xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision de37d9f1ed8c270827db4eacb43fb676a106cecc)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
4           C = A * B
5 */
6 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
7 #include <../src/mat/utils/freespace.h>
8 #include <../src/mat/impls/aij/mpi/mpiaij.h>
9 #include <petscbt.h>
10 #include <../src/mat/impls/dense/mpi/mpidense.h>
11 #include <petsc/private/vecimpl.h>
12 #include <petsc/private/sfimpl.h>
13 
14 #if defined(PETSC_HAVE_HYPRE)
15 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
16 #endif
17 
18 PETSC_INTERN PetscErrorCode MatProductSymbolic_ABt_MPIAIJ_MPIAIJ(Mat C)
19 {
20   Mat_Product         *product = C->product;
21   Mat                 B=product->B;
22 
23   PetscFunctionBegin;
24   PetscCall(MatTranspose(B,MAT_INITIAL_MATRIX,&product->B));
25   PetscCall(MatDestroy(&B));
26   PetscCall(MatProductSymbolic_AB_MPIAIJ_MPIAIJ(C));
27   PetscFunctionReturn(0);
28 }
29 
30 PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
31 {
32   Mat_Product         *product = C->product;
33   Mat                 A=product->A,B=product->B;
34   MatProductAlgorithm alg=product->alg;
35   PetscReal           fill=product->fill;
36   PetscBool           flg;
37 
38   PetscFunctionBegin;
39   /* scalable */
40   PetscCall(PetscStrcmp(alg,"scalable",&flg));
41   if (flg) {
42     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C));
43     PetscFunctionReturn(0);
44   }
45 
46   /* nonscalable */
47   PetscCall(PetscStrcmp(alg,"nonscalable",&flg));
48   if (flg) {
49     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C));
50     PetscFunctionReturn(0);
51   }
52 
53   /* seqmpi */
54   PetscCall(PetscStrcmp(alg,"seqmpi",&flg));
55   if (flg) {
56     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C));
57     PetscFunctionReturn(0);
58   }
59 
60   /* backend general code */
61   PetscCall(PetscStrcmp(alg,"backend",&flg));
62   if (flg) {
63     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
64     PetscFunctionReturn(0);
65   }
66 
67 #if defined(PETSC_HAVE_HYPRE)
68   PetscCall(PetscStrcmp(alg,"hypre",&flg));
69   if (flg) {
70     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C));
71     PetscFunctionReturn(0);
72   }
73 #endif
74   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
75 }
76 
77 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
78 {
79   Mat_APMPI      *ptap = (Mat_APMPI*)data;
80 
81   PetscFunctionBegin;
82   PetscCall(PetscFree2(ptap->startsj_s,ptap->startsj_r));
83   PetscCall(PetscFree(ptap->bufa));
84   PetscCall(MatDestroy(&ptap->P_loc));
85   PetscCall(MatDestroy(&ptap->P_oth));
86   PetscCall(MatDestroy(&ptap->Pt));
87   PetscCall(PetscFree(ptap->api));
88   PetscCall(PetscFree(ptap->apj));
89   PetscCall(PetscFree(ptap->apa));
90   PetscCall(PetscFree(ptap));
91   PetscFunctionReturn(0);
92 }
93 
94 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
95 {
96   Mat_MPIAIJ        *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
97   Mat_SeqAIJ        *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
98   Mat_SeqAIJ        *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
99   PetscScalar       *cda=cd->a,*coa=co->a;
100   Mat_SeqAIJ        *p_loc,*p_oth;
101   PetscScalar       *apa,*ca;
102   PetscInt          cm =C->rmap->n;
103   Mat_APMPI         *ptap;
104   PetscInt          *api,*apj,*apJ,i,k;
105   PetscInt          cstart=C->cmap->rstart;
106   PetscInt          cdnz,conz,k0,k1;
107   const PetscScalar *dummy;
108   MPI_Comm          comm;
109   PetscMPIInt       size;
110 
111   PetscFunctionBegin;
112   MatCheckProduct(C,3);
113   ptap = (Mat_APMPI*)C->product->data;
114   PetscCheck(ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
115   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
116   PetscCallMPI(MPI_Comm_size(comm,&size));
117 
118   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
119 
120   /* flag CPU mask for C */
121 #if defined(PETSC_HAVE_DEVICE)
122   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
123   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
124   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
125 #endif
126 
127   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
128   /*-----------------------------------------------------*/
129   /* update numerical values of P_oth and P_loc */
130   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth));
131   PetscCall(MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc));
132 
133   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
134   /*----------------------------------------------------------*/
135   /* get data from symbolic products */
136   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
137   p_oth = NULL;
138   if (size >1) {
139     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
140   }
141 
142   /* get apa for storing dense row A[i,:]*P */
143   apa = ptap->apa;
144 
145   api = ptap->api;
146   apj = ptap->apj;
147   /* trigger copy to CPU */
148   PetscCall(MatSeqAIJGetArrayRead(a->A,&dummy));
149   PetscCall(MatSeqAIJRestoreArrayRead(a->A,&dummy));
150   PetscCall(MatSeqAIJGetArrayRead(a->B,&dummy));
151   PetscCall(MatSeqAIJRestoreArrayRead(a->B,&dummy));
152   for (i=0; i<cm; i++) {
153     /* compute apa = A[i,:]*P */
154     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
155 
156     /* set values in C */
157     apJ  = apj + api[i];
158     cdnz = cd->i[i+1] - cd->i[i];
159     conz = co->i[i+1] - co->i[i];
160 
161     /* 1st off-diagonal part of C */
162     ca = coa + co->i[i];
163     k  = 0;
164     for (k0=0; k0<conz; k0++) {
165       if (apJ[k] >= cstart) break;
166       ca[k0]      = apa[apJ[k]];
167       apa[apJ[k++]] = 0.0;
168     }
169 
170     /* diagonal part of C */
171     ca = cda + cd->i[i];
172     for (k1=0; k1<cdnz; k1++) {
173       ca[k1]      = apa[apJ[k]];
174       apa[apJ[k++]] = 0.0;
175     }
176 
177     /* 2nd off-diagonal part of C */
178     ca = coa + co->i[i];
179     for (; k0<conz; k0++) {
180       ca[k0]      = apa[apJ[k]];
181       apa[apJ[k++]] = 0.0;
182     }
183   }
184   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
185   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
186   PetscFunctionReturn(0);
187 }
188 
189 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
190 {
191   MPI_Comm           comm;
192   PetscMPIInt        size;
193   Mat_APMPI          *ptap;
194   PetscFreeSpaceList free_space=NULL,current_space=NULL;
195   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
196   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
197   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
198   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
199   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
200   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
201   PetscBT            lnkbt;
202   PetscReal          afill;
203   MatType            mtype;
204 
205   PetscFunctionBegin;
206   MatCheckProduct(C,4);
207   PetscCheck(!C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
208   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
209   PetscCallMPI(MPI_Comm_size(comm,&size));
210 
211   /* create struct Mat_APMPI and attached it to C later */
212   PetscCall(PetscNew(&ptap));
213 
214   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
215   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth));
216 
217   /* get P_loc by taking all local rows of P */
218   PetscCall(MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc));
219 
220   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
221   pi_loc = p_loc->i; pj_loc = p_loc->j;
222   if (size > 1) {
223     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
224     pi_oth = p_oth->i; pj_oth = p_oth->j;
225   } else {
226     p_oth = NULL;
227     pi_oth = NULL; pj_oth = NULL;
228   }
229 
230   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
231   /*-------------------------------------------------------------------*/
232   PetscCall(PetscMalloc1(am+2,&api));
233   ptap->api = api;
234   api[0]    = 0;
235 
236   /* create and initialize a linked list */
237   PetscCall(PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt));
238 
239   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
240   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space));
241   current_space = free_space;
242 
243   MatPreallocateBegin(comm,am,pn,dnz,onz);
244   for (i=0; i<am; i++) {
245     /* diagonal portion of A */
246     nzi = adi[i+1] - adi[i];
247     for (j=0; j<nzi; j++) {
248       row  = *adj++;
249       pnz  = pi_loc[row+1] - pi_loc[row];
250       Jptr = pj_loc + pi_loc[row];
251       /* add non-zero cols of P into the sorted linked list lnk */
252       PetscCall(PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt));
253     }
254     /* off-diagonal portion of A */
255     nzi = aoi[i+1] - aoi[i];
256     for (j=0; j<nzi; j++) {
257       row  = *aoj++;
258       pnz  = pi_oth[row+1] - pi_oth[row];
259       Jptr = pj_oth + pi_oth[row];
260       PetscCall(PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt));
261     }
262     /* add possible missing diagonal entry */
263     if (C->force_diagonals) {
264       j = i + rstart; /* column index */
265       PetscCall(PetscLLCondensedAddSorted(1,&j,lnk,lnkbt));
266     }
267 
268     apnz     = lnk[0];
269     api[i+1] = api[i] + apnz;
270 
271     /* if free space is not available, double the total space in the list */
272     if (current_space->local_remaining<apnz) {
273       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space));
274       nspacedouble++;
275     }
276 
277     /* Copy data into free space, then initialize lnk */
278     PetscCall(PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt));
