xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 3c859ba3a04a72e8efcb87bc7ffc046a6cbab413)
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_AB_MPIAIJ_MPIAIJ(Mat C)
19 {
20   PetscErrorCode      ierr;
21   Mat_Product         *product = C->product;
22   Mat                 A=product->A,B=product->B;
23   MatProductAlgorithm alg=product->alg;
24   PetscReal           fill=product->fill;
25   PetscBool           flg;
26 
27   PetscFunctionBegin;
28   /* scalable */
29   ierr = PetscStrcmp(alg,"scalable",&flg);CHKERRQ(ierr);
30   if (flg) {
31     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
32     PetscFunctionReturn(0);
33   }
34 
35   /* nonscalable */
36   ierr = PetscStrcmp(alg,"nonscalable",&flg);CHKERRQ(ierr);
37   if (flg) {
38     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
39     PetscFunctionReturn(0);
40   }
41 
42   /* seqmpi */
43   ierr = PetscStrcmp(alg,"seqmpi",&flg);CHKERRQ(ierr);
44   if (flg) {
45     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);CHKERRQ(ierr);
46     PetscFunctionReturn(0);
47   }
48 
49   /* backend general code */
50   ierr = PetscStrcmp(alg,"backend",&flg);CHKERRQ(ierr);
51   if (flg) {
52     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
53     PetscFunctionReturn(0);
54   }
55 
56 #if defined(PETSC_HAVE_HYPRE)
57   ierr = PetscStrcmp(alg,"hypre",&flg);CHKERRQ(ierr);
58   if (flg) {
59     ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
60     PetscFunctionReturn(0);
61   }
62 #endif
63   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
64 }
65 
66 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
67 {
68   PetscErrorCode ierr;
69   Mat_APMPI      *ptap = (Mat_APMPI*)data;
70 
71   PetscFunctionBegin;
72   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
73   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
74   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
75   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
76   ierr = MatDestroy(&ptap->Pt);CHKERRQ(ierr);
77   ierr = PetscFree(ptap->api);CHKERRQ(ierr);
78   ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
79   ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
80   ierr = PetscFree(ptap);CHKERRQ(ierr);
81   PetscFunctionReturn(0);
82 }
83 
84 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
85 {
86   PetscErrorCode    ierr;
87   Mat_MPIAIJ        *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
88   Mat_SeqAIJ        *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
89   Mat_SeqAIJ        *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
90   PetscScalar       *cda=cd->a,*coa=co->a;
91   Mat_SeqAIJ        *p_loc,*p_oth;
92   PetscScalar       *apa,*ca;
93   PetscInt          cm =C->rmap->n;
94   Mat_APMPI         *ptap;
95   PetscInt          *api,*apj,*apJ,i,k;
96   PetscInt          cstart=C->cmap->rstart;
97   PetscInt          cdnz,conz,k0,k1;
98   const PetscScalar *dummy;
99   MPI_Comm          comm;
100   PetscMPIInt       size;
101 
102   PetscFunctionBegin;
103   MatCheckProduct(C,3);
104   ptap = (Mat_APMPI*)C->product->data;
105   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
106   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
107   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
108 
109   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
110 
111   /* flag CPU mask for C */
112 #if defined(PETSC_HAVE_DEVICE)
113   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
114   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
115   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
116 #endif
117 
118   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
119   /*-----------------------------------------------------*/
120   /* update numerical values of P_oth and P_loc */
121   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
122   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
123 
124   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
125   /*----------------------------------------------------------*/
126   /* get data from symbolic products */
127   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
128   p_oth = NULL;
129   if (size >1) {
130     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
131   }
132 
133   /* get apa for storing dense row A[i,:]*P */
134   apa = ptap->apa;
135 
136   api = ptap->api;
137   apj = ptap->apj;
138   /* trigger copy to CPU */
139   ierr = MatSeqAIJGetArrayRead(a->A,&dummy);CHKERRQ(ierr);
140   ierr = MatSeqAIJRestoreArrayRead(a->A,&dummy);CHKERRQ(ierr);
141   ierr = MatSeqAIJGetArrayRead(a->B,&dummy);CHKERRQ(ierr);
142   ierr = MatSeqAIJRestoreArrayRead(a->B,&dummy);CHKERRQ(ierr);
143   for (i=0; i<cm; i++) {
144     /* compute apa = A[i,:]*P */
145     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
146 
147     /* set values in C */
148     apJ  = apj + api[i];
149     cdnz = cd->i[i+1] - cd->i[i];
150     conz = co->i[i+1] - co->i[i];
151 
152     /* 1st off-diagonal part of C */
153     ca = coa + co->i[i];
154     k  = 0;
155     for (k0=0; k0<conz; k0++) {
156       if (apJ[k] >= cstart) break;
157       ca[k0]      = apa[apJ[k]];
158       apa[apJ[k++]] = 0.0;
159     }
160 
161     /* diagonal part of C */
162     ca = cda + cd->i[i];
163     for (k1=0; k1<cdnz; k1++) {
164       ca[k1]      = apa[apJ[k]];
165       apa[apJ[k++]] = 0.0;
166     }
167 
168     /* 2nd off-diagonal part of C */
169     ca = coa + co->i[i];
170     for (; k0<conz; k0++) {
171       ca[k0]      = apa[apJ[k]];
172       apa[apJ[k++]] = 0.0;
173     }
174   }
175   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
176   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
177   PetscFunctionReturn(0);
178 }
179 
180 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
181 {
182   PetscErrorCode     ierr;
183   MPI_Comm           comm;
184   PetscMPIInt        size;
185   Mat_APMPI          *ptap;
186   PetscFreeSpaceList free_space=NULL,current_space=NULL;
187   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
188   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
189   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
190   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
191   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
192   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
193   PetscBT            lnkbt;
194   PetscReal          afill;
195   MatType            mtype;
196 
197   PetscFunctionBegin;
198   MatCheckProduct(C,4);
199   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
200   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
201   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
202 
203   /* create struct Mat_APMPI and attached it to C later */
204   ierr = PetscNew(&ptap);CHKERRQ(ierr);
205 
206   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
207   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
208 
209   /* get P_loc by taking all local rows of P */
210   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
211 
212   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
213   pi_loc = p_loc->i; pj_loc = p_loc->j;
214   if (size > 1) {
215     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
216     pi_oth = p_oth->i; pj_oth = p_oth->j;
217   } else {
218     p_oth = NULL;
219     pi_oth = NULL; pj_oth = NULL;
220   }
221 
222   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
223   /*-------------------------------------------------------------------*/
224   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
225   ptap->api = api;
226   api[0]    = 0;
227 
228   /* create and initialize a linked list */
229   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
230 
231   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
232   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
233   current_space = free_space;
234 
235   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
236   for (i=0; i<am; i++) {
237     /* diagonal portion of A */
238     nzi = adi[i+1] - adi[i];
239     for (j=0; j<nzi; j++) {
240       row  = *adj++;
241       pnz  = pi_loc[row+1] - pi_loc[row];
242       Jptr = pj_loc + pi_loc[row];
243       /* add non-zero cols of P into the sorted linked list lnk */
244       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
245     }
246     /* off-diagonal portion of A */
247     nzi = aoi[i+1] - aoi[i];
248     for (j=0; j<nzi; j++) {
249       row  = *aoj++;
250       pnz  = pi_oth[row+1] - pi_oth[row];
251       Jptr = pj_oth + pi_oth[row];
252       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
253     }
254     /* add possible missing diagonal entry */
255     if (C->force_diagonals) {
256       j = i + rstart; /* column index */
257       ierr = PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);CHKERRQ(ierr);
258     }
259 
260     apnz     = lnk[0];
261     api[i+1] = api[i] + apnz;
262 
263     /* if free space is not available, double the total space in the list */
264     if (current_space->local_remaining<apnz) {
265       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
266       nspacedouble++;
267     }
268 
269     /* Copy data into free space, then initialize lnk */
270     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
271     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
272 
273     current_space->array           += apnz;
274     current_space->local_used      += apnz;
275     current_space->local_remaining -= apnz;
276   }
277 
278   /* Allocate space for apj, initialize apj, and */
279   /* destroy list of free space and other temporary array(s) */
280   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
281   apj  = ptap->apj;
282   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
