xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision af4fa82cc29c77689f3cd2af837601dbdc3602c2)
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   if (!ptap) SETERRQ(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   if (!ptap->P_oth && size>1) SETERRQ(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   if (C->product->data) SETERRQ(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 = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
320     ierr = PetscInfo1(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     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",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     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",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,clda,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   if (C->product->data) SETERRQ(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 = MatDenseGetLDA(C,&clda);CHKERRQ(ierr);
440   ierr = PetscNew(&contents);CHKERRQ(ierr);
441 
442   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
443   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
444 
445   /* Create column block of B and C for memory scalability when BN is too large */
446   /* Estimate Bbn, column size of Bb */
447   if (nz) {
448     Bbn1 = 2*Am*BN/nz;
449     if (!Bbn1) Bbn1 = 1;
450   } else Bbn1 = BN;
451 
452   bs = PetscAbs(B->cmap->bs);
453   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
454   if (Bbn1 > BN) Bbn1 = BN;
455   ierr = MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);CHKERRMPI(ierr);
456 
457   /* Enable runtime option for Bbn */
458   ierr = PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
459   ierr = PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);CHKERRQ(ierr);
460   ierr = PetscOptionsEnd();CHKERRQ(ierr);
461   Bbn  = PetscMin(Bbn,BN);
462 
463   if (Bbn > 0 && Bbn < BN) {
464     numBb = BN/Bbn;
465     Bbn1 = BN - numBb*Bbn;
466   } else numBb = 0;
467 
468   if (numBb) {
469     ierr = PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);CHKERRQ(ierr);
470     if (Bbn1) { /* Create workB1 for the remaining columns */
471       ierr = PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);CHKERRQ(ierr);
472       /* Create work matrix used to store off processor rows of B needed for local product */
473       ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);CHKERRQ(ierr);
474     } else contents->workB1 = NULL;
475   }
476 
477   /* Create work matrix used to store off processor rows of B needed for local product */
478   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);CHKERRQ(ierr);
479 
480   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
481   ierr = PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);CHKERRQ(ierr);
482   contents->stype  = stype;
483   contents->nsends = nsends;
484 
485   contents->rtype  = rtype;
486   contents->nrecvs = nrecvs;
487   contents->blda   = blda;
488 
489   ierr = PetscMalloc1(Bm+1,&disp);CHKERRQ(ierr);
490   for (i=0; i<nsends; i++) {
491     nrows_to = sstarts[i+1]-sstarts[i];
492     for (j=0; j<nrows_to; j++){
493       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
494     }
495     ierr = MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);CHKERRMPI(ierr);
496 
497     ierr = MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);CHKERRMPI(ierr);
498     ierr = MPI_Type_commit(&stype[i]);CHKERRMPI(ierr);
499     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
500   }
501 
502   for (i=0; i<nrecvs; i++) {
503     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
504     nrows_from = rstarts[i+1]-rstarts[i];
505     disp[0] = 0;
506     ierr = MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);CHKERRMPI(ierr);
507     ierr = MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);CHKERRMPI(ierr);
508     ierr = MPI_Type_commit(&rtype[i]);CHKERRMPI(ierr);
509     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
510   }
511 
512   ierr = PetscFree(disp);CHKERRQ(ierr);
513   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
514   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
515   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
516   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
517   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
518   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
519 
520   C->product->data = contents;
521   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
522   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
523   PetscFunctionReturn(0);
524 }
525 
526 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
527 /*
528     Performs an efficient scatter on the rows of B needed by this process; this is
529     a modification of the VecScatterBegin_() routines.
530 
531     Input: Bbidx = 0: B = Bb
532                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
533 */
534 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
535 {
536   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
537   PetscErrorCode    ierr;
538   const PetscScalar *b;
539   PetscScalar       *rvalues;
540   VecScatter        ctx = aij->Mvctx;
541   const PetscInt    *sindices,*sstarts,*rstarts;
542   const PetscMPIInt *sprocs,*rprocs;
543   PetscInt          i,nsends,nrecvs;
544   MPI_Request       *swaits,*rwaits;
545   MPI_Comm          comm;
546   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
547   MPIAIJ_MPIDense   *contents;
548   Mat               workB;
549   MPI_Datatype      *stype,*rtype;
550   PetscInt          blda;
551 
552   PetscFunctionBegin;
553   MatCheckProduct(C,4);
554   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
555   contents = (MPIAIJ_MPIDense*)C->product->data;
556   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);CHKERRQ(ierr);
557   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);CHKERRQ(ierr);
558   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
559   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
560   if (Bbidx == 0) {
561     workB = *outworkB = contents->workB;
562   } else {
563     workB = *outworkB = contents->workB1;
564   }
565   if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
566   swaits = contents->swaits;
567   rwaits = contents->rwaits;
568 
569   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
570   ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
571   if (blda != contents->blda) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %D != %D",blda,contents->blda);
572   ierr = MatDenseGetArray(workB,&rvalues);CHKERRQ(ierr);
573 
574   /* Post recv, use MPI derived data type to save memory */
575   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
576   rtype = contents->rtype;
577   for (i=0; i<nrecvs; i++) {
578     ierr = MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);CHKERRMPI(ierr);
579   }
580 
581   stype = contents->stype;
582   for (i=0; i<nsends; i++) {
583     ierr = MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);CHKERRMPI(ierr);
584   }
585 
586   if (nrecvs) {ierr = MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr);}
587   if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr);}
588 
589   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);CHKERRQ(ierr);
590   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);CHKERRQ(ierr);
591   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
592   ierr = MatDenseRestoreArray(workB,&rvalues);CHKERRQ(ierr);
593   PetscFunctionReturn(0);
594 }
595 
596 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
597 {
598   PetscErrorCode  ierr;
599   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
600   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
601   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
602   Mat             workB;
603   MPIAIJ_MPIDense *contents;
604 
605   PetscFunctionBegin;
606   MatCheckProduct(C,3);
607   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
608   contents = (MPIAIJ_MPIDense*)C->product->data;
609   /* diagonal block of A times all local rows of B */
610   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
611   ierr = MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);CHKERRQ(ierr);
612   if (contents->workB->cmap->n == B->cmap->N) {
613     /* get off processor parts of B needed to complete C=A*B */
614     ierr = MatMPIDenseScatter(A,B,0,C,&workB);CHKERRQ(ierr);
615 
616     /* off-diagonal block of A times nonlocal rows of B */
617     ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
618   } else {
619     Mat      Bb,Cb;
620     PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
621     if (n <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %D must be positive",n);
622 
623     for (i=0; i<BN; i+=n) {
624       ierr = MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);CHKERRQ(ierr);
625       ierr = MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);CHKERRQ(ierr);
626 
627       /* get off processor parts of B needed to complete C=A*B */
628       ierr = MatMPIDenseScatter(A,Bb,i+n>BN,C,&workB);CHKERRQ(ierr);
629 
630       /* off-diagonal block of A times nonlocal rows of B */
631       cdense = (Mat_MPIDense*)Cb->data;
632       ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
633 
634       ierr = MatDenseRestoreSubMatrix(B,&Bb);CHKERRQ(ierr);
635       ierr = MatDenseRestoreSubMatrix(C,&Cb);CHKERRQ(ierr);
636     }
637   }
638   PetscFunctionReturn(0);
639 }
640 
641 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
642 {
643   PetscErrorCode    ierr;
644   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
645   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
646   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
647   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
648   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
649   Mat_SeqAIJ        *p_loc,*p_oth;
650   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