279     PetscCall(MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz));
280 
281     current_space->array           += apnz;
282     current_space->local_used      += apnz;
283     current_space->local_remaining -= apnz;
284   }
285 
286   /* Allocate space for apj, initialize apj, and */
287   /* destroy list of free space and other temporary array(s) */
288   PetscCall(PetscMalloc1(api[am]+1,&ptap->apj));
289   apj  = ptap->apj;
290   PetscCall(PetscFreeSpaceContiguous(&free_space,ptap->apj));
291   PetscCall(PetscLLDestroy(lnk,lnkbt));
292 
293   /* malloc apa to store dense row A[i,:]*P */
294   PetscCall(PetscCalloc1(pN,&ptap->apa));
295 
296   /* set and assemble symbolic parallel matrix C */
297   /*---------------------------------------------*/
298   PetscCall(MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE));
299   PetscCall(MatSetBlockSizesFromMats(C,A,P));
300 
301   PetscCall(MatGetType(A,&mtype));
302   PetscCall(MatSetType(C,mtype));
303   PetscCall(MatMPIAIJSetPreallocation(C,0,dnz,0,onz));
304   MatPreallocateEnd(dnz,onz);
305 
306   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
307   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
308   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
309   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
310 
311   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
312   C->ops->productnumeric = MatProductNumeric_AB;
313 
314   /* attach the supporting struct to C for reuse */
315   C->product->data    = ptap;
316   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
317 
318   /* set MatInfo */
319   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
320   if (afill < 1.0) afill = 1.0;
321   C->info.mallocs           = nspacedouble;
322   C->info.fill_ratio_given  = fill;
323   C->info.fill_ratio_needed = afill;
324 
325 #if defined(PETSC_USE_INFO)
326   if (api[am]) {
327     PetscCall(PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill));
328     PetscCall(PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill));
329   } else {
330     PetscCall(PetscInfo(C,"Empty matrix product\n"));
331   }
332 #endif
333   PetscFunctionReturn(0);
334 }
335 
336 /* ------------------------------------------------------- */
337 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
338 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);
339 
340 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
341 {
342   Mat_Product *product = C->product;
343   Mat         A = product->A,B=product->B;
344 
345   PetscFunctionBegin;
346   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
347     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);
348 
349   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
350   C->ops->productsymbolic = MatProductSymbolic_AB;
351   PetscFunctionReturn(0);
352 }
353 /* -------------------------------------------------------------------- */
354 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
355 {
356   Mat_Product *product = C->product;
357   Mat         A = product->A,B=product->B;
358 
359   PetscFunctionBegin;
360   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
361     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);
362 
363   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
364   C->ops->productsymbolic          = MatProductSymbolic_AtB;
365   PetscFunctionReturn(0);
366 }
367 
368 /* --------------------------------------------------------------------- */
369 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
370 {
371   Mat_Product    *product = C->product;
372 
373   PetscFunctionBegin;
374   switch (product->type) {
375   case MATPRODUCT_AB:
376     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
377     break;
378   case MATPRODUCT_AtB:
379     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
380     break;
381   default:
382     break;
383   }
384   PetscFunctionReturn(0);
385 }
386 /* ------------------------------------------------------- */
387 
388 typedef struct {
389   Mat          workB,workB1;
390   MPI_Request  *rwaits,*swaits;
391   PetscInt     nsends,nrecvs;
392   MPI_Datatype *stype,*rtype;
393   PetscInt     blda;
394 } MPIAIJ_MPIDense;
395 
396 PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
397 {
398   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
399   PetscInt        i;
400 
401   PetscFunctionBegin;
402   PetscCall(MatDestroy(&contents->workB));
403   PetscCall(MatDestroy(&contents->workB1));
404   for (i=0; i<contents->nsends; i++) {
405     PetscCallMPI(MPI_Type_free(&contents->stype[i]));
406   }
407   for (i=0; i<contents->nrecvs; i++) {
408     PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
409   }
410   PetscCall(PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits));
411   PetscCall(PetscFree(contents));
412   PetscFunctionReturn(0);
413 }
414 
415 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
416 {
417   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
418   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,m,M,n,N;
419   MPIAIJ_MPIDense *contents;
420   VecScatter      ctx=aij->Mvctx;
421   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
422   MPI_Comm        comm;
423   MPI_Datatype    type1,*stype,*rtype;
424   const PetscInt  *sindices,*sstarts,*rstarts;
425   PetscMPIInt     *disp;
426   PetscBool       cisdense;
427 
428   PetscFunctionBegin;
429   MatCheckProduct(C,4);
430   PetscCheck(!C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
431   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
432   PetscCall(PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense));
433   if (!cisdense) {
434     PetscCall(MatSetType(C,((PetscObject)B)->type_name));
435   }
436   PetscCall(MatGetLocalSize(C,&m,&n));
437   PetscCall(MatGetSize(C,&M,&N));
438   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
439     PetscCall(MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN));
440   }
441   PetscCall(MatSetBlockSizesFromMats(C,A,B));
442   PetscCall(MatSetUp(C));
443   PetscCall(MatDenseGetLDA(B,&blda));
444   PetscCall(PetscNew(&contents));
445 
446   PetscCall(VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL));
447   PetscCall(VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL));
448 
449   /* Create column block of B and C for memory scalability when BN is too large */
450   /* Estimate Bbn, column size of Bb */
451   if (nz) {
452     Bbn1 = 2*Am*BN/nz;
453     if (!Bbn1) Bbn1 = 1;
454   } else Bbn1 = BN;
455 
456   bs = PetscAbs(B->cmap->bs);
457   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
458   if (Bbn1 > BN) Bbn1 = BN;
459   PetscCallMPI(MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm));
460 
461   /* Enable runtime option for Bbn */
462   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
463   PetscCall(PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL));
464   PetscOptionsEnd();
465   Bbn  = PetscMin(Bbn,BN);
466 
467   if (Bbn > 0 && Bbn < BN) {
468     numBb = BN/Bbn;
469     Bbn1 = BN - numBb*Bbn;
470   } else numBb = 0;
471 
472   if (numBb) {
473     PetscCall(PetscInfo(C,"use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n",BN,Bbn,numBb));
474     if (Bbn1) { /* Create workB1 for the remaining columns */
475       PetscCall(PetscInfo(C,"use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n",BN,Bbn1));
476       /* Create work matrix used to store off processor rows of B needed for local product */
477       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1));
478     } else contents->workB1 = NULL;
479   }
480 
481   /* Create work matrix used to store off processor rows of B needed for local product */
482   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB));
483 
484   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
485   PetscCall(PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits));
486   contents->stype  = stype;
487   contents->nsends = nsends;
488 
489   contents->rtype  = rtype;
490   contents->nrecvs = nrecvs;
491   contents->blda   = blda;
492 
493   PetscCall(PetscMalloc1(Bm+1,&disp));
494   for (i=0; i<nsends; i++) {
495     nrows_to = sstarts[i+1]-sstarts[i];
496     for (j=0; j<nrows_to; j++) disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
497     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to,1,disp,MPIU_SCALAR,&type1));
498     PetscCallMPI(MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]));
499     PetscCallMPI(MPI_Type_commit(&stype[i]));
500     PetscCallMPI(MPI_Type_free(&type1));
501   }
502 
503   for (i=0; i<nrecvs; i++) {
504     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
505     nrows_from = rstarts[i+1]-rstarts[i];
506     disp[0] = 0;
507     PetscCallMPI(MPI_Type_create_indexed_block(1,nrows_from,disp,MPIU_SCALAR,&type1));
508     PetscCallMPI(MPI_Type_create_resized(type1,0,nz*sizeof(PetscScalar),&rtype[i]));
509     PetscCallMPI(MPI_Type_commit(&rtype[i]));
510     PetscCallMPI(MPI_Type_free(&type1));
511   }
512 
513   PetscCall(PetscFree(disp));
514   PetscCall(VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL));
515   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL));
516   PetscCall(MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
517   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
518   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
519   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
520 
521   C->product->data = contents;
522   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
523   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
524   PetscFunctionReturn(0);
525 }
526 
527 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
528 /*
529     Performs an efficient scatter on the rows of B needed by this process; this is
530     a modification of the VecScatterBegin_() routines.