283   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
284 
285   /* malloc apa to store dense row A[i,:]*P */
286   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
287 
288   /* set and assemble symbolic parallel matrix C */
289   /*---------------------------------------------*/
290   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
291   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
292 
293   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
294   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
295   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
296   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
297 
298   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
299   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
300   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
301   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
302 
303   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
304   C->ops->productnumeric = MatProductNumeric_AB;
305 
306   /* attach the supporting struct to C for reuse */
307   C->product->data    = ptap;
308   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
309 
310   /* set MatInfo */
311   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
312   if (afill < 1.0) afill = 1.0;
313   C->info.mallocs           = nspacedouble;
314   C->info.fill_ratio_given  = fill;
315   C->info.fill_ratio_needed = afill;
316 
317 #if defined(PETSC_USE_INFO)
318   if (api[am]) {
319     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
320     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
321   } else {
322     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
323   }
324 #endif
325   PetscFunctionReturn(0);
326 }
327 
328 /* ------------------------------------------------------- */
329 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
330 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);
331 
332 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
333 {
334   Mat_Product *product = C->product;
335   Mat         A = product->A,B=product->B;
336 
337   PetscFunctionBegin;
338   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
339     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);
340 
341   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
342   C->ops->productsymbolic = MatProductSymbolic_AB;
343   PetscFunctionReturn(0);
344 }
345 /* -------------------------------------------------------------------- */
346 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
347 {
348   Mat_Product *product = C->product;
349   Mat         A = product->A,B=product->B;
350 
351   PetscFunctionBegin;
352   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
353     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);
354 
355   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
356   C->ops->productsymbolic          = MatProductSymbolic_AtB;
357   PetscFunctionReturn(0);
358 }
359 
360 /* --------------------------------------------------------------------- */
361 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
362 {
363   PetscErrorCode ierr;
364   Mat_Product    *product = C->product;
365 
366   PetscFunctionBegin;
367   switch (product->type) {
368   case MATPRODUCT_AB:
369     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);CHKERRQ(ierr);
370     break;
371   case MATPRODUCT_AtB:
372     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);CHKERRQ(ierr);
373     break;
374   default:
375     break;
376   }
377   PetscFunctionReturn(0);
378 }
379 /* ------------------------------------------------------- */
380 
381 typedef struct {
382   Mat          workB,workB1;
383   MPI_Request  *rwaits,*swaits;
384   PetscInt     nsends,nrecvs;
385   MPI_Datatype *stype,*rtype;
386   PetscInt     blda;
387 } MPIAIJ_MPIDense;
388 
389 PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
390 {
391   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
392   PetscErrorCode  ierr;
393   PetscInt        i;
394 
395   PetscFunctionBegin;
396   ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
397   ierr = MatDestroy(&contents->workB1);CHKERRQ(ierr);
398   for (i=0; i<contents->nsends; i++) {
399     ierr = MPI_Type_free(&contents->stype[i]);CHKERRMPI(ierr);
400   }
401   for (i=0; i<contents->nrecvs; i++) {
402     ierr = MPI_Type_free(&contents->rtype[i]);CHKERRMPI(ierr);
403   }
404   ierr = PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);CHKERRQ(ierr);
405   ierr = PetscFree(contents);CHKERRQ(ierr);
406   PetscFunctionReturn(0);
407 }
408 
409 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
410 {
411   PetscErrorCode  ierr;
412   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
413   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,m,M,n,N;
414   MPIAIJ_MPIDense *contents;
415   VecScatter      ctx=aij->Mvctx;
416   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
417   MPI_Comm        comm;
418   MPI_Datatype    type1,*stype,*rtype;
419   const PetscInt  *sindices,*sstarts,*rstarts;
420   PetscMPIInt     *disp;
421   PetscBool       cisdense;
422 
423   PetscFunctionBegin;
424   MatCheckProduct(C,4);
425   PetscCheckFalse(C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
426   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
427   ierr = PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);CHKERRQ(ierr);
428   if (!cisdense) {
429     ierr = MatSetType(C,((PetscObject)B)->type_name);CHKERRQ(ierr);
430   }
431   ierr = MatGetLocalSize(C,&m,&n);CHKERRQ(ierr);
432   ierr = MatGetSize(C,&M,&N);CHKERRQ(ierr);
433   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
434     ierr = MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);CHKERRQ(ierr);
435   }
436   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
437   ierr = MatSetUp(C);CHKERRQ(ierr);
438   ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
439   ierr = PetscNew(&contents);CHKERRQ(ierr);
440 
441   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
442   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
443 
444   /* Create column block of B and C for memory scalability when BN is too large */
445   /* Estimate Bbn, column size of Bb */
446   if (nz) {
447     Bbn1 = 2*Am*BN/nz;
448     if (!Bbn1) Bbn1 = 1;
449   } else Bbn1 = BN;
450 
451   bs = PetscAbs(B->cmap->bs);
452   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
453   if (Bbn1 > BN) Bbn1 = BN;
454   ierr = MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);CHKERRMPI(ierr);
455 
456   /* Enable runtime option for Bbn */
457   ierr = PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
458   ierr = PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);CHKERRQ(ierr);
459   ierr = PetscOptionsEnd();CHKERRQ(ierr);
460   Bbn  = PetscMin(Bbn,BN);
461 
462   if (Bbn > 0 && Bbn < BN) {
463     numBb = BN/Bbn;
464     Bbn1 = BN - numBb*Bbn;
465   } else numBb = 0;
466 
467   if (numBb) {
468     ierr = PetscInfo(C,"use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n",BN,Bbn,numBb);CHKERRQ(ierr);
469     if (Bbn1) { /* Create workB1 for the remaining columns */
470       ierr = PetscInfo(C,"use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n",BN,Bbn1);CHKERRQ(ierr);
471       /* Create work matrix used to store off processor rows of B needed for local product */
472       ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);CHKERRQ(ierr);
473     } else contents->workB1 = NULL;
474   }
475 
476   /* Create work matrix used to store off processor rows of B needed for local product */
477   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);CHKERRQ(ierr);
478 
479   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
480   ierr = PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);CHKERRQ(ierr);
481   contents->stype  = stype;
482   contents->nsends = nsends;
483 
484   contents->rtype  = rtype;
485   contents->nrecvs = nrecvs;
486   contents->blda   = blda;
487 
488   ierr = PetscMalloc1(Bm+1,&disp);CHKERRQ(ierr);
489   for (i=0; i<nsends; i++) {
490     nrows_to = sstarts[i+1]-sstarts[i];
491     for (j=0; j<nrows_to; j++) disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
492     ierr = MPI_Type_create_indexed_block(nrows_to,1,disp,MPIU_SCALAR,&type1);CHKERRMPI(ierr);
493     ierr = MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);CHKERRMPI(ierr);
494     ierr = MPI_Type_commit(&stype[i]);CHKERRMPI(ierr);
495     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
496   }
497 
498   for (i=0; i<nrecvs; i++) {
499     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
500     nrows_from = rstarts[i+1]-rstarts[i];
501     disp[0] = 0;
502     ierr = MPI_Type_create_indexed_block(1,nrows_from,disp,MPIU_SCALAR,&type1);CHKERRMPI(ierr);
503     ierr = MPI_Type_create_resized(type1,0,nz*sizeof(PetscScalar),&rtype[i]);CHKERRMPI(ierr);
504     ierr = MPI_Type_commit(&rtype[i]);CHKERRMPI(ierr);
505     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
506   }
507 
508   ierr = PetscFree(disp);CHKERRQ(ierr);
509   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
510   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
511   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
512   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
513   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
514   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
515 
516   C->product->data = contents;
517   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
518   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
519   PetscFunctionReturn(0);
520 }
521 
522 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
523 /*
524     Performs an efficient scatter on the rows of B needed by this process; this is
525     a modification of the VecScatterBegin_() routines.
