnk, i, k, rstart;
1255:   PetscBT                  lnkbt;
1256:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1257:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1258:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1259:   PetscInt                 len, *dnz, *onz, *owners, nzi;
1260:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1261:   MPI_Request             *swaits, *rwaits;
1262:   MPI_Status              *sstatus, rstatus;
1263:   PetscLayout              rowmap;
1264:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1265:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1266:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1267:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1268:   PetscHMapI               ta;
1269:   MatType                  mtype;
1270:   const char              *prefix;

1272:   PetscFunctionBegin;
1273:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1274:   PetscCallMPI(MPI_Comm_size(comm, &size));
1275:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1277:   /* create symbolic parallel matrix C */
1278:   PetscCall(MatGetType(A, &mtype));
1279:   PetscCall(MatSetType(C, mtype));

1281:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1283:   /* create struct MatProductCtx_APMPI and attached it to C later */
1284:   PetscCall(PetscNew(&ptap));

1286:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1287:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1288:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1290:   /* (1) compute symbolic A_loc */
1291:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1293:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1294:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1295:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1296:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1297:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1298:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1300:   /* (3) send coj of C_oth to other processors  */
1301:   /* determine row ownership */
1302:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1303:   rowmap->n  = pn;
1304:   rowmap->bs = 1;
1305:   PetscCall(PetscLayoutSetUp(rowmap));
1306:   owners = rowmap->range;

1308:   /* determine the number of messages to send, their lengths */
1309:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1310:   PetscCall(PetscArrayzero(len_s, size));
1311:   PetscCall(PetscArrayzero(len_si, size));

1313:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1314:   coi   = c_oth->i;
1315:   coj   = c_oth->j;
1316:   con   = ptap->C_oth->rmap->n;
1317:   proc  = 0;
1318:   for (i = 0; i < con; i++) {
1319:     while (prmap[i] >= owners[proc + 1]) proc++;
1320:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1321:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1322:   }

1324:   len          = 0; /* max length of buf_si[], see (4) */
1325:   owners_co[0] = 0;
1326:   nsend        = 0;
1327:   for (proc = 0; proc < size; proc++) {
1328:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1329:     if (len_s[proc]) {
1330:       nsend++;
1331:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1332:       len += len_si[proc];
1333:     }
1334:   }

1336:   /* determine the number and length of messages to receive for coi and coj  */
1337:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1338:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1340:   /* post the Irecv and Isend of coj */
1341:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1342:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1343:   PetscCall(PetscMalloc1(nsend, &swaits));
1344:   for (proc = 0, k = 0; proc < size; proc++) {
1345:     if (!len_s[proc]) continue;
1346:     i = owners_co[proc];
1347:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1348:     k++;
1349:   }

1351:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1352:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1353:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1354:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1355:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1356:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1358:   /* receives coj are complete */
1359:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1360:   PetscCall(PetscFree(rwaits));
1361:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1363:   /* add received column indices into ta to update Crmax */
1364:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1366:   /* create and initialize a linked list */
1367:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1368:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1370:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1371:     Jptr = buf_rj[k];
1372:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1373:   }
1374:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1375:   PetscCall(PetscHMapIDestroy(&ta));

1377:   /* (4) send and recv coi */
1378:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1379:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1380:   PetscCall(PetscMalloc1(len, &buf_s));
1381:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1382:   for (proc = 0, k = 0; proc < size; proc++) {
1383:     if (!len_s[proc]) continue;
1384:     /* form outgoing message for i-structure:
1385:          buf_si[0]:                 nrows to be sent
1386:                [1:nrows]:           row index (global)
1387:                [nrows+1:2*nrows+1]: i-structure index
1388:     */
1389:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1390:     buf_si_i    = buf_si + nrows + 1;
1391:     buf_si[0]   = nrows;
1392:     buf_si_i[0] = 0;
1393:     nrows       = 0;
1394:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1395:       nzi                 = coi[i + 1] - coi[i];
1396:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1397:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1398:       nrows++;
1399:     }
1400:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1401:     k++;
1402:     buf_si += len_si[proc];
1403:   }
1404:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1405:   PetscCall(PetscFree(rwaits));
1406:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1408:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1409:   PetscCall(PetscFree(len_ri));
1410:   PetscCall(PetscFree(swaits));
1411:   PetscCall(PetscFree(buf_s));