531 
532     Input: Bbidx = 0: B = Bb
533                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
534 */
535 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
536 {
537   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
538   const PetscScalar *b;
539   PetscScalar       *rvalues;
540   VecScatter        ctx = aij->Mvctx;
541   const PetscInt    *sindices,*sstarts,*rstarts;
542   const PetscMPIInt *sprocs,*rprocs;
543   PetscInt          i,nsends,nrecvs;
544   MPI_Request       *swaits,*rwaits;
545   MPI_Comm          comm;
546   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
547   MPIAIJ_MPIDense   *contents;
548   Mat               workB;
549   MPI_Datatype      *stype,*rtype;
550   PetscInt          blda;
551 
552   PetscFunctionBegin;
553   MatCheckProduct(C,4);
554   PetscCheck(C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
555   contents = (MPIAIJ_MPIDense*)C->product->data;
556   PetscCall(VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/));
557   PetscCall(VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/));
558   PetscCall(PetscMPIIntCast(nsends,&nsends_mpi));
559   PetscCall(PetscMPIIntCast(nrecvs,&nrecvs_mpi));
560   if (Bbidx == 0) workB = *outworkB = contents->workB;
561   else workB = *outworkB = contents->workB1;
562   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);
563   swaits = contents->swaits;
564   rwaits = contents->rwaits;
565 
566   PetscCall(MatDenseGetArrayRead(B,&b));
567   PetscCall(MatDenseGetLDA(B,&blda));
568   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);
569   PetscCall(MatDenseGetArray(workB,&rvalues));
570 
571   /* Post recv, use MPI derived data type to save memory */
572   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
573   rtype = contents->rtype;
574   for (i=0; i<nrecvs; i++) {
575     PetscCallMPI(MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i));
576   }
577 
578   stype = contents->stype;
579   for (i=0; i<nsends; i++) {
580     PetscCallMPI(MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i));
581   }
582 
583   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE));
584   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE));
585 
586   PetscCall(VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL));
587   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL));
588   PetscCall(MatDenseRestoreArrayRead(B,&b));
589   PetscCall(MatDenseRestoreArray(workB,&rvalues));
590   PetscFunctionReturn(0);
591 }
592 
593 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
594 {
595   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
596   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
597   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
598   Mat             workB;
599   MPIAIJ_MPIDense *contents;
600 
601   PetscFunctionBegin;
602   MatCheckProduct(C,3);
603   PetscCheck(C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
604   contents = (MPIAIJ_MPIDense*)C->product->data;
605   /* diagonal block of A times all local rows of B */
606   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
607   PetscCall(MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A));
608   if (contents->workB->cmap->n == B->cmap->N) {
609     /* get off processor parts of B needed to complete C=A*B */
610     PetscCall(MatMPIDenseScatter(A,B,0,C,&workB));
611 
612     /* off-diagonal block of A times nonlocal rows of B */
613     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE));
614   } else {
615     Mat       Bb,Cb;
616     PetscInt  BN=B->cmap->N,n=contents->workB->cmap->n,i;
617     PetscBool ccpu;
618 
619     PetscCheck(n > 0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %" PetscInt_FMT " must be positive",n);
620     /* Prevent from unneeded copies back and forth from the GPU
621        when getting and restoring the submatrix
622        We need a proper GPU code for AIJ * dense in parallel */
623     PetscCall(MatBoundToCPU(C,&ccpu));
624     PetscCall(MatBindToCPU(C,PETSC_TRUE));
625     for (i=0; i<BN; i+=n) {
626       PetscCall(MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb));
627       PetscCall(MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb));
628 
629       /* get off processor parts of B needed to complete C=A*B */
630       PetscCall(MatMPIDenseScatter(A,Bb,(i+n)>BN,C,&workB));
631 
632       /* off-diagonal block of A times nonlocal rows of B */
633       cdense = (Mat_MPIDense*)Cb->data;
634       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE));
635       PetscCall(MatDenseRestoreSubMatrix(B,&Bb));
636       PetscCall(MatDenseRestoreSubMatrix(C,&Cb));
637     }
638     PetscCall(MatBindToCPU(C,ccpu));
639   }
640   PetscFunctionReturn(0);
641 }
642 
643 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
644 {
645   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
646   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
647   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
648   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
649   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
650   Mat_SeqAIJ        *p_loc,*p_oth;
651   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
652   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
653   PetscInt          cm    = C->rmap->n,anz,pnz;
654   Mat_APMPI         *ptap;
655   PetscScalar       *apa_sparse;
656   const PetscScalar *dummy;
657   PetscInt          *api,*apj,*apJ,i,j,k,row;
658   PetscInt          cstart = C->cmap->rstart;
659   PetscInt          cdnz,conz,k0,k1,nextp;
660   MPI_Comm          comm;
661   PetscMPIInt       size;
662 
663   PetscFunctionBegin;
664   MatCheckProduct(C,3);
665   ptap = (Mat_APMPI*)C->product->data;
666   PetscCheck(ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
667   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
668   PetscCallMPI(MPI_Comm_size(comm,&size));
669   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
670 
671   /* flag CPU mask for C */
672 #if defined(PETSC_HAVE_DEVICE)
673   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
674   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
675   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
676 #endif
677   apa_sparse = ptap->apa;
678 
679   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
680   /*-----------------------------------------------------*/
681   /* update numerical values of P_oth and P_loc */
682   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth));
683   PetscCall(MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc));
684 
685   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
686   /*----------------------------------------------------------*/
687   /* get data from symbolic products */
688   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
689   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
690   if (size >1) {
691     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
692     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
693   } else {
694     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
695   }
696 
697   /* trigger copy to CPU */
698   PetscCall(MatSeqAIJGetArrayRead(a->A,&dummy));
699   PetscCall(MatSeqAIJRestoreArrayRead(a->A,&dummy));
700   PetscCall(MatSeqAIJGetArrayRead(a->B,&dummy));
701   PetscCall(MatSeqAIJRestoreArrayRead(a->B,&dummy));
702   api = ptap->api;
703   apj = ptap->apj;
704   for (i=0; i<cm; i++) {
705     apJ = apj + api[i];
706 
707     /* diagonal portion of A */
708     anz = adi[i+1] - adi[i];
709     adj = ad->j + adi[i];
710     ada = ad->a + adi[i];
711     for (j=0; j<anz; j++) {
712       row = adj[j];
713       pnz = pi_loc[row+1] - pi_loc[row];
714       pj  = pj_loc + pi_loc[row];
715       pa  = pa_loc + pi_loc[row];
716       /* perform sparse axpy */
717       valtmp = ada[j];
718       nextp  = 0;
719       for (k=0; nextp<pnz; k++) {
720         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
721           apa_sparse[k] += valtmp*pa[nextp++];
722         }
723       }
724       PetscCall(PetscLogFlops(2.0*pnz));
725     }
726 
727     /* off-diagonal portion of A */
728     anz = aoi[i+1] - aoi[i];
729     aoj = ao->j + aoi[i];
730     aoa = ao->a + aoi[i];
731     for (j=0; j<anz; j++) {
732       row = aoj[j];
733       pnz = pi_oth[row+1] - pi_oth[row];
734       pj  = pj_oth + pi_oth[row];
735       pa  = pa_oth + pi_oth[row];
736       /* perform sparse axpy */
737       valtmp = aoa[j];
738       nextp  = 0;
739       for (k=0; nextp<pnz; k++) {
740         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
741           apa_sparse[k] += valtmp*pa[nextp++];
742         }
743       }
744       PetscCall(PetscLogFlops(2.0*pnz));
745     }
746 
747     /* set values in C */
748     cdnz = cd->i[i+1] - cd->i[i];
749     conz = co->i[i+1] - co->i[i];
750 
751     /* 1st off-diagonal part of C */
752     ca = coa + co->i[i];
753     k  = 0;
754     for (k0=0; k0<conz; k0++) {
755       if (apJ[k] >= cstart) break;
756       ca[k0]        = apa_sparse[k];
757       apa_sparse[k] = 0.0;
758       k++;
759     }
760 
761     /* diagonal part of C */
762     ca = cda + cd->i[i];
763     for (k1=0; k1<cdnz; k1++) {
764       ca[k1]        = apa_sparse[k];
765       apa_sparse[k] = 0.0;
766       k++;
767     }
768 
769     /* 2nd off-diagonal part of C */
770     ca = coa + co->i[i];
771     for (; k0<conz; k0++) {
772       ca[k0]        = apa_sparse[k];
773       apa_sparse[k] = 0.0;
774       k++;
775     }
776   }
777   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
778   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
779   PetscFunctionReturn(0);
780 }
781 
782 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
783 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
784 {
785   MPI_Comm           comm;
786   PetscMPIInt        size;
787   Mat_APMPI          *ptap;
788   PetscFreeSpaceList free_space = NULL,current_space=NULL;
789   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
790   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
791   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
792   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
793   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
794   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
795   PetscReal          afill;
796   MatType            mtype;
797 
798   PetscFunctionBegin;
799   MatCheckProduct(C,4);
800   PetscCheck(!C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
801   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
802   PetscCallMPI(MPI_Comm_size(comm,&size));
803 
804   /* create struct Mat_APMPI and attached it to C later */
805   PetscCall(PetscNew(&ptap));
806 
807   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
808   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth));
809 
810   /* get P_loc by taking all local rows of P */
811   PetscCall(MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc));
812 
813   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
814   pi_loc = p_loc->i; pj_loc = p_loc->j;
815   if (size > 1) {
816     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
817     pi_oth = p_oth->i; pj_oth = p_oth->j;
818   } else {
819     p_oth  = NULL;
820     pi_oth = NULL; pj_oth = NULL;
821   }
822 
823   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
824   /*-------------------------------------------------------------------*/
825   PetscCall(PetscMalloc1(am+2,&api));
826   ptap->api = api;
827   api[0]    = 0;
828 
829   PetscCall(PetscLLCondensedCreate_Scalable(lsize,&lnk));
830 
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     }
870 
871     /* add missing diagonal entry */
872     if (C->force_diagonals) {
873       j = i + rstart; /* column index */
874       PetscCall(PetscLLCondensedAddSorted_Scalable(1,&j,lnk));
875     }
876 
877     apnz     = *lnk;
878     api[i+1] = api[i] + apnz;