526 
527     Input: Bbidx = 0: B = Bb
528                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
529 */
530 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
531 {
532   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
533   PetscErrorCode    ierr;
534   const PetscScalar *b;
535   PetscScalar       *rvalues;
536   VecScatter        ctx = aij->Mvctx;
537   const PetscInt    *sindices,*sstarts,*rstarts;
538   const PetscMPIInt *sprocs,*rprocs;
539   PetscInt          i,nsends,nrecvs;
540   MPI_Request       *swaits,*rwaits;
541   MPI_Comm          comm;
542   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
543   MPIAIJ_MPIDense   *contents;
544   Mat               workB;
545   MPI_Datatype      *stype,*rtype;
546   PetscInt          blda;
547 
548   PetscFunctionBegin;
549   MatCheckProduct(C,4);
550   PetscCheckFalse(!C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
551   contents = (MPIAIJ_MPIDense*)C->product->data;
552   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);CHKERRQ(ierr);
553   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);CHKERRQ(ierr);
554   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
555   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
556   if (Bbidx == 0) workB = *outworkB = contents->workB;
557   else workB = *outworkB = contents->workB1;
558   PetscCheckFalse(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);
559   swaits = contents->swaits;
560   rwaits = contents->rwaits;
561 
562   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
563   ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
564   PetscCheckFalse(blda != contents->blda,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %" PetscInt_FMT " != %" PetscInt_FMT,blda,contents->blda);
565   ierr = MatDenseGetArray(workB,&rvalues);CHKERRQ(ierr);
566 
567   /* Post recv, use MPI derived data type to save memory */
568   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
569   rtype = contents->rtype;
570   for (i=0; i<nrecvs; i++) {
571     ierr = MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);CHKERRMPI(ierr);
572   }
573 
574   stype = contents->stype;
575   for (i=0; i<nsends; i++) {
576     ierr = MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);CHKERRMPI(ierr);
577   }
578 
579   if (nrecvs) { ierr = MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr); }
580   if (nsends) { ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr); }
581 
582   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);CHKERRQ(ierr);
583   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);CHKERRQ(ierr);
584   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
585   ierr = MatDenseRestoreArray(workB,&rvalues);CHKERRQ(ierr);
586   PetscFunctionReturn(0);
587 }
588 
589 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
590 {
591   PetscErrorCode  ierr;
592   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
593   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
594   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
595   Mat             workB;
596   MPIAIJ_MPIDense *contents;
597 
598   PetscFunctionBegin;
599   MatCheckProduct(C,3);
600   PetscCheckFalse(!C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
601   contents = (MPIAIJ_MPIDense*)C->product->data;
602   /* diagonal block of A times all local rows of B */
603   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
604   ierr = MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);CHKERRQ(ierr);
605   if (contents->workB->cmap->n == B->cmap->N) {
606     /* get off processor parts of B needed to complete C=A*B */
607     ierr = MatMPIDenseScatter(A,B,0,C,&workB);CHKERRQ(ierr);
608 
609     /* off-diagonal block of A times nonlocal rows of B */
610     ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
611   } else {
612     Mat       Bb,Cb;
613     PetscInt  BN=B->cmap->N,n=contents->workB->cmap->n,i;
614     PetscBool ccpu;
615 
616     PetscCheckFalse(n <= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %" PetscInt_FMT " must be positive",n);
617     /* Prevent from unneeded copies back and forth from the GPU
618        when getting and restoring the submatrix
619        We need a proper GPU code for AIJ * dense in parallel */
620     ierr = MatBoundToCPU(C,&ccpu);CHKERRQ(ierr);
621     ierr = MatBindToCPU(C,PETSC_TRUE);CHKERRQ(ierr);
622     for (i=0; i<BN; i+=n) {
623       ierr = MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);CHKERRQ(ierr);
624       ierr = MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);CHKERRQ(ierr);
625 
626       /* get off processor parts of B needed to complete C=A*B */
627       ierr = MatMPIDenseScatter(A,Bb,(i+n)>BN,C,&workB);CHKERRQ(ierr);
628 
629       /* off-diagonal block of A times nonlocal rows of B */
630       cdense = (Mat_MPIDense*)Cb->data;
631       ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
632       ierr = MatDenseRestoreSubMatrix(B,&Bb);CHKERRQ(ierr);
633       ierr = MatDenseRestoreSubMatrix(C,&Cb);CHKERRQ(ierr);
634     }
635     ierr = MatBindToCPU(C,ccpu);CHKERRQ(ierr);
636   }
637   PetscFunctionReturn(0);
638 }
639 
640 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
641 {
642   PetscErrorCode    ierr;
643   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
644   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
645   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
646   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
647   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
648   Mat_SeqAIJ        *p_loc,*p_oth;
649   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
650   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
651   PetscInt          cm    = C->rmap->n,anz,pnz;
652   Mat_APMPI         *ptap;
653   PetscScalar       *apa_sparse;
654   const PetscScalar *dummy;
655   PetscInt          *api,*apj,*apJ,i,j,k,row;
656   PetscInt          cstart = C->cmap->rstart;
657   PetscInt          cdnz,conz,k0,k1,nextp;
658   MPI_Comm          comm;
659   PetscMPIInt       size;
660 
661   PetscFunctionBegin;
662   MatCheckProduct(C,3);
663   ptap = (Mat_APMPI*)C->product->data;
664   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
665   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
666   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
667   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
668 
669   /* flag CPU mask for C */
670 #if defined(PETSC_HAVE_DEVICE)
671   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
672   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
673   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
674 #endif
675   apa_sparse = ptap->apa;
676 
677   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
678   /*-----------------------------------------------------*/
679   /* update numerical values of P_oth and P_loc */
680   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
681   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
682 
683   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
684   /*----------------------------------------------------------*/
685   /* get data from symbolic products */
686   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
687   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
688   if (size >1) {
689     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
690     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
691   } else {
692     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
693   }
694 
695   /* trigger copy to CPU */
696   ierr = MatSeqAIJGetArrayRead(a->A,&dummy);CHKERRQ(ierr);
697   ierr = MatSeqAIJRestoreArrayRead(a->A,&dummy);CHKERRQ(ierr);
698   ierr = MatSeqAIJGetArrayRead(a->B,&dummy);CHKERRQ(ierr);
699   ierr = MatSeqAIJRestoreArrayRead(a->B,&dummy);CHKERRQ(ierr);
700   api = ptap->api;
701   apj = ptap->apj;
702   for (i=0; i<cm; i++) {
703     apJ = apj + api[i];
704 
705     /* diagonal portion of A */
706     anz = adi[i+1] - adi[i];
707     adj = ad->j + adi[i];
708     ada = ad->a + adi[i];
709     for (j=0; j<anz; j++) {
710       row = adj[j];
711       pnz = pi_loc[row+1] - pi_loc[row];
712       pj  = pj_loc + pi_loc[row];
713       pa  = pa_loc + pi_loc[row];
714       /* perform sparse axpy */
715       valtmp = ada[j];
716       nextp  = 0;
717       for (k=0; nextp<pnz; k++) {
718         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
719           apa_sparse[k] += valtmp*pa[nextp++];
720         }
721       }
722       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
723     }
724 
725     /* off-diagonal portion of A */
726     anz = aoi[i+1] - aoi[i];
727     aoj = ao->j + aoi[i];
728     aoa = ao->a + aoi[i];
729     for (j=0; j<anz; j++) {
730       row = aoj[j];
731       pnz = pi_oth[row+1] - pi_oth[row];
732       pj  = pj_oth + pi_oth[row];
733       pa  = pa_oth + pi_oth[row];
734       /* perform sparse axpy */
735       valtmp = aoa[j];
736       nextp  = 0;
737       for (k=0; nextp<pnz; k++) {
738         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
739           apa_sparse[k] += valtmp*pa[nextp++];
740         }
741       }
742       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
743     }
744 
745     /* set values in C */
746     cdnz = cd->i[i+1] - cd->i[i];
747     conz = co->i[i+1] - co->i[i];
748 
749     /* 1st off-diagonal part of C */
750     ca = coa + co->i[i];
751     k  = 0;
752     for (k0=0; k0<conz; k0++) {
753       if (apJ[k] >= cstart) break;
754       ca[k0]        = apa_sparse[k];
755       apa_sparse[k] = 0.0;
756       k++;
757     }
758 
759     /* diagonal part of C */
760     ca = cda + cd->i[i];
761     for (k1=0; k1<cdnz; k1++) {
762       ca[k1]        = apa_sparse[k];
763       apa_sparse[k] = 0.0;
764       k++;
765     }
766 
767     /* 2nd off-diagonal part of C */
768     ca = coa + co->i[i];
769     for (; k0<conz; k0++) {
770       ca[k0]        = apa_sparse[k];
771       apa_sparse[k] = 0.0;
772       k++;
773     }
774   }
775   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
776   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
777   PetscFunctionReturn(0);
778 }
779 
780 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
781 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
782 {
783   PetscErrorCode     ierr;
784   MPI_Comm           comm;
785   PetscMPIInt        size;
786   Mat_APMPI          *ptap;
787   PetscFreeSpaceList free_space = NULL,current_space=NULL;
788   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
789   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
790   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
791   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
792   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
793   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
794   PetscReal          afill;
795   MatType            mtype;
796 
797   PetscFunctionBegin;
798   MatCheckProduct(C,4);
799   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
800   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
801   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
802 
803   /* create struct Mat_APMPI and attached it to C later */
804   ierr = PetscNew(&ptap);CHKERRQ(ierr);
805 
806   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
807   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
808 
809   /* get P_loc by taking all local rows of P */
810   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
811 
812   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
813   pi_loc = p_loc->i; pj_loc = p_loc->j;
814   if (size > 1) {
815     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
816     pi_oth = p_oth->i; pj_oth = p_oth->j;
817   } else {
818     p_oth  = NULL;
819     pi_oth = NULL; pj_oth = NULL;
820   }
821 
822   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