1413:   /* (5) compute the local portion of C      */
1414:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1415:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1416:   current_space = free_space;

1418:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1419:   for (k = 0; k < nrecv; k++) {
1420:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1421:     nrows       = *buf_ri_k[k];
1422:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1423:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1424:   }

1426:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1427:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1428:   for (i = 0; i < pn; i++) { /* for each local row of C */
1429:     /* add C_loc into C */
1430:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1431:     Jptr = c_loc->j + c_loc->i[i];
1432:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1434:     /* add received col data into lnk */
1435:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1436:       if (i == *nextrow[k]) {     /* i-th row */
1437:         nzi  = *(nextci[k] + 1) - *nextci[k];
1438:         Jptr = buf_rj[k] + *nextci[k];
1439:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1440:         nextrow[k]++;
1441:         nextci[k]++;
1442:       }
1443:     }

1445:     /* add missing diagonal entry */
1446:     if (C->force_diagonals) {
1447:       k = i + owners[rank]; /* column index */
1448:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1449:     }

1451:     nzi = lnk[0];

1453:     /* copy data into free space, then initialize lnk */
1454:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1455:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1456:   }
1457:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1458:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1459:   PetscCall(PetscFreeSpaceDestroy(free_space));

1461:   /* local sizes and preallocation */
1462:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1463:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1464:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1465:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1466:   MatPreallocateEnd(dnz, onz);

1468:   /* add C_loc and C_oth to C */
1469:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1470:   for (i = 0; i < pn; i++) {
1471:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1472:     cols  = c_loc->j + c_loc->i[i];
1473:     row   = rstart + i;
1474:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1476:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1477:   }
1478:   for (i = 0; i < con; i++) {
1479:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1480:     cols  = c_oth->j + c_oth->i[i];
1481:     row   = prmap[i];
1482:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1483:   }
1484:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1485:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1486:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1488:   /* members in merge */
1489:   PetscCall(PetscFree(id_r));
1490:   PetscCall(PetscFree(len_r));
1491:   PetscCall(PetscFree(buf_ri[0]));
1492:   PetscCall(PetscFree(buf_ri));
1493:   PetscCall(PetscFree(buf_rj[0]));
1494:   PetscCall(PetscFree(buf_rj));
1495:   PetscCall(PetscLayoutDestroy(&rowmap));

1497:   /* attach the supporting struct to C for reuse */
1498:   C->product->data    = ptap;
1499:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
1500:   PetscFunctionReturn(PETSC_SUCCESS);
1501: }

1503: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1504: {
1505:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1506:   Mat_SeqAIJ          *c_seq;
1507:   MatProductCtx_APMPI *ptap;
1508:   Mat                  A_loc, C_loc, C_oth;
1509:   PetscInt             i, rstart, rend, cm, ncols, row;
1510:   const PetscInt      *cols;
1511:   const PetscScalar   *vals;

1513:   PetscFunctionBegin;
1514:   MatCheckProduct(C, 3);
1515:   ptap = (MatProductCtx_APMPI *)C->product->data;
1516:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1517:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1518:   PetscCall(MatZeroEntries(C));

1520:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1521:   /* 1) get R = Pd^T, Ro = Po^T */
1522:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1523:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1524:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1525:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1527:   /* 2) compute numeric A_loc */
1528:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1530:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1531:   A_loc = ptap->A_loc;
1532:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1533:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1534:   C_loc = ptap->C_loc;
1535:   C_oth = ptap->C_oth;