879     if (apnz > apnz_max) apnz_max = apnz;
880 
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     }
886 
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));
890 
891     current_space->array           += apnz;
892     current_space->local_used      += apnz;
893     current_space->local_remaining -= apnz;
894   }
895 
896   /* Allocate space for apj, initialize apj, and */
897   /* destroy list of free space and other temporary array(s) */
898   PetscCall(PetscMalloc1(api[am]+1,&ptap->apj));
899   apj  = ptap->apj;
900   PetscCall(PetscFreeSpaceContiguous(&free_space,ptap->apj));
901   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
902 
903   /* create and assemble symbolic parallel matrix C */
904   /*----------------------------------------------------*/
905   PetscCall(MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE));
906   PetscCall(MatSetBlockSizesFromMats(C,A,P));
907   PetscCall(MatGetType(A,&mtype));
908   PetscCall(MatSetType(C,mtype));
909   PetscCall(MatMPIAIJSetPreallocation(C,0,dnz,0,onz));
910   MatPreallocateEnd(dnz,onz);
911 
912   /* malloc apa for assembly C */
913   PetscCall(PetscCalloc1(apnz_max,&ptap->apa));
914 
915   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
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));
919 
920   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
921   C->ops->productnumeric = MatProductNumeric_AB;
922 
923   /* attach the supporting struct to C for reuse */
924   C->product->data    = ptap;
925   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
926 
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;
933 
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(0);
943 }
944 
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,
949                                PetscInt  size2, PetscInt *in2,
950                                PetscInt  size3, PetscInt *in3,
951                                PetscInt *size4, PetscInt *out)
952 {
953   int i = 0, j = 0, k = 0, l = 0;
954 
955   /* Traverse all three arrays */
956   while (i<size1 && j<size2 && k<size3) {
957     if (in1[i] < in2[j] && in1[i] < in3[k]) {
958       out[l++] = in1[i++];
959     }
960     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
961       out[l++] = in2[j++];
962     }
963     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
964       out[l++] = in3[k++];
965     }
966     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
967       out[l++] = in1[i];
968       i++, j++;
969     }
970     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
971       out[l++] = in1[i];
972       i++, k++;
973     }
974     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
975       out[l++] = in2[j];
976       k++, j++;
977     }
978     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
979       out[l++] = in1[i];
980       i++, j++, k++;
981     }
982   }
983 
984   /* Traverse two remaining arrays */
985   while (i<size1 && j<size2) {
986     if (in1[i] < in2[j]) {
987       out[l++] = in1[i++];
988     }
989     else if (in1[i] > in2[j]) {
990       out[l++] = in2[j++];
991     }
992     else {
993       out[l++] = in1[i];
994       i++, j++;
995     }
996   }
997 
998   while (i<size1 && k<size3) {
999     if (in1[i] < in3[k]) {
1000       out[l++] = in1[i++];
1001     }
1002     else if (in1[i] > in3[k]) {
1003       out[l++] = in3[k++];
1004     }
1005     else {
1006       out[l++] = in1[i];
1007       i++, k++;
1008     }
1009   }
1010 
1011   while (k<size3 && j<size2)  {
1012     if (in3[k] < in2[j]) {
1013       out[l++] = in3[k++];
1014     }
1015     else if (in3[k] > in2[j]) {
1016       out[l++] = in2[j++];
1017     }
1018     else {
1019       out[l++] = in3[k];
1020       k++, j++;
1021     }
1022   }
1023 
1024   /* Traverse one remaining array */
1025   while (i<size1) out[l++] = in1[i++];
1026   while (j<size2) out[l++] = in2[j++];
1027   while (k<size3) out[l++] = in3[k++];
1028 
1029   *size4 = l;
1030 }
1031 
1032 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1033 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1034 /* matrix-matrix multiplications.  */
1035 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1036 {
1037   MPI_Comm           comm;
1038   PetscMPIInt        size;
1039   Mat_APMPI          *ptap;
1040   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1041   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
1042   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1043   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
1044   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1045   PetscInt           adponz, adpdnz;
1046   PetscInt           *pi_loc,*dnz,*onz;
1047   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1048   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1049                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1050   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1051   PetscBT            lnkbt;
1052   PetscReal          afill;
1053   PetscMPIInt        rank;
1054   Mat                adpd, aopoth;
1055   MatType            mtype;
1056   const char         *prefix;
1057 
1058   PetscFunctionBegin;
1059   MatCheckProduct(C,4);
1060   PetscCheck(!C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1061   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
1062   PetscCallMPI(MPI_Comm_size(comm,&size));
1063   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1064   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));
1065 
1066   /* create struct Mat_APMPI and attached it to C later */
1067   PetscCall(PetscNew(&ptap));
1068 
1069   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1070   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth));
1071 
1072   /* get P_loc by taking all local rows of P */
1073   PetscCall(MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc));
1074 
1075   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1076   pi_loc = p_loc->i;
1077 
1078   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1079   PetscCall(PetscMalloc1(am+2,&api));
1080   PetscCall(PetscMalloc1(am+2,&adpoi));
1081 
1082   adpoi[0]    = 0;
1083   ptap->api = api;
1084   api[0] = 0;
1085 
1086   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1087   PetscCall(PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt));
1088   MatPreallocateBegin(comm,am,pn,dnz,onz);
1089 
1090   /* Symbolic calc of A_loc_diag * P_loc_diag */
1091   PetscCall(MatGetOptionsPrefix(A,&prefix));
1092   PetscCall(MatProductCreate(a->A,p->A,NULL,&adpd));
1093   PetscCall(MatGetOptionsPrefix(A,&prefix));
1094   PetscCall(MatSetOptionsPrefix(adpd,prefix));
1095   PetscCall(MatAppendOptionsPrefix(adpd,"inner_diag_"));
1096 
1097   PetscCall(MatProductSetType(adpd,MATPRODUCT_AB));
1098   PetscCall(MatProductSetAlgorithm(adpd,"sorted"));
1099   PetscCall(MatProductSetFill(adpd,fill));
1100   PetscCall(MatProductSetFromOptions(adpd));
1101 
1102   adpd->force_diagonals = C->force_diagonals;
1103   PetscCall(MatProductSymbolic(adpd));
1104 
1105   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1106   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1107   p_off = (Mat_SeqAIJ*)((p->B)->data);
1108   poff_i = p_off->i; poff_j = p_off->j;
1109 
1110   /* j_temp stores indices of a result row before they are added to the linked list */
1111   PetscCall(PetscMalloc1(pN+2,&j_temp));
1112 
1113   /* Symbolic calc of the A_diag * p_loc_off */
1114   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1115   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag));
1116   current_space = free_space_diag;
1117 
1118   for (i=0; i<am; i++) {
1119     /* A_diag * P_loc_off */
1120     nzi = adi[i+1] - adi[i];
1121     for (j=0; j<nzi; j++) {
1122       row  = *adj++;
1123       pnz  = poff_i[row+1] - poff_i[row];
1124       Jptr = poff_j + poff_i[row];
1125       for (i1 = 0; i1 < pnz; i1++) {
1126         j_temp[i1] = p->garray[Jptr[i1]];
1127       }
1128       /* add non-zero cols of P into the sorted linked list lnk */
1129       PetscCall(PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt));
1130     }
1131 
1132     adponz     = lnk[0];
1133     adpoi[i+1] = adpoi[i] + adponz;
1134 
1135     /* if free space is not available, double the total space in the list */
1136     if (current_space->local_remaining<adponz) {
1137       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space));
1138       nspacedouble++;
1139     }
1140 
1141     /* Copy data into free space, then initialize lnk */
1142     PetscCall(PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt));
1143 
1144     current_space->array           += adponz;
1145     current_space->local_used      += adponz;
1146     current_space->local_remaining -= adponz;
1147   }
1148 
1149   /* Symbolic calc of A_off * P_oth */
1150   PetscCall(MatSetOptionsPrefix(a->B,prefix));
1151   PetscCall(MatAppendOptionsPrefix(a->B,"inner_offdiag_"));
1152   PetscCall(MatCreate(PETSC_COMM_SELF,&aopoth));
1153   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1154   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1155   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1156 
1157   /* Allocate space for apj, adpj, aopj, ... */
1158   /* destroy lists of free space and other temporary array(s) */
1159 
1160   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj));
1161   PetscCall(PetscMalloc1(adpoi[am]+2, &adpoj));
1162 
1163   /* Copy from linked list to j-array */
1164   PetscCall(PetscFreeSpaceContiguous(&free_space_diag,adpoj));
1165   PetscCall(PetscLLDestroy(lnk,lnkbt));
1166 
1167   adpoJ = adpoj;
1168   adpdJ = adpdj;
1169   aopJ = aopothj;
1170   apj  = ptap->apj;
1171   apJ = apj; /* still empty */
1172 
1173   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1174   /* A_diag * P_loc_diag to get A*P */
1175   for (i = 0; i < am; i++) {
1176     aopnz  =  aopothi[i+1] -  aopothi[i];
1177     adponz = adpoi[i+1] - adpoi[i];
1178     adpdnz = adpdi[i+1] - adpdi[i];
1179 
1180     /* Correct indices from A_diag*P_diag */
1181     for (i1 = 0; i1 < adpdnz; i1++) {
1182       adpdJ[i1] += p_colstart;
1183     }
1184     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1185     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1186     PetscCall(MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz));
1187 
1188     aopJ += aopnz;
1189     adpoJ += adponz;
1190     adpdJ += adpdnz;
1191     apJ += apnz;
1192     api[i+1] = api[i] + apnz;
1193   }
1194 
1195   /* malloc apa to store dense row A[i,:]*P */
1196   PetscCall(PetscCalloc1(pN+2,&ptap->apa));
1197 
1198   /* create and assemble symbolic parallel matrix C */
1199   PetscCall(MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE));
1200   PetscCall(MatSetBlockSizesFromMats(C,A,P));
1201   PetscCall(MatGetType(A,&mtype));
1202   PetscCall(MatSetType(C,mtype));
1203   PetscCall(MatMPIAIJSetPreallocation(C,0,dnz,0,onz));
1204   MatPreallocateEnd(dnz,onz);
1205 
1206   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1207   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
1208   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
1209   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
1210 
1211   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1212   C->ops->productnumeric = MatProductNumeric_AB;
1213 
1214   /* attach the supporting struct to C for reuse */
1215   C->product->data    = ptap;
1216   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1217 
1218   /* set MatInfo */
1219   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1220   if (afill < 1.0) afill = 1.0;
1221   C->info.mallocs           = nspacedouble;
1222   C->info.fill_ratio_given  = fill;
1223   C->info.fill_ratio_needed = afill;
1224 
1225 #if defined(PETSC_USE_INFO)
1226   if (api[am]) {
1227     PetscCall(PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill));