823   /*-------------------------------------------------------------------*/
824   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
825   ptap->api = api;
826   api[0]    = 0;
827 
828   ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr);
829 
830   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
831   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
832   current_space = free_space;
833   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
834   for (i=0; i<am; i++) {
835     /* diagonal portion of A */
836     nzi = adi[i+1] - adi[i];
837     for (j=0; j<nzi; j++) {
838       row  = *adj++;
839       pnz  = pi_loc[row+1] - pi_loc[row];
840       Jptr = pj_loc + pi_loc[row];
841       /* Expand list if it is not long enough */
842       if (pnz+apnz_max > lsize) {
843         lsize = pnz+apnz_max;
844         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
845       }
846       /* add non-zero cols of P into the sorted linked list lnk */
847       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
848       apnz     = *lnk; /* The first element in the list is the number of items in the list */
849       api[i+1] = api[i] + apnz;
850       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
851     }
852     /* off-diagonal portion of A */
853     nzi = aoi[i+1] - aoi[i];
854     for (j=0; j<nzi; j++) {
855       row  = *aoj++;
856       pnz  = pi_oth[row+1] - pi_oth[row];
857       Jptr = pj_oth + pi_oth[row];
858       /* Expand list if it is not long enough */
859       if (pnz+apnz_max > lsize) {
860         lsize = pnz + apnz_max;
861         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
862       }
863       /* add non-zero cols of P into the sorted linked list lnk */
864       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
865       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
866       api[i+1] = api[i] + apnz;
867       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
868     }
869 
870     /* add missing diagonal entry */
871     if (C->force_diagonals) {
872       j = i + rstart; /* column index */
873       ierr = PetscLLCondensedAddSorted_Scalable(1,&j,lnk);CHKERRQ(ierr);
874     }
875 
876     apnz     = *lnk;
877     api[i+1] = api[i] + apnz;
878     if (apnz > apnz_max) apnz_max = apnz;
879 
880     /* if free space is not available, double the total space in the list */
881     if (current_space->local_remaining<apnz) {
882       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
883       nspacedouble++;
884     }
885 
886     /* Copy data into free space, then initialize lnk */
887     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
888     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
889 
890     current_space->array           += apnz;
891     current_space->local_used      += apnz;
892     current_space->local_remaining -= apnz;
893   }
894 
895   /* Allocate space for apj, initialize apj, and */
896   /* destroy list of free space and other temporary array(s) */
897   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
898   apj  = ptap->apj;
899   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
900   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
901 
902   /* create and assemble symbolic parallel matrix C */
903   /*----------------------------------------------------*/
904   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
905   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
906   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
907   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
908   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
909   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
910 
911   /* malloc apa for assembly C */
912   ierr = PetscCalloc1(apnz_max,&ptap->apa);CHKERRQ(ierr);
913 
914   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
915   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
916   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
917   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
918 
919   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
920   C->ops->productnumeric = MatProductNumeric_AB;
921 
922   /* attach the supporting struct to C for reuse */
923   C->product->data    = ptap;
924   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
925 
926   /* set MatInfo */
927   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
928   if (afill < 1.0) afill = 1.0;
929   C->info.mallocs           = nspacedouble;
930   C->info.fill_ratio_given  = fill;
931   C->info.fill_ratio_needed = afill;
932 
933 #if defined(PETSC_USE_INFO)
934   if (api[am]) {
935     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
936     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
937   } else {
938     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
939   }
940 #endif
941   PetscFunctionReturn(0);
942 }
943 
944 /* This function is needed for the seqMPI matrix-matrix multiplication.  */
945 /* Three input arrays are merged to one output array. The size of the    */
946 /* output array is also output. Duplicate entries only show up once.     */
947 static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
948                                PetscInt  size2, PetscInt *in2,
949                                PetscInt  size3, PetscInt *in3,
950                                PetscInt *size4, PetscInt *out)
951 {
952   int i = 0, j = 0, k = 0, l = 0;
953 
954   /* Traverse all three arrays */
955   while (i<size1 && j<size2 && k<size3) {
956     if (in1[i] < in2[j] && in1[i] < in3[k]) {
957       out[l++] = in1[i++];
958     }
959     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
960       out[l++] = in2[j++];
961     }
962     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
963       out[l++] = in3[k++];
964     }
965     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
966       out[l++] = in1[i];
967       i++, j++;
968     }
969     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
970       out[l++] = in1[i];
971       i++, k++;
972     }
973     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
974       out[l++] = in2[j];
975       k++, j++;
976     }
977     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
978       out[l++] = in1[i];
979       i++, j++, k++;
980     }
981   }
982 
983   /* Traverse two remaining arrays */
984   while (i<size1 && j<size2) {
985     if (in1[i] < in2[j]) {
986       out[l++] = in1[i++];
987     }
988     else if (in1[i] > in2[j]) {
989       out[l++] = in2[j++];
990     }
991     else {
992       out[l++] = in1[i];
993       i++, j++;
994     }
995   }
996 
997   while (i<size1 && k<size3) {
998     if (in1[i] < in3[k]) {
999       out[l++] = in1[i++];
1000     }
1001     else if (in1[i] > in3[k]) {
1002       out[l++] = in3[k++];
1003     }
1004     else {
1005       out[l++] = in1[i];
1006       i++, k++;
1007     }
1008   }
1009 
1010   while (k<size3 && j<size2)  {
1011     if (in3[k] < in2[j]) {
1012       out[l++] = in3[k++];
1013     }
1014     else if (in3[k] > in2[j]) {
1015       out[l++] = in2[j++];
1016     }
1017     else {
1018       out[l++] = in3[k];
1019       k++, j++;
1020     }
1021   }
1022 
1023   /* Traverse one remaining array */
1024   while (i<size1) out[l++] = in1[i++];
1025   while (j<size2) out[l++] = in2[j++];
1026   while (k<size3) out[l++] = in3[k++];
1027 
1028   *size4 = l;
1029 }
1030 
1031 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1032 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1033 /* matrix-matrix multiplications.  */
1034 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1035 {
1036   PetscErrorCode     ierr;
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   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1061   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1062   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1063   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
1064   ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);CHKERRQ(ierr);
1065 
1066   /* create struct Mat_APMPI and attached it to C later */
1067   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1068 
1069   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1070   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1071 
1072   /* get P_loc by taking all local rows of P */
1073   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
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   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1080   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
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   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1088   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1089 
1090   /* Symbolic calc of A_loc_diag * P_loc_diag */
1091   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1092   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1093   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1094   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1095   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1096 
1097   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1098   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1099   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1100   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1101 
1102   adpd->force_diagonals = C->force_diagonals;
1103   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
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   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1112 
1113   /* Symbolic calc of the A_diag * p_loc_off */
1114   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1115   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
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       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
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       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1138       nspacedouble++;
1139     }
1140 
1141     /* Copy data into free space, then initialize lnk */
1142     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
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   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1151   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1152   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1153   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
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   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1161   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1162 
1163   /* Copy from linked list to j-array */
1164   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1165   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
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     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);CHKERRQ(ierr);
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   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1197 
1198   /* create and assemble symbolic parallel matrix C */
1199   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1200   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1201   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1202   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1203   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1204   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1205 
1206   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1207   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1208   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1209   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
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     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1228     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1229   } else {