651   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
652   PetscInt          cm    = C->rmap->n,anz,pnz;
653   Mat_APMPI         *ptap;
654   PetscScalar       *apa_sparse;
655   const PetscScalar *dummy;
656   PetscInt          *api,*apj,*apJ,i,j,k,row;
657   PetscInt          cstart = C->cmap->rstart;
658   PetscInt          cdnz,conz,k0,k1,nextp;
659   MPI_Comm          comm;
660   PetscMPIInt       size;
661 
662   PetscFunctionBegin;
663   MatCheckProduct(C,3);
664   ptap = (Mat_APMPI*)C->product->data;
665   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
666   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
667   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
668   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
669 
670   /* flag CPU mask for C */
671 #if defined(PETSC_HAVE_DEVICE)
672   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
673   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
674   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
675 #endif
676   apa_sparse = ptap->apa;
677 
678   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
679   /*-----------------------------------------------------*/
680   /* update numerical values of P_oth and P_loc */
681   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
682   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
683 
684   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
685   /*----------------------------------------------------------*/
686   /* get data from symbolic products */
687   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
688   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
689   if (size >1) {
690     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
691     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
692   } else {
693     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
694   }
695 
696   /* trigger copy to CPU */
697   ierr = MatSeqAIJGetArrayRead(a->A,&dummy);CHKERRQ(ierr);
698   ierr = MatSeqAIJRestoreArrayRead(a->A,&dummy);CHKERRQ(ierr);
699   ierr = MatSeqAIJGetArrayRead(a->B,&dummy);CHKERRQ(ierr);
700   ierr = MatSeqAIJRestoreArrayRead(a->B,&dummy);CHKERRQ(ierr);
701   api = ptap->api;
702   apj = ptap->apj;
703   for (i=0; i<cm; i++) {
704     apJ = apj + api[i];
705 
706     /* diagonal portion of A */
707     anz = adi[i+1] - adi[i];
708     adj = ad->j + adi[i];
709     ada = ad->a + adi[i];
710     for (j=0; j<anz; j++) {
711       row = adj[j];
712       pnz = pi_loc[row+1] - pi_loc[row];
713       pj  = pj_loc + pi_loc[row];
714       pa  = pa_loc + pi_loc[row];
715       /* perform sparse axpy */
716       valtmp = ada[j];
717       nextp  = 0;
718       for (k=0; nextp<pnz; k++) {
719         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
720           apa_sparse[k] += valtmp*pa[nextp++];
721         }
722       }
723       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
724     }
725 
726     /* off-diagonal portion of A */
727     anz = aoi[i+1] - aoi[i];
728     aoj = ao->j + aoi[i];
729     aoa = ao->a + aoi[i];
730     for (j=0; j<anz; j++) {
731       row = aoj[j];
732       pnz = pi_oth[row+1] - pi_oth[row];
733       pj  = pj_oth + pi_oth[row];
734       pa  = pa_oth + pi_oth[row];
735       /* perform sparse axpy */
736       valtmp = aoa[j];
737       nextp  = 0;
738       for (k=0; nextp<pnz; k++) {
739         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
740           apa_sparse[k] += valtmp*pa[nextp++];
741         }
742       }
743       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
744     }
745 
746     /* set values in C */
747     cdnz = cd->i[i+1] - cd->i[i];
748     conz = co->i[i+1] - co->i[i];
749 
750     /* 1st off-diagonal part of C */
751     ca = coa + co->i[i];
752     k  = 0;
753     for (k0=0; k0<conz; k0++) {
754       if (apJ[k] >= cstart) break;
755       ca[k0]        = apa_sparse[k];
756       apa_sparse[k] = 0.0;
757       k++;
758     }
759 
760     /* diagonal part of C */
761     ca = cda + cd->i[i];
762     for (k1=0; k1<cdnz; k1++) {
763       ca[k1]        = apa_sparse[k];
764       apa_sparse[k] = 0.0;
765       k++;
766     }
767 
768     /* 2nd off-diagonal part of C */
769     ca = coa + co->i[i];
770     for (; k0<conz; k0++) {
771       ca[k0]        = apa_sparse[k];
772       apa_sparse[k] = 0.0;
773       k++;
774     }
775   }
776   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
777   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
778   PetscFunctionReturn(0);
779 }
780 
781 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
782 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
783 {
784   PetscErrorCode     ierr;
785   MPI_Comm           comm;
786   PetscMPIInt        size;
787   Mat_APMPI          *ptap;
788   PetscFreeSpaceList free_space = NULL,current_space=NULL;
789   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
790   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
791   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
792   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
793   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
794   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
795   PetscReal          afill;
796   MatType            mtype;
797 
798   PetscFunctionBegin;
799   MatCheckProduct(C,4);
800   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
801   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
802   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
803 
804   /* create struct Mat_APMPI and attached it to C later */
805   ierr = PetscNew(&ptap);CHKERRQ(ierr);
806 
807   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
808   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
809 
810   /* get P_loc by taking all local rows of P */
811   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
812 
813   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
814   pi_loc = p_loc->i; pj_loc = p_loc->j;
815   if (size > 1) {
816     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
817     pi_oth = p_oth->i; pj_oth = p_oth->j;
818   } else {
819     p_oth  = NULL;
820     pi_oth = NULL; pj_oth = NULL;
821   }
822 
823   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
824   /*-------------------------------------------------------------------*/
825   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
826   ptap->api = api;
827   api[0]    = 0;
828 
829   ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr);
830 
831   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
832   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
833   current_space = free_space;
834   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
835   for (i=0; i<am; i++) {
836     /* diagonal portion of A */
837     nzi = adi[i+1] - adi[i];
838     for (j=0; j<nzi; j++) {
839       row  = *adj++;
840       pnz  = pi_loc[row+1] - pi_loc[row];
841       Jptr = pj_loc + pi_loc[row];
842       /* Expand list if it is not long enough */
843       if (pnz+apnz_max > lsize) {
844         lsize = pnz+apnz_max;
845         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
846       }
847       /* add non-zero cols of P into the sorted linked list lnk */
848       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
849       apnz     = *lnk; /* The first element in the list is the number of items in the list */
850       api[i+1] = api[i] + apnz;
851       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
852     }
853     /* off-diagonal portion of A */
854     nzi = aoi[i+1] - aoi[i];
855     for (j=0; j<nzi; j++) {
856       row  = *aoj++;
857       pnz  = pi_oth[row+1] - pi_oth[row];
858       Jptr = pj_oth + pi_oth[row];
859       /* Expand list if it is not long enough */
860       if (pnz+apnz_max > lsize) {
861         lsize = pnz + apnz_max;
862         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
863       }
864       /* add non-zero cols of P into the sorted linked list lnk */
865       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
866       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
867       api[i+1] = api[i] + apnz;
868       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
869     }
870 
871     /* add missing diagonal entry */
872     if (C->force_diagonals) {
873       j = i + rstart; /* column index */
874       ierr = PetscLLCondensedAddSorted_Scalable(1,&j,lnk);CHKERRQ(ierr);
875     }
876 
877     apnz     = *lnk;
878     api[i+1] = api[i] + apnz;
879     if (apnz > apnz_max) apnz_max = apnz;
880 
881     /* if free space is not available, double the total space in the list */
882     if (current_space->local_remaining<apnz) {
883       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
884       nspacedouble++;
885     }
886 
887     /* Copy data into free space, then initialize lnk */
888     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
889     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
890 
891     current_space->array           += apnz;
892     current_space->local_used      += apnz;
893     current_space->local_remaining -= apnz;
894   }
895 
896   /* Allocate space for apj, initialize apj, and */
897   /* destroy list of free space and other temporary array(s) */
898   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
899   apj  = ptap->apj;
900   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
901   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
902 
903   /* create and assemble symbolic parallel matrix C */
904   /*----------------------------------------------------*/
905   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
906   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
907   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
908   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
909   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