1228     PetscCall(PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill));
1229   } else {
1230     PetscCall(PetscInfo(C,"Empty matrix product\n"));
1231   }
1232 #endif
1233 
1234   PetscCall(MatDestroy(&aopoth));
1235   PetscCall(MatDestroy(&adpd));
1236   PetscCall(PetscFree(j_temp));
1237   PetscCall(PetscFree(adpoj));
1238   PetscCall(PetscFree(adpoi));
1239   PetscFunctionReturn(0);
1240 }
1241 
1242 /*-------------------------------------------------------------------------*/
1243 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1244 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1245 {
1246   Mat_APMPI      *ptap;
1247   Mat            Pt;
1248 
1249   PetscFunctionBegin;
1250   MatCheckProduct(C,3);
1251   ptap = (Mat_APMPI*)C->product->data;
1252   PetscCheck(ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1253   PetscCheck(ptap->Pt,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1254 
1255   Pt   = ptap->Pt;
1256   PetscCall(MatTranspose(P,MAT_REUSE_MATRIX,&Pt));
1257   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C));
1258   PetscFunctionReturn(0);
1259 }
1260 
1261 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1262 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1263 {
1264   Mat_APMPI           *ptap;
1265   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1266   MPI_Comm            comm;
1267   PetscMPIInt         size,rank;
1268   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1269   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1270   PetscInt            *lnk,i,k,nsend,rstart;
1271   PetscBT             lnkbt;
1272   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1273   PETSC_UNUSED PetscMPIInt icompleted=0;
1274   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1275   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1276   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1277   MPI_Request         *swaits,*rwaits;
1278   MPI_Status          *sstatus,rstatus;
1279   PetscLayout         rowmap;
1280   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1281   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1282   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1283   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1284   PetscTable          ta;
1285   MatType             mtype;
1286   const char          *prefix;
1287 
1288   PetscFunctionBegin;
1289   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
1290   PetscCallMPI(MPI_Comm_size(comm,&size));
1291   PetscCallMPI(MPI_Comm_rank(comm,&rank));
1292 
1293   /* create symbolic parallel matrix C */
1294   PetscCall(MatGetType(A,&mtype));
1295   PetscCall(MatSetType(C,mtype));
1296 
1297   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1298 
1299   /* create struct Mat_APMPI and attached it to C later */
1300   PetscCall(PetscNew(&ptap));
1301   ptap->reuse = MAT_INITIAL_MATRIX;
1302 
1303   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1304   /* --------------------------------- */
1305   PetscCall(MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd));
1306   PetscCall(MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro));
1307 
1308   /* (1) compute symbolic A_loc */
1309   /* ---------------------------*/
1310   PetscCall(MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc));
1311 
1312   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1313   /* ------------------------------------ */
1314   PetscCall(MatGetOptionsPrefix(A,&prefix));
1315   PetscCall(MatSetOptionsPrefix(ptap->Ro,prefix));
1316   PetscCall(MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_"));
1317   PetscCall(MatCreate(PETSC_COMM_SELF,&ptap->C_oth));
1318   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth));
1319 
1320   /* (3) send coj of C_oth to other processors  */
1321   /* ------------------------------------------ */
1322   /* determine row ownership */
1323   PetscCall(PetscLayoutCreate(comm,&rowmap));
1324   rowmap->n  = pn;
1325   rowmap->bs = 1;
1326   PetscCall(PetscLayoutSetUp(rowmap));
1327   owners = rowmap->range;
1328 
1329   /* determine the number of messages to send, their lengths */
1330   PetscCall(PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co));
1331   PetscCall(PetscArrayzero(len_s,size));
1332   PetscCall(PetscArrayzero(len_si,size));
1333 
1334   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1335   coi   = c_oth->i; coj = c_oth->j;
1336   con   = ptap->C_oth->rmap->n;
1337   proc  = 0;
1338   for (i=0; i<con; i++) {
1339     while (prmap[i] >= owners[proc+1]) proc++;
1340     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1341     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1342   }
1343 
1344   len          = 0; /* max length of buf_si[], see (4) */
1345   owners_co[0] = 0;
1346   nsend        = 0;
1347   for (proc=0; proc<size; proc++) {
1348     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1349     if (len_s[proc]) {
1350       nsend++;
1351       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1352       len         += len_si[proc];
1353     }
1354   }
1355 
1356   /* determine the number and length of messages to receive for coi and coj  */
1357   PetscCall(PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv));
1358   PetscCall(PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri));
1359 
1360   /* post the Irecv and Isend of coj */
1361   PetscCall(PetscCommGetNewTag(comm,&tagj));
1362   PetscCall(PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits));
1363   PetscCall(PetscMalloc1(nsend+1,&swaits));
1364   for (proc=0, k=0; proc<size; proc++) {
1365     if (!len_s[proc]) continue;
1366     i    = owners_co[proc];
1367     PetscCallMPI(MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k));
1368     k++;
1369   }
1370 
1371   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1372   /* ---------------------------------------- */
1373   PetscCall(MatSetOptionsPrefix(ptap->Rd,prefix));
1374   PetscCall(MatAppendOptionsPrefix(ptap->Rd,"inner_diag_"));
1375   PetscCall(MatCreate(PETSC_COMM_SELF,&ptap->C_loc));
1376   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc));
1377   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1378 
1379   /* receives coj are complete */
1380   for (i=0; i<nrecv; i++) {
1381     PetscCallMPI(MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus));
1382   }
1383   PetscCall(PetscFree(rwaits));
1384   if (nsend) PetscCallMPI(MPI_Waitall(nsend,swaits,sstatus));
1385 
1386   /* add received column indices into ta to update Crmax */
1387   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1388 
1389   /* create and initialize a linked list */
1390   PetscCall(PetscTableCreate(an,aN,&ta)); /* for compute Crmax */
1391   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1392 
1393   for (k=0; k<nrecv; k++) {/* k-th received message */
1394     Jptr = buf_rj[k];
1395     for (j=0; j<len_r[k]; j++) {
1396       PetscCall(PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES));
1397     }
1398   }
1399   PetscCall(PetscTableGetCount(ta,&Crmax));
1400   PetscCall(PetscTableDestroy(&ta));
1401 
1402   /* (4) send and recv coi */
1403   /*-----------------------*/
1404   PetscCall(PetscCommGetNewTag(comm,&tagi));
1405   PetscCall(PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits));
1406   PetscCall(PetscMalloc1(len+1,&buf_s));
1407   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1408   for (proc=0,k=0; proc<size; proc++) {
1409     if (!len_s[proc]) continue;
1410     /* form outgoing message for i-structure:
1411          buf_si[0]:                 nrows to be sent
1412                [1:nrows]:           row index (global)
1413                [nrows+1:2*nrows+1]: i-structure index
1414     */
1415     /*-------------------------------------------*/
1416     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1417     buf_si_i    = buf_si + nrows+1;
1418     buf_si[0]   = nrows;
1419     buf_si_i[0] = 0;
1420     nrows       = 0;
1421     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1422       nzi = coi[i+1] - coi[i];
1423       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1424       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1425       nrows++;
1426     }
1427     PetscCallMPI(MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k));
1428     k++;
1429     buf_si += len_si[proc];
1430   }
1431   for (i=0; i<nrecv; i++) {
1432     PetscCallMPI(MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus));
1433   }
1434   PetscCall(PetscFree(rwaits));
1435   if (nsend) PetscCallMPI(MPI_Waitall(nsend,swaits,sstatus));
1436 
1437   PetscCall(PetscFree4(len_s,len_si,sstatus,owners_co));
1438   PetscCall(PetscFree(len_ri));
1439   PetscCall(PetscFree(swaits));
1440   PetscCall(PetscFree(buf_s));
1441 
1442   /* (5) compute the local portion of C      */
1443   /* ------------------------------------------ */
1444   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1445   PetscCall(PetscFreeSpaceGet(Crmax,&free_space));
1446   current_space = free_space;
1447 
1448   PetscCall(PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci));
1449   for (k=0; k<nrecv; k++) {
1450     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1451     nrows       = *buf_ri_k[k];
1452     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1453     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1454   }
1455 
1456   MatPreallocateBegin(comm,pn,an,dnz,onz);
1457   PetscCall(PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt));
1458   for (i=0; i<pn; i++) { /* for each local row of C */
1459     /* add C_loc into C */
1460     nzi  = c_loc->i[i+1] - c_loc->i[i];
1461     Jptr = c_loc->j + c_loc->i[i];
1462     PetscCall(PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt));
1463 
1464     /* add received col data into lnk */
1465     for (k=0; k<nrecv; k++) { /* k-th received message */
1466       if (i == *nextrow[k]) { /* i-th row */
1467         nzi  = *(nextci[k]+1) - *nextci[k];
1468         Jptr = buf_rj[k] + *nextci[k];
1469         PetscCall(PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt));
1470         nextrow[k]++; nextci[k]++;
1471       }
1472     }
1473 
1474     /* add missing diagonal entry */
1475     if (C->force_diagonals) {
1476       k = i + owners[rank]; /* column index */
1477       PetscCall(PetscLLCondensedAddSorted(1,&k,lnk,lnkbt));
1478     }
1479 
1480     nzi = lnk[0];
1481 
1482     /* copy data into free space, then initialize lnk */
1483     PetscCall(PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt));
1484     PetscCall(MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz));
1485   }
1486   PetscCall(PetscFree3(buf_ri_k,nextrow,nextci));
1487   PetscCall(PetscLLDestroy(lnk,lnkbt));
1488   PetscCall(PetscFreeSpaceDestroy(free_space));
1489 
1490   /* local sizes and preallocation */
1491   PetscCall(MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE));
1492   if (P->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap,P->cmap->bs));
1493   if (A->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap,A->cmap->bs));
1494   PetscCall(MatMPIAIJSetPreallocation(C,0,dnz,0,onz));
1495   MatPreallocateEnd(dnz,onz);
1496 
1497   /* add C_loc and C_oth to C */
1498   PetscCall(MatGetOwnershipRange(C,&rstart,NULL));
1499   for (i=0; i<pn; i++) {
1500     ncols = c_loc->i[i+1] - c_loc->i[i];
1501     cols  = c_loc->j + c_loc->i[i];
1502     row   = rstart + i;
1503     PetscCall(MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES));
1504 
1505     if (C->force_diagonals) {
1506       PetscCall(MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES));
1507     }
1508   }
1509   for (i=0; i<con; i++) {
1510     ncols = c_oth->i[i+1] - c_oth->i[i];
1511     cols  = c_oth->j + c_oth->i[i];
1512     row   = prmap[i];
1513     PetscCall(MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES));