1230     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1231   }
1232 #endif
1233 
1234   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1235   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1236   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1237   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1238   ierr = PetscFree(adpoi);CHKERRQ(ierr);
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   PetscErrorCode ierr;
1247   Mat_APMPI      *ptap;
1248   Mat            Pt;
1249 
1250   PetscFunctionBegin;
1251   MatCheckProduct(C,3);
1252   ptap = (Mat_APMPI*)C->product->data;
1253   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1254   PetscCheckFalse(!ptap->Pt,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1255 
1256   Pt   = ptap->Pt;
1257   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1258   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1259   PetscFunctionReturn(0);
1260 }
1261 
1262 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1263 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1264 {
1265   PetscErrorCode      ierr;
1266   Mat_APMPI           *ptap;
1267   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1268   MPI_Comm            comm;
1269   PetscMPIInt         size,rank;
1270   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1271   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1272   PetscInt            *lnk,i,k,nsend,rstart;
1273   PetscBT             lnkbt;
1274   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1275   PETSC_UNUSED PetscMPIInt icompleted=0;
1276   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1277   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1278   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1279   MPI_Request         *swaits,*rwaits;
1280   MPI_Status          *sstatus,rstatus;
1281   PetscLayout         rowmap;
1282   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1283   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1284   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1285   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1286   PetscTable          ta;
1287   MatType             mtype;
1288   const char          *prefix;
1289 
1290   PetscFunctionBegin;
1291   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1292   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1293   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1294 
1295   /* create symbolic parallel matrix C */
1296   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1297   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1298 
1299   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1300 
1301   /* create struct Mat_APMPI and attached it to C later */
1302   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1303   ptap->reuse = MAT_INITIAL_MATRIX;
1304 
1305   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1306   /* --------------------------------- */
1307   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1308   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1309 
1310   /* (1) compute symbolic A_loc */
1311   /* ---------------------------*/
1312   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1313 
1314   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1315   /* ------------------------------------ */
1316   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1317   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1318   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1319   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1320   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1321 
1322   /* (3) send coj of C_oth to other processors  */
1323   /* ------------------------------------------ */
1324   /* determine row ownership */
1325   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1326   rowmap->n  = pn;
1327   rowmap->bs = 1;
1328   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1329   owners = rowmap->range;
1330 
1331   /* determine the number of messages to send, their lengths */
1332   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1333   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1334   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1335 
1336   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1337   coi   = c_oth->i; coj = c_oth->j;
1338   con   = ptap->C_oth->rmap->n;
1339   proc  = 0;
1340   for (i=0; i<con; i++) {
1341     while (prmap[i] >= owners[proc+1]) proc++;
1342     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1343     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1344   }
1345 
1346   len          = 0; /* max length of buf_si[], see (4) */
1347   owners_co[0] = 0;
1348   nsend        = 0;
1349   for (proc=0; proc<size; proc++) {
1350     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1351     if (len_s[proc]) {
1352       nsend++;
1353       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1354       len         += len_si[proc];
1355     }
1356   }
1357 
1358   /* determine the number and length of messages to receive for coi and coj  */
1359   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1360   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1361 
1362   /* post the Irecv and Isend of coj */
1363   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1364   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1365   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1366   for (proc=0, k=0; proc<size; proc++) {
1367     if (!len_s[proc]) continue;
1368     i    = owners_co[proc];
1369     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1370     k++;
1371   }
1372 
1373   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1374   /* ---------------------------------------- */
1375   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1376   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1377   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1378   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1379   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1380 
1381   /* receives coj are complete */
1382   for (i=0; i<nrecv; i++) {
1383     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1384   }
1385   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1386   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1387 
1388   /* add received column indices into ta to update Crmax */
1389   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1390 
1391   /* create and initialize a linked list */
1392   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1393   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1394 
1395   for (k=0; k<nrecv; k++) {/* k-th received message */
1396     Jptr = buf_rj[k];
1397     for (j=0; j<len_r[k]; j++) {
1398       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1399     }
1400   }
1401   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1402   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1403 
1404   /* (4) send and recv coi */
1405   /*-----------------------*/
1406   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1407   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1408   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1409   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1410   for (proc=0,k=0; proc<size; proc++) {
1411     if (!len_s[proc]) continue;
1412     /* form outgoing message for i-structure:
1413          buf_si[0]:                 nrows to be sent
1414                [1:nrows]:           row index (global)
1415                [nrows+1:2*nrows+1]: i-structure index
1416     */
1417     /*-------------------------------------------*/
1418     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1419     buf_si_i    = buf_si + nrows+1;
1420     buf_si[0]   = nrows;
1421     buf_si_i[0] = 0;
1422     nrows       = 0;
1423     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1424       nzi = coi[i+1] - coi[i];
1425       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1426       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1427       nrows++;
1428     }
1429     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1430     k++;
1431     buf_si += len_si[proc];
1432   }
1433   for (i=0; i<nrecv; i++) {
1434     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1435   }
1436   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1437   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1438 
1439   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1440   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1441   ierr = PetscFree(swaits);CHKERRQ(ierr);
1442   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1443 
1444   /* (5) compute the local portion of C      */
1445   /* ------------------------------------------ */
1446   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1447   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1448   current_space = free_space;
1449 
1450   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1451   for (k=0; k<nrecv; k++) {
1452     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1453     nrows       = *buf_ri_k[k];
1454     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1455     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1456   }
1457 
1458   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1459   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1460   for (i=0; i<pn; i++) { /* for each local row of C */
1461     /* add C_loc into C */
1462     nzi  = c_loc->i[i+1] - c_loc->i[i];
1463     Jptr = c_loc->j + c_loc->i[i];
1464     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1465 
1466     /* add received col data into lnk */
1467     for (k=0; k<nrecv; k++) { /* k-th received message */
1468       if (i == *nextrow[k]) { /* i-th row */
1469         nzi  = *(nextci[k]+1) - *nextci[k];
1470         Jptr = buf_rj[k] + *nextci[k];
1471         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1472         nextrow[k]++; nextci[k]++;
1473       }
1474     }
1475 
1476     /* add missing diagonal entry */
1477     if (C->force_diagonals) {
1478       k = i + owners[rank]; /* column index */
1479       ierr = PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);CHKERRQ(ierr);
1480     }
1481 
1482     nzi = lnk[0];
1483 
1484     /* copy data into free space, then initialize lnk */
1485     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1486     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1487   }
1488   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1489   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1490   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1491 
1492   /* local sizes and preallocation */
1493   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1494   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1495   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1496   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1497   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1498 
1499   /* add C_loc and C_oth to C */
1500   ierr = MatGetOwnershipRange(C,&rstart,NULL);CHKERRQ(ierr);
1501   for (i=0; i<pn; i++) {
1502     ncols = c_loc->i[i+1] - c_loc->i[i];
1503     cols  = c_loc->j + c_loc->i[i];
1504     row   = rstart + i;
1505     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1506 
1507     if (C->force_diagonals) {
1508       ierr = MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);CHKERRQ(ierr);
1509     }
1510   }
1511   for (i=0; i<con; i++) {
1512     ncols = c_oth->i[i+1] - c_oth->i[i];
1513     cols  = c_oth->j + c_oth->i[i];
1514     row   = prmap[i];
1515     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1516   }
1517   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1518   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1519   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1520 