910   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
911 
912   /* malloc apa for assembly C */
913   ierr = PetscCalloc1(apnz_max,&ptap->apa);CHKERRQ(ierr);
914 
915   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
916   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
917   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
918   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
919 
920   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
921   C->ops->productnumeric = MatProductNumeric_AB;
922 
923   /* attach the supporting struct to C for reuse */
924   C->product->data    = ptap;
925   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
926 
927   /* set MatInfo */
928   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
929   if (afill < 1.0) afill = 1.0;
930   C->info.mallocs           = nspacedouble;
931   C->info.fill_ratio_given  = fill;
932   C->info.fill_ratio_needed = afill;
933 
934 #if defined(PETSC_USE_INFO)
935   if (api[am]) {
936     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
937     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
938   } else {
939     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
940   }
941 #endif
942   PetscFunctionReturn(0);
943 }
944 
945 /* This function is needed for the seqMPI matrix-matrix multiplication.  */
946 /* Three input arrays are merged to one output array. The size of the    */
947 /* output array is also output. Duplicate entries only show up once.     */
948 static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
949                                PetscInt  size2, PetscInt *in2,
950                                PetscInt  size3, PetscInt *in3,
951                                PetscInt *size4, PetscInt *out)
952 {
953   int i = 0, j = 0, k = 0, l = 0;
954 
955   /* Traverse all three arrays */
956   while (i<size1 && j<size2 && k<size3) {
957     if (in1[i] < in2[j] && in1[i] < in3[k]) {
958       out[l++] = in1[i++];
959     }
960     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
961       out[l++] = in2[j++];
962     }
963     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
964       out[l++] = in3[k++];
965     }
966     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
967       out[l++] = in1[i];
968       i++, j++;
969     }
970     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
971       out[l++] = in1[i];
972       i++, k++;
973     }
974     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
975       out[l++] = in2[j];
976       k++, j++;
977     }
978     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
979       out[l++] = in1[i];
980       i++, j++, k++;
981     }
982   }
983 
984   /* Traverse two remaining arrays */
985   while (i<size1 && j<size2) {
986     if (in1[i] < in2[j]) {
987       out[l++] = in1[i++];
988     }
989     else if (in1[i] > in2[j]) {
990       out[l++] = in2[j++];
991     }
992     else {
993       out[l++] = in1[i];
994       i++, j++;
995     }
996   }
997 
998   while (i<size1 && k<size3) {
999     if (in1[i] < in3[k]) {
1000       out[l++] = in1[i++];
1001     }
1002     else if (in1[i] > in3[k]) {
1003       out[l++] = in3[k++];
1004     }
1005     else {
1006       out[l++] = in1[i];
1007       i++, k++;
1008     }
1009   }
1010 
1011   while (k<size3 && j<size2)  {
1012     if (in3[k] < in2[j]) {
1013       out[l++] = in3[k++];
1014     }
1015     else if (in3[k] > in2[j]) {
1016       out[l++] = in2[j++];
1017     }
1018     else {
1019       out[l++] = in3[k];
1020       k++, j++;
1021     }
1022   }
1023 
1024   /* Traverse one remaining array */
1025   while (i<size1) out[l++] = in1[i++];
1026   while (j<size2) out[l++] = in2[j++];
1027   while (k<size3) out[l++] = in3[k++];
1028 
1029   *size4 = l;
1030 }
1031 
1032 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1033 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1034 /* matrix-matrix multiplications.  */
1035 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1036 {
1037   PetscErrorCode     ierr;
1038   MPI_Comm           comm;
1039   PetscMPIInt        size;
1040   Mat_APMPI          *ptap;
1041   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1042   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
1043   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1044   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
1045   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1046   PetscInt           adponz, adpdnz;
1047   PetscInt           *pi_loc,*dnz,*onz;
1048   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1049   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1050                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1051   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1052   PetscBT            lnkbt;
1053   PetscReal          afill;
1054   PetscMPIInt        rank;
1055   Mat                adpd, aopoth;
1056   MatType            mtype;
1057   const char         *prefix;
1058 
1059   PetscFunctionBegin;
1060   MatCheckProduct(C,4);
1061   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1062   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1063   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1064   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
1065   ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);CHKERRQ(ierr);
1066 
1067   /* create struct Mat_APMPI and attached it to C later */
1068   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1069 
1070   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1071   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1072 
1073   /* get P_loc by taking all local rows of P */
1074   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1075 
1076 
1077   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1078   pi_loc = p_loc->i;
1079 
1080   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1081   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1082   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
1083 
1084   adpoi[0]    = 0;
1085   ptap->api = api;
1086   api[0] = 0;
1087 
1088   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1089   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1090   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1091 
1092   /* Symbolic calc of A_loc_diag * P_loc_diag */
1093   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1094   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1095   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1096   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1097   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1098 
1099   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1100   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1101   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1102   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1103 
1104   adpd->force_diagonals = C->force_diagonals;
1105   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
1106 
1107   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1108   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1109   p_off = (Mat_SeqAIJ*)((p->B)->data);
1110   poff_i = p_off->i; poff_j = p_off->j;
1111 
1112   /* j_temp stores indices of a result row before they are added to the linked list */
1113   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1114 
1115 
1116   /* Symbolic calc of the A_diag * p_loc_off */
1117   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1118   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
1119   current_space = free_space_diag;
1120 
1121   for (i=0; i<am; i++) {
1122     /* A_diag * P_loc_off */
1123     nzi = adi[i+1] - adi[i];
1124     for (j=0; j<nzi; j++) {
1125       row  = *adj++;
1126       pnz  = poff_i[row+1] - poff_i[row];
1127       Jptr = poff_j + poff_i[row];
1128       for (i1 = 0; i1 < pnz; i1++) {
1129         j_temp[i1] = p->garray[Jptr[i1]];
1130       }
1131       /* add non-zero cols of P into the sorted linked list lnk */
1132       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
1133     }
1134 
1135     adponz     = lnk[0];
1136     adpoi[i+1] = adpoi[i] + adponz;
1137 
1138     /* if free space is not available, double the total space in the list */
1139     if (current_space->local_remaining<adponz) {
1140       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1141       nspacedouble++;
1142     }
1143 
1144     /* Copy data into free space, then initialize lnk */
1145     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1146 
1147     current_space->array           += adponz;
1148     current_space->local_used      += adponz;
1149     current_space->local_remaining -= adponz;
1150   }
1151 
1152   /* Symbolic calc of A_off * P_oth */
1153   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1154   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1155   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1156   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
1157   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1158   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1159 
1160   /* Allocate space for apj, adpj, aopj, ... */
1161   /* destroy lists of free space and other temporary array(s) */
1162 
1163   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1164   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1165 
1166   /* Copy from linked list to j-array */
1167   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1168   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1169 
1170   adpoJ = adpoj;
1171   adpdJ = adpdj;
1172   aopJ = aopothj;
1173   apj  = ptap->apj;
1174   apJ = apj; /* still empty */
1175 
1176   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1177   /* A_diag * P_loc_diag to get A*P */
1178   for (i = 0; i < am; i++) {
1179     aopnz  =  aopothi[i+1] -  aopothi[i];
1180     adponz = adpoi[i+1] - adpoi[i];
