xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 2fa40bb9206b96114faa7cb222621ec184d31cd2)
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   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1077   pi_loc = p_loc->i;
1078 
1079   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1080   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1081   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
1082 
1083   adpoi[0]    = 0;
1084   ptap->api = api;
1085   api[0] = 0;
1086 
1087   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1088   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1089   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1090 
1091   /* Symbolic calc of A_loc_diag * P_loc_diag */
1092   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1093   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1094   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1095   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1096   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1097 
1098   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1099   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1100   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1101   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1102 
1103   adpd->force_diagonals = C->force_diagonals;
1104   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
1105 
1106   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1107   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1108   p_off = (Mat_SeqAIJ*)((p->B)->data);
1109   poff_i = p_off->i; poff_j = p_off->j;
1110 
1111   /* j_temp stores indices of a result row before they are added to the linked list */
1112   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1113 
1114   /* Symbolic calc of the A_diag * p_loc_off */
1115   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1116   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
1117   current_space = free_space_diag;
1118 
1119   for (i=0; i<am; i++) {
1120     /* A_diag * P_loc_off */
1121     nzi = adi[i+1] - adi[i];
1122     for (j=0; j<nzi; j++) {
1123       row  = *adj++;
1124       pnz  = poff_i[row+1] - poff_i[row];
1125       Jptr = poff_j + poff_i[row];
1126       for (i1 = 0; i1 < pnz; i1++) {
1127         j_temp[i1] = p->garray[Jptr[i1]];
1128       }
1129       /* add non-zero cols of P into the sorted linked list lnk */
1130       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
1131     }
1132 
1133     adponz     = lnk[0];
1134     adpoi[i+1] = adpoi[i] + adponz;
1135 
1136     /* if free space is not available, double the total space in the list */
1137     if (current_space->local_remaining<adponz) {
1138       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1139       nspacedouble++;
1140     }
1141 
1142     /* Copy data into free space, then initialize lnk */
1143     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1144 
1145     current_space->array           += adponz;
1146     current_space->local_used      += adponz;
1147     current_space->local_remaining -= adponz;
1148   }
1149 
1150   /* Symbolic calc of A_off * P_oth */
1151   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1152   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1153   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1154   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
1155   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1156   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1157 
1158   /* Allocate space for apj, adpj, aopj, ... */
1159   /* destroy lists of free space and other temporary array(s) */
1160 
1161   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1162   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1163 
1164   /* Copy from linked list to j-array */
1165   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1166   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1167 
1168   adpoJ = adpoj;
1169   adpdJ = adpdj;
1170   aopJ = aopothj;
1171   apj  = ptap->apj;
1172   apJ = apj; /* still empty */
1173 
1174   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1175   /* A_diag * P_loc_diag to get A*P */
1176   for (i = 0; i < am; i++) {
1177     aopnz  =  aopothi[i+1] -  aopothi[i];
1178     adponz = adpoi[i+1] - adpoi[i];
1179     adpdnz = adpdi[i+1] - adpdi[i];
1180 
1181     /* Correct indices from A_diag*P_diag */
1182     for (i1 = 0; i1 < adpdnz; i1++) {
1183       adpdJ[i1] += p_colstart;
1184     }
1185     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1186     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1187     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);CHKERRQ(ierr);
1188 
1189     aopJ += aopnz;
1190     adpoJ += adponz;
1191     adpdJ += adpdnz;
1192     apJ += apnz;
1193     api[i+1] = api[i] + apnz;
1194   }
1195 
1196   /* malloc apa to store dense row A[i,:]*P */
1197   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1198 
1199   /* create and assemble symbolic parallel matrix C */
1200   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1201   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1202   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1203   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1204   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1205   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1206 
1207   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1208   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1209   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1210   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1211 
1212   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1213   C->ops->productnumeric = MatProductNumeric_AB;
1214 
1215   /* attach the supporting struct to C for reuse */
1216   C->product->data    = ptap;
1217   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1218 
1219   /* set MatInfo */
1220   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1221   if (afill < 1.0) afill = 1.0;
1222   C->info.mallocs           = nspacedouble;
1223   C->info.fill_ratio_given  = fill;
1224   C->info.fill_ratio_needed = afill;
1225 
1226 #if defined(PETSC_USE_INFO)
1227   if (api[am]) {
1228     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1229     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1230   } else {
1231     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1232   }
1233 #endif
1234 
1235   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1236   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1237   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1238   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1239   ierr = PetscFree(adpoi);CHKERRQ(ierr);