1521   /* members in merge */
1522   ierr = PetscFree(id_r);CHKERRQ(ierr);
1523   ierr = PetscFree(len_r);CHKERRQ(ierr);
1524   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1525   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1526   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1527   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1528   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1529 
1530   /* attach the supporting struct to C for reuse */
1531   C->product->data    = ptap;
1532   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1533   PetscFunctionReturn(0);
1534 }
1535 
1536 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1537 {
1538   PetscErrorCode    ierr;
1539   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1540   Mat_SeqAIJ        *c_seq;
1541   Mat_APMPI         *ptap;
1542   Mat               A_loc,C_loc,C_oth;
1543   PetscInt          i,rstart,rend,cm,ncols,row;
1544   const PetscInt    *cols;
1545   const PetscScalar *vals;
1546 
1547   PetscFunctionBegin;
1548   MatCheckProduct(C,3);
1549   ptap = (Mat_APMPI*)C->product->data;
1550   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1551   PetscCheckFalse(!ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1552   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1553 
1554   if (ptap->reuse == MAT_REUSE_MATRIX) {
1555     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1556     /* 1) get R = Pd^T, Ro = Po^T */
1557     /*----------------------------*/
1558     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1559     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1560 
1561     /* 2) compute numeric A_loc */
1562     /*--------------------------*/
1563     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1564   }
1565 
1566   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1567   A_loc = ptap->A_loc;
1568   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1569   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1570   C_loc = ptap->C_loc;
1571   C_oth = ptap->C_oth;
1572 
1573   /* add C_loc and C_oth to C */
1574   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1575 
1576   /* C_loc -> C */
1577   cm    = C_loc->rmap->N;
1578   c_seq = (Mat_SeqAIJ*)C_loc->data;
1579   cols = c_seq->j;
1580   vals = c_seq->a;
1581   for (i=0; i<cm; i++) {
1582     ncols = c_seq->i[i+1] - c_seq->i[i];
1583     row = rstart + i;
1584     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1585     cols += ncols; vals += ncols;
1586   }
1587 
1588   /* Co -> C, off-processor part */
1589   cm    = C_oth->rmap->N;
1590   c_seq = (Mat_SeqAIJ*)C_oth->data;
1591   cols  = c_seq->j;
1592   vals  = c_seq->a;
1593   for (i=0; i<cm; i++) {
1594     ncols = c_seq->i[i+1] - c_seq->i[i];
1595     row = p->garray[i];
1596     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1597     cols += ncols; vals += ncols;
1598   }
1599   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1600   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1601   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1602 
1603   ptap->reuse = MAT_REUSE_MATRIX;
1604   PetscFunctionReturn(0);
1605 }
1606 
1607 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1608 {
1609   PetscErrorCode      ierr;
1610   Mat_Merge_SeqsToMPI *merge;
1611   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1612   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1613   Mat_APMPI           *ptap;
1614   PetscInt            *adj;
1615   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1616   MatScalar           *ada,*ca,valtmp;
1617   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1618   MPI_Comm            comm;
1619   PetscMPIInt         size,rank,taga,*len_s;
1620   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1621   PetscInt            **buf_ri,**buf_rj;
1622   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1623   MPI_Request         *s_waits,*r_waits;
1624   MPI_Status          *status;
1625   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1626   const PetscScalar   *dummy;
1627   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1628   Mat                 A_loc;
1629   Mat_SeqAIJ          *a_loc;
1630 
1631   PetscFunctionBegin;
1632   MatCheckProduct(C,3);
1633   ptap = (Mat_APMPI*)C->product->data;
1634   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1635   PetscCheckFalse(!ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1636   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1637   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1638   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1639 
1640   merge = ptap->merge;
1641 
1642   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1643   /*------------------------------------------*/
1644   /* get data from symbolic products */
1645   coi    = merge->coi; coj = merge->coj;
1646   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1647   bi     = merge->bi; bj = merge->bj;
1648   owners = merge->rowmap->range;
1649   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1650 
1651   /* get A_loc by taking all local rows of A */
1652   A_loc = ptap->A_loc;
1653   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1654   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1655   ai    = a_loc->i;
1656   aj    = a_loc->j;
1657 
1658   /* trigger copy to CPU */
1659   ierr = MatSeqAIJGetArrayRead(p->A,&dummy);CHKERRQ(ierr);
1660   ierr = MatSeqAIJRestoreArrayRead(p->A,&dummy);CHKERRQ(ierr);
1661   ierr = MatSeqAIJGetArrayRead(p->B,&dummy);CHKERRQ(ierr);
1662   ierr = MatSeqAIJRestoreArrayRead(p->B,&dummy);CHKERRQ(ierr);
1663   for (i=0; i<am; i++) {
1664     anz = ai[i+1] - ai[i];
1665     adj = aj + ai[i];
1666     ada = a_loc->a + ai[i];
1667 
1668     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1669     /*-------------------------------------------------------------*/
1670     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1671     pnz = po->i[i+1] - po->i[i];
1672     poJ = po->j + po->i[i];
1673     pA  = po->a + po->i[i];
1674     for (j=0; j<pnz; j++) {
1675       row = poJ[j];
1676       cj  = coj + coi[row];
1677       ca  = coa + coi[row];
1678       /* perform sparse axpy */
1679       nexta  = 0;
1680       valtmp = pA[j];
1681       for (k=0; nexta<anz; k++) {
1682         if (cj[k] == adj[nexta]) {
1683           ca[k] += valtmp*ada[nexta];
1684           nexta++;
1685         }
1686       }
1687       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1688     }
1689 
1690     /* put the value into Cd (diagonal part) */
1691     pnz = pd->i[i+1] - pd->i[i];
1692     pdJ = pd->j + pd->i[i];
1693     pA  = pd->a + pd->i[i];
1694     for (j=0; j<pnz; j++) {
1695       row = pdJ[j];
1696       cj  = bj + bi[row];
1697       ca  = ba + bi[row];
1698       /* perform sparse axpy */
1699       nexta  = 0;
1700       valtmp = pA[j];
1701       for (k=0; nexta<anz; k++) {
1702         if (cj[k] == adj[nexta]) {
1703           ca[k] += valtmp*ada[nexta];
1704           nexta++;
1705         }
1706       }
1707       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1708     }
1709   }
1710 
1711   /* 3) send and recv matrix values coa */
1712   /*------------------------------------*/
1713   buf_ri = merge->buf_ri;
1714   buf_rj = merge->buf_rj;
1715   len_s  = merge->len_s;
1716   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1717   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1718 
1719   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1720   for (proc=0,k=0; proc<size; proc++) {
1721     if (!len_s[proc]) continue;
1722     i    = merge->owners_co[proc];
1723     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRMPI(ierr);
1724     k++;
1725   }
1726   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRMPI(ierr);}
1727   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRMPI(ierr);}
1728 
1729   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1730   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1731   ierr = PetscFree(coa);CHKERRQ(ierr);
1732 
1733   /* 4) insert local Cseq and received values into Cmpi */
1734   /*----------------------------------------------------*/
1735   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1736   for (k=0; k<merge->nrecv; k++) {
1737     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1738     nrows       = *(buf_ri_k[k]);
1739     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1740     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1741   }
1742 
1743   for (i=0; i<cm; i++) {
1744     row  = owners[rank] + i; /* global row index of C_seq */
1745     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1746     ba_i = ba + bi[i];
1747     bnz  = bi[i+1] - bi[i];
1748     /* add received vals into ba */
1749     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1750       /* i-th row */
1751       if (i == *nextrow[k]) {
1752         cnz    = *(nextci[k]+1) - *nextci[k];
1753         cj     = buf_rj[k] + *(nextci[k]);
1754         ca     = abuf_r[k] + *(nextci[k]);
1755         nextcj = 0;
1756         for (j=0; nextcj<cnz; j++) {
1757           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1758             ba_i[j] += ca[nextcj++];
1759           }
1760         }
1761         nextrow[k]++; nextci[k]++;
1762         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1763       }
1764     }
1765     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1766   }
1767   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1768   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1769 
1770   ierr = PetscFree(ba);CHKERRQ(ierr);
1771   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1772   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1773   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1774   PetscFunctionReturn(0);
1775 }
1776 
1777 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1778 {
1779   PetscErrorCode      ierr;
1780   Mat                 A_loc;
1781   Mat_APMPI           *ptap;
1782   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1783   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1784   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1785   PetscInt            nnz;
1786   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1787   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1788   MPI_Comm            comm;
1789   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1790   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1791   PetscInt            len,proc,*dnz,*onz,*owners;
1792   PetscInt            nzi,*bi,*bj;
1793   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1794   MPI_Request         *swaits,*rwaits;
1795   MPI_Status          *sstatus,rstatus;
1796   Mat_Merge_SeqsToMPI *merge;
1797   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1798   PetscReal           afill  =1.0,afill_tmp;
1799   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1800   Mat_SeqAIJ          *a_loc;
1801   PetscTable          ta;
1802   MatType             mtype;
1803 
1804   PetscFunctionBegin;
1805   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1806   /* check if matrix local sizes are compatible */
1807   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);
1808 
1809   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1810   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1811 
1812   /* create struct Mat_APMPI and attached it to C later */
1813   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1814 
1815   /* get A_loc by taking all local rows of A */
1816   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1817 
1818   ptap->A_loc = A_loc;
1819   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1820   ai          = a_loc->i;