1181     adpdnz = adpdi[i+1] - adpdi[i];
1182 
1183     /* Correct indices from A_diag*P_diag */
1184     for (i1 = 0; i1 < adpdnz; i1++) {
1185       adpdJ[i1] += p_colstart;
1186     }
1187     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1188     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1189     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);CHKERRQ(ierr);
1190 
1191     aopJ += aopnz;
1192     adpoJ += adponz;
1193     adpdJ += adpdnz;
1194     apJ += apnz;
1195     api[i+1] = api[i] + apnz;
1196   }
1197 
1198   /* malloc apa to store dense row A[i,:]*P */
1199   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1200 
1201   /* create and assemble symbolic parallel matrix C */
1202   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1203   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1204   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1205   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1206   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1207   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1208 
1209   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1210   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1211   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1212   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1213 
1214   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1215   C->ops->productnumeric = MatProductNumeric_AB;
1216 
1217   /* attach the supporting struct to C for reuse */
1218   C->product->data    = ptap;
1219   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1220 
1221   /* set MatInfo */
1222   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1223   if (afill < 1.0) afill = 1.0;
1224   C->info.mallocs           = nspacedouble;
1225   C->info.fill_ratio_given  = fill;
1226   C->info.fill_ratio_needed = afill;
1227 
1228 #if defined(PETSC_USE_INFO)
1229   if (api[am]) {
1230     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1231     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1232   } else {
1233     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1234   }
1235 #endif
1236 
1237   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1238   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1239   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1240   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1241   ierr = PetscFree(adpoi);CHKERRQ(ierr);
1242   PetscFunctionReturn(0);
1243 }
1244 
1245 /*-------------------------------------------------------------------------*/
1246 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1247 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1248 {
1249   PetscErrorCode ierr;
1250   Mat_APMPI      *ptap;
1251   Mat            Pt;
1252 
1253   PetscFunctionBegin;
1254   MatCheckProduct(C,3);
1255   ptap = (Mat_APMPI*)C->product->data;
1256   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1257   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1258 
1259   Pt   = ptap->Pt;
1260   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1261   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1262   PetscFunctionReturn(0);
1263 }
1264 
1265 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1266 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1267 {
1268   PetscErrorCode      ierr;
1269   Mat_APMPI           *ptap;
1270   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1271   MPI_Comm            comm;
1272   PetscMPIInt         size,rank;
1273   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1274   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1275   PetscInt            *lnk,i,k,nsend,rstart;
1276   PetscBT             lnkbt;
1277   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1278   PETSC_UNUSED PetscMPIInt icompleted=0;
1279   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1280   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1281   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1282   MPI_Request         *swaits,*rwaits;
1283   MPI_Status          *sstatus,rstatus;
1284   PetscLayout         rowmap;
1285   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1286   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1287   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1288   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1289   PetscTable          ta;
1290   MatType             mtype;
1291   const char          *prefix;
1292 
1293   PetscFunctionBegin;
1294   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1295   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1296   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1297 
1298   /* create symbolic parallel matrix C */
1299   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1300   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1301 
1302   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1303 
1304   /* create struct Mat_APMPI and attached it to C later */
1305   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1306   ptap->reuse = MAT_INITIAL_MATRIX;
1307 
1308   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1309   /* --------------------------------- */
1310   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1311   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1312 
1313   /* (1) compute symbolic A_loc */
1314   /* ---------------------------*/
1315   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1316 
1317   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1318   /* ------------------------------------ */
1319   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1320   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1321   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1322   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1323   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1324 
1325   /* (3) send coj of C_oth to other processors  */
1326   /* ------------------------------------------ */
1327   /* determine row ownership */
1328   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1329   rowmap->n  = pn;
1330   rowmap->bs = 1;
1331   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1332   owners = rowmap->range;
1333 
1334   /* determine the number of messages to send, their lengths */
1335   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1336   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1337   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1338 
1339   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1340   coi   = c_oth->i; coj = c_oth->j;
1341   con   = ptap->C_oth->rmap->n;
1342   proc  = 0;
1343   for (i=0; i<con; i++) {
1344     while (prmap[i] >= owners[proc+1]) proc++;
1345     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1346     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1347   }
1348 
1349   len          = 0; /* max length of buf_si[], see (4) */
1350   owners_co[0] = 0;
1351   nsend        = 0;
1352   for (proc=0; proc<size; proc++) {
1353     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1354     if (len_s[proc]) {
1355       nsend++;
1356       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1357       len         += len_si[proc];
1358     }
1359   }
1360 
1361   /* determine the number and length of messages to receive for coi and coj  */
1362   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1363   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1364 
1365   /* post the Irecv and Isend of coj */
1366   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1367   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1368   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1369   for (proc=0, k=0; proc<size; proc++) {
1370     if (!len_s[proc]) continue;
1371     i    = owners_co[proc];
1372     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1373     k++;
1374   }
1375 
1376   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1377   /* ---------------------------------------- */
1378   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1379   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1380   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1381   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1382   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1383 
1384   /* receives coj are complete */
1385   for (i=0; i<nrecv; i++) {
1386     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1387   }
1388   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1389   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1390 
1391   /* add received column indices into ta to update Crmax */
1392   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1393 
1394   /* create and initialize a linked list */
1395   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1396   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1397 
1398   for (k=0; k<nrecv; k++) {/* k-th received message */
1399     Jptr = buf_rj[k];
1400     for (j=0; j<len_r[k]; j++) {
1401       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1402     }
1403   }
1404   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1405   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1406 
1407   /* (4) send and recv coi */
1408   /*-----------------------*/
1409   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1410   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1411   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1412   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1413   for (proc=0,k=0; proc<size; proc++) {
1414     if (!len_s[proc]) continue;
1415     /* form outgoing message for i-structure:
1416          buf_si[0]:                 nrows to be sent
1417                [1:nrows]:           row index (global)
1418                [nrows+1:2*nrows+1]: i-structure index
1419     */
1420     /*-------------------------------------------*/