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 /*-------------------------------------------------------------------------*/
1244 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1245 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1246 {
1247   PetscErrorCode ierr;
1248   Mat_APMPI      *ptap;
1249   Mat            Pt;
1250 
1251   PetscFunctionBegin;
1252   MatCheckProduct(C,3);
1253   ptap = (Mat_APMPI*)C->product->data;
1254   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1255   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1256 
1257   Pt   = ptap->Pt;
1258   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1259   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1260   PetscFunctionReturn(0);
1261 }
1262 
1263 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1264 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1265 {
1266   PetscErrorCode      ierr;
1267   Mat_APMPI           *ptap;
1268   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1269   MPI_Comm            comm;
1270   PetscMPIInt         size,rank;
1271   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1272   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1273   PetscInt            *lnk,i,k,nsend,rstart;
1274   PetscBT             lnkbt;
1275   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1276   PETSC_UNUSED PetscMPIInt icompleted=0;
1277   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1278   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1279   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1280   MPI_Request         *swaits,*rwaits;
1281   MPI_Status          *sstatus,rstatus;
1282   PetscLayout         rowmap;
1283   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1284   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1285   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1286   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1287   PetscTable          ta;
1288   MatType             mtype;
1289   const char          *prefix;
1290 
1291   PetscFunctionBegin;
1292   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1293   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1294   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1295 
1296   /* create symbolic parallel matrix C */
1297   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1298   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1299 
1300   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1301 
1302   /* create struct Mat_APMPI and attached it to C later */
1303   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1304   ptap->reuse = MAT_INITIAL_MATRIX;
1305 
1306   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1307   /* --------------------------------- */
1308   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1309   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1310 
1311   /* (1) compute symbolic A_loc */
1312   /* ---------------------------*/
1313   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1314 
1315   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1316   /* ------------------------------------ */
1317   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1318   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1319   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1320   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1321   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1322 
1323   /* (3) send coj of C_oth to other processors  */
1324   /* ------------------------------------------ */
1325   /* determine row ownership */
1326   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1327   rowmap->n  = pn;
1328   rowmap->bs = 1;
1329   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1330   owners = rowmap->range;
1331 
1332   /* determine the number of messages to send, their lengths */
1333   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1334   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1335   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1336 
1337   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1338   coi   = c_oth->i; coj = c_oth->j;
1339   con   = ptap->C_oth->rmap->n;
1340   proc  = 0;
1341   for (i=0; i<con; i++) {
1342     while (prmap[i] >= owners[proc+1]) proc++;
1343     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1344     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1345   }
1346 
1347   len          = 0; /* max length of buf_si[], see (4) */
1348   owners_co[0] = 0;
1349   nsend        = 0;
1350   for (proc=0; proc<size; proc++) {
1351     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1352     if (len_s[proc]) {
1353       nsend++;
1354       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1355       len         += len_si[proc];
1356     }
1357   }
1358 
1359   /* determine the number and length of messages to receive for coi and coj  */
1360   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1361   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1362 
1363   /* post the Irecv and Isend of coj */
1364   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1365   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1366   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1367   for (proc=0, k=0; proc<size; proc++) {
1368     if (!len_s[proc]) continue;
1369     i    = owners_co[proc];
1370     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1371     k++;
1372   }
1373 
1374   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1375   /* ---------------------------------------- */
1376   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1377   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1378   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1379   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1380   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1381 
1382   /* receives coj are complete */
1383   for (i=0; i<nrecv; i++) {
1384     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1385   }
1386   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1387   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1388 
1389   /* add received column indices into ta to update Crmax */
1390   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1391 
1392   /* create and initialize a linked list */
1393   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1394   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1395 
1396   for (k=0; k<nrecv; k++) {/* k-th received message */
1397     Jptr = buf_rj[k];
1398     for (j=0; j<len_r[k]; j++) {
1399       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1400     }
1401   }