1821   aj          = a_loc->j;
1822 
1823   /* determine symbolic Co=(p->B)^T*A - send to others */
1824   /*----------------------------------------------------*/
1825   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1826   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1827   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1828                          >= (num of nonzero rows of C_seq) - pn */
1829   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1830   coi[0] = 0;
1831 
1832   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1833   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1834   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1835   current_space = free_space;
1836 
1837   /* create and initialize a linked list */
1838   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1839   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1840   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1841 
1842   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1843 
1844   for (i=0; i<pon; i++) {
1845     pnz = poti[i+1] - poti[i];
1846     ptJ = potj + poti[i];
1847     for (j=0; j<pnz; j++) {
1848       row  = ptJ[j]; /* row of A_loc == col of Pot */
1849       anz  = ai[row+1] - ai[row];
1850       Jptr = aj + ai[row];
1851       /* add non-zero cols of AP into the sorted linked list lnk */
1852       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1853     }
1854     nnz = lnk[0];
1855 
1856     /* If free space is not available, double the total space in the list */
1857     if (current_space->local_remaining<nnz) {
1858       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1859       nspacedouble++;
1860     }
1861 
1862     /* Copy data into free space, and zero out denserows */
1863     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1864 
1865     current_space->array           += nnz;
1866     current_space->local_used      += nnz;
1867     current_space->local_remaining -= nnz;
1868 
1869     coi[i+1] = coi[i] + nnz;
1870   }
1871 
1872   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1873   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1874   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1875 
1876   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1877   if (afill_tmp > afill) afill = afill_tmp;
1878 
1879   /* send j-array (coj) of Co to other processors */
1880   /*----------------------------------------------*/
1881   /* determine row ownership */
1882   ierr = PetscNew(&merge);CHKERRQ(ierr);
1883   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1884 
1885   merge->rowmap->n  = pn;
1886   merge->rowmap->bs = 1;
1887 
1888   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1889   owners = merge->rowmap->range;
1890 
1891   /* determine the number of messages to send, their lengths */
1892   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1893   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1894 
1895   len_s        = merge->len_s;
1896   merge->nsend = 0;
1897 
1898   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1899 
1900   proc = 0;
1901   for (i=0; i<pon; i++) {
1902     while (prmap[i] >= owners[proc+1]) proc++;
1903     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1904     len_s[proc] += coi[i+1] - coi[i];
1905   }
1906 
1907   len          = 0; /* max length of buf_si[] */
1908   owners_co[0] = 0;
1909   for (proc=0; proc<size; proc++) {
1910     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1911     if (len_si[proc]) {
1912       merge->nsend++;
1913       len_si[proc] = 2*(len_si[proc] + 1);
1914       len         += len_si[proc];
1915     }
1916   }
1917 
1918   /* determine the number and length of messages to receive for coi and coj  */
1919   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1920   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1921 
1922   /* post the Irecv and Isend of coj */
1923   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1924   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1925   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1926   for (proc=0, k=0; proc<size; proc++) {
1927     if (!len_s[proc]) continue;
1928     i    = owners_co[proc];
1929     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1930     k++;
1931   }
1932 
1933   /* receives and sends of coj are complete */
1934   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
1935   for (i=0; i<merge->nrecv; i++) {
1936     PETSC_UNUSED PetscMPIInt icompleted;
1937     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1938   }
1939   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1940   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1941 
1942   /* add received column indices into table to update Armax */
1943   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1944   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1945     Jptr = buf_rj[k];
1946     for (j=0; j<merge->len_r[k]; j++) {
1947       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1948     }
1949   }
1950   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1951 
1952   /* send and recv coi */
1953   /*-------------------*/
1954   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1955   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1956   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1957   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1958   for (proc=0,k=0; proc<size; proc++) {
1959     if (!len_s[proc]) continue;
1960     /* form outgoing message for i-structure:
1961          buf_si[0]:                 nrows to be sent
1962                [1:nrows]:           row index (global)
1963                [nrows+1:2*nrows+1]: i-structure index
1964     */
1965     /*-------------------------------------------*/
1966     nrows       = len_si[proc]/2 - 1;
1967     buf_si_i    = buf_si + nrows+1;
1968     buf_si[0]   = nrows;
1969     buf_si_i[0] = 0;
1970     nrows       = 0;
1971     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1972       nzi               = coi[i+1] - coi[i];
1973       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1974       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1975       nrows++;
1976     }
1977     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1978     k++;
1979     buf_si += len_si[proc];
1980   }
1981   i = merge->nrecv;
1982   while (i--) {
1983     PETSC_UNUSED PetscMPIInt icompleted;
1984     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1985   }
1986   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1987   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1988   ierr = PetscFree(len_si);CHKERRQ(ierr);
1989   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1990   ierr = PetscFree(swaits);CHKERRQ(ierr);
1991   ierr = PetscFree(sstatus);CHKERRQ(ierr);
1992   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1993 
1994   /* compute the local portion of C (mpi mat) */
1995   /*------------------------------------------*/
1996   /* allocate bi array and free space for accumulating nonzero column info */
1997   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
1998   bi[0] = 0;
1999 
2000   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2001   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2002   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
2003   current_space = free_space;
2004 
2005   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2006   for (k=0; k<merge->nrecv; k++) {
2007     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2008     nrows       = *buf_ri_k[k];
2009     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2010     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2011   }
2012 
2013   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2014   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2015   rmax = 0;
2016   for (i=0; i<pn; i++) {
2017     /* add pdt[i,:]*AP into lnk */
2018     pnz = pdti[i+1] - pdti[i];
2019     ptJ = pdtj + pdti[i];
2020     for (j=0; j<pnz; j++) {
2021       row  = ptJ[j];  /* row of AP == col of Pt */
2022       anz  = ai[row+1] - ai[row];
2023       Jptr = aj + ai[row];
2024       /* add non-zero cols of AP into the sorted linked list lnk */
2025       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2026     }
2027 
2028     /* add received col data into lnk */
2029     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2030       if (i == *nextrow[k]) { /* i-th row */
2031         nzi  = *(nextci[k]+1) - *nextci[k];
2032         Jptr = buf_rj[k] + *nextci[k];
2033         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2034         nextrow[k]++; nextci[k]++;
2035       }
2036     }
2037 
2038     /* add missing diagonal entry */
2039     if (C->force_diagonals) {
2040       k = i + owners[rank]; /* column index */
2041       ierr = PetscLLCondensedAddSorted_Scalable(1,&k,lnk);CHKERRQ(ierr);
2042     }
2043 
2044     nnz = lnk[0];
2045 
2046     /* if free space is not available, make more free space */
2047     if (current_space->local_remaining<nnz) {
2048       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2049       nspacedouble++;
2050     }
2051     /* copy data into free space, then initialize lnk */
2052     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2053     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2054 
2055     current_space->array           += nnz;
2056     current_space->local_used      += nnz;
2057     current_space->local_remaining -= nnz;
2058 
2059     bi[i+1] = bi[i] + nnz;
2060     if (nnz > rmax) rmax = nnz;
2061   }
2062   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2063 
2064   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2065   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2066   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2067   if (afill_tmp > afill) afill = afill_tmp;
2068   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2069   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2070   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
2071   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
2072 
2073   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2074   /*-------------------------------------------------------------------------------*/
2075   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2076   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2077   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2078   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2079   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2080   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2081   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2082   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
2083   for (i=0; i<pn; i++) {
2084     row  = i + rstart;
2085     nnz  = bi[i+1] - bi[i];
2086     Jptr = bj + bi[i];
2087     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2088   }
2089   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2090   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2091   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2092   merge->bi        = bi;
2093   merge->bj        = bj;
2094   merge->coi       = coi;
2095   merge->coj       = coj;
2096   merge->buf_ri    = buf_ri;
2097   merge->buf_rj    = buf_rj;
2098   merge->owners_co = owners_co;
2099 
2100   /* attach the supporting struct to C for reuse */
2101   C->product->data    = ptap;
2102   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2103   ptap->merge         = merge;
2104 
2105   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2106 
2107 #if defined(PETSC_USE_INFO)
2108   if (bi[pn] != 0) {
2109     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2110     ierr = PetscInfo(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2111   } else {