1514   }
1515   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
1516   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
1517   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
1518 
1519   /* members in merge */
1520   PetscCall(PetscFree(id_r));
1521   PetscCall(PetscFree(len_r));
1522   PetscCall(PetscFree(buf_ri[0]));
1523   PetscCall(PetscFree(buf_ri));
1524   PetscCall(PetscFree(buf_rj[0]));
1525   PetscCall(PetscFree(buf_rj));
1526   PetscCall(PetscLayoutDestroy(&rowmap));
1527 
1528   /* attach the supporting struct to C for reuse */
1529   C->product->data    = ptap;
1530   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1531   PetscFunctionReturn(0);
1532 }
1533 
1534 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1535 {
1536   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1537   Mat_SeqAIJ        *c_seq;
1538   Mat_APMPI         *ptap;
1539   Mat               A_loc,C_loc,C_oth;
1540   PetscInt          i,rstart,rend,cm,ncols,row;
1541   const PetscInt    *cols;
1542   const PetscScalar *vals;
1543 
1544   PetscFunctionBegin;
1545   MatCheckProduct(C,3);
1546   ptap = (Mat_APMPI*)C->product->data;
1547   PetscCheck(ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1548   PetscCheck(ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1549   PetscCall(MatZeroEntries(C));
1550 
1551   if (ptap->reuse == MAT_REUSE_MATRIX) {
1552     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1553     /* 1) get R = Pd^T, Ro = Po^T */
1554     /*----------------------------*/
1555     PetscCall(MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd));
1556     PetscCall(MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro));
1557 
1558     /* 2) compute numeric A_loc */
1559     /*--------------------------*/
1560     PetscCall(MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc));
1561   }
1562 
1563   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1564   A_loc = ptap->A_loc;
1565   PetscCall(((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc));
1566   PetscCall(((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth));
1567   C_loc = ptap->C_loc;
1568   C_oth = ptap->C_oth;
1569 
1570   /* add C_loc and C_oth to C */
1571   PetscCall(MatGetOwnershipRange(C,&rstart,&rend));
1572 
1573   /* C_loc -> C */
1574   cm    = C_loc->rmap->N;
1575   c_seq = (Mat_SeqAIJ*)C_loc->data;
1576   cols = c_seq->j;
1577   vals = c_seq->a;
1578   for (i=0; i<cm; i++) {
1579     ncols = c_seq->i[i+1] - c_seq->i[i];
1580     row = rstart + i;
1581     PetscCall(MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES));
1582     cols += ncols; vals += ncols;
1583   }
1584 
1585   /* Co -> C, off-processor part */
1586   cm    = C_oth->rmap->N;
1587   c_seq = (Mat_SeqAIJ*)C_oth->data;
1588   cols  = c_seq->j;
1589   vals  = c_seq->a;
1590   for (i=0; i<cm; i++) {
1591     ncols = c_seq->i[i+1] - c_seq->i[i];
1592     row = p->garray[i];
1593     PetscCall(MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES));
1594     cols += ncols; vals += ncols;
1595   }
1596   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
1597   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
1598   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
1599 
1600   ptap->reuse = MAT_REUSE_MATRIX;
1601   PetscFunctionReturn(0);
1602 }
1603 
1604 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1605 {
1606   Mat_Merge_SeqsToMPI *merge;
1607   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1608   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1609   Mat_APMPI           *ptap;
1610   PetscInt            *adj;
1611   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1612   MatScalar           *ada,*ca,valtmp;
1613   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1614   MPI_Comm            comm;
1615   PetscMPIInt         size,rank,taga,*len_s;
1616   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1617   PetscInt            **buf_ri,**buf_rj;
1618   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1619   MPI_Request         *s_waits,*r_waits;
1620   MPI_Status          *status;
1621   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1622   const PetscScalar   *dummy;
1623   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1624   Mat                 A_loc;
1625   Mat_SeqAIJ          *a_loc;
1626 
1627   PetscFunctionBegin;
1628   MatCheckProduct(C,3);
1629   ptap = (Mat_APMPI*)C->product->data;
1630   PetscCheck(ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1631   PetscCheck(ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1632   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
1633   PetscCallMPI(MPI_Comm_size(comm,&size));
1634   PetscCallMPI(MPI_Comm_rank(comm,&rank));
1635 
1636   merge = ptap->merge;
1637 
1638   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1639   /*------------------------------------------*/
1640   /* get data from symbolic products */
1641   coi    = merge->coi; coj = merge->coj;
1642   PetscCall(PetscCalloc1(coi[pon]+1,&coa));
1643   bi     = merge->bi; bj = merge->bj;
1644   owners = merge->rowmap->range;
1645   PetscCall(PetscCalloc1(bi[cm]+1,&ba));
1646 
1647   /* get A_loc by taking all local rows of A */
1648   A_loc = ptap->A_loc;
1649   PetscCall(MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc));
1650   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1651   ai    = a_loc->i;
1652   aj    = a_loc->j;
1653 
1654   /* trigger copy to CPU */
1655   PetscCall(MatSeqAIJGetArrayRead(p->A,&dummy));
1656   PetscCall(MatSeqAIJRestoreArrayRead(p->A,&dummy));
1657   PetscCall(MatSeqAIJGetArrayRead(p->B,&dummy));
1658   PetscCall(MatSeqAIJRestoreArrayRead(p->B,&dummy));
1659   for (i=0; i<am; i++) {
1660     anz = ai[i+1] - ai[i];
1661     adj = aj + ai[i];
1662     ada = a_loc->a + ai[i];
1663 
1664     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1665     /*-------------------------------------------------------------*/
1666     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1667     pnz = po->i[i+1] - po->i[i];
1668     poJ = po->j + po->i[i];
1669     pA  = po->a + po->i[i];
1670     for (j=0; j<pnz; j++) {
1671       row = poJ[j];
1672       cj  = coj + coi[row];
1673       ca  = coa + coi[row];
1674       /* perform sparse axpy */
1675       nexta  = 0;
1676       valtmp = pA[j];
1677       for (k=0; nexta<anz; k++) {
1678         if (cj[k] == adj[nexta]) {
1679           ca[k] += valtmp*ada[nexta];
1680           nexta++;
1681         }
1682       }
1683       PetscCall(PetscLogFlops(2.0*anz));
1684     }
1685 
1686     /* put the value into Cd (diagonal part) */
1687     pnz = pd->i[i+1] - pd->i[i];
1688     pdJ = pd->j + pd->i[i];
1689     pA  = pd->a + pd->i[i];
1690     for (j=0; j<pnz; j++) {
1691       row = pdJ[j];
1692       cj  = bj + bi[row];
1693       ca  = ba + bi[row];
1694       /* perform sparse axpy */
1695       nexta  = 0;
1696       valtmp = pA[j];
1697       for (k=0; nexta<anz; k++) {
1698         if (cj[k] == adj[nexta]) {
1699           ca[k] += valtmp*ada[nexta];
1700           nexta++;
1701         }
1702       }
1703       PetscCall(PetscLogFlops(2.0*anz));
1704     }
1705   }
1706 
1707   /* 3) send and recv matrix values coa */
1708   /*------------------------------------*/
1709   buf_ri = merge->buf_ri;
1710   buf_rj = merge->buf_rj;
1711   len_s  = merge->len_s;
1712   PetscCall(PetscCommGetNewTag(comm,&taga));
1713   PetscCall(PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits));
1714 
1715   PetscCall(PetscMalloc2(merge->nsend+1,&s_waits,size,&status));
1716   for (proc=0,k=0; proc<size; proc++) {
1717     if (!len_s[proc]) continue;
1718     i    = merge->owners_co[proc];
1719     PetscCallMPI(MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k));
1720     k++;
1721   }
1722   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv,r_waits,status));
1723   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,s_waits,status));
1724 
1725   PetscCall(PetscFree2(s_waits,status));
1726   PetscCall(PetscFree(r_waits));
1727   PetscCall(PetscFree(coa));
1728 
1729   /* 4) insert local Cseq and received values into Cmpi */
1730   /*----------------------------------------------------*/
1731   PetscCall(PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci));
1732   for (k=0; k<merge->nrecv; k++) {
1733     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1734     nrows       = *(buf_ri_k[k]);
1735     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1736     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1737   }
1738 
1739   for (i=0; i<cm; i++) {
1740     row  = owners[rank] + i; /* global row index of C_seq */
1741     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1742     ba_i = ba + bi[i];
1743     bnz  = bi[i+1] - bi[i];
1744     /* add received vals into ba */
1745     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1746       /* i-th row */
1747       if (i == *nextrow[k]) {
1748         cnz    = *(nextci[k]+1) - *nextci[k];
1749         cj     = buf_rj[k] + *(nextci[k]);
1750         ca     = abuf_r[k] + *(nextci[k]);
1751         nextcj = 0;
1752         for (j=0; nextcj<cnz; j++) {
1753           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1754             ba_i[j] += ca[nextcj++];
1755           }
1756         }
1757         nextrow[k]++; nextci[k]++;
1758         PetscCall(PetscLogFlops(2.0*cnz));
1759       }
1760     }
1761     PetscCall(MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES));
1762   }
1763   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
1764   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
1765 
1766   PetscCall(PetscFree(ba));
1767   PetscCall(PetscFree(abuf_r[0]));
1768   PetscCall(PetscFree(abuf_r));
1769   PetscCall(PetscFree3(buf_ri_k,nextrow,nextci));
1770   PetscFunctionReturn(0);
1771 }
1772 
1773 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1774 {
1775   Mat                 A_loc;
1776   Mat_APMPI           *ptap;
1777   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1778   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1779   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1780   PetscInt            nnz;
1781   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1782   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1783   MPI_Comm            comm;
1784   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1785   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1786   PetscInt            len,proc,*dnz,*onz,*owners;
1787   PetscInt            nzi,*bi,*bj;
1788   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1789   MPI_Request         *swaits,*rwaits;
1790   MPI_Status          *sstatus,rstatus;
1791   Mat_Merge_SeqsToMPI *merge;
1792   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1793   PetscReal           afill  =1.0,afill_tmp;
1794   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1795   Mat_SeqAIJ          *a_loc;
1796   PetscTable          ta;
1797   MatType             mtype;
1798 
1799   PetscFunctionBegin;
1800   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
1801   /* check if matrix local sizes are compatible */
1802   PetscCheckFalse(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,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
1803 
1804   PetscCallMPI(MPI_Comm_size(comm,&size));
1805   PetscCallMPI(MPI_Comm_rank(comm,&rank));
1806 
1807   /* create struct Mat_APMPI and attached it to C later */
1808   PetscCall(PetscNew(&ptap));
1809 
1810   /* get A_loc by taking all local rows of A */
1811   PetscCall(MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc));
1812 
1813   ptap->A_loc = A_loc;
1814   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1815   ai          = a_loc->i;
1816   aj          = a_loc->j;
1817 
1818   /* determine symbolic Co=(p->B)^T*A - send to others */