1402   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1403   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1404 
1405   /* (4) send and recv coi */
1406   /*-----------------------*/
1407   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1408   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1409   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1410   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1411   for (proc=0,k=0; proc<size; proc++) {
1412     if (!len_s[proc]) continue;
1413     /* form outgoing message for i-structure:
1414          buf_si[0]:                 nrows to be sent
1415                [1:nrows]:           row index (global)
1416                [nrows+1:2*nrows+1]: i-structure index
1417     */
1418     /*-------------------------------------------*/
1419     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1420     buf_si_i    = buf_si + nrows+1;
1421     buf_si[0]   = nrows;
1422     buf_si_i[0] = 0;
1423     nrows       = 0;
1424     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1425       nzi = coi[i+1] - coi[i];
1426       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1427       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1428       nrows++;
1429     }
1430     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1431     k++;
1432     buf_si += len_si[proc];
1433   }
1434   for (i=0; i<nrecv; i++) {
1435     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1436   }
1437   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1438   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1439 
1440   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1441   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1442   ierr = PetscFree(swaits);CHKERRQ(ierr);
1443   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1444 
1445   /* (5) compute the local portion of C      */
1446   /* ------------------------------------------ */
1447   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1448   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1449   current_space = free_space;
1450 
1451   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1452   for (k=0; k<nrecv; k++) {
1453     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1454     nrows       = *buf_ri_k[k];
1455     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1456     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1457   }
1458 
1459   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1460   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1461   for (i=0; i<pn; i++) { /* for each local row of C */
1462     /* add C_loc into C */
1463     nzi  = c_loc->i[i+1] - c_loc->i[i];
1464     Jptr = c_loc->j + c_loc->i[i];
1465     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1466 
1467     /* add received col data into lnk */
1468     for (k=0; k<nrecv; k++) { /* k-th received message */
1469       if (i == *nextrow[k]) { /* i-th row */
1470         nzi  = *(nextci[k]+1) - *nextci[k];
1471         Jptr = buf_rj[k] + *nextci[k];
1472         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1473         nextrow[k]++; nextci[k]++;
1474       }
1475     }
1476 
1477     /* add missing diagonal entry */
1478     if (C->force_diagonals) {
1479       k = i + owners[rank]; /* column index */
1480       ierr = PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);CHKERRQ(ierr);
1481     }
1482 
1483     nzi = lnk[0];
1484 
1485     /* copy data into free space, then initialize lnk */
1486     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1487     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1488   }
1489   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1490   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1491   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1492 
1493   /* local sizes and preallocation */
1494   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1495   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1496   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1497   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1498   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1499 
1500   /* add C_loc and C_oth to C */
1501   ierr = MatGetOwnershipRange(C,&rstart,NULL);CHKERRQ(ierr);
1502   for (i=0; i<pn; i++) {
1503     ncols = c_loc->i[i+1] - c_loc->i[i];
1504     cols  = c_loc->j + c_loc->i[i];
1505     row   = rstart + i;
1506     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1507 
1508     if (C->force_diagonals) {
1509       ierr = MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);CHKERRQ(ierr);
1510     }
1511   }
1512   for (i=0; i<con; i++) {
1513     ncols = c_oth->i[i+1] - c_oth->i[i];
1514     cols  = c_oth->j + c_oth->i[i];
1515     row   = prmap[i];
1516     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1517   }
1518   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1519   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1520   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1521 
1522   /* members in merge */
1523   ierr = PetscFree(id_r);CHKERRQ(ierr);
1524   ierr = PetscFree(len_r);CHKERRQ(ierr);
1525   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1526   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1527   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1528   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1529   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1530 
1531   /* attach the supporting struct to C for reuse */
1532   C->product->data    = ptap;
1533   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1534   PetscFunctionReturn(0);
1535 }
1536 
1537 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1538 {
1539   PetscErrorCode    ierr;
1540   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1541   Mat_SeqAIJ        *c_seq;
1542   Mat_APMPI         *ptap;
1543   Mat               A_loc,C_loc,C_oth;
1544   PetscInt          i,rstart,rend,cm,ncols,row;
1545   const PetscInt    *cols;
1546   const PetscScalar *vals;
1547 
1548   PetscFunctionBegin;
1549   MatCheckProduct(C,3);
1550   ptap = (Mat_APMPI*)C->product->data;
1551   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1552   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1553   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1554 
1555   if (ptap->reuse == MAT_REUSE_MATRIX) {
1556     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1557     /* 1) get R = Pd^T, Ro = Po^T */
1558     /*----------------------------*/
1559     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1560     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1561 
1562     /* 2) compute numeric A_loc */
1563     /*--------------------------*/
1564     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1565   }