1537:   /* add C_loc and C_oth to C */
1538:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1540:   /* C_loc -> C */
1541:   cm    = C_loc->rmap->N;
1542:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1543:   cols  = c_seq->j;
1544:   vals  = c_seq->a;
1545:   for (i = 0; i < cm; i++) {
1546:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1547:     row   = rstart + i;
1548:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1549:     cols += ncols;
1550:     vals += ncols;
1551:   }

1553:   /* Co -> C, off-processor part */
1554:   cm    = C_oth->rmap->N;
1555:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1556:   cols  = c_seq->j;
1557:   vals  = c_seq->a;
1558:   for (i = 0; i < cm; i++) {
1559:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1560:     row   = p->garray[i];
1561:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1562:     cols += ncols;
1563:     vals += ncols;
1564:   }
1565:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1566:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1567:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1568:   PetscFunctionReturn(PETSC_SUCCESS);
1569: }

1571: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1572: {
1573:   MatMergeSeqsToMPI   *merge;
1574:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1575:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1576:   MatProductCtx_APMPI *ap;
1577:   PetscInt            *adj;
1578:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1579:   MatScalar           *ada, *ca, valtmp;
1580:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1581:   MPI_Comm             comm;
1582:   PetscMPIInt          size, rank, taga, *len_s, proc;
1583:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1584:   PetscInt           **buf_ri, **buf_rj;
1585:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1586:   MPI_Request         *s_waits, *r_waits;
1587:   MPI_Status          *status;
1588:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1589:   const PetscScalar   *dummy;
1590:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1591:   Mat                  A_loc;
1592:   Mat_SeqAIJ          *a_loc;

1594:   PetscFunctionBegin;
1595:   MatCheckProduct(C, 3);
1596:   ap = (MatProductCtx_APMPI *)C->product->data;
1597:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1598:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1599:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1600:   PetscCallMPI(MPI_Comm_size(comm, &size));
1601:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1603:   merge = ap->merge;

1605:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1606:   /* get data from symbolic products */
1607:   coi = merge->coi;
1608:   coj = merge->coj;
1609:   PetscCall(PetscCalloc1(coi[pon], &coa));
1610:   bi     = merge->bi;
1611:   bj     = merge->bj;
1612:   owners = merge->rowmap->range;
1613:   PetscCall(PetscCalloc1(bi[cm], &ba));

1615:   /* get A_loc by taking all local rows of A */
1616:   A_loc = ap->A_loc;
1617:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1618:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1619:   ai    = a_loc->i;
1620:   aj    = a_loc->j;

1622:   /* trigger copy to CPU */
1623:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1624:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1625:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1626:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1627:   for (i = 0; i < am; i++) {
1628:     anz = ai[i + 1] - ai[i];
1629:     adj = aj + ai[i];
1630:     ada = a_loc->a + ai[i];

1632:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1633:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1634:     pnz = po->i[i + 1] - po->i[i];
1635:     poJ = po->j + po->i[i];
1636:     pA  = po->a + po->i[i];
1637:     for (j = 0; j < pnz; j++) {
1638:       row = poJ[j];
1639:       cj  = coj + coi[row];
1640:       ca  = coa + coi[row];
1641:       /* perform sparse axpy */
1642:       nexta  = 0;
1643:       valtmp = pA[j];
1644:       for (k = 0; nexta < anz; k++) {
1645:         if (cj[k] == adj[nexta]) {
1646:           ca[k] += valtmp * ada[nexta];
1647:           nexta++;
1648:         }
1649:       }
1650:       PetscCall(PetscLogFlops(2.0 * anz));
1651:     }

1653:     /* put the value into Cd (diagonal part) */
1654:     pnz = pd->i[i + 1] - pd->i[i];
1655:     pdJ = pd->j + pd->i[i];
1656:     pA  = pd->a + pd->i[i];
1657:     for (j = 0; j < pnz; j++) {
1658:       row = pdJ[j];
1659:       cj  = bj + bi[row];
1660:       ca  = ba + bi[row];
1661:       /* perform sparse axpy */
1662:       nexta  = 0;
1663:       valtmp = pA[j];
1664:       for (k = 0; nexta < anz; k++) {
1665:         if (cj[k] == adj[nexta]) {
1666:           ca[k] += valtmp * ada[nexta];
1667:           nexta++;
1668:         }
1669:       }
1670:       PetscCall(PetscLogFlops(2.0 * anz));
1671:     }
1672:   }