1819   /*----------------------------------------------------*/
1820   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj));
1821   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj));
1822   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1823                          >= (num of nonzero rows of C_seq) - pn */
1824   PetscCall(PetscMalloc1(pon+1,&coi));
1825   coi[0] = 0;
1826 
1827   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1828   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1829   PetscCall(PetscFreeSpaceGet(nnz,&free_space));
1830   current_space = free_space;
1831 
1832   /* create and initialize a linked list */
1833   PetscCall(PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta));
1834   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1835   PetscCall(PetscTableGetCount(ta,&Armax));
1836 
1837   PetscCall(PetscLLCondensedCreate_Scalable(Armax,&lnk));
1838 
1839   for (i=0; i<pon; i++) {
1840     pnz = poti[i+1] - poti[i];
1841     ptJ = potj + poti[i];
1842     for (j=0; j<pnz; j++) {
1843       row  = ptJ[j]; /* row of A_loc == col of Pot */
1844       anz  = ai[row+1] - ai[row];
1845       Jptr = aj + ai[row];
1846       /* add non-zero cols of AP into the sorted linked list lnk */
1847       PetscCall(PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk));
1848     }
1849     nnz = lnk[0];
1850 
1851     /* If free space is not available, double the total space in the list */
1852     if (current_space->local_remaining<nnz) {
1853       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space));
1854       nspacedouble++;
1855     }
1856 
1857     /* Copy data into free space, and zero out denserows */
1858     PetscCall(PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk));
1859 
1860     current_space->array           += nnz;
1861     current_space->local_used      += nnz;
1862     current_space->local_remaining -= nnz;
1863 
1864     coi[i+1] = coi[i] + nnz;
1865   }
1866 
1867   PetscCall(PetscMalloc1(coi[pon]+1,&coj));
1868   PetscCall(PetscFreeSpaceContiguous(&free_space,coj));
1869   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */
1870 
1871   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1872   if (afill_tmp > afill) afill = afill_tmp;
1873 
1874   /* send j-array (coj) of Co to other processors */
1875   /*----------------------------------------------*/
1876   /* determine row ownership */
1877   PetscCall(PetscNew(&merge));
1878   PetscCall(PetscLayoutCreate(comm,&merge->rowmap));
1879 
1880   merge->rowmap->n  = pn;
1881   merge->rowmap->bs = 1;
1882 
1883   PetscCall(PetscLayoutSetUp(merge->rowmap));
1884   owners = merge->rowmap->range;
1885 
1886   /* determine the number of messages to send, their lengths */
1887   PetscCall(PetscCalloc1(size,&len_si));
1888   PetscCall(PetscCalloc1(size,&merge->len_s));
1889 
1890   len_s        = merge->len_s;
1891   merge->nsend = 0;
1892 
1893   PetscCall(PetscMalloc1(size+2,&owners_co));
1894 
1895   proc = 0;
1896   for (i=0; i<pon; i++) {
1897     while (prmap[i] >= owners[proc+1]) proc++;
1898     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1899     len_s[proc] += coi[i+1] - coi[i];
1900   }
1901 
1902   len          = 0; /* max length of buf_si[] */
1903   owners_co[0] = 0;
1904   for (proc=0; proc<size; proc++) {
1905     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1906     if (len_si[proc]) {
1907       merge->nsend++;
1908       len_si[proc] = 2*(len_si[proc] + 1);
1909       len         += len_si[proc];
1910     }
1911   }
1912 
1913   /* determine the number and length of messages to receive for coi and coj  */
1914   PetscCall(PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv));
1915   PetscCall(PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri));
1916 
1917   /* post the Irecv and Isend of coj */
1918   PetscCall(PetscCommGetNewTag(comm,&tagj));
1919   PetscCall(PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits));
1920   PetscCall(PetscMalloc1(merge->nsend+1,&swaits));
1921   for (proc=0, k=0; proc<size; proc++) {
1922     if (!len_s[proc]) continue;
1923     i    = owners_co[proc];
1924     PetscCallMPI(MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k));
1925     k++;
1926   }
1927 
1928   /* receives and sends of coj are complete */
1929   PetscCall(PetscMalloc1(size,&sstatus));
1930   for (i=0; i<merge->nrecv; i++) {
1931     PETSC_UNUSED PetscMPIInt icompleted;
1932     PetscCallMPI(MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus));
1933   }
1934   PetscCall(PetscFree(rwaits));
1935   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,swaits,sstatus));
1936 
1937   /* add received column indices into table to update Armax */
1938   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1939   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1940     Jptr = buf_rj[k];
1941     for (j=0; j<merge->len_r[k]; j++) {
1942       PetscCall(PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES));
1943     }
1944   }
1945   PetscCall(PetscTableGetCount(ta,&Armax));
1946 
1947   /* send and recv coi */
1948   /*-------------------*/
1949   PetscCall(PetscCommGetNewTag(comm,&tagi));
1950   PetscCall(PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits));
1951   PetscCall(PetscMalloc1(len+1,&buf_s));
1952   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1953   for (proc=0,k=0; proc<size; proc++) {
1954     if (!len_s[proc]) continue;
1955     /* form outgoing message for i-structure:
1956          buf_si[0]:                 nrows to be sent
1957                [1:nrows]:           row index (global)
1958                [nrows+1:2*nrows+1]: i-structure index
1959     */
1960     /*-------------------------------------------*/
1961     nrows       = len_si[proc]/2 - 1;
1962     buf_si_i    = buf_si + nrows+1;
1963     buf_si[0]   = nrows;
1964     buf_si_i[0] = 0;
1965     nrows       = 0;
1966     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1967       nzi               = coi[i+1] - coi[i];
1968       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1969       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1970       nrows++;
1971     }
1972     PetscCallMPI(MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k));
1973     k++;
1974     buf_si += len_si[proc];
1975   }
1976   i = merge->nrecv;
1977   while (i--) {
1978     PETSC_UNUSED PetscMPIInt icompleted;
1979     PetscCallMPI(MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus));
1980   }
1981   PetscCall(PetscFree(rwaits));
1982   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,swaits,sstatus));
1983   PetscCall(PetscFree(len_si));
1984   PetscCall(PetscFree(len_ri));
1985   PetscCall(PetscFree(swaits));
1986   PetscCall(PetscFree(sstatus));
1987   PetscCall(PetscFree(buf_s));
1988 
1989   /* compute the local portion of C (mpi mat) */
1990   /*------------------------------------------*/
1991   /* allocate bi array and free space for accumulating nonzero column info */
1992   PetscCall(PetscMalloc1(pn+1,&bi));
1993   bi[0] = 0;
1994 
1995   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1996   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1997   PetscCall(PetscFreeSpaceGet(nnz,&free_space));
1998   current_space = free_space;
1999 
2000   PetscCall(PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci));
2001   for (k=0; k<merge->nrecv; k++) {
2002     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2003     nrows       = *buf_ri_k[k];
2004     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2005     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2006   }
2007 
2008   PetscCall(PetscLLCondensedCreate_Scalable(Armax,&lnk));
2009   MatPreallocateBegin(comm,pn,A->cmap->n,dnz,onz);
2010   rmax = 0;
2011   for (i=0; i<pn; i++) {
2012     /* add pdt[i,:]*AP into lnk */
2013     pnz = pdti[i+1] - pdti[i];
2014     ptJ = pdtj + pdti[i];
2015     for (j=0; j<pnz; j++) {
2016       row  = ptJ[j];  /* row of AP == col of Pt */
2017       anz  = ai[row+1] - ai[row];
2018       Jptr = aj + ai[row];
2019       /* add non-zero cols of AP into the sorted linked list lnk */
2020       PetscCall(PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk));
2021     }
2022 
2023     /* add received col data into lnk */
2024     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2025       if (i == *nextrow[k]) { /* i-th row */
2026         nzi  = *(nextci[k]+1) - *nextci[k];
2027         Jptr = buf_rj[k] + *nextci[k];
2028         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk));
2029         nextrow[k]++; nextci[k]++;
2030       }
2031     }
2032 
2033     /* add missing diagonal entry */
2034     if (C->force_diagonals) {
2035       k = i + owners[rank]; /* column index */
2036       PetscCall(PetscLLCondensedAddSorted_Scalable(1,&k,lnk));
2037     }
2038 
2039     nnz = lnk[0];
2040 
2041     /* if free space is not available, make more free space */
2042     if (current_space->local_remaining<nnz) {
2043       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space));
2044       nspacedouble++;
2045     }
2046     /* copy data into free space, then initialize lnk */
2047     PetscCall(PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk));
2048     PetscCall(MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz));
2049 
2050     current_space->array           += nnz;
2051     current_space->local_used      += nnz;
2052     current_space->local_remaining -= nnz;
2053 
2054     bi[i+1] = bi[i] + nnz;
2055     if (nnz > rmax) rmax = nnz;
2056   }
2057   PetscCall(PetscFree3(buf_ri_k,nextrow,nextci));
2058 
2059   PetscCall(PetscMalloc1(bi[pn]+1,&bj));
2060   PetscCall(PetscFreeSpaceContiguous(&free_space,bj));
2061   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2062   if (afill_tmp > afill) afill = afill_tmp;
2063   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2064   PetscCall(PetscTableDestroy(&ta));
2065   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj));
2066   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj));
2067 
2068   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2069   /*-------------------------------------------------------------------------------*/
2070   PetscCall(MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE));
2071   PetscCall(MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs)));
2072   PetscCall(MatGetType(A,&mtype));
2073   PetscCall(MatSetType(C,mtype));
2074   PetscCall(MatMPIAIJSetPreallocation(C,0,dnz,0,onz));
2075   MatPreallocateEnd(dnz,onz);
2076   PetscCall(MatSetBlockSize(C,1));
2077   PetscCall(MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
2078   for (i=0; i<pn; i++) {
2079     row  = i + rstart;
2080     nnz  = bi[i+1] - bi[i];
2081     Jptr = bj + bi[i];
2082     PetscCall(MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES));
2083   }
2084   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
2085   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));
2086   PetscCall(MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
2087   merge->bi        = bi;
2088   merge->bj        = bj;
2089   merge->coi       = coi;
2090   merge->coj       = coj;
2091   merge->buf_ri    = buf_ri;
2092   merge->buf_rj    = buf_rj;
2093   merge->owners_co = owners_co;
2094 
2095   /* attach the supporting struct to C for reuse */
2096   C->product->data    = ptap;
2097   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2098   ptap->merge         = merge;
2099 
2100   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2101 
2102 #if defined(PETSC_USE_INFO)
2103   if (bi[pn] != 0) {
2104     PetscCall(PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill));
2105     PetscCall(PetscInfo(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill));
2106   } else {
2107     PetscCall(PetscInfo(C,"Empty matrix product\n"));
2108   }
2109 #endif
2110   PetscFunctionReturn(0);
2111 }
2112 