1421     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1422     buf_si_i    = buf_si + nrows+1;
1423     buf_si[0]   = nrows;
1424     buf_si_i[0] = 0;
1425     nrows       = 0;
1426     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1427       nzi = coi[i+1] - coi[i];
1428       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1429       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1430       nrows++;
1431     }
1432     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1433     k++;
1434     buf_si += len_si[proc];
1435   }
1436   for (i=0; i<nrecv; i++) {
1437     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1438   }
1439   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1440   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1441 
1442   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1443   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1444   ierr = PetscFree(swaits);CHKERRQ(ierr);
1445   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1446 
1447   /* (5) compute the local portion of C      */
1448   /* ------------------------------------------ */
1449   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1450   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1451   current_space = free_space;
1452 
1453   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1454   for (k=0; k<nrecv; k++) {
1455     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1456     nrows       = *buf_ri_k[k];
1457     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1458     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1459   }
1460 
1461   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1462   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1463   for (i=0; i<pn; i++) { /* for each local row of C */
1464     /* add C_loc into C */
1465     nzi  = c_loc->i[i+1] - c_loc->i[i];
1466     Jptr = c_loc->j + c_loc->i[i];
1467     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1468 
1469     /* add received col data into lnk */
1470     for (k=0; k<nrecv; k++) { /* k-th received message */
1471       if (i == *nextrow[k]) { /* i-th row */
1472         nzi  = *(nextci[k]+1) - *nextci[k];
1473         Jptr = buf_rj[k] + *nextci[k];
1474         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1475         nextrow[k]++; nextci[k]++;
1476       }
1477     }
1478 
1479     /* add missing diagonal entry */
1480     if (C->force_diagonals) {
1481       k = i + owners[rank]; /* column index */
1482       ierr = PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);CHKERRQ(ierr);
1483     }
1484 
1485     nzi = lnk[0];
1486 
1487     /* copy data into free space, then initialize lnk */
1488     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1489     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1490   }
1491   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1492   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1493   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1494 
1495   /* local sizes and preallocation */
1496   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1497   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1498   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1499   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1500   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1501 
1502   /* add C_loc and C_oth to C */
1503   ierr = MatGetOwnershipRange(C,&rstart,NULL);CHKERRQ(ierr);
1504   for (i=0; i<pn; i++) {
1505     ncols = c_loc->i[i+1] - c_loc->i[i];
1506     cols  = c_loc->j + c_loc->i[i];
1507     row   = rstart + i;
1508     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1509 
1510     if (C->force_diagonals) {
1511       ierr = MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);CHKERRQ(ierr);
1512     }
1513   }
1514   for (i=0; i<con; i++) {
1515     ncols = c_oth->i[i+1] - c_oth->i[i];
1516     cols  = c_oth->j + c_oth->i[i];
1517     row   = prmap[i];
1518     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1519   }
1520   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1521   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1522   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1523 
1524   /* members in merge */
1525   ierr = PetscFree(id_r);CHKERRQ(ierr);
1526   ierr = PetscFree(len_r);CHKERRQ(ierr);
1527   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1528   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1529   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1530   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1531   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1532 
1533   /* attach the supporting struct to C for reuse */
1534   C->product->data    = ptap;
1535   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1536   PetscFunctionReturn(0);
1537 }
1538 
1539 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1540 {
1541   PetscErrorCode    ierr;
1542   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1543   Mat_SeqAIJ        *c_seq;
1544   Mat_APMPI         *ptap;
1545   Mat               A_loc,C_loc,C_oth;
1546   PetscInt          i,rstart,rend,cm,ncols,row;
1547   const PetscInt    *cols;
1548   const PetscScalar *vals;
1549 
1550   PetscFunctionBegin;
1551   MatCheckProduct(C,3);
1552   ptap = (Mat_APMPI*)C->product->data;
1553   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1554   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1555   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1556 
1557   if (ptap->reuse == MAT_REUSE_MATRIX) {
1558     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1559     /* 1) get R = Pd^T, Ro = Po^T */
1560     /*----------------------------*/
1561     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1562     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1563 
1564     /* 2) compute numeric A_loc */
1565     /*--------------------------*/
1566     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1567   }
1568 
1569   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1570   A_loc = ptap->A_loc;
1571   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1572   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1573   C_loc = ptap->C_loc;
1574   C_oth = ptap->C_oth;
1575 
1576   /* add C_loc and C_oth to C */
1577   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1578 
1579   /* C_loc -> C */
1580   cm    = C_loc->rmap->N;
1581   c_seq = (Mat_SeqAIJ*)C_loc->data;
1582   cols = c_seq->j;
1583   vals = c_seq->a;
1584   for (i=0; i<cm; i++) {
1585     ncols = c_seq->i[i+1] - c_seq->i[i];
1586     row = rstart + i;
1587     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1588     cols += ncols; vals += ncols;
1589   }
1590 
1591   /* Co -> C, off-processor part */
1592   cm    = C_oth->rmap->N;
1593   c_seq = (Mat_SeqAIJ*)C_oth->data;
1594   cols  = c_seq->j;
1595   vals  = c_seq->a;
1596   for (i=0; i<cm; i++) {
1597     ncols = c_seq->i[i+1] - c_seq->i[i];
1598     row = p->garray[i];
1599     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1600     cols += ncols; vals += ncols;
1601   }
1602   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1603   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1604   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1605 
1606   ptap->reuse = MAT_REUSE_MATRIX;
1607   PetscFunctionReturn(0);
1608 }
1609 
1610 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1611 {
1612   PetscErrorCode      ierr;
1613   Mat_Merge_SeqsToMPI *merge;
1614   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1615   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1616   Mat_APMPI           *ptap;
1617   PetscInt            *adj;
1618   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1619   MatScalar           *ada,*ca,valtmp;
1620   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1621   MPI_Comm            comm;
1622   PetscMPIInt         size,rank,taga,*len_s;
1623   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1624   PetscInt            **buf_ri,**buf_rj;
1625   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1626   MPI_Request         *s_waits,*r_waits;
1627   MPI_Status          *status;
1628   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1629   const PetscScalar   *dummy;
1630   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1631   Mat                 A_loc;
1632   Mat_SeqAIJ          *a_loc;
1633 
1634   PetscFunctionBegin;
1635   MatCheckProduct(C,3);
1636   ptap = (Mat_APMPI*)C->product->data;
1637   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1638   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1639   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1640   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1641   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1642 
1643   merge = ptap->merge;
1644 
1645   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1646   /*------------------------------------------*/
1647   /* get data from symbolic products */
1648   coi    = merge->coi; coj = merge->coj;
1649   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1650   bi     = merge->bi; bj = merge->bj;
1651   owners = merge->rowmap->range;
1652   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1653 
1654   /* get A_loc by taking all local rows of A */
1655   A_loc = ptap->A_loc;
1656   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1657   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1658   ai    = a_loc->i;
1659   aj    = a_loc->j;
1660 
1661   /* trigger copy to CPU */
1662   ierr = MatSeqAIJGetArrayRead(p->A,&dummy);CHKERRQ(ierr);
1663   ierr = MatSeqAIJRestoreArrayRead(p->A,&dummy);CHKERRQ(ierr);
1664   ierr = MatSeqAIJGetArrayRead(p->B,&dummy);CHKERRQ(ierr);
1665   ierr = MatSeqAIJRestoreArrayRead(p->B,&dummy);CHKERRQ(ierr);
1666   for (i=0; i<am; i++) {
1667     anz = ai[i+1] - ai[i];
1668     adj = aj + ai[i];