1674:   /* 3) send and recv matrix values coa */
1675:   buf_ri = merge->buf_ri;
1676:   buf_rj = merge->buf_rj;
1677:   len_s  = merge->len_s;
1678:   PetscCall(PetscCommGetNewTag(comm, &taga));
1679:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1681:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1682:   for (proc = 0, k = 0; proc < size; proc++) {
1683:     if (!len_s[proc]) continue;
1684:     i = merge->owners_co[proc];
1685:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1686:     k++;
1687:   }
1688:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1689:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1691:   PetscCall(PetscFree2(s_waits, status));
1692:   PetscCall(PetscFree(r_waits));
1693:   PetscCall(PetscFree(coa));

1695:   /* 4) insert local Cseq and received values into Cmpi */
1696:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1697:   for (k = 0; k < merge->nrecv; k++) {
1698:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1699:     nrows       = *buf_ri_k[k];
1700:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1701:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1702:   }

1704:   for (i = 0; i < cm; i++) {
1705:     row  = owners[rank] + i; /* global row index of C_seq */
1706:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1707:     ba_i = ba + bi[i];
1708:     bnz  = bi[i + 1] - bi[i];
1709:     /* add received vals into ba */
1710:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1711:       /* i-th row */
1712:       if (i == *nextrow[k]) {
1713:         cnz    = *(nextci[k] + 1) - *nextci[k];
1714:         cj     = buf_rj[k] + *nextci[k];
1715:         ca     = abuf_r[k] + *nextci[k];
1716:         nextcj = 0;
1717:         for (j = 0; nextcj < cnz; j++) {
1718:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1719:             ba_i[j] += ca[nextcj++];
1720:           }
1721:         }
1722:         nextrow[k]++;
1723:         nextci[k]++;
1724:         PetscCall(PetscLogFlops(2.0 * cnz));
1725:       }
1726:     }
1727:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1728:   }
1729:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1730:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1732:   PetscCall(PetscFree(ba));
1733:   PetscCall(PetscFree(abuf_r[0]));
1734:   PetscCall(PetscFree(abuf_r));
1735:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1736:   PetscFunctionReturn(PETSC_SUCCESS);
1737: }

1739: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1740: {
1741:   Mat                  A_loc;
1742:   MatProductCtx_APMPI *ap;
1743:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1744:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1745:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1746:   PetscInt             nnz;
1747:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1748:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1749:   MPI_Comm             comm;
1750:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1751:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1752:   PetscInt             len, *dnz, *onz, *owners;
1753:   PetscInt             nzi, *bi, *bj;
1754:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1755:   MPI_Request         *swaits, *rwaits;
1756:   MPI_Status          *sstatus, rstatus;
1757:   MatMergeSeqsToMPI   *merge;
1758:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1759:   PetscReal            afill  = 1.0, afill_tmp;
1760:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1761:   Mat_SeqAIJ          *a_loc;
1762:   PetscHMapI           ta;
1763:   MatType              mtype;

1765:   PetscFunctionBegin;
1766:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1767:   /* check if matrix local sizes are compatible */
1768:   PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, comm, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != P (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart,
1769:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1771:   PetscCallMPI(MPI_Comm_size(comm, &size));
1772:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1774:   /* create struct MatProductCtx_APMPI and attached it to C later */
1775:   PetscCall(PetscNew(&ap));

1777:   /* get A_loc by taking all local rows of A */
1778:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1780:   ap->A_loc = A_loc;
1781:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1782:   ai        = a_loc->i;
1783:   aj        = a_loc->j;

1785:   /* determine symbolic Co=(p->B)^T*A - send to others */
1786:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1787:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1788:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1789:                          >= (num of nonzero rows of C_seq) - pn */
1790:   PetscCall(PetscMalloc1(pon + 1, &coi));
1791:   coi[0] = 0;