2113 /* ---------------------------------------------------------------- */
2114 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2115 {
2116   Mat_Product    *product = C->product;
2117   Mat            A=product->A,B=product->B;
2118   PetscReal      fill=product->fill;
2119   PetscBool      flg;
2120 
2121   PetscFunctionBegin;
2122   /* scalable */
2123   PetscCall(PetscStrcmp(product->alg,"scalable",&flg));
2124   if (flg) {
2125     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C));
2126     goto next;
2127   }
2128 
2129   /* nonscalable */
2130   PetscCall(PetscStrcmp(product->alg,"nonscalable",&flg));
2131   if (flg) {
2132     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C));
2133     goto next;
2134   }
2135 
2136   /* matmatmult */
2137   PetscCall(PetscStrcmp(product->alg,"at*b",&flg));
2138   if (flg) {
2139     Mat       At;
2140     Mat_APMPI *ptap;
2141 
2142     PetscCall(MatTranspose(A,MAT_INITIAL_MATRIX,&At));
2143     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C));
2144     ptap = (Mat_APMPI*)C->product->data;
2145     if (ptap) {
2146       ptap->Pt = At;
2147       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2148     }
2149     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2150     goto next;
2151   }
2152 
2153   /* backend general code */
2154   PetscCall(PetscStrcmp(product->alg,"backend",&flg));
2155   if (flg) {
2156     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2157     PetscFunctionReturn(0);
2158   }
2159 
2160   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2161 
2162 next:
2163   C->ops->productnumeric = MatProductNumeric_AtB;
2164   PetscFunctionReturn(0);
2165 }
2166 
2167 /* ---------------------------------------------------------------- */
2168 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2169 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2170 {
2171   Mat_Product    *product = C->product;
2172   Mat            A=product->A,B=product->B;
2173 #if defined(PETSC_HAVE_HYPRE)
2174   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2175   PetscInt       nalg = 5;
2176 #else
2177   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2178   PetscInt       nalg = 4;
2179 #endif
2180   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2181   PetscBool      flg;
2182   MPI_Comm       comm;
2183 
2184   PetscFunctionBegin;
2185   /* Check matrix local sizes */
2186   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
2187 
2188   /* Set "nonscalable" as default algorithm */
2189   PetscCall(PetscStrcmp(C->product->alg,"default",&flg));
2190   if (flg) {
2191     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2192 
2193     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2194     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2195       MatInfo     Ainfo,Binfo;
2196       PetscInt    nz_local;
2197       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2198 
2199       PetscCall(MatGetInfo(A,MAT_LOCAL,&Ainfo));
2200       PetscCall(MatGetInfo(B,MAT_LOCAL,&Binfo));
2201       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2202 
2203       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2204       PetscCall(MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm));
2205 
2206       if (alg_scalable) {
2207         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2208         PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2209         PetscCall(PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local)));
2210       }
2211     }
2212   }
2213 
2214   /* Get runtime option */
2215   if (product->api_user) {
2216     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
2217     PetscCall(PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg));
2218     PetscOptionsEnd();
2219   } else {
2220     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
2221     PetscCall(PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg));
2222     PetscOptionsEnd();
2223   }
2224   if (flg) {
2225     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2226   }
2227 
2228   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2229   PetscFunctionReturn(0);
2230 }
2231 
2232 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2233 {
2234   PetscFunctionBegin;
2235   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2236   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2237   PetscFunctionReturn(0);
2238 }
2239 
2240 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2241 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2242 {
2243   Mat_Product    *product = C->product;
2244   Mat            A=product->A,B=product->B;
2245   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2246   PetscInt       nalg = 4;
2247   PetscInt       alg = 1; /* set default algorithm  */
2248   PetscBool      flg;
2249   MPI_Comm       comm;
2250 
2251   PetscFunctionBegin;
2252   /* Check matrix local sizes */
2253   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
2254   PetscCheckFalse(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 ")",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
2255 
2256   /* Set default algorithm */
2257   PetscCall(PetscStrcmp(C->product->alg,"default",&flg));
2258   if (flg) {
2259     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2260   }
2261 
2262   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2263   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2264     MatInfo     Ainfo,Binfo;
2265     PetscInt    nz_local;
2266     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2267 
2268     PetscCall(MatGetInfo(A,MAT_LOCAL,&Ainfo));
2269     PetscCall(MatGetInfo(B,MAT_LOCAL,&Binfo));
2270     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2271 
2272     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2273     PetscCall(MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm));
2274 
2275     if (alg_scalable) {
2276       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2277       PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2278       PetscCall(PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local)));
2279     }
2280   }
2281 
2282   /* Get runtime option */
2283   if (product->api_user) {
2284     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
2285     PetscCall(PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg));
2286     PetscOptionsEnd();
2287   } else {
2288     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
2289     PetscCall(PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg));
2290     PetscOptionsEnd();
2291   }
2292   if (flg) {
2293     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2294   }
2295 
2296   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2297   PetscFunctionReturn(0);
2298 }
2299 
2300 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2301 {
2302   Mat_Product    *product = C->product;
2303   Mat            A=product->A,P=product->B;
2304   MPI_Comm       comm;
2305   PetscBool      flg;
2306   PetscInt       alg=1; /* set default algorithm */
2307 #if !defined(PETSC_HAVE_HYPRE)
2308   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2309   PetscInt       nalg=5;
2310 #else
2311   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2312   PetscInt       nalg=6;
2313 #endif
2314   PetscInt       pN=P->cmap->N;
2315 
2316   PetscFunctionBegin;
2317   /* Check matrix local sizes */
2318   PetscCall(PetscObjectGetComm((PetscObject)C,&comm));
2319   PetscCheckFalse(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 ")",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
2320   PetscCheckFalse(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 ")",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
2321 
2322   /* Set "nonscalable" as default algorithm */
2323   PetscCall(PetscStrcmp(C->product->alg,"default",&flg));
2324   if (flg) {
2325     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2326 
2327     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2328     if (pN > 100000) {
2329       MatInfo     Ainfo,Pinfo;
2330       PetscInt    nz_local;
2331       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2332 
2333       PetscCall(MatGetInfo(A,MAT_LOCAL,&Ainfo));
2334       PetscCall(MatGetInfo(P,MAT_LOCAL,&Pinfo));
2335       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2336 
2337       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2338       PetscCall(MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm));
2339 
2340       if (alg_scalable) {
2341         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2342         PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2343       }
2344     }
2345   }
2346 
2347   /* Get runtime option */
2348   if (product->api_user) {
2349     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
2350     PetscCall(PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg));
2351     PetscOptionsEnd();
2352   } else {
2353     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
2354     PetscCall(PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg));
2355     PetscOptionsEnd();
2356   }
2357   if (flg) {
2358     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2359   }
2360 
2361   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2362   PetscFunctionReturn(0);
2363 }
2364 
2365 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2366 {
2367   Mat_Product *product = C->product;
2368   Mat         A = product->A,R=product->B;
2369 
2370   PetscFunctionBegin;
2371   /* Check matrix local sizes */
2372   PetscCheckFalse(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,A->rmap->n,R->rmap->n,R->cmap->n);
2373 
2374   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 /*
2379  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2380 */
2381 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2382 {
2383   Mat_Product    *product = C->product;
2384   PetscBool      flg = PETSC_FALSE;
2385   PetscInt       alg = 1; /* default algorithm */
2386   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2387   PetscInt       nalg = 3;
2388 
2389   PetscFunctionBegin;
2390   /* Set default algorithm */
2391   PetscCall(PetscStrcmp(C->product->alg,"default",&flg));
2392   if (flg) {
2393     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2394   }
2395 
2396   /* Get runtime option */
2397   if (product->api_user) {
2398     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
2399     PetscCall(PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg));
2400     PetscOptionsEnd();
2401   } else {
2402     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
2403     PetscCall(PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg));
2404     PetscOptionsEnd();
2405   }
2406   if (flg) {
2407     PetscCall(MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]));
2408   }
2409 
2410   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2411   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2412   PetscFunctionReturn(0);
2413 }
2414 
2415 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2416 {
2417   Mat_Product    *product = C->product;
2418 
2419   PetscFunctionBegin;
2420   switch (product->type) {
2421   case MATPRODUCT_AB:
2422     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2423     break;
2424   case MATPRODUCT_ABt:
2425     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2426     break;
2427   case MATPRODUCT_AtB:
2428     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2429     break;
2430   case MATPRODUCT_PtAP:
2431     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2432     break;
2433   case MATPRODUCT_RARt:
2434     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2435     break;
2436   case MATPRODUCT_ABC:
2437     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2438     break;
2439   default:
2440     break;
2441   }
2442   PetscFunctionReturn(0);
2443 }
2444