2112     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2113   }
2114 #endif
2115   PetscFunctionReturn(0);
2116 }
2117 
2118 /* ---------------------------------------------------------------- */
2119 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2120 {
2121   PetscErrorCode ierr;
2122   Mat_Product    *product = C->product;
2123   Mat            A=product->A,B=product->B;
2124   PetscReal      fill=product->fill;
2125   PetscBool      flg;
2126 
2127   PetscFunctionBegin;
2128   /* scalable */
2129   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2130   if (flg) {
2131     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2132     goto next;
2133   }
2134 
2135   /* nonscalable */
2136   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2137   if (flg) {
2138     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2139     goto next;
2140   }
2141 
2142   /* matmatmult */
2143   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2144   if (flg) {
2145     Mat       At;
2146     Mat_APMPI *ptap;
2147 
2148     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2149     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2150     ptap = (Mat_APMPI*)C->product->data;
2151     if (ptap) {
2152       ptap->Pt = At;
2153       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2154     }
2155     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2156     goto next;
2157   }
2158 
2159   /* backend general code */
2160   ierr = PetscStrcmp(product->alg,"backend",&flg);CHKERRQ(ierr);
2161   if (flg) {
2162     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
2163     PetscFunctionReturn(0);
2164   }
2165 
2166   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2167 
2168 next:
2169   C->ops->productnumeric = MatProductNumeric_AtB;
2170   PetscFunctionReturn(0);
2171 }
2172 
2173 /* ---------------------------------------------------------------- */
2174 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2175 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2176 {
2177   PetscErrorCode ierr;
2178   Mat_Product    *product = C->product;
2179   Mat            A=product->A,B=product->B;
2180 #if defined(PETSC_HAVE_HYPRE)
2181   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2182   PetscInt       nalg = 5;
2183 #else
2184   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2185   PetscInt       nalg = 4;
2186 #endif
2187   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2188   PetscBool      flg;
2189   MPI_Comm       comm;
2190 
2191   PetscFunctionBegin;
2192   /* Check matrix local sizes */
2193   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2194   PetscCheckFalse(A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend,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);
2195 
2196   /* Set "nonscalable" as default algorithm */
2197   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2198   if (flg) {
2199     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2200 
2201     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2202     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2203       MatInfo     Ainfo,Binfo;
2204       PetscInt    nz_local;
2205       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2206 
2207       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2208       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2209       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2210 
2211       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2212       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2213 
2214       if (alg_scalable) {
2215         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2216         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2217         ierr = PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));CHKERRQ(ierr);
2218       }
2219     }
2220   }
2221 
2222   /* Get runtime option */
2223   if (product->api_user) {
2224     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2225     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2226     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2227   } else {
2228     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2229     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2230     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2231   }
2232   if (flg) {
2233     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2234   }
2235 
2236   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2237   PetscFunctionReturn(0);
2238 }
2239 
2240 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2241 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2242 {
2243   PetscErrorCode ierr;
2244   Mat_Product    *product = C->product;
2245   Mat            A=product->A,B=product->B;
2246   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2247   PetscInt       nalg = 4;
2248   PetscInt       alg = 1; /* set default algorithm  */
2249   PetscBool      flg;
2250   MPI_Comm       comm;
2251 
2252   PetscFunctionBegin;
2253   /* Check matrix local sizes */
2254   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2255   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);
2256 
2257   /* Set default algorithm */
2258   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2259   if (flg) {
2260     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2261   }
2262 
2263   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2264   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2265     MatInfo     Ainfo,Binfo;
2266     PetscInt    nz_local;
2267     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2268 
2269     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2270     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2271     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2272 
2273     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2274     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2275 
2276     if (alg_scalable) {
2277       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2278       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2279       ierr = PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));CHKERRQ(ierr);
2280     }
2281   }
2282 
2283   /* Get runtime option */
2284   if (product->api_user) {
2285     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2286     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2287     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2288   } else {
2289     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2290     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2291     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2292   }
2293   if (flg) {
2294     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2295   }
2296 
2297   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2298   PetscFunctionReturn(0);
2299 }
2300 
2301 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2302 {
2303   PetscErrorCode ierr;
2304   Mat_Product    *product = C->product;
2305   Mat            A=product->A,P=product->B;
2306   MPI_Comm       comm;
2307   PetscBool      flg;
2308   PetscInt       alg=1; /* set default algorithm */
2309 #if !defined(PETSC_HAVE_HYPRE)
2310   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2311   PetscInt       nalg=5;
2312 #else
2313   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2314   PetscInt       nalg=6;
2315 #endif
2316   PetscInt       pN=P->cmap->N;
2317 
2318   PetscFunctionBegin;
2319   /* Check matrix local sizes */
2320   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2321   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);
2322   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);
2323 
2324   /* Set "nonscalable" as default algorithm */
2325   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2326   if (flg) {
2327     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2328 
2329     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2330     if (pN > 100000) {
2331       MatInfo     Ainfo,Pinfo;
2332       PetscInt    nz_local;
2333       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2334 
2335       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2336       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2337       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2338 
2339       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2340       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2341 
2342       if (alg_scalable) {
2343         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2344         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2345       }
2346     }
2347   }
2348 
2349   /* Get runtime option */
2350   if (product->api_user) {
2351     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2352     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2353     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2354   } else {
2355     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2356     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2357     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2358   }
2359   if (flg) {
2360     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2361   }
2362 
2363   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2364   PetscFunctionReturn(0);
2365 }
2366 
2367 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2368 {
2369   Mat_Product *product = C->product;
2370   Mat         A = product->A,R=product->B;
2371 
2372   PetscFunctionBegin;
2373   /* Check matrix local sizes */
2374   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);
2375 
2376   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2377   PetscFunctionReturn(0);
2378 }
2379 
2380 /*
2381  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2382 */
2383 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2384 {
2385   PetscErrorCode ierr;
2386   Mat_Product    *product = C->product;
2387   PetscBool      flg = PETSC_FALSE;
2388   PetscInt       alg = 1; /* default algorithm */
2389   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2390   PetscInt       nalg = 3;
2391 
2392   PetscFunctionBegin;
2393   /* Set default algorithm */
2394   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2395   if (flg) {
2396     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2397   }
2398 
2399   /* Get runtime option */
2400   if (product->api_user) {
2401     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2402     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2403     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2404   } else {
2405     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2406     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2407     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2408   }
2409   if (flg) {
2410     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2411   }
2412 
2413   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2414   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2415   PetscFunctionReturn(0);
2416 }
2417 
2418 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2419 {
2420   PetscErrorCode ierr;
2421   Mat_Product    *product = C->product;
2422 
2423   PetscFunctionBegin;
2424   switch (product->type) {
2425   case MATPRODUCT_AB:
2426     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2427     break;
2428   case MATPRODUCT_AtB:
2429     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2430     break;
2431   case MATPRODUCT_PtAP:
2432     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2433     break;
2434   case MATPRODUCT_RARt:
2435     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2436     break;
2437   case MATPRODUCT_ABC:
2438     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2439     break;
2440   default:
2441     break;
2442   }
2443   PetscFunctionReturn(0);
2444 }
2445