1669     ada = a_loc->a + ai[i];
1670 
1671     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1672     /*-------------------------------------------------------------*/
1673     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1674     pnz = po->i[i+1] - po->i[i];
1675     poJ = po->j + po->i[i];
1676     pA  = po->a + po->i[i];
1677     for (j=0; j<pnz; j++) {
1678       row = poJ[j];
1679       cj  = coj + coi[row];
1680       ca  = coa + coi[row];
1681       /* perform sparse axpy */
1682       nexta  = 0;
1683       valtmp = pA[j];
1684       for (k=0; nexta<anz; k++) {
1685         if (cj[k] == adj[nexta]) {
1686           ca[k] += valtmp*ada[nexta];
1687           nexta++;
1688         }
1689       }
1690       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1691     }
1692 
1693     /* put the value into Cd (diagonal part) */
1694     pnz = pd->i[i+1] - pd->i[i];
1695     pdJ = pd->j + pd->i[i];
1696     pA  = pd->a + pd->i[i];
1697     for (j=0; j<pnz; j++) {
1698       row = pdJ[j];
1699       cj  = bj + bi[row];
1700       ca  = ba + bi[row];
1701       /* perform sparse axpy */
1702       nexta  = 0;
1703       valtmp = pA[j];
1704       for (k=0; nexta<anz; k++) {
1705         if (cj[k] == adj[nexta]) {
1706           ca[k] += valtmp*ada[nexta];
1707           nexta++;
1708         }
1709       }
1710       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1711     }
1712   }
1713 
1714   /* 3) send and recv matrix values coa */
1715   /*------------------------------------*/
1716   buf_ri = merge->buf_ri;
1717   buf_rj = merge->buf_rj;
1718   len_s  = merge->len_s;
1719   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1720   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1721 
1722   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1723   for (proc=0,k=0; proc<size; proc++) {
1724     if (!len_s[proc]) continue;
1725     i    = merge->owners_co[proc];
1726     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRMPI(ierr);
1727     k++;
1728   }
1729   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRMPI(ierr);}
1730   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRMPI(ierr);}
1731 
1732   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1733   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1734   ierr = PetscFree(coa);CHKERRQ(ierr);
1735 
1736   /* 4) insert local Cseq and received values into Cmpi */
1737   /*----------------------------------------------------*/
1738   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1739   for (k=0; k<merge->nrecv; k++) {
1740     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1741     nrows       = *(buf_ri_k[k]);
1742     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1743     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1744   }
1745 
1746   for (i=0; i<cm; i++) {
1747     row  = owners[rank] + i; /* global row index of C_seq */
1748     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1749     ba_i = ba + bi[i];
1750     bnz  = bi[i+1] - bi[i];
1751     /* add received vals into ba */
1752     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1753       /* i-th row */
1754       if (i == *nextrow[k]) {
1755         cnz    = *(nextci[k]+1) - *nextci[k];
1756         cj     = buf_rj[k] + *(nextci[k]);
1757         ca     = abuf_r[k] + *(nextci[k]);
1758         nextcj = 0;
1759         for (j=0; nextcj<cnz; j++) {
1760           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1761             ba_i[j] += ca[nextcj++];
1762           }
1763         }
1764         nextrow[k]++; nextci[k]++;
1765         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1766       }
1767     }
1768     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1769   }
1770   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1771   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1772 
1773   ierr = PetscFree(ba);CHKERRQ(ierr);
1774   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1775   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1776   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1777   PetscFunctionReturn(0);
1778 }
1779 
1780 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1781 {
1782   PetscErrorCode      ierr;
1783   Mat                 A_loc;
1784   Mat_APMPI           *ptap;
1785   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1786   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1787   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1788   PetscInt            nnz;
1789   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1790   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1791   MPI_Comm            comm;
1792   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1793   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1794   PetscInt            len,proc,*dnz,*onz,*owners;
1795   PetscInt            nzi,*bi,*bj;
1796   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1797   MPI_Request         *swaits,*rwaits;
1798   MPI_Status          *sstatus,rstatus;
1799   Mat_Merge_SeqsToMPI *merge;
1800   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1801   PetscReal           afill  =1.0,afill_tmp;
1802   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1803   Mat_SeqAIJ          *a_loc;
1804   PetscTable          ta;
1805   MatType             mtype;
1806 
1807   PetscFunctionBegin;
1808   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1809   /* check if matrix local sizes are compatible */
1810   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
1811 
1812   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1813   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1814 
1815   /* create struct Mat_APMPI and attached it to C later */
1816   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1817 
1818   /* get A_loc by taking all local rows of A */
1819   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1820 
1821   ptap->A_loc = A_loc;
1822   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1823   ai          = a_loc->i;
1824   aj          = a_loc->j;
1825 
1826   /* determine symbolic Co=(p->B)^T*A - send to others */
1827   /*----------------------------------------------------*/
1828   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1829   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1830   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1831                          >= (num of nonzero rows of C_seq) - pn */
1832   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1833   coi[0] = 0;
1834 
1835   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1836   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1837   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1838   current_space = free_space;
1839 
1840   /* create and initialize a linked list */
1841   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1842   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1843   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1844 
1845   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1846 
1847   for (i=0; i<pon; i++) {
1848     pnz = poti[i+1] - poti[i];
1849     ptJ = potj + poti[i];
1850     for (j=0; j<pnz; j++) {
1851       row  = ptJ[j]; /* row of A_loc == col of Pot */
1852       anz  = ai[row+1] - ai[row];
1853       Jptr = aj + ai[row];
1854       /* add non-zero cols of AP into the sorted linked list lnk */
1855       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1856     }
1857     nnz = lnk[0];
1858 
1859     /* If free space is not available, double the total space in the list */
1860     if (current_space->local_remaining<nnz) {
1861       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1862       nspacedouble++;
1863     }
1864 
1865     /* Copy data into free space, and zero out denserows */
1866     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1867 
1868     current_space->array           += nnz;
1869     current_space->local_used      += nnz;
1870     current_space->local_remaining -= nnz;
1871 
1872     coi[i+1] = coi[i] + nnz;
1873   }
1874 
1875   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1876   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1877   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1878 
1879   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1880   if (afill_tmp > afill) afill = afill_tmp;
1881 
1882   /* send j-array (coj) of Co to other processors */
1883   /*----------------------------------------------*/
1884   /* determine row ownership */
1885   ierr = PetscNew(&merge);CHKERRQ(ierr);
1886   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1887 
1888   merge->rowmap->n  = pn;
1889   merge->rowmap->bs = 1;
1890 
1891   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1892   owners = merge->rowmap->range;
1893 
1894   /* determine the number of messages to send, their lengths */
1895   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1896   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1897 
1898   len_s        = merge->len_s;
1899   merge->nsend = 0;
1900 
1901   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1902 
1903   proc = 0;
1904   for (i=0; i<pon; i++) {
1905     while (prmap[i] >= owners[proc+1]) proc++;
1906     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1907     len_s[proc] += coi[i+1] - coi[i];
1908   }
1909 
1910   len          = 0; /* max length of buf_si[] */
1911   owners_co[0] = 0;
1912   for (proc=0; proc<size; proc++) {
1913     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1914     if (len_si[proc]) {
1915       merge->nsend++;
1916       len_si[proc] = 2*(len_si[proc] + 1);
1917       len         += len_si[proc];
1918     }
1919   }
1920 
1921   /* determine the number and length of messages to receive for coi and coj  */
1922   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1923   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1924 