1566 
1567   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1568   A_loc = ptap->A_loc;
1569   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1570   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1571   C_loc = ptap->C_loc;
1572   C_oth = ptap->C_oth;
1573 
1574   /* add C_loc and C_oth to C */
1575   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1576 
1577   /* C_loc -> C */
1578   cm    = C_loc->rmap->N;
1579   c_seq = (Mat_SeqAIJ*)C_loc->data;
1580   cols = c_seq->j;
1581   vals = c_seq->a;
1582   for (i=0; i<cm; i++) {
1583     ncols = c_seq->i[i+1] - c_seq->i[i];
1584     row = rstart + i;
1585     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1586     cols += ncols; vals += ncols;
1587   }
1588 
1589   /* Co -> C, off-processor part */
1590   cm    = C_oth->rmap->N;
1591   c_seq = (Mat_SeqAIJ*)C_oth->data;
1592   cols  = c_seq->j;
1593   vals  = c_seq->a;
1594   for (i=0; i<cm; i++) {
1595     ncols = c_seq->i[i+1] - c_seq->i[i];
1596     row = p->garray[i];
1597     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1598     cols += ncols; vals += ncols;
1599   }
1600   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1601   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1602   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1603 
1604   ptap->reuse = MAT_REUSE_MATRIX;
1605   PetscFunctionReturn(0);
1606 }
1607 
1608 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1609 {
1610   PetscErrorCode      ierr;
1611   Mat_Merge_SeqsToMPI *merge;
1612   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1613   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1614   Mat_APMPI           *ptap;
1615   PetscInt            *adj;
1616   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1617   MatScalar           *ada,*ca,valtmp;
1618   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1619   MPI_Comm            comm;
1620   PetscMPIInt         size,rank,taga,*len_s;
1621   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1622   PetscInt            **buf_ri,**buf_rj;
1623   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1624   MPI_Request         *s_waits,*r_waits;
1625   MPI_Status          *status;
1626   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1627   const PetscScalar   *dummy;
1628   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1629   Mat                 A_loc;
1630   Mat_SeqAIJ          *a_loc;
1631 
1632   PetscFunctionBegin;
1633   MatCheckProduct(C,3);
1634   ptap = (Mat_APMPI*)C->product->data;
1635   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1636   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1637   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1638   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1639   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1640 
1641   merge = ptap->merge;
1642 
1643   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1644   /*------------------------------------------*/
1645   /* get data from symbolic products */
1646   coi    = merge->coi; coj = merge->coj;
1647   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1648   bi     = merge->bi; bj = merge->bj;
1649   owners = merge->rowmap->range;
1650   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1651 
1652   /* get A_loc by taking all local rows of A */
1653   A_loc = ptap->A_loc;
1654   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1655   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1656   ai    = a_loc->i;
1657   aj    = a_loc->j;
1658 
1659   /* trigger copy to CPU */
1660   ierr = MatSeqAIJGetArrayRead(p->A,&dummy);CHKERRQ(ierr);
1661   ierr = MatSeqAIJRestoreArrayRead(p->A,&dummy);CHKERRQ(ierr);
1662   ierr = MatSeqAIJGetArrayRead(p->B,&dummy);CHKERRQ(ierr);
1663   ierr = MatSeqAIJRestoreArrayRead(p->B,&dummy);CHKERRQ(ierr);
1664   for (i=0; i<am; i++) {
1665     anz = ai[i+1] - ai[i];
1666     adj = aj + ai[i];
1667     ada = a_loc->a + ai[i];
1668 
1669     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1670     /*-------------------------------------------------------------*/
1671     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1672     pnz = po->i[i+1] - po->i[i];
1673     poJ = po->j + po->i[i];
1674     pA  = po->a + po->i[i];
1675     for (j=0; j<pnz; j++) {
1676       row = poJ[j];
1677       cj  = coj + coi[row];
1678       ca  = coa + coi[row];
1679       /* perform sparse axpy */
1680       nexta  = 0;
1681       valtmp = pA[j];
1682       for (k=0; nexta<anz; k++) {
1683         if (cj[k] == adj[nexta]) {
1684           ca[k] += valtmp*ada[nexta];
1685           nexta++;
1686         }
1687       }
1688       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1689     }
1690 
1691     /* put the value into Cd (diagonal part) */
1692     pnz = pd->i[i+1] - pd->i[i];
1693     pdJ = pd->j + pd->i[i];
1694     pA  = pd->a + pd->i[i];
1695     for (j=0; j<pnz; j++) {
1696       row = pdJ[j];
1697       cj  = bj + bi[row];
1698       ca  = ba + bi[row];
1699       /* perform sparse axpy */
1700       nexta  = 0;
1701       valtmp = pA[j];
1702       for (k=0; nexta<anz; k++) {
1703         if (cj[k] == adj[nexta]) {
1704           ca[k] += valtmp*ada[nexta];
1705           nexta++;
1706         }
1707       }
1708       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1709     }
1710   }
1711 
1712   /* 3) send and recv matrix values coa */
1713   /*------------------------------------*/
1714   buf_ri = merge->buf_ri;
1715   buf_rj = merge->buf_rj;
1716   len_s  = merge->len_s;
1717   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1718   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1719 
1720   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1721   for (proc=0,k=0; proc<size; proc++) {
1722     if (!len_s[proc]) continue;
1723     i    = merge->owners_co[proc];
1724     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRMPI(ierr);
1725     k++;
1726   }
1727   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRMPI(ierr);}
1728   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRMPI(ierr);}
1729 
1730   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1731   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1732   ierr = PetscFree(coa);CHKERRQ(ierr);
1733 
1734   /* 4) insert local Cseq and received values into Cmpi */
1735   /*----------------------------------------------------*/
1736   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1737   for (k=0; k<merge->nrecv; k++) {
1738     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1739     nrows       = *(buf_ri_k[k]);
1740     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1741     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1742   }