1793:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1794:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1795:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1796:   current_space = free_space;

1798:   /* create and initialize a linked list */
1799:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1800:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1801:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1803:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1805:   for (i = 0; i < pon; i++) {
1806:     pnz = poti[i + 1] - poti[i];
1807:     ptJ = potj + poti[i];
1808:     for (j = 0; j < pnz; j++) {
1809:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1810:       anz  = ai[row + 1] - ai[row];
1811:       Jptr = aj + ai[row];
1812:       /* add non-zero cols of AP into the sorted linked list lnk */
1813:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1814:     }
1815:     nnz = lnk[0];

1817:     /* If free space is not available, double the total space in the list */
1818:     if (current_space->local_remaining < nnz) {
1819:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1820:       nspacedouble++;
1821:     }

1823:     /* Copy data into free space, and zero out denserows */
1824:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1826:     current_space->array += nnz;
1827:     current_space->local_used += nnz;
1828:     current_space->local_remaining -= nnz;

1830:     coi[i + 1] = coi[i] + nnz;
1831:   }

1833:   PetscCall(PetscMalloc1(coi[pon], &coj));
1834:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1835:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1837:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1838:   if (afill_tmp > afill) afill = afill_tmp;

1840:   /* send j-array (coj) of Co to other processors */
1841:   /* determine row ownership */
1842:   PetscCall(PetscNew(&merge));
1843:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1845:   merge->rowmap->n  = pn;
1846:   merge->rowmap->bs = 1;

1848:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1849:   owners = merge->rowmap->range;

1851:   /* determine the number of messages to send, their lengths */
1852:   PetscCall(PetscCalloc1(size, &len_si));
1853:   PetscCall(PetscCalloc1(size, &merge->len_s));

1855:   len_s        = merge->len_s;
1856:   merge->nsend = 0;

1858:   PetscCall(PetscMalloc1(size + 1, &owners_co));

1860:   proc = 0;
1861:   for (i = 0; i < pon; i++) {
1862:     while (prmap[i] >= owners[proc + 1]) proc++;
1863:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1864:     len_s[proc] += coi[i + 1] - coi[i];
1865:   }

1867:   len          = 0; /* max length of buf_si[] */
1868:   owners_co[0] = 0;
1869:   for (proc = 0; proc < size; proc++) {
1870:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1871:     if (len_s[proc]) {
1872:       merge->nsend++;
1873:       len_si[proc] = 2 * (len_si[proc] + 1);
1874:       len += len_si[proc];
1875:     }
1876:   }

1878:   /* determine the number and length of messages to receive for coi and coj  */
1879:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1880:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1882:   /* post the Irecv and Isend of coj */
1883:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1884:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1885:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
1886:   for (proc = 0, k = 0; proc < size; proc++) {
1887:     if (!len_s[proc]) continue;
1888:     i = owners_co[proc];
1889:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1890:     k++;
1891:   }

1893:   /* receives and sends of coj are complete */
1894:   PetscCall(PetscMalloc1(size, &sstatus));
1895:   for (i = 0; i < merge->nrecv; i++) {
1896:     PETSC_UNUSED PetscMPIInt icompleted;
1897:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1898:   }
1899:   PetscCall(PetscFree(rwaits));
1900:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1902:   /* add received column indices into table to update Armax */
1903:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1904:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1905:     Jptr = buf_rj[k];
1906:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1907:   }
1908:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1910:   /* send and recv coi */
1911:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1912:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1913:   PetscCall(PetscMalloc1(len, &buf_s));
1914:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1915:   for (proc = 0, k = 0; proc < size; proc++) {
1916:     if (!len_s[proc]) continue;
1917:     /* form outgoing message for i-structure:
1918:          buf_si[0]:                 nrows to be sent
1919:                [1:nrows]:           row index (global)
1920:                [nrows+1:2*nrows+1]: i-structure index
1921:     */
1922:     nrows       = len_si[proc] / 2 - 1;
1923:     buf_si_i    = buf_si + nrows + 1;
1924:     buf_si[0]   = nrows;
1925:     buf_si_i[0] = 0;
1926:     nrows       = 0;
1927:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1928:       nzi                 = coi[i + 1] - coi[i];
1929:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1930:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1931:       nrows++;
1932:     }
1933:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1934:     k++;
1935:     buf_si += len_si[proc];
1936:   }
1937:   i = merge->nrecv;
1938:   while (i--) {
1939:     PETSC_UNUSED PetscMPIInt icompleted;
1940:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1941:   }
1942:   PetscCall(PetscFree(rwaits));
1943:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1944:   PetscCall(PetscFree(len_si));
1945:   PetscCall(PetscFree(len_ri));
1946:   PetscCall(PetscFree(swaits));
1947:   PetscCall(PetscFree(sstatus));
1948:   PetscCall(PetscFree(buf_s));