1925   /* post the Irecv and Isend of coj */
1926   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1927   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1928   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1929   for (proc=0, k=0; proc<size; proc++) {
1930     if (!len_s[proc]) continue;
1931     i    = owners_co[proc];
1932     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1933     k++;
1934   }
1935 
1936   /* receives and sends of coj are complete */
1937   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
1938   for (i=0; i<merge->nrecv; i++) {
1939     PETSC_UNUSED PetscMPIInt icompleted;
1940     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1941   }
1942   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1943   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1944 
1945   /* add received column indices into table to update Armax */
1946   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1947   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1948     Jptr = buf_rj[k];
1949     for (j=0; j<merge->len_r[k]; j++) {
1950       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1951     }
1952   }
1953   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1954   /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */
1955 
1956   /* send and recv coi */
1957   /*-------------------*/
1958   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1959   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1960   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1961   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1962   for (proc=0,k=0; proc<size; proc++) {
1963     if (!len_s[proc]) continue;
1964     /* form outgoing message for i-structure:
1965          buf_si[0]:                 nrows to be sent
1966                [1:nrows]:           row index (global)
1967                [nrows+1:2*nrows+1]: i-structure index
1968     */
1969     /*-------------------------------------------*/
1970     nrows       = len_si[proc]/2 - 1;
1971     buf_si_i    = buf_si + nrows+1;
1972     buf_si[0]   = nrows;
1973     buf_si_i[0] = 0;
1974     nrows       = 0;
1975     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1976       nzi               = coi[i+1] - coi[i];
1977       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1978       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1979       nrows++;
1980     }
1981     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1982     k++;
1983     buf_si += len_si[proc];
1984   }
1985   i = merge->nrecv;
1986   while (i--) {
1987     PETSC_UNUSED PetscMPIInt icompleted;
1988     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1989   }
1990   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1991   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1992   ierr = PetscFree(len_si);CHKERRQ(ierr);
1993   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1994   ierr = PetscFree(swaits);CHKERRQ(ierr);
1995   ierr = PetscFree(sstatus);CHKERRQ(ierr);
1996   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1997 
1998   /* compute the local portion of C (mpi mat) */
1999   /*------------------------------------------*/
2000   /* allocate bi array and free space for accumulating nonzero column info */
2001   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
2002   bi[0] = 0;
2003 
2004   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2005   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2006   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
2007   current_space = free_space;
2008 
2009   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2010   for (k=0; k<merge->nrecv; k++) {
2011     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2012     nrows       = *buf_ri_k[k];
2013     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2014     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2015   }
2016 
2017   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2018   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2019   rmax = 0;
2020   for (i=0; i<pn; i++) {
2021     /* add pdt[i,:]*AP into lnk */
2022     pnz = pdti[i+1] - pdti[i];
2023     ptJ = pdtj + pdti[i];
2024     for (j=0; j<pnz; j++) {
2025       row  = ptJ[j];  /* row of AP == col of Pt */
2026       anz  = ai[row+1] - ai[row];
2027       Jptr = aj + ai[row];
2028       /* add non-zero cols of AP into the sorted linked list lnk */
2029       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2030     }
2031 
2032     /* add received col data into lnk */
2033     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2034       if (i == *nextrow[k]) { /* i-th row */
2035         nzi  = *(nextci[k]+1) - *nextci[k];
2036         Jptr = buf_rj[k] + *nextci[k];
2037         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2038         nextrow[k]++; nextci[k]++;
2039       }
2040     }
2041 
2042     /* add missing diagonal entry */
2043     if (C->force_diagonals) {
2044       k = i + owners[rank]; /* column index */
2045       ierr = PetscLLCondensedAddSorted_Scalable(1,&k,lnk);CHKERRQ(ierr);
2046     }
2047 
2048     nnz = lnk[0];
2049 
2050     /* if free space is not available, make more free space */
2051     if (current_space->local_remaining<nnz) {
2052       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2053       nspacedouble++;
2054     }
2055     /* copy data into free space, then initialize lnk */
2056     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2057     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2058 
2059     current_space->array           += nnz;
2060     current_space->local_used      += nnz;
2061     current_space->local_remaining -= nnz;
2062 
2063     bi[i+1] = bi[i] + nnz;
2064     if (nnz > rmax) rmax = nnz;
2065   }
2066   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2067 
2068   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2069   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2070   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2071   if (afill_tmp > afill) afill = afill_tmp;
2072   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2073   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2074   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
2075   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
2076 
2077   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2078   /*-------------------------------------------------------------------------------*/
2079   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2080   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2081   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2082   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2083   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2084   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2085   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2086   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
2087   for (i=0; i<pn; i++) {
2088     row  = i + rstart;
2089     nnz  = bi[i+1] - bi[i];
2090     Jptr = bj + bi[i];
2091     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2092   }
2093   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2094   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2095   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2096   merge->bi        = bi;
2097   merge->bj        = bj;
2098   merge->coi       = coi;
2099   merge->coj       = coj;
2100   merge->buf_ri    = buf_ri;
2101   merge->buf_rj    = buf_rj;
2102   merge->owners_co = owners_co;
2103 
2104   /* attach the supporting struct to C for reuse */
2105   C->product->data    = ptap;
2106   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2107   ptap->merge         = merge;
2108 
2109   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2110 
2111 #if defined(PETSC_USE_INFO)
2112   if (bi[pn] != 0) {
2113     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2114     ierr = PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2115   } else {
2116     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2117   }
2118 #endif
2119   PetscFunctionReturn(0);
2120 }
2121 
2122 /* ---------------------------------------------------------------- */
2123 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2124 {
2125   PetscErrorCode ierr;
2126   Mat_Product    *product = C->product;
2127   Mat            A=product->A,B=product->B;
2128   PetscReal      fill=product->fill;
2129   PetscBool      flg;
2130 
2131   PetscFunctionBegin;
2132   /* scalable */
2133   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2134   if (flg) {
2135     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2136     goto next;
2137   }
2138 
2139   /* nonscalable */
2140   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2141   if (flg) {
2142     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2143     goto next;
2144   }
2145 
2146   /* matmatmult */
2147   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2148   if (flg) {
2149     Mat       At;
2150     Mat_APMPI *ptap;
2151 
2152     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2153     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2154     ptap = (Mat_APMPI*)C->product->data;
2155     if (ptap) {
2156       ptap->Pt = At;
2157       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2158     }
2159     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2160     goto next;
2161   }
2162 
2163   /* backend general code */
2164   ierr = PetscStrcmp(product->alg,"backend",&flg);CHKERRQ(ierr);
2165   if (flg) {
2166     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
2167     PetscFunctionReturn(0);
2168   }
2169 
2170   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2171 
2172 next:
2173   C->ops->productnumeric = MatProductNumeric_AtB;
2174   PetscFunctionReturn(0);
2175 }
2176 
2177 /* ---------------------------------------------------------------- */