1743 
1744   for (i=0; i<cm; i++) {
1745     row  = owners[rank] + i; /* global row index of C_seq */
1746     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1747     ba_i = ba + bi[i];
1748     bnz  = bi[i+1] - bi[i];
1749     /* add received vals into ba */
1750     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1751       /* i-th row */
1752       if (i == *nextrow[k]) {
1753         cnz    = *(nextci[k]+1) - *nextci[k];
1754         cj     = buf_rj[k] + *(nextci[k]);
1755         ca     = abuf_r[k] + *(nextci[k]);
1756         nextcj = 0;
1757         for (j=0; nextcj<cnz; j++) {
1758           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1759             ba_i[j] += ca[nextcj++];
1760           }
1761         }
1762         nextrow[k]++; nextci[k]++;
1763         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1764       }
1765     }
1766     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1767   }
1768   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1769   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1770 
1771   ierr = PetscFree(ba);CHKERRQ(ierr);
1772   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1773   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1774   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1775   PetscFunctionReturn(0);
1776 }
1777 
1778 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1779 {
1780   PetscErrorCode      ierr;
1781   Mat                 A_loc;
1782   Mat_APMPI           *ptap;
1783   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1784   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1785   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1786   PetscInt            nnz;
1787   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1788   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1789   MPI_Comm            comm;
1790   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1791   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1792   PetscInt            len,proc,*dnz,*onz,*owners;
1793   PetscInt            nzi,*bi,*bj;
1794   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1795   MPI_Request         *swaits,*rwaits;
1796   MPI_Status          *sstatus,rstatus;
1797   Mat_Merge_SeqsToMPI *merge;
1798   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1799   PetscReal           afill  =1.0,afill_tmp;
1800   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1801   Mat_SeqAIJ          *a_loc;
1802   PetscTable          ta;
1803   MatType             mtype;
1804 
1805   PetscFunctionBegin;
1806   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1807   /* check if matrix local sizes are compatible */
1808   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);
1809 
1810   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1811   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1812 
1813   /* create struct Mat_APMPI and attached it to C later */
1814   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1815 
1816   /* get A_loc by taking all local rows of A */
1817   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1818 
1819   ptap->A_loc = A_loc;
1820   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1821   ai          = a_loc->i;
1822   aj          = a_loc->j;
1823 
1824   /* determine symbolic Co=(p->B)^T*A - send to others */
1825   /*----------------------------------------------------*/
1826   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1827   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1828   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1829                          >= (num of nonzero rows of C_seq) - pn */
1830   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1831   coi[0] = 0;
1832 
1833   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1834   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1835   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1836   current_space = free_space;
1837 
1838   /* create and initialize a linked list */
1839   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1840   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1841   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1842 
1843   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1844 
1845   for (i=0; i<pon; i++) {
1846     pnz = poti[i+1] - poti[i];
1847     ptJ = potj + poti[i];
1848     for (j=0; j<pnz; j++) {
1849       row  = ptJ[j]; /* row of A_loc == col of Pot */
1850       anz  = ai[row+1] - ai[row];
1851       Jptr = aj + ai[row];
1852       /* add non-zero cols of AP into the sorted linked list lnk */
1853       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1854     }
1855     nnz = lnk[0];
1856 
1857     /* If free space is not available, double the total space in the list */
1858     if (current_space->local_remaining<nnz) {
1859       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1860       nspacedouble++;
1861     }
1862 
1863     /* Copy data into free space, and zero out denserows */
1864     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1865 
1866     current_space->array           += nnz;
1867     current_space->local_used      += nnz;
1868     current_space->local_remaining -= nnz;
1869 
1870     coi[i+1] = coi[i] + nnz;
1871   }
1872 
1873   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1874   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1875   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1876 
1877   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1878   if (afill_tmp > afill) afill = afill_tmp;
1879 
1880   /* send j-array (coj) of Co to other processors */
1881   /*----------------------------------------------*/
1882   /* determine row ownership */
1883   ierr = PetscNew(&merge);CHKERRQ(ierr);
1884   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1885 
1886   merge->rowmap->n  = pn;
1887   merge->rowmap->bs = 1;
1888 
1889   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1890   owners = merge->rowmap->range;
1891 
1892   /* determine the number of messages to send, their lengths */
1893   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1894   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1895 
1896   len_s        = merge->len_s;
1897   merge->nsend = 0;
1898 
1899   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1900 
1901   proc = 0;
1902   for (i=0; i<pon; i++) {
1903     while (prmap[i] >= owners[proc+1]) proc++;
1904     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1905     len_s[proc] += coi[i+1] - coi[i];
1906   }
1907 
1908   len          = 0; /* max length of buf_si[] */
1909   owners_co[0] = 0;
1910   for (proc=0; proc<size; proc++) {
1911     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1912     if (len_si[proc]) {