1950:   /* compute the local portion of C (mpi mat) */
1951:   /* allocate bi array and free space for accumulating nonzero column info */
1952:   PetscCall(PetscMalloc1(pn + 1, &bi));
1953:   bi[0] = 0;

1955:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1956:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1957:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1958:   current_space = free_space;

1960:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1961:   for (k = 0; k < merge->nrecv; k++) {
1962:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1963:     nrows       = *buf_ri_k[k];
1964:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1965:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1966:   }

1968:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1969:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1970:   rmax = 0;
1971:   for (i = 0; i < pn; i++) {
1972:     /* add pdt[i,:]*AP into lnk */
1973:     pnz = pdti[i + 1] - pdti[i];
1974:     ptJ = pdtj + pdti[i];
1975:     for (j = 0; j < pnz; j++) {
1976:       row  = ptJ[j]; /* row of AP == col of Pt */
1977:       anz  = ai[row + 1] - ai[row];
1978:       Jptr = aj + ai[row];
1979:       /* add non-zero cols of AP into the sorted linked list lnk */
1980:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1981:     }

1983:     /* add received col data into lnk */
1984:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1985:       if (i == *nextrow[k]) {            /* i-th row */
1986:         nzi  = *(nextci[k] + 1) - *nextci[k];
1987:         Jptr = buf_rj[k] + *nextci[k];
1988:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1989:         nextrow[k]++;
1990:         nextci[k]++;
1991:       }
1992:     }

1994:     /* add missing diagonal entry */
1995:     if (C->force_diagonals) {
1996:       k = i + owners[rank]; /* column index */
1997:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1998:     }

2000:     nnz = lnk[0];

2002:     /* if free space is not available, make more free space */
2003:     if (current_space->local_remaining < nnz) {
2004:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
2005:       nspacedouble++;
2006:     }
2007:     /* copy data into free space, then initialize lnk */
2008:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
2009:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

2011:     current_space->array += nnz;
2012:     current_space->local_used += nnz;
2013:     current_space->local_remaining -= nnz;

2015:     bi[i + 1] = bi[i] + nnz;
2016:     if (nnz > rmax) rmax = nnz;
2017:   }
2018:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2020:   PetscCall(PetscMalloc1(bi[pn], &bj));
2021:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2022:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2023:   if (afill_tmp > afill) afill = afill_tmp;
2024:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2025:   PetscCall(PetscHMapIDestroy(&ta));
2026:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2027:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2029:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2030:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2031:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2032:   PetscCall(MatGetType(A, &mtype));
2033:   PetscCall(MatSetType(C, mtype));
2034:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2035:   MatPreallocateEnd(dnz, onz);
2036:   PetscCall(MatSetBlockSize(C, 1));
2037:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2038:   for (i = 0; i < pn; i++) {
2039:     row  = i + rstart;
2040:     nnz  = bi[i + 1] - bi[i];
2041:     Jptr = bj + bi[i];
2042:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2043:   }
2044:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2045:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2046:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2047:   merge->bi        = bi;
2048:   merge->bj        = bj;
2049:   merge->coi       = coi;
2050:   merge->coj       = coj;
2051:   merge->buf_ri    = buf_ri;
2052:   merge->buf_rj    = buf_rj;
2053:   merge->owners_co = owners_co;