2178 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2179 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2180 {
2181   PetscErrorCode ierr;
2182   Mat_Product    *product = C->product;
2183   Mat            A=product->A,B=product->B;
2184 #if defined(PETSC_HAVE_HYPRE)
2185   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2186   PetscInt       nalg = 5;
2187 #else
2188   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2189   PetscInt       nalg = 4;
2190 #endif
2191   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2192   PetscBool      flg;
2193   MPI_Comm       comm;
2194 
2195   PetscFunctionBegin;
2196   /* Check matrix local sizes */
2197   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2198   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
2199 
2200   /* Set "nonscalable" as default algorithm */
2201   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2202   if (flg) {
2203     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2204 
2205     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2206     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2207       MatInfo     Ainfo,Binfo;
2208       PetscInt    nz_local;
2209       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2210 
2211       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2212       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2213       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2214 
2215       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2216       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2217 
2218       if (alg_scalable) {
2219         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2220         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2221         ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2222       }
2223     }
2224   }
2225 
2226   /* Get runtime option */
2227   if (product->api_user) {
2228     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2229     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2230     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2231   } else {
2232     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2233     ierr = PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2234     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2235   }
2236   if (flg) {
2237     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2238   }
2239 
2240   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2241   PetscFunctionReturn(0);
2242 }
2243 
2244 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2245 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2246 {
2247   PetscErrorCode ierr;
2248   Mat_Product    *product = C->product;
2249   Mat            A=product->A,B=product->B;
2250   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2251   PetscInt       nalg = 4;
2252   PetscInt       alg = 1; /* set default algorithm  */
2253   PetscBool      flg;
2254   MPI_Comm       comm;
2255 
2256   PetscFunctionBegin;
2257   /* Check matrix local sizes */
2258   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2259   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != B (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
2260 
2261   /* Set default algorithm */
2262   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2263   if (flg) {
2264     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2265   }
2266 
2267   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2268   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2269     MatInfo     Ainfo,Binfo;
2270     PetscInt    nz_local;
2271     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2272 
2273     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2274     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2275     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2276 
2277     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2278     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2279 
2280     if (alg_scalable) {
2281       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2282       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2283       ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2284     }
2285   }
2286 
2287   /* Get runtime option */
2288   if (product->api_user) {
2289     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2290     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2291     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2292   } else {
2293     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2294     ierr = PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2295     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2296   }
2297   if (flg) {
2298     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2299   }
2300 
2301   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2306 {
2307   PetscErrorCode ierr;
2308   Mat_Product    *product = C->product;
2309   Mat            A=product->A,P=product->B;
2310   MPI_Comm       comm;
2311   PetscBool      flg;
2312   PetscInt       alg=1; /* set default algorithm */
2313 #if !defined(PETSC_HAVE_HYPRE)
2314   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2315   PetscInt       nalg=5;
2316 #else
2317   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2318   PetscInt       nalg=6;
2319 #endif
2320   PetscInt       pN=P->cmap->N;
2321 
2322   PetscFunctionBegin;
2323   /* Check matrix local sizes */
2324   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2325   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
2326   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
2327 
2328   /* Set "nonscalable" as default algorithm */
2329   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2330   if (flg) {
2331     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2332 
2333     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2334     if (pN > 100000) {
2335       MatInfo     Ainfo,Pinfo;
2336       PetscInt    nz_local;
2337       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2338 
2339       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2340       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2341       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2342 
2343       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2344       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2345 
2346       if (alg_scalable) {
2347         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2348         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2349       }
2350     }
2351   }
2352 
2353   /* Get runtime option */
2354   if (product->api_user) {
2355     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2356     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2357     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2358   } else {
2359     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2360     ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2361     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2362   }
2363   if (flg) {
2364     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2365   }
2366 
2367   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2368   PetscFunctionReturn(0);
2369 }
2370 
2371 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2372 {
2373   Mat_Product *product = C->product;
2374   Mat         A = product->A,R=product->B;
2375 
2376   PetscFunctionBegin;
2377   /* Check matrix local sizes */
2378   if (A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%D, %D), R local (%D,%D)",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);
2379 
2380   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2381   PetscFunctionReturn(0);
2382 }
2383 
2384 /*
2385  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2386 */
2387 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2388 {
2389   PetscErrorCode ierr;
2390   Mat_Product    *product = C->product;
2391   PetscBool      flg = PETSC_FALSE;
2392   PetscInt       alg = 1; /* default algorithm */
2393   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2394   PetscInt       nalg = 3;
2395 
2396   PetscFunctionBegin;
2397   /* Set default algorithm */
2398   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2399   if (flg) {
2400     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2401   }
2402 
2403   /* Get runtime option */
2404   if (product->api_user) {
2405     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2406     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2407     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2408   } else {
2409     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2410     ierr = PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2411     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2412   }
2413   if (flg) {
2414     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2415   }
2416 
2417   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2418   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2419   PetscFunctionReturn(0);
2420 }
2421 
2422 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2423 {
2424   PetscErrorCode ierr;
2425   Mat_Product    *product = C->product;
2426 
2427   PetscFunctionBegin;
2428   switch (product->type) {
2429   case MATPRODUCT_AB:
2430     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2431     break;
2432   case MATPRODUCT_AtB:
2433     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2434     break;
2435   case MATPRODUCT_PtAP:
2436     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2437     break;
2438   case MATPRODUCT_RARt:
2439     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2440     break;
2441   case MATPRODUCT_ABC:
2442     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2443     break;
2444   default:
2445     break;
2446   }
2447   PetscFunctionReturn(0);
2448 }
2449