1913       merge->nsend++;
1914       len_si[proc] = 2*(len_si[proc] + 1);
1915       len         += len_si[proc];
1916     }
1917   }
1918 
1919   /* determine the number and length of messages to receive for coi and coj  */
1920   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1921   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1922 
1923   /* post the Irecv and Isend of coj */
1924   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1925   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1926   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1927   for (proc=0, k=0; proc<size; proc++) {
1928     if (!len_s[proc]) continue;
1929     i    = owners_co[proc];
1930     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1931     k++;
1932   }
1933 
1934   /* receives and sends of coj are complete */
1935   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
1936   for (i=0; i<merge->nrecv; i++) {
1937     PETSC_UNUSED PetscMPIInt icompleted;
1938     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1939   }
1940   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1941   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1942 
1943   /* add received column indices into table to update Armax */
1944   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1945   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1946     Jptr = buf_rj[k];
1947     for (j=0; j<merge->len_r[k]; j++) {
1948       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1949     }
1950   }
1951   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1952   /* 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); */
1953 
1954   /* send and recv coi */
1955   /*-------------------*/
1956   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1957   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1958   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1959   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1960   for (proc=0,k=0; proc<size; proc++) {
1961     if (!len_s[proc]) continue;
1962     /* form outgoing message for i-structure:
1963          buf_si[0]:                 nrows to be sent
1964                [1:nrows]:           row index (global)
1965                [nrows+1:2*nrows+1]: i-structure index
1966     */
1967     /*-------------------------------------------*/
1968     nrows       = len_si[proc]/2 - 1;
1969     buf_si_i    = buf_si + nrows+1;
1970     buf_si[0]   = nrows;
1971     buf_si_i[0] = 0;
1972     nrows       = 0;
1973     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1974       nzi               = coi[i+1] - coi[i];
1975       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1976       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1977       nrows++;
1978     }
1979     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1980     k++;
1981     buf_si += len_si[proc];
1982   }
1983   i = merge->nrecv;
1984   while (i--) {
1985     PETSC_UNUSED PetscMPIInt icompleted;
1986     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1987   }
1988   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1989   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1990   ierr = PetscFree(len_si);CHKERRQ(ierr);
1991   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1992   ierr = PetscFree(swaits);CHKERRQ(ierr);
1993   ierr = PetscFree(sstatus);CHKERRQ(ierr);
1994   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1995 
1996   /* compute the local portion of C (mpi mat) */
1997   /*------------------------------------------*/
1998   /* allocate bi array and free space for accumulating nonzero column info */
1999   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
2000   bi[0] = 0;
2001 
2002   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2003   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2004   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
2005   current_space = free_space;
2006 
2007   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2008   for (k=0; k<merge->nrecv; k++) {
2009     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2010     nrows       = *buf_ri_k[k];
2011     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2012     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2013   }
2014 
2015   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2016   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2017   rmax = 0;
2018   for (i=0; i<pn; i++) {
2019     /* add pdt[i,:]*AP into lnk */
2020     pnz = pdti[i+1] - pdti[i];
2021     ptJ = pdtj + pdti[i];
2022     for (j=0; j<pnz; j++) {
2023       row  = ptJ[j];  /* row of AP == col of Pt */
2024       anz  = ai[row+1] - ai[row];
2025       Jptr = aj + ai[row];
2026       /* add non-zero cols of AP into the sorted linked list lnk */
2027       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2028     }
2029 
2030     /* add received col data into lnk */
2031     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2032       if (i == *nextrow[k]) { /* i-th row */
2033         nzi  = *(nextci[k]+1) - *nextci[k];
2034         Jptr = buf_rj[k] + *nextci[k];
2035         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2036         nextrow[k]++; nextci[k]++;
2037       }
2038     }
2039 
2040     /* add missing diagonal entry */
2041     if (C->force_diagonals) {
2042       k = i + owners[rank]; /* column index */
2043       ierr = PetscLLCondensedAddSorted_Scalable(1,&k,lnk);CHKERRQ(ierr);
2044     }
2045 
2046     nnz = lnk[0];
2047 
2048     /* if free space is not available, make more free space */
2049     if (current_space->local_remaining<nnz) {
2050       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2051       nspacedouble++;
2052     }
2053     /* copy data into free space, then initialize lnk */
2054     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2055     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2056 
2057     current_space->array           += nnz;
2058     current_space->local_used      += nnz;
2059     current_space->local_remaining -= nnz;
2060 
2061     bi[i+1] = bi[i] + nnz;
2062     if (nnz > rmax) rmax = nnz;
2063   }
2064   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2065 
2066   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2067   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2068   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2069   if (afill_tmp > afill) afill = afill_tmp;
2070   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2071   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2072   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
2073   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
2074 