2055:   /* attach the supporting struct to C for reuse */
2056:   C->product->data    = ap;
2057:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2058:   ap->merge           = merge;

2060:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2062: #if defined(PETSC_USE_INFO)
2063:   if (bi[pn] != 0) {
2064:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2065:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2066:   } else {
2067:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2068:   }
2069: #endif
2070:   PetscFunctionReturn(PETSC_SUCCESS);
2071: }

2073: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2074: {
2075:   Mat_Product *product = C->product;
2076:   Mat          A = product->A, B = product->B;
2077:   PetscReal    fill = product->fill;
2078:   PetscBool    flg;

2080:   PetscFunctionBegin;
2081:   /* scalable */
2082:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2083:   if (flg) {
2084:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2085:     goto next;
2086:   }

2088:   /* nonscalable */
2089:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2090:   if (flg) {
2091:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2092:     goto next;
2093:   }

2095:   /* matmatmult */
2096:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2097:   if (flg) {
2098:     Mat                  At;
2099:     MatProductCtx_APMPI *ptap;

2101:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2102:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2103:     ptap = (MatProductCtx_APMPI *)C->product->data;
2104:     if (ptap) {
2105:       ptap->Pt            = At;
2106:       C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2107:     }
2108:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2109:     goto next;
2110:   }

2112:   /* backend general code */
2113:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2114:   if (flg) {
2115:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2116:     PetscFunctionReturn(PETSC_SUCCESS);
2117:   }

2119:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2121: next:
2122:   C->ops->productnumeric = MatProductNumeric_AtB;
2123:   PetscFunctionReturn(PETSC_SUCCESS);
2124: }

2126: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2127: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2128: {
2129:   Mat_Product *product = C->product;
2130:   Mat          A = product->A, B = product->B;
2131: #if defined(PETSC_HAVE_HYPRE)
2132:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2133:   PetscInt    nalg        = 5;
2134: #else
2135:   const char *algTypes[4] = {
2136:     "scalable",
2137:     "nonscalable",
2138:     "seqmpi",
2139:     "backend",
2140:   };
2141:   PetscInt nalg = 4;
2142: #endif
2143:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2144:   PetscBool flg;
2145:   MPI_Comm  comm;

2147:   PetscFunctionBegin;
2148:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

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

2155:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2156:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2157:       MatInfo   Ainfo, Binfo;
2158:       PetscInt  nz_local;
2159:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2161:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2162:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2163:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2165:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2166:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2168:       if (alg_scalable) {
2169:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2170:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2171:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2172:       }
2173:     }
2174:   }

2176:   /* Get runtime option */
2177:   if (product->api_user) {
2178:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2179:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2180:     PetscOptionsEnd();
2181:   } else {
2182:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2183:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2184:     PetscOptionsEnd();
2185:   }
2186:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2188:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2189:   PetscFunctionReturn(PETSC_SUCCESS);
2190: }

2192: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2193: {
2194:   PetscFunctionBegin;
2195:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2196:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2197:   PetscFunctionReturn(PETSC_SUCCESS);
2198: }

2200: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2201: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2202: {
2203:   Mat_Product *product = C->product;
2204:   Mat          A = product->A, B = product->B;
2205:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2206:   PetscInt     nalg        = 4;
2207:   PetscInt     alg         = 1; /* set default algorithm  */
2208:   PetscBool    flg;
2209:   MPI_Comm     comm;

2211:   PetscFunctionBegin;
2212:   /* Check matrix local sizes */
2213:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2214:   PetscCheck(A->rmap->rstart == B->rmap->rstart && A->rmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2215:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2217:   /* Set default algorithm */
2218:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2219:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2221:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2222:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2223:     MatInfo   Ainfo, Binfo;
2224:     PetscInt  nz_local;
2225:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2227:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2228:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2229:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2231:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2232:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2234:     if (alg_scalable) {
2235:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2236:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2237:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2238:     }
2239:   }