2075   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2076   /*-------------------------------------------------------------------------------*/
2077   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2078   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2079   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2080   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2081   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2082   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2083   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2084   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
2085   for (i=0; i<pn; i++) {
2086     row  = i + rstart;
2087     nnz  = bi[i+1] - bi[i];
2088     Jptr = bj + bi[i];
2089     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2090   }
2091   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2092   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2093   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2094   merge->bi        = bi;
2095   merge->bj        = bj;
2096   merge->coi       = coi;
2097   merge->coj       = coj;
2098   merge->buf_ri    = buf_ri;
2099   merge->buf_rj    = buf_rj;
2100   merge->owners_co = owners_co;
2101 
2102   /* attach the supporting struct to C for reuse */
2103   C->product->data    = ptap;
2104   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2105   ptap->merge         = merge;
2106 
2107   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2108 
2109 #if defined(PETSC_USE_INFO)
2110   if (bi[pn] != 0) {
2111     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2112     ierr = PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2113   } else {
2114     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2115   }
2116 #endif
2117   PetscFunctionReturn(0);
2118 }
2119 
2120 /* ---------------------------------------------------------------- */
2121 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2122 {
2123   PetscErrorCode ierr;
2124   Mat_Product    *product = C->product;
2125   Mat            A=product->A,B=product->B;
2126   PetscReal      fill=product->fill;
2127   PetscBool      flg;
2128 
2129   PetscFunctionBegin;
2130   /* scalable */
2131   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2132   if (flg) {
2133     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2134     goto next;
2135   }
2136 
2137   /* nonscalable */
2138   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2139   if (flg) {
2140     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2141     goto next;
2142   }
2143 
2144   /* matmatmult */
2145   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2146   if (flg) {
2147     Mat       At;
2148     Mat_APMPI *ptap;
2149 
2150     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2151     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2152     ptap = (Mat_APMPI*)C->product->data;
2153     if (ptap) {
2154       ptap->Pt = At;
2155       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2156     }
2157     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2158     goto next;
2159   }
2160 
2161   /* backend general code */
2162   ierr = PetscStrcmp(product->alg,"backend",&flg);CHKERRQ(ierr);
2163   if (flg) {
2164     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
2165     PetscFunctionReturn(0);
2166   }
2167 
2168   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2169 
2170 next:
2171   C->ops->productnumeric = MatProductNumeric_AtB;
2172   PetscFunctionReturn(0);
2173 }
2174 
2175 /* ---------------------------------------------------------------- */
2176 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2177 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2178 {
2179   PetscErrorCode ierr;
2180   Mat_Product    *product = C->product;
2181   Mat            A=product->A,B=product->B;
2182 #if defined(PETSC_HAVE_HYPRE)
2183   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2184   PetscInt       nalg = 5;
2185 #else
2186   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2187   PetscInt       nalg = 4;
2188 #endif
2189   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2190   PetscBool      flg;
2191   MPI_Comm       comm;
2192 
2193   PetscFunctionBegin;
2194   /* Check matrix local sizes */
2195   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2196   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);
2197 
2198   /* Set "nonscalable" as default algorithm */
2199   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2200   if (flg) {
2201     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2202 
2203     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2204     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2205       MatInfo     Ainfo,Binfo;
2206       PetscInt    nz_local;
2207       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2208 
2209       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2210       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2211       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2212 
2213       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2214       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2215 
2216       if (alg_scalable) {
2217         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2218         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2219         ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2220       }
2221     }
2222   }
2223 
2224   /* Get runtime option */
2225   if (product->api_user) {
2226     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2227     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2228     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2229   } else {
2230     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2231     ierr = PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2232     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2233   }
2234   if (flg) {
2235     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2236   }
2237 
2238   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2239   PetscFunctionReturn(0);
2240 }
2241 
2242 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2243 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2244 {
2245   PetscErrorCode ierr;
2246   Mat_Product    *product = C->product;
2247   Mat            A=product->A,B=product->B;
2248   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2249   PetscInt       nalg = 4;
2250   PetscInt       alg = 1; /* set default algorithm  */
2251   PetscBool      flg;
2252   MPI_Comm       comm;
2253 
2254   PetscFunctionBegin;
2255   /* Check matrix local sizes */
2256   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2257   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);