2241:   /* Get runtime option */
2242:   if (product->api_user) {
2243:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2244:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2245:     PetscOptionsEnd();
2246:   } else {
2247:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2248:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2249:     PetscOptionsEnd();
2250:   }
2251:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2253:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2254:   PetscFunctionReturn(PETSC_SUCCESS);
2255: }

2257: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2258: {
2259:   Mat_Product *product = C->product;
2260:   Mat          A = product->A, P = product->B;
2261:   MPI_Comm     comm;
2262:   PetscBool    flg;
2263:   PetscInt     alg = 1; /* set default algorithm */
2264: #if !defined(PETSC_HAVE_HYPRE)
2265:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2266:   PetscInt    nalg        = 5;
2267: #else
2268:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2269:   PetscInt    nalg        = 6;
2270: #endif
2271:   PetscInt pN = P->cmap->N;

2273:   PetscFunctionBegin;
2274:   /* Check matrix local sizes */
2275:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2276:   PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Arow (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2277:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2278:   PetscCheck(A->cmap->rstart == P->rmap->rstart && A->cmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Acol (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2279:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2281:   /* Set "nonscalable" as default algorithm */
2282:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2283:   if (flg) {
2284:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2286:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2287:     if (pN > 100000) {
2288:       MatInfo   Ainfo, Pinfo;
2289:       PetscInt  nz_local;
2290:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2292:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2293:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2294:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2296:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2297:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2299:       if (alg_scalable) {
2300:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2301:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2302:       }
2303:     }
2304:   }

2306:   /* Get runtime option */
2307:   if (product->api_user) {
2308:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2309:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2310:     PetscOptionsEnd();
2311:   } else {
2312:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2313:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2314:     PetscOptionsEnd();
2315:   }
2316:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2318:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2319:   PetscFunctionReturn(PETSC_SUCCESS);
2320: }

2322: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2323: {
2324:   Mat_Product *product = C->product;
2325:   Mat          A = product->A, R = product->B;

2327:   PetscFunctionBegin;
2328:   /* Check matrix local sizes */
2329:   PetscCheck(A->cmap->n == R->cmap->n && A->rmap->n == R->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A local (%" PetscInt_FMT ", %" PetscInt_FMT "), R local (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->n,
2330:              A->rmap->n, R->rmap->n, R->cmap->n);

2332:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2333:   PetscFunctionReturn(PETSC_SUCCESS);
2334: }

2336: /*
2337:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2338: */
2339: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2340: {
2341:   Mat_Product *product     = C->product;
2342:   PetscBool    flg         = PETSC_FALSE;
2343:   PetscInt     alg         = 1; /* default algorithm */
2344:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2345:   PetscInt     nalg        = 3;

2347:   PetscFunctionBegin;
2348:   /* Set default algorithm */
2349:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2350:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2352:   /* Get runtime option */
2353:   if (product->api_user) {
2354:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2355:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2356:     PetscOptionsEnd();
2357:   } else {
2358:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2359:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2360:     PetscOptionsEnd();
2361:   }
2362:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2364:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2365:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2366:   PetscFunctionReturn(PETSC_SUCCESS);
2367: }

2369: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2370: {
2371:   Mat_Product *product = C->product;

2373:   PetscFunctionBegin;
2374:   switch (product->type) {
2375:   case MATPRODUCT_AB:
2376:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2377:     break;
2378:   case MATPRODUCT_ABt:
2379:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2380:     break;
2381:   case MATPRODUCT_AtB:
2382:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2383:     break;
2384:   case MATPRODUCT_PtAP:
2385:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2386:     break;
2387:   case MATPRODUCT_RARt:
2388:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2389:     break;
2390:   case MATPRODUCT_ABC:
2391:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2392:     break;
2393:   default:
2394:     break;
2395:   }
2396:   PetscFunctionReturn(PETSC_SUCCESS);
2397: }