2258 
2259   /* Set default algorithm */
2260   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2261   if (flg) {
2262     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2263   }
2264 
2265   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2266   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2267     MatInfo     Ainfo,Binfo;
2268     PetscInt    nz_local;
2269     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2270 
2271     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2272     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2273     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2274 
2275     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2276     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2277 
2278     if (alg_scalable) {
2279       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2280       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2281       ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2282     }
2283   }
2284 
2285   /* Get runtime option */
2286   if (product->api_user) {
2287     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2288     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2289     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2290   } else {
2291     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2292     ierr = PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2293     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2294   }
2295   if (flg) {
2296     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2297   }
2298 
2299   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2300   PetscFunctionReturn(0);
2301 }
2302 
2303 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2304 {
2305   PetscErrorCode ierr;
2306   Mat_Product    *product = C->product;
2307   Mat            A=product->A,P=product->B;
2308   MPI_Comm       comm;
2309   PetscBool      flg;
2310   PetscInt       alg=1; /* set default algorithm */
2311 #if !defined(PETSC_HAVE_HYPRE)
2312   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2313   PetscInt       nalg=5;
2314 #else
2315   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2316   PetscInt       nalg=6;
2317 #endif
2318   PetscInt       pN=P->cmap->N;
2319 
2320   PetscFunctionBegin;
2321   /* Check matrix local sizes */
2322   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2323   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);
2324   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);
2325 
2326   /* Set "nonscalable" as default algorithm */
2327   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2328   if (flg) {
2329     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2330 
2331     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2332     if (pN > 100000) {
2333       MatInfo     Ainfo,Pinfo;
2334       PetscInt    nz_local;
2335       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2336 
2337       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2338       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2339       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2340 
2341       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2342       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2343 
2344       if (alg_scalable) {
2345         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2346         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2347       }
2348     }
2349   }
2350 
2351   /* Get runtime option */
2352   if (product->api_user) {
2353     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2354     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2355     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2356   } else {
2357     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2358     ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2359     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2360   }
2361   if (flg) {
2362     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2363   }
2364 
2365   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2366   PetscFunctionReturn(0);
2367 }
2368 
2369 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2370 {
2371   Mat_Product *product = C->product;
2372   Mat         A = product->A,R=product->B;
2373 
2374   PetscFunctionBegin;
2375   /* Check matrix local sizes */
2376   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);
2377 
2378   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2379   PetscFunctionReturn(0);
2380 }
2381 
2382 /*
2383  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2384 */
2385 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2386 {
2387   PetscErrorCode ierr;
2388   Mat_Product    *product = C->product;
2389   PetscBool      flg = PETSC_FALSE;
2390   PetscInt       alg = 1; /* default algorithm */
2391   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2392   PetscInt       nalg = 3;
2393 
2394   PetscFunctionBegin;
2395   /* Set default algorithm */
2396   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2397   if (flg) {
2398     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2399   }
2400 
2401   /* Get runtime option */
2402   if (product->api_user) {
2403     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2404     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2405     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2406   } else {
2407     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2408     ierr = PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2409     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2410   }
2411   if (flg) {
2412     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2413   }
2414 
2415   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2416   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2417   PetscFunctionReturn(0);
2418 }
2419 
2420 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2421 {
2422   PetscErrorCode ierr;
2423   Mat_Product    *product = C->product;
2424 
2425   PetscFunctionBegin;
2426   switch (product->type) {
2427   case MATPRODUCT_AB:
2428     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2429     break;
2430   case MATPRODUCT_AtB:
2431     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2432     break;
2433   case MATPRODUCT_PtAP:
2434     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2435     break;
2436   case MATPRODUCT_RARt:
2437     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2438     break;
2439   case MATPRODUCT_ABC:
2440     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2441     break;
2442   default:
2443     break;
2444   }
2445   PetscFunctionReturn(0);
2446 